Molinism and the Grounding Objection, Part 1

0. Introduction 

Molinism is the view that there are true counterfactuals involving agents making libertarian free choices, and that these counterfactuals are known by God. See this for more background.

Perhaps the most common objection to Molinism is referred to as the ‘grounding problem’. The issue is just that there seems to be nothing which explains why true Molinist counterfactuals are true. They seem to be just true, but not true because of anything in particular. Here is how Craig puts it in his paper Middle Knowledge, Truth–Makers, and the “Grounding Objection” (henceforth MK, and from which all the Craig quotes will come in this post):

“What is the grounding objection? It is the claim that there are no true counterfactuals concerning what creatures would freely do under certain specified circumstances–the propositions expressed by such counterfactual sentences are said either to have no truth value or to be uniformly false–, since there is nothing to make these counterfactuals true. Because they are contrary–to–fact conditionals and are supposed to be true logically prior to God’s creative decree, there is no ground of the truth of such counterfactual propositions. Thus, they cannot be known by God.”

One way of thinking about this issue is that the grounding problem itself presupposes the ‘truth-maker’ principle. According to this principle, every true proposition is made true by something. If the truth-maker principle is correct, and if nothing makes Molinist counterfactuals true, it follows that they are not true. Hence, it follows that there are no such truths for God to know.

In response to this, a Molinist can either deny the truth-maker principle, or accept it and provide a truth-maker for the counterfactuals. As Craig makes explicit, he believes he can make the case that either strategy is plausible:

“For it is far from evident that counterfactuals of creaturely freedom must have truth-makers or, if they must, that appropriate candidates for their truth-makers are not available.”

Craig gives reasons that one might want to deny the truth-maker principle in general. He also explains how one might think about Molinist counterfactuals not having truth-makers. He also offers an account of how they could have truth-makers. If any of these works, it seems that the grounding objection has been rebutted. In this series I will look at his proposals, and argue against them. In this first post, I will just look at the positive case that Craig sets out for Molinism.

  1. The (supposedly) intuitive case

Craig mentions a comment from Plantinga that he agrees with, about how plausible it is that there should be true Molinist counterfactuals:

“No anti–Molinist has, to my knowledge, yet responded to Alvin Plantinga’s simple retort to the grounding objection: “It seems to me much clearer that some counterfactuals of freedom are at least possibly true than that the truth of propositions must, in general, be grounded in this way.””

Craig goes on to say that the grounding problem is:

“…a bold and positive assertion and therefore requires warrant in excess of that which attends the Molinist assumption that there are true counterfactuals about creaturely free actions.”

Plantinga is saying that the fact that there are Molinist counterfactuals is more plausible than the truth-maker principle. To show that we should prefer the truth-maker principle to Molinist counterfactuals, we need warrant for the truth-maker principle “in excess” of that for Molinist counterfactuals. Not an easy job, thinks Craig, who says that the warrant for Molinist counterfactuals is “not inconsiderable”.

In his ‘Warrant for the Molinist Assumption’ section of MK, Craig provides three aspects of the case which supposedly shows that Molinist counterfactuals have ‘not inconsiderable’ warrant already. These are as follows:

  1. First, we ourselves often appear to know such true counterfactuals.”
  2. Second, it is plausible that the Law of Conditional Excluded Middle (LCEM) holds for counterfactuals of a certain special form, usually called “counterfactuals of creaturely freedom.””
  3. Third, the Scriptures are replete with counterfactual statements, so that the Christian theist, at least, should be committed to the truth of certain counterfactuals about free, creaturely actions.”

In this post, I will focus on the first of these three.

2. The epistemic objection – Molinist counterfactuals are unknowable

The first one of these, along with the third and Plantinga’s quote from above, are all related. They are rebutted by what I will call the ‘epistemic objection’.  According to this objection, even if they were true, it isn’t possible for an agent to know Molinist counterfactuals.

It seems to Craig to be obvious that we “often appear to know” Molinist counterfactuals to be true. Yet, there seems to be good reason to think that we cannot know Molinist counterfactuals.

In order to help explain things, I want to make an important distinction, which is between Molinist counterfactuals and what I will call ‘probably-counterfactuals’. So, an example of a Molinist counterfactual is:

a) Had Louis been tempted, he would have given in.

An example of a probably-counterfactual is:

b) Had Louis been tempted, he probably would have given in.

The difference between a) and b) is merely the word ‘probably’. The difference it plays is huge though. I think that it makes the difference between being crucial to rational reasoning generally (like b), and being utterly useless (like a). I think that Craig’s claims about Molinist counterfactuals only really make sense if they are ultimately being made about probably-counterfactuals, and I will explain why I think this in what follows.

First of all, Craig thinks that we “often appear to know” Molinist counterfactuals, like a). But this is strange. Maybe God could know them (although, I don’t think that can be maintained either), but how could a mere mortal like me know them? All I can really know, we might suppose, is i) what I have some kind of access to empirically (a posteriori), and ii) what I can reason about abstractly (a priori). And neither of these routes can get me to the conclusion that Louis would have freely chosen to give in to the sin had he been tempted.

I don’t have empirical access to counterfactual situations, so that rules out the first epistemological route; nothing about the empirical world that I can investigate can tell me which of the two options Louis would have freely chosen to make.

But mere abstract reasoning cannot ever decide which of two options an agent with libertarian free choice would make either; it doesn’t follow logically from any purely a priori antecedent conditions. Thus, Louis’ choice seems literally unknowable to an agent like me. Not only that, but all Molinist counterfactuals become unknowable for the same reason.

On the other hand, knowing b) seems relatively straightforward, at least in principle. Let’s suppose Louis has a strong track record of giving in to sin when tempted, and that I know this because I have witnessed it personally. Perhaps he has also told me about how much he hates living in the stuffy confines of the monastery and yearns for some temptation to give into. Any number of scenarios like this could support the idea that I could come to believe with good reason that he probably would have given in had he been tempted.

Thus, a) seems literally unknowable, whereas b) is eminently knowable. They are therefore, epistemically asymmetric.

3. The utility objection – Molinist counterfactuals are useless

Craig says:

“Very little reflection is required to reveal how pervasive and indispensable a role such counterfactuals play in rational conduct and planning. We not infrequently base our very lives upon the assumption of their truth or falsity.”

He is right about the fact that counterfactuals play a “pervasive and indispensable” role in “rational conduct and planning”. But where is wrong is that it is probably-counterfactuals which are doing most of the work, and Molinist counterfactuals do none (and indeed, could not do any). The reason for this difference in utility is because of the epistemic asymmetry between probably-counterfactuals and Molinist counterfactuals.

Here is an example to play with to make this point clear. Imagine I am deciding whether or not to leave my bike unlocked or not while I go into the library. Let’s suppose that I see the well-known bike thief, Louis, lurking just round the corner. I decide to lock my bike up. When I return after finding the book I want, I am glad to find my bike is still there. I begin to unlock my bike, and at this point you ask me: “Why did you lock your bike up?” My answer is going to be something like this:

c) Had I not locked up my bike, Louis probably would have stolen it.

It is the likelihood of Louis stealing the bike that motivated me to lock it up. My reasoning process included the fact that I had good reasons to think that e) was true. The place that the probably-counterfactual plays in my reasoning is completely clear. It makes perfect sense for a probably-counterfactual to be what I am using here to come to my decision to lock the bike up.

The idea that I used a Molinist counterfactual is almost unintelligible though. Imagine my reply had been the following:

d) Had I not locked up my bike, Louis would have freely chosen to steal it.

It would be bizarre for me to say that, because there is no way for me to know that d) is true rather than false. Given that Louis has libertarian free will, he could have chosen to steal the bike, but he could have also chosen not to steal the bike. The scenario where he freely chooses to steal the bike, and the scenario where he freely chooses refrain from stealing the bike, are literally identical in every respect up to the point where he makes a decision. There is nothing at all, even in principle, that could justify my belief that one would happen rather than the other. Possibly, God knows something I don’t, but it is clear that I do not. Thus, there is no way it can be part of my (rational) decision making process, for I have no reason to think that it is true rather than false.

If this wasn’t bad enough, we can develop the worry. Imagine that standing next to Louis is Louise, who I know has never stolen a bike, or indeed anything, in her entire life. My belief is that she is unlikely to steal my bike. Her presence is therefore not a consideration I took into account when I locked my bike up. If you asked me when I got back to my why I did not consider her presence, I would have said that it was because of something like the following:

e) Had I not locked up my bike, Louise probably would not have stolen it.

I was under the belief that even if I had not locked my bike up, Louise probably wouldn’t have stolen it. While the presence of Louis plays a role in my reasoning, and the presence of Louise does not, and this is easily cashed out in terms of probably-counterfactuals.

But when we come to consider that it wasn’t probably-counterfactuals, but Molinist counterfactuals that were part of my reasoning, we run into a problem. This is because an entirely symmetric Molinist counterfactual can be created for Louise:

f) Had I not locked up my bike, Louise would have freely chosen to steal it.

Given that Louise has libertarian free will, she could have chosen to steal the bike, but she could have also chosen not to steal the bike. The scenario where she freely chooses to steal the bike, and the scenario where she freely chooses refrain from stealing the bike, are literally identical in every respect up to the point where she makes a decision. Each of Louis and Louise are perfectly symmetrical in this respect, so there is no reason for me to believe both that e) is true and f) is false. But unless I do have this (non-Molinist) asymmetric view about e) and f), my inclination to treat them differently utterly inexplicable.

The very thing that the counterfactual would need to do to be an ‘indispensable’ part of my reasoning process is inexplicable if they are Molinist counterfactuals.

4. A possible reply

There is a possible reply that could be made on behalf of the Molinist at this point though. Clearly, our Molinist friend might reply, we cannot know for sure whether a Molinist counterfactual like a) or d) or f) is true rather than false. Only God can know that for certain. However, I have set the bar too high. We can reasonably infer such counterfactuals from the truth of the probably-counterfactuals, which I already conceded are not problematic to know. So, for example, it is from the premise that Louis probably would have stolen the bike, that I infer that he would have freely chosen to steal the bike. Obviously, this is not a deductive inference (for it is not deductively valid), but it is a reasonable inductive inference.

Here is the inference:

  1. Had I not locked the bike, Louis probably would have stolen it
  2. Therefore, had I not locked the bike, Louis would have freely chosen to steel it

This reply has a lot going for it. Things can be known via such inductions. I think that premise 1 is true, and that it’s truth can be plausibly construed as something which increases the (epistemic) probability of 2. Thus, the inference, though inductive, seems pretty good.

I actually don’t think that 2 could be true, but that is for semantic reasons that we do not have to get into here. Let’s just say that for the sake of the argument, I accept this type of move. Where does it get us?

It might be thought that Molinist counterfactuals can indeed be known (via inductive inference from known probably-counterfactuals). Thus, the epistemic objection seems to have been countered. Indeed, once we make this move, counterfactuals like d) (i.e. had I not locked up my bike, Louis would have freely chosen to steal it) can be believed by me with justification. Thus, it is now no longer problematic to see how they might fit into my reasoning process. I believe (via inference from a probably-counterfactual) that Louis would have freely stolen my bike, and that belief is what motivates me to lock it up. Thus, the utility objection has a rebuttal as well.

5. The redundancy reply

As I said,  I think this is a good line of response. I think it is about the best there is to be had. But even if we concede it, I don’t think much has happened of any importance. Ultimately, they rescue Molinist counterfactuals at the cost of making them redundant. If they can known and can be put to work in decision making, then they necessarily do not need to be used, because there will already be something we believe (or know) which does all of their work for them.

Even if Molinist counterfactuals, like d), can be inductively inferred from probably-counterfactuals, like c), it is not clear that they can be derived from anything else. Consider the case where someone believes that Louis will freely choose to steal the bike, but does not believe that he probably will steal the bike. Such a belief can be had, but surely it is irrational. It is like holding that this lottery ticket is the winner, even while believing that it is unlikely to be the winner. Such beliefs may be commonplace (and maybe it is beneficial to believe that you will beat the odds when fighting with a disease, etc), but they are paradigmatically irrational nonetheless. Unless you believe that something is probably going to happen, you should not believe (i.e. should lack a belief) that it is going to happen.

If that is right, then it has a similar consequence for Molinist counterfactuals being used in rational processes. Unless I have inferred it from a probably-counterfactual, I cannot reasonably believe a Molinist-counterfactual. But the only way I can use a belief in a Molinist counterfactual as part of a rational decision-making process is if I reasonably believe it. Therefore, the only way I can use a belief in a Molinist counterfactual as part of a decision making process is if I already believe the corresponding probably-counterfactual.

Here is an example to make this clear.

Let’s say that I can infer that ‘Louis would freely choose to steal the bike if left unlocked’ from the premise that ‘he probably would steal the bike if left unlocked’, and from no other premise. Let’s also say that I use believe that ‘he would freely choose to steal the bike if left unlocked’, and that I use that as part of my decision process to lock the bike up. It follows that because I used that belief as part of my rational process, that I must also believe that he probably would steal the bike.

This means that even if Molinist counterfactuals played the role that Craig thinks they do in decision making, they must come with an accompanying belief about the corresponding probably-counterfactual.

And this means that, maybe Molinist counterfactuals can be known, and maybe they can be used in reasoning processes, but they can do so only if there is a reasonably believed probably-counterfactual present as well. This makes Molinist counterfactuals completely dependent on probably-counterfactuals from both an epistemic and decision theoretic point of view. You never get to rationally believe a Molinist counterfactual unless you already believe the corresponding probably-counterfactual. And you can never use your belief in a Molinist counterfactual in some reasoning process unless you also already believe the corresponding probably-counterfactual.

And as we saw, probably-counterfactuals can already do all the explanatory work in explaining why I decided to lock my bike up. I don’t need Molinist counterfactuals if I have the right probably-counterfactual, and I never have a Molinist counterfactual unless I already have the right probably-counterfactual. That makes them necessarily redundant. Maybe they can play the role Craig wants them to play, but only if the need not play it.

 

6. Conclusion

Craig’s first aspect of the warrant for Molinist counterfactuals was that we commonly know such counterfactuals. However, I showed how it seems quite hard to see how we could know such counterfactuals directly. They are not things we can experience ourselves, and they are not deducible a priori. Probably-counterfactuals, on the other hand, are eminently knowable. Craig also claimed that Molinist counterfactuals play an indispensable role in decision making, however their disconnection from our direct ways of knowing their truth-values makes them irrelevant to decision making, unlike probably-counterfactuals.

The only response to this seems to be to claim that Molinist counterfactuals can be known via inference from probably counterfactuals. While this may be true (although I still have problems with that), all it would get a Molinist would be something which can only be known because the probably-counterfactual was also known, and only does any work explaining decision making if that work could be done by the epistemically prior probably-counterfactual. They can only be saved by being made redundant.

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Inspiring Philosophy and the Laws of Logic: Part 1

0. Introduction

There is a YouTube channel, called Inspiring Philosophy (henceforth IP), which is about philosophical apologetics. It has about 45k subscribers, and the videos have high visual production values. One video in particular caught my attention, as it was about the laws of logic.

Despite the relatively large audience and good production values, IP makes some pretty baffling mistakes, and a lot of them are very easy to spell out. I will try to explain the main ones here.

  1. Confusions

IP’s lack of understanding about the issues involved contributes to a confusion about what is being claimed by his imagined ‘opponents’, and what he is trying to say in reply to them. This fundamental confusion is at the heart of the entire video.

In the very opening section, IP asks two general questions:

“Can we trust the laws of logic? Is logic safe from criticism, or is it just another man made construct built on sand?”

These questions are actually quite vague. What does it mean to ‘trust‘ the laws of logic? Does it just mean ‘Are the laws of logic true?’

More importantly, what exactly does he mean by ‘the laws of logic’? He never specifies what he takes the ‘laws of logic’ to actually be. Commonly in discussions like this, they are taken to be the law of excluded middle, the law of non-contradiction, and the law of identity. They are part of what is known as ‘classical logic‘, which we can think of as a group of logical systems which all share a number of principles, including those laws. We must assume that this is what IP means. Let’s refer to these three laws as the ‘classical laws of logic’

The historical development of logic shows that, in one sense, classical logic is not safe from criticism. Just like mathematics, logic has evolved over time, and it has gone through various changes (see this, and this). In particular, there are logical systems which do not include the classical laws of logic; there are systems of logic which have contradictions in, or which have exceptions to excluded middle, or where identity is treated very differently. So, suppose that IP is asking: ‘are there logical systems which do not include those particular logical laws?’ The answer is: ‘yes, there are non-classical logics‘.

Surely though IP thinks he is asking a more interesting question than this. He wants to ask whether some other non-classical logical system should be regarded as the right one. This is a much more interesting question, and much more difficult to answer. I assume that IP wants to say that the classical laws of logic are the right ones, and all the other non-classical alternatives are not right. That would be a coherent position for him to take: he is defending classical logic against rival non-classical logics.

However, this is not what IP actually articulates throughout the video. The video starts off with a claim which seems to be the target that IP wants to argue against. He says

“Many argue that the laws of logic are not true”.

Here we see the fundamental confusion right at the heart of the video. There are two distinct issues IP never distinguishes between a kind of local challenge to classical logic, and a global challenge to all logic:

Local) “Many argue that classical logic is not the right logic

Global) “Many argue that there is no right logic at all

While the first option is clearly something many people do argue, it is not quite clear whether the second option even makes sense. Are there really such people who argue that there is no such thing as logic? Who are these people? IP doesn’t ever say.

One of the main problems in what follows is that IP switches back and forth between the local and global challenge, as if he is unaware of the distinction.

2. The argument

In the first half of the video, IP offers what he calls a “simple argument” to use as a foil to respond to. He does not say where he got this argument from, but I suspect that he got it from here.

The argument goes like this:

  1. Assume that the laws of logic are true
  2. All propositions are either true or false
  3. The proposition “This proposition is false” is neither true nor false
  4. There exists at least one proposition that is neither true nor false
  5. It is not the case that all propositions are either true or false
  6. It both is and is not the case that all propositions are either true nor false
  7. Therefore, the laws of logic are not true

We need to ignore the fact that the first premise is an example of a command, and is not expressing a proposition. We also need to ignore that the argument is not formally valid; strictly speaking, the conclusion does not formally follow from the premises. You have to assume that by ‘the laws of logic’ we mean to include the law of bivalence. If you want an argument to be formally valid, you cannot keep these sorts of assumptions implicit.

Basically, what is going on with this argument is a challenge to classical logic, or really any logic which has the semantic principle of ‘bivalence’. So it is an example of a local challenge. The principle of bivalence is expressed in premise 2, and it says that each proposition has exactly one of the following two truth values: ‘true’ or ‘false’. This principle is the target of the argument.

The liar’s paradox is notoriously difficult to give a satisfying account of within the constraints of classical logic. Therefore, some people say that the only way to account for it is to give up some aspect of classical logic. Thus, considerations of the liar’s paradox provide some reason for people who argue that classical logic needs to be rejected. In this case, the idea implicit in premise 3 is that the liar’s paradox requires bivalence to be false. They say that the Liar Proposition, i.e. “This proposition is false”, is itself neither true nor false. If they are right about this, then classical logic must be wrong. This is because classical logic says that all propositions are either true or false, but there is a proposition which is neither (i.e. the Liar Proposition).

To defend classical logic against this charge, we would expect IP to argue that the liar’s paradox is not solved by treating the Liar Proposition as neither true nor false, but that it can be solved without giving up any of the assumptions of classical logic. This would undermine the reason given here for thinking that bivalence had an exception.

However, at this point IP starts to show just what a poor grasp he has of what this argument is supposed to be showing, and what he needs to do to defend classical logic against it.

He says that “there are several problems with this argument”, but he criticises premise 2. Now, this is odd, because premise 2 is just an expression of bivalence, which is part of classical logic. If he is defending classical logic, then he should be defending premise 2; yet, he is about to offer a reason to doubt it.

IP says that the problem with premise 2 is that not all propositions are either true or false; some are neither true nor false. His example is the following:

“Easter is the best holiday”.

His reasons for thinking that “Easter is the best holiday” is neither true nor false are strange. He says that that proposition “Cannot be proven true or false” and that it is “just an expression of opinion”. “So,” he continues, “you can have propositions that are neither true nor false. Nothing in either logic or language denies this”.

Now, just hold on a minute. Let’s grant IP’s claim that the proposition “Easter is the best holiday” merely expresses an opinion. This is ambiguous between two different things.  On one hand, saying that it merely expresses an opinion might mean that it is just shorthand for:

“My opinion is that Easter is the best holiday”

If that is what IP means, then surely “Easter is the best holiday” can be true. After all, I have opinions, and sometimes they are true. In particular, the proposition “My opinion is that Easter is the best holiday” is true just so long as I really do prefer Easter to all other holidays. It would be false if I happened to prefer Halloween to Easter, etc. What is supposed to be the problem here? If such propositions are expressions of opinion in this sense, that doesn’t mean that they are not true or false.

On the other hand, “Easter is the best holiday” might not be shorthand for “My opinion is that Easter is the best holiday”. It might be taken to be something like: “Yey! Easter!” If that is what IP means, then it doesn’t have a truth-value, but then it isn’t really a proposition at all.

So, it seems like either “Easter is the best holiday” is a proposition with a truth-value, or it lacks a truth-value precisely because it isn’t a proposition. Either way round, it doesn’t seem to be any reason to doubt bivalence.

He also says that it cannot be proven. But if “Easter is the best holiday” is just taken as a proposition, then it can be proven in the same way as any other proposition:

  1. If p, then “Easter is the best holiday”.
  2. p
  3. Therefore, “Easter is the best holiday”.

Why IP thinks we cannot enter “Easter is the best holiday” into a proof like this is a mystery.

IP concludes that the argument doesn’t work, on the basis that propositions like “Easter is the best holiday” are neither true nor false. As we have just seen, his reasons for thinking that this sort of proposition is neither true nor false are pretty unconvincing. But let’s just grant them for the sake of the argument.

He doesn’t seem to realise that if “Easter is the best holiday” is neither true nor false, then he is effectively conceding exactly the thing that the argument was supposed to be showing, i.e. that there are exceptions to classical logic. If his own example were genuinely an example of a proposition that lacked a truth value, this would be enough to undermine classical logic. So, he isn’t showing something about the argument that is wrong; he is just giving another (albeit more flawed) instance of a counterexample to classical logic.

3. Gödel

At around 2:20, IP moves on to talk about Kurt Gödel:

“The argument itself is based on Gödel’s theorems, which many think shows logic doesn’t work”.

I think what IP has in mind is that there is another type of challenge to classical logic, this time coming from Gödel’s incompleteness theorems. He gives a statement about what the incompleteness theorems show, but it crucially mistakes (and overstates) their true significance. This leaves IP drawing all the wrong consequences.

IP says that Gödel’s incompleteness theorems show that:

“No consistent system of axioms whose theorems can be listed by an ‘effective procedure’ is capable of proving all truth”

This statement stands out a bit in the video, and it sounds like IP has got it from somewhere, but he never gives any citations for this quote, so we have to guess. My first guess was Wikipedia, and I was right. What is revealing about the quote is what he leaves off. Here is how it shows on Wikipedia:

sjdksds

The quote in full (with the bit he missed off in italics) is:

“No consistent system of axioms whose theorems can be listed by an ‘effective procedure’ is capable of proving all truths about the arithmetic of the natural numbers“.

There is a very big difference between showing that no consistent system of axioms can prove all truth, and showing that they cannot prove all truths about the arithmetic of the natural numbers. I don’t know if he didn’t think the extra bit he left off wasn’t important, or if he did it on purpose to jazz up his point, but either way leaving it off completely changes the significance of Gödel’s incompleteness theorems.

The thing is that (when we look at it properly) Gödel’s incompleteness theorems do not pose a direct local challenge to classical logic. What they show is compatible with non-contradiction, excluded middle and the law of identity all being true (along with all the other principles of classical logic).

What the theorems show is that any system of logic that is powerful enough to express all the arithmetic propositions cannot prove all of them.

So, the result applies to a certain type of logic, called ‘mathematical logic’. This logic is built up out of first-order logic, which is itself a very basic type of classical logic (one that respects all the principles IP presumably wants to defend). If you add the right axioms to this logic, then it becomes capable of expressing things like 1+1=2, etc. Once it is able to do that, we call it mathematical logic. Gödel’s incompleteness theorems apply specifically to mathematical logic.

And because this mathematical logic itself respects the classical principles (it is a type of classical logic), this means that Gödel is just telling us something about the limits of a certain type of classical logic (classical logic that is capable of expressing arithmetic). It is pointing out a limitation in mathematical logic. That is not itself a straightforwardly a reason to think that classical logic is not the correct logic, or that the ‘laws of logic’ are not true.

Except… it might be.

The strange thing about Gödel’s proof is that it shows that arithmetic, and any more complex bit of mathematics, cannot be modelled in classical logic without having ‘blind spots’, where there is something which is true but not provable in that logic. Yet, we might just think that we obviously can prove everything in arithmetic; we might just find the limits of proof in mathematical logic to be an unacceptable consequence. Well, if you did think this, then you could use this as a reason to think that there must be contradictions.

This is because the actual theorems can be thought of as ‘either-or’ statements. They can be thought of as saying ‘either mathematical logic is consistent but has blind-spots, or it has no blind-spots but it has some contradictions in it’ – Gödel is telling us that mathematical logic is either incomplete or inconsistent – either there is something that is true but not provable, or the law of non-contradiction is false.

If you thought that the price (of denying non-contradiction) was worth it so that you didn’t have any of these weird blind-spots in your proof-theory, then you might be willing to accept the inconsistent option. Most people find contradictions more troubling than blind-spots though, and so don’t go that route. But, that is probably the most direct sort of attack you could make from Gödel against classical logic.

If you were feeling charitable, you might think that this is the sort of challenge that IP had in mind. But he dropped off the bit of the quote from Wikipedia which specifically says that Gödel’s theorems are about mathematical logic, not all logic (or even all of classical logic). I find it hard to believe that he didn’t read the end of the sentence he quoted, so either he didn’t understand that the bit he left off is crucial to understand the theorems, or he is deliberately overstating their importance. Either way, it is not great.

Now, if you know a little bit about Gödel, then you might know that in addition to his incompleteness theorems, he is also well known for his completeness theorem. This showed that the basic (classical) first-order logic is actually complete, meaning that it definitely doesn’t have any of those weird blind-spots that the extended mathematical logic has. So without the extra axioms added to first-order logic, it is capable of proving all its own truths.

And this is where we see why leaving off that bit from the Wikipedia quote was so telling. The way IP tells it, the significance of Gödel’s incompleteness theorems is that logic ‘cannot prove all truths’, which sounds like a very profound, almost mystical insight into what people can know and what they can’t. But, in reality, Gödel’s incompleteness theorems only show that some types of logic cannot prove all of their own truths. Admittedly, it is a very important class of logical systems, as it is the ones that model mathematical logic, but it is not as widespread as IP makes out. And Gödel’s completeness theorem actually proves that there are other types of logic for which this is not the case. There are also many other famous completeness theorems in logic (such as Kripke’s celebrated completeness theorem for the modal logic S5, which wouldn’t be possible if IP was right about what Gödel’s incompleteness theorems said!).

IP summarises what he thinks Gödel showed us as follows:

“All Gödel did was show that we are limited in having a total proof of something, but even without Gödel that is intuitively obvious. Many things will only be 99% probably true. But absolute certainty will always be beyond our reach”.

In reality, the significance of Gödel’s incompleteness theorems is not at all intuitive. Almost nobody expected mathematical logic to be limited in the way he showed it was. IP seems to think that Gödel just used maths to show that we can never really know anything for certain. This is demonstrably a bad interpretation of Gödel, and IP clearly has no idea what Gödel really showed us.

On the other hand, I agree that there is no particularly compelling reason to give up classical logic due to Gödel’s incompleteness theorems. I don’t find the idea of accepting contradictions just to get around incompleteness of arithmetic to be persuasive. It’s just a pity that IP wasn’t able to explain what Gödel said, how that was relevant to classical logic, and how it doesn’t mean we should reject classical logic. It’s more a case of a stopped clock accidentally showing the right time.

4. G Spencer-Brown

In the next main bit (around 3:10), IP brings up a different philosopher (or mathematician, depending on how you look at it), G Spencer-Brown, and the section he takes up is from Spencer-Brown’s book, Laws of Form. Now, this is a very strange book on logic, and not within the mainstream work on logic that philosophers usually debate. That is not to say that it is not of any value, but just to be aware that it is already a weird reference. The bit of that book that IP seems to have read is merely the preface, so it is quite easy to check for yourself (just pages ix – xii).

Anyway, IP is going back to the 3rd premise of the argument, which is the idea that the Liar Proposition is neither true nor false. He seems to be saying that Spencer-Brown advocates a solution to the problem which avoids having to postulate that the proposition is neither true nor false. This is presumably done in order to rescue the ‘laws of logic’ from the attack, and to defend classical logic.

So, the thing about the liar proposition, i.e. “This proposition is false”, is that if you assume it has a truth-value (true or false), then it sort of switches that truth-value on you. To see that, assume it is true. That would mean that what it says is the case. But what it says is that it is false. So if it is true, then it is false. The same thing happens if we assume it is false. So, we might say that any input value gets transformed into its opposite output value; true goes to false, false goes to true.

And this feature, or something similar to it, is also seen in the following mathematical example that Spencer-Brown brings up in the preface to Laws of Form. So consider the following equation:

X = -1/X

If you try to solve the equation by assuming that X = 1 (i.e. if we substitute X for 1), then we get:

1 = -1/1

However, -1 divided by 1 equals -1 (because any number divided by 1 equals itself), so: -1/1 = -1. But that means that:

1 = -1/1 = -1

The ‘input’ of 1 gets turned into the ‘output’ of -1. If we try to solve the equation by assuming that X = -1, then we get the converse result (because any number divided by itself equals 1):

-1 = -1/-1 = 1

So the assumption of X = 1, results in an output of -1. And the assumption of X = -1 results in the output of 1. This is a bit like what is going on with the liar proposition if we think of 1 being like ‘true’, and -1 being like ‘false’. In both cases, the input value gets switched to the alternative value.

IP says that the ‘solution’ to this problem is to use an ‘imaginary number‘ i, which is √-1. What he means is that if we assume that X = i, then we get the following solution to the equation:

i = -1/i

Because is the square root of -1, it is already -1/i. So:

i = -1/i = i

Unlike when we assumed X was 1 or -1, where the output got switched, if we assume the input is i, then the output doesn’t get switched. Ok, got it.

The first thing to note here is that this sort of consideration is what motivated mathematicians to consider changing how they thought about mathematics. And not without some resistance. Descartes apparently used the term ‘imaginary’ as a derogatory term. Nevertheless, mathematicians were convinced that introducing imaginary numbers into their understanding of mathematics, despite being unintuitive to some extent, was warranted due to the utility that doing so brought about. What Spencer-Brown is pointing to is a reason for re-conceiving traditional mathematics.

How does this relate to the liar proposition? Unfortunately for IP, it doesn’t relate in the way he wants it to. Also, he says almost nothing about how this is supposed to relate to the liar’s paradox. He says something, it is not helpful. What he says is:

“The only problem is that we cannot epistemically understand the mathematical usage of i. And thus Gödel was proven right and not the absolute skeptic who doubts logic is true”.

Now, IP is obviously wandering off down the wrong path here. Clearly, IP finds imaginary numbers hard to think about, but it is not clear what that has to do with anything. His comment about Gödel betrays his poor grasp of his work as well. Because Spencer-Brown explained how to use i in an equation, that proves that Gödel was right? Hardly.

What is actually going on here, what IP seems unable to get, is that Spencer-Brown is not advocating for classical logic. In fact, he is quite out-there as a thinker, and proposing something quite radical. Let’s look at what Spencer-Brown says about the mathematical example that IP brought up, and how it relates to the liar paradox:

“Of course, as everybody knows, the [mathematical] paradox in this case is resolved by introducing a fourth class of number, called imaginary, so that we can say the roots of the equation above are ±i, where is a new kind of entity that consists of a square root of minus one.” (Spencer-Brown, Laws of Form, page xi, bold added by me)

Spencer-Brown is saying that the solution to the mathematical puzzle requires the addition of a “new kind of entity” to mathematics. A new kind of number. He then goes on in the next paragraph to explain how this mathematical lesson applies to logic:

“What we do in Chapter 11 is extend the concept to Boolean algebras, which means that a valid argument may contain not just three classes of statement, but four: true false, meaningless and imaginary.” (ibid)

So Spencer-Brown is playing around with a type of logic which has four truth-values, not two like classical logic has. This makes it a very exotic type of non-classical logic! IP doesn’t mention this passage, which clearly shows Spencer-Brown freely speculating on a type of logic which is very different from classical logic.

So, what we have here is an example of someone saying that the right way to solve the liars paradox is to modify classical logic in some fundamental way. IP seems to think that this example makes the point he wants to make, but if anything it points in the opposite direction completely. Far from showing that the laws of classical logic cannot be questioned, it is an example of someone questioning the laws of classical logic.

5. Conclusion

So far we have seen that IP has no real idea what the skeptical challenge to logic really consists in. He knows that sometimes people talk about reasons to doubt things like non-contradiction or the law of excluded middle, and he seems to take this to be a very radical attack on logic itself. However, we saw that he presented an argument that attempted to attack the claim that the laws of logic are true, and he hopelessly misunderstood it. It was showing that if the Liar Proposition is neither true nor false, then classical logic isn’t correct. In response, he proposed that “Easter is the best holiday” was neither true nor false, which is itself very poorly argued for, but even if it were correct would be another reason to reject classical logic. He then utterly failed to grasp Gödel, and may have deliberately misstated the theorem’s significance. Lastly, he looked at a passage from Spencer-Brown, but failed to see that if it was correct, it would be a reason to prefer a four-valued logic over the classical two-valued logic.

There is still another half of his video to go, and I will try to get round to debunking the claims made in that half as well when I get a chance.

A New Problem for Divine Conceptualism?

0. Introduction

Divine Conceptualism (DC) is an idea about the ontological relationship between God and abstract objects, defended by Greg Welty, in his M.Phil thesis “An Examination of Theistic Conceptual Realism as an Alternative to Theistic Activism“(Welty (2000)), his Philosophia Christi paper “The Lord of Non-Contradiction” (Anderson and Welty (2011)), and his contributions to the book “Beyond the Control of God” edited by Paul Gould (Welty (2016)). Put simply, (DC) identifies abstract objects as something like ideas in the mind of God.

Welty sees his view as being quite close to that of Morris & Menzel‘s (1986) ‘theistic activism’ (TA), according to which:

“…all properties and relations are God’s concepts; the products, or perhaps better, the contents of a divine intellective activity.” (Morris & Menzel (1986), p. 166)

Morris & Menzel’s TA asserts that God created everything which is distinct from God, and that includes the divine concepts themselves. However, as Welty (2000) p.29 observes, TA is vulnerable to ‘bootstrapping’ objections. If God is supposed to be able to create his own properties, then he creates his own omnipotence (because omnipotence is a property); yet it seems that one would already have to have omnipotence in order to be able to create omnipotence. Even more forcefully: God already needs to possess the property of ‘being able to create properties’ in order to create properties. The idea of self-creation is therefore seemingly incoherent.

Welty’s DC can be seen as a modified version of TA; it is TA without the troublesome doctrine of self-creation. On DC:

“…abstract objects … are uncreated ideas in the divine mind; i.e. God’s thoughts.” (Welty, (2000), p. 43

Postulating abstract objects as uncreated divine ideas is designed to avoid the bootstrapping objections from above.

There are of course lots of different types of abstract objects, including propositions, properties, possible worlds, mathematical objects, etc. Here we will only look at propositions. One of the motivations for thinking that propositions in particular are divine thoughts is the argument from intentionality (seen in Anderson and Welty (2011), p 15-18). Propositions are intentional, in that they are about things. So the proposition ‘the cat is on the mat’ is about the cat having a certain relationship to the mat; the proposition is about the cat being in this relation to the mat. In a similar manner, thoughts are also about things. Consciousness is always consciousness of something or other. In Anderson and Welty (2011), it is argued that the laws of logic are propositions, which are necessarily true and really existing things. Given the intrinsic intentionality of propositions, these are argued to be thoughts. However, they cannot be thoughts had by contingently existing entities, like humans, as humans could have failed to exist, whereas laws of logic could not. Thus:

“If the laws of logic are necessarily existent thoughts, they can only be the thoughts of a necessarily existent mind.” (Anderson and Welty, (2011), p.19).

However, I want to point out an objection to this picture, which I have not seen in the literature (a nice summary of existing objections is found here). It is about the definition of the word ‘thought’. (It may be that this problem has been adequately documented in the literature somewhere that I have not seen. Maybe someone can let me know in the comments section.)

  1. Thought

It seems to have gone unnoticed that Welty in particular oscillates between DC being construed in two different and incompatible ways. It has to do with the word ‘thought’. There is no completely standardised usage of this term in the philosophy literature. And it is a term which needs careful definition in a philosophical argument because in natural language the word ‘thought’ is sometimes used to refer to the thinking and sometimes the thought-of; it is either the token of a type of mental activity called ‘thinking’, or it is the content, or object, of the thinking. For example, we may have the intuition that my thought is private, and that it is metaphysically impossible for you to have my thought (which makes thoughts similar to perceptions in this respect). But we may also have the intuition that we can ‘put our thoughts on paper’ or ‘share our thoughts’ with other people. It seems to me that this ambiguity infects Welty’s version of DC due to his not clearly and carefully defining what he means by ‘thought’ so as to disambiguate the term between thinking and thought-of. Welty (2000), for example, doesn’t actually contain a definition of a ‘thought’ anywhere in it, even though it mentions ‘thought’ 135 times in 85 pages.

According to Anderson and Welty (2011), they seem to indicate that a thought is not the content of thinking, but the token of the act of thinking. In a footnote on page 20, they say:

We could not have had your thoughts (except in the weaker sense that we could have thoughts with the same content as your thoughts, which presupposes a distinction between human thoughts and the content of those thoughts, e.g., propositions).”

The distinction that is being made here is between thoughts, which are individualised occurrences not shareable by multiple thinkers, and the contents of those thoughts, which are generalised and shareable by multiple thinkers. I can have a thought with the same content as you, even though we cannot have the same thought. In Fregean terms, a ‘thought’ (as Anderson and Welty use the term above) is an ‘apprehension’. When one thinks about the Pythagorean theorem, one is apprehending the proposition. In order to be explicit about what I mean, I will disambiguate the term ‘thought’ by referring to the token act of thinking as an ‘apprehension’, and the content of the thought as the ‘proposition’.

2. Blurred Lines

However, in Welty (2000), this distinction is repeatedly blurred. One of the main thrusts of the position defended there is that God’s thoughts function as abstract objects:

“God and I can have the same thought, ‘2+2=4’, in terms of content. But my thought doesn’t function in the same way that God’s thought does. My thought doesn’t determine or delimit anything about the actual world, or about any possible world. But God’s thought does. Thus, it plays a completely different role in the scheme of things, even though God and I have the same thought in terms of content. Thus, God’s thought uniquely functions as an abstract object, because of his role as creator of any possible world. I am not the creator of the actual world (much less, any possible world), and thus my thoughts, though they are in many cases the same thoughts as God’s, don’t function as abstract objects in any relevant sense.” (Welty, (2000), p. 51)

Welty says that God and I can have ‘the same thought in terms of content’, which blatantly smudges the sharp distinction between the apprehension and proposition. We can each apprehend the same proposition. But can I share in God’s apprehension of the proposition? It seems that the answer would have to be: no. God’s apprehension of a proposition is surely private to God, just as my apprehension of a proposition is private to me.

Then Welty ends the passage with “my thoughts, though they are in many cases the same thoughts as God’s, don’t function as abstract objects in any relevant sense”. The only sense in which my thoughts are “the same thoughts as God’s” is in terms of the propositions that I think about being the same as the ones that God thinks about. In that sense they do function as abstract objects, precisely because they are abstract objects, namely propositions! The sense in which ‘my thoughts’ don’t function as abstract objects is in terms of the token act of thinking (the apprehension). That doesn’t function as an abstract object, but then that is not something I share with God. So Welty cannot have it that there is something, x, which is both something I share with God and which doesn’t function as an abstract object. The only reason it seems like this is possible is because of a failure to distinguish clearly between thought as apprehension, and thought as propositional content.

This confusion pops up again and again. Take the argument from intentionality, found in all three Welty publications referenced in this post. Part of the motivation for DC is that propositions are (supposedly) thoughts (because they are intentional) but that they cannot be human thoughts; a non-divine conceptualism, the doctrine that abstract objects like propositions are human thoughts, cannot do the job here. The reason for thinking that they cannot be human thoughts is as follows:

“There aren’t enough human thoughts to go around…, human thoughts don’t necessarily exist, and whose thoughts will serve as the intersubjectively available and mind-independent referents of propositional attitudes (referents that are also named by that-clauses)?”

There are three reasons given against human thoughts being able to play the role of propositions: a) there aren’t enough of them, b) their existence isn’t necessary, c) they aren’t intersubjectively available.

While these considerations look somewhat compelling when trying to think of a human conceptualism without the benefit of the distinction between apprehension and proposition, it quickly loses its force when we apply the distinction. The problem is the combination of two types of properties that propositions need. One type of property is associated with divine apprehensions, and the other type of property is associated with divinely apprehended propositions. Being of sufficient plentitude to play the role of propositions (a), and having necessary existence (b), are of one type, and being ‘intersubjectively available’ (c) is of the other. As I shall show, you cannot have both of these types at the same time, without smudging the distinction between apprehensions and propositions.

Firstly, let’s consider non-divine conceptualism, where thoughts are construed as apprehensions.

There are, of course, only finitely many human apprehensions of propositions; there are only finitely many times people have apprehended propositions. Also, human apprehensions of propositions are contingently existing things, because human minds are themselves only contingently existing things. Human apprehensions are also inherently private, and thus not intersubjectively available. So apprehensions cannot be thought of as ‘doing the job’ of abstract objects for these reasons. That much is quite clear.

On the other hand, there may be infinitely many divine apprehensions, so there would be ‘enough to go round’, and perhaps they each exists necessarily. In this sense, they seem suited to play the role of propositions. However, as apprehensions, they would not be ‘intersubjectively available’. Can I actually share in God’s apprehension of a proposition? Unless I can, they cannot play the role of an abstract object.

Thus, when considering apprehensions, although non-divine conceptualism is not suited to play the job, neither is divine conceptualism. The problem is just that apprehensions are private. So let’s compare non-divine and divine conceptualism, where we construe ‘thought’ as the contents of thoughts.

Right away it is obvious that there is no reason to think that the content of human apprehensions are limited in the same way as their apprehensions were. The contents of human apprehensions just are propositions, so of course they can play the role of propositions!

Equally, if divine thoughts are construed as divinely apprehended propositions, then there will be enough to go round, they will exist necessarily, and they will be intersubjectively available. But in both cases, this is just because propositions themselves are sufficiently plentiful, necessary and intersubjective to play the role of propositions. Obviously, propositions can play the role of propositions. Being apprehended by God, rather than humans, is not what bestows the required properties on them.

3. Begging the question?

But perhaps I have begged the question somehow. Maybe the defender of DC can stipulate that, although my apprehensions are private, God’s apprehensions are somehow intersubjectively available. Call this theory ‘divine accessibility’ (DA). So on DA, propositions are divine apprehensions (which are plentiful, and necessary existing) and crucially also intersubjectively available to humans; they can be the content of humans’ apprehensions.

So, let’s say that I am thinking about the Pythagorean theorem. Let’s say that my apprehension is A. According to DA, the content of my apprehension, what A is about, is a divinely accessible apprehension, D. But the question is, what is the content of the divine apprehension, D? What is it that God is thinking about when he has the thought which is the Pythagorean theorem? There seem to be only a few options:

Either God’s apprehension, D, has content, or it does not. If it has no content, then what is it about D which links it to the Pythagorean theorem, rather than to some other theorem, or to nothing at all? It would be empty and featureless without content.

But, if it does have content, then either the content is that ‘the square of the hypotenuse is equal to the sum of the squares of the other two sides’, or it is something else.

If it does have this as its content, then it seems like the content of D is doing all the work. It seems like the only reason God’s apprehension is linked in any way to the Pythagorean theorem is that it has the theorem as its content. If that is right, then we need to have the proposition itself in the picture for God’s apprehension to be in any way relevant.

Consider what would be the case if the content of God’s apprehension was of something else entirely, like the fact that it all bachelors are unmarried men or something. In that situation, there  would be no reason to say that this apprehension was the Pythagorean theorem. The only divine apprehension that could, even plausibly, look like it is playing the role of the proposition is one which has the proposition as its content.

And if we ask what role God’s apprehension plays here it seems that the answer is that it is just a middle man in between my apprehension and the theorem. It seems to be doing nothing. When I think of the theorem, I have an apprehension, A, and all this is about is one of God’s apprehensions, D, which is itself about the theorem. If p is the Pythagorean therem, and x ⇒ y means ‘x is about y’, then we have:

A ⇒ D ⇒ p

God’s apprehension is just an idle cog which does nothing. Why not just have:

A ⇒ p

Why not just say that I have the theorem as the content of my thought? It would be a much simpler suggestion. Given that for God’s apprehension to be in any way relevant to the proposition in question it has to have the proposition as its content, we seem to require the proposition in the picture anyway. Ockham’s razor should suggest shaving off the unnecessary extra entity in the picture, which is the divine apprehension.

4. Conclusion

Thus, there are really two problems with DC. If construed as the contents of God’s thoughts, divine ‘thoughts’ just are propositions. So for DC to be in any way different from the traditional Fregean picture (where propositions are abstract objects), we have no other option but to construe divine thoughts as divine apprehensions. However, it seems that apprehensions are inherently private, and so they are unsuited to play the role of propositions. Even if we postulate that somehow divine apprehensions are accessible to everyone, they seem to become idle cogs doing nothing.

Problems with ‘The Lord of non-Contradiction’

0. Introduction

In this post, I will not be focusing on a blog post or a non-professional apologetical argument. Rather, I will be focusing on an argument in a peer-reviewed academic journal, called Philosophia Christi (it is published by the Evangelical Philosophical Society). The paper is entitled ‘The Lord of Non-Contradiction‘, and the authors are James Anderson and Greg Welty. They are professional academics, with PhDs in respected institutions (Edinburgh and Oxford, respectively). These guys are proper academics, by any standards. I believe this to be the most philosophically rigorous version of their argument that I have come across.

The argument they present in the paper is a version of the ‘argument from logic’, in which the existence of God is argued for using the nature of logic as the motivating factor. This is a sophisticated version of the familiar presuppositionalist refrain, and is the sort of thing I imagine Matt Slick would be arguing for had he received a graduate education in philosophy as well as theology. It is an interesting paper, which certainly doesn’t fall prey to the usual fallacies that we see repeated over and over again in the non-professional internet apologetics communities. They are presuppositionalists (as far as I can gather), but this is not a presuppositional argument as such.

Despite their obvious qualities as theologians and philosophers, I still see reason to reject the argument, which I will explain here. Before we get to my reasons for criticising the argument, we should have a look at the argument as they present it.

  1. The argument

The paper is divided into nine sections, the first eight of which have headings that are claims about the laws of logic; ‘the laws of logic are truths’, ‘the laws of logic are truths about truths’, ‘the laws of logic are necessary truths’, ‘the laws of logic really exist’, ‘the laws of logic necessarily exist’, ‘the laws of logic are non-physical’, ‘the laws of logic are thoughts’, and ‘the laws of logic are divine thoughts’. Here is how they summarise the argument in their conclusion:

The laws of logic are necessary truths about truths; they are necessarily true propositions. Propositions are real entities, but cannot be physical entities; they are essentially thoughts. So the laws of logic are necessarily true thoughts. Since they are true in every possible world, they must exist in every possible world. But if there are necessarily existent thoughts, there must be a necessarily existent mind; and if there is a necessarily existent mind, there must be a necessarily existent person. A necessarily existent person must be spiritual in nature, because no physical entity exists necessarily. Thus, if there are laws of logic, there must also be a necessarily existent, personal, spiritual being. The laws of logic imply the existence of God.” (p. 20)

So we see a plausible looking string of inferences from various claims, each of which has a section in the paper defending it, and often presenting citations to other papers for elaborations. We seem to be moving from simple observations about the nature of the laws of logic, that they are necessary truths, etc, to the claim that they indicate the presence of a divine mind.

Here is the argument from above in something closer to premise/conclusion form. I have had to construct this, as the authors leave the logical form of the argument informal, and in doing so, I have tried to represent the reasoning as we find it above:

  1. The laws of logic are necessarily true propositions.
  2. Propositions are real entities, but cannot be physical entities; they are essentially thoughts.
  3. But if there are necessarily existent thoughts, there must be a necessarily existent mind.
  4. If there is a necessarily existent mind, there must be a necessarily existent person.
  5.  A necessarily existent person must be spiritual in nature, because no physical entity exists necessarily.
  6. If there are laws of logic, there must also be a necessarily existent, personal, spiritual being.
  7. A necessarily existent, personal, spiritual being is God
  8. The laws of logic imply the existence of God.
  9. Therefore, God exists.

The final step I have had to add in myself, as Anderson and Welty do not explicitly draw it out as such. They stop their argument at the conditional ‘logic implies God’, leaving the reader to join the dots. There are some terms that don’t quite match up properly in the above (true propositions and real entities, etc), which stop it from being formally valid.

1.1 A more formal version of the argument

Here is a more formal way of thinking about the argument, with the presentation cleaned up a bit, and as a result more stilted:

 

1.  If something is a law of logic, then it is necessarily true. (premise)

1a. If something is necessarily true, then it is true all possible worlds. (premise).

 1b. There is something which is a law of logic. (premise)

 1c. There is something such that it exists in all possible worlds. (from 1 and 1b.)

2. For everything that exists, it is either a physical thing or a thought. (premise)

2a. If something is a law of logic, then it is either a physical thing or a thought. (from 1 and 2.).

2b. If a thing exists necessarily, then it is not a physical thing. (premise)

2c. If something is a law of logic, then it is not a physical thing. (from 1 and 2b.)

2d. If something is a law of logic, then it is a thought. (from 2a. and 2c.)

2e. There is something which is a thought. (from 1a. and 2d.)

 2f. There is something such that it is is a thought and that it is necessary that it exists. (from 1b and 2e)

3. If there is a thought, then there is a mind (of which it is a part). (premise)

3a. There is a thought and there is a mind (of which it is part). (from 2e. and 3)

3b. There is something such that it is is a thought and that it is necessary that it exists, and that there is a mind (of which it is part). (from 2f., 3.)

4. If something is a mind, then it is a person. (premise)

4a. There is a person. (from 3a and 4)

4b. There is something such that it is is a thought and that it is necessary that it exists, and that there is a mind (of which it is part) and this is a person. (from 3b. and 4)

 5. If it is necessary that there is a person, that person must be spiritual. (premise)

5a. It is necessary that there is a person such that they are spiritual. (from 4b and 5).

6. If the laws of logic exist, then it is necessary that there is person who is spiritual. (1a and 5a)

7. If it is necessary that there is a spiritual person, that person is God. (premise)

8. Therefore, God exists (from 5a. and 7)

 

The argument presented above is valid. It has the advantage of showing what the various inferences are and how many assumptions need to be given in order for the argument to work. I will present two initial problems, before going into more detail about three more serious problems.

1.2 Initial problems

There are two initial problems with the argument. Firstly, the conclusion arrived at is actually weaker than ‘God exists’, and secondly there is a false dichotomy involved in one of the premises.

1.2.1 Polytheism

The first problem is in premise 3, the inference from the existence of thoughts to the existence of a mind. Take a particular law, say the law of non-contradiction. We can run through the argument up to premise 3 and show that there is a thought, then we deduce the existence of a mind from it; call that mind ‘M1’. But now run the argument again, this time with the law of excluded middle as the example. Once again, when we arrive at step 3, we deduce the existence of a mind; call it ‘M2’. The question is, does M1 = M2? It doesn’t follow logically that they are the same mind, and they could be distinct minds for all the truth of the premises entail. If so, then we would end up with two Gods at the end. Given that there are three laws of logic considered in the paper, Anderson and Welty’s argument is compatible with there being three non-identical necessarily existing minds, or Gods, which would be polytheism. The argument is not specific to laws of logic, but could use any necessary proposition, such as those of mathematics, meaning that we could be looking at an infinite number of minds.

In order to avoid this, we would have to add in as an additional premise that in all cases such as this, M1 = M2. But this seems rather implausible. Now the argument basically says, ‘laws of logic are thoughts, and so are all necessary propositions, and they are all had by the same mind, and that mind is God’. The addition of this premise is ad hoc, meaning it has no intuitive support apart from the fact that it gets us to the conclusion. For it to be considered at all plausible, there should be some independent reason given to think that it is true. Anderson and Welty consider something close to this objection:

It might be objected that the necessary existence of certain thoughts entails only that, necessarily, some minds exist.” (p.19)

However, they cash this out with a scenario in which there are multiple contingent minds, and then produce a counter-argument against this. They seem to miss the possibility that there are multiple necessary minds (i.e. polytheism), and as such their counter-argument misses my point entirely.

At the moment, even if you grant all the premises and assumptions, the argument establishes only that at least one god exists, which is presumably a lot weaker than the conclusion they intend to establish.

1.2.2 False dichotomy

Another problem with the argument above is that premise 2 (everything is either a physical thing or a thought) is a false dichotomy. In addition to arguing that laws of logic are not physical, one would have to present an argument for why the only two options are physical or thought. Anderson and Welty do not present any such argument, and as such there is no reason to accept premise 2. One might want to argue that everything has to be in one of two categories, but then one has to say something about difficult cases. We often say things like ‘there is an opportunity for a promotion’. On the face of it, we are quantifying existentially over opportunities. So opportunities exist. Are they physical things? Are they thoughts? Take haircuts as another example. Are they physical things? Are they thoughts? We could come up with some way of categorising things such that opportunities are a kind of mental entity, and haircuts are a type of physical entity, or explain away the apparent existential quantification as a mere turn of phrase, but the point is that is it is not straightforward to merely claim that everything is either mental or physical, and any argument which relies on this as a basic assumption inherits all the difficulties associated with it.

However, if I left things like that, then I think I would be seriously misrepresenting their actual argument. In reality, this premise is a product of trying to stick to the wording of what they say in the quoted section above. In the paper, they actually provide a positive argument for why laws of logic have to be considered as thoughts. So we could just change premise 2 to ‘the laws of logic are thoughts’, and have it supported independently by their sub-argument. I will come to their sub-argument, that the laws of logic have to be thoughts, in section 3 below.

In what follows, I will look at three aspects of their argument where I think there are weaknesses. These aspects will be with a) the claim that the laws of logic are necessary (part 2), b) with the inference from intentionality to mentality (part 3), and c) with a modal shift from necessary thoughts to necessary minds (part 4). They are not presented in order of importance, or any particular order.

2. The Necessary Truth Hypothesis

The first premise of the argument as stated above (‘If something is a law of logic, then it is necessarily true’) is ambiguous over the variety of necessity involved. There are several likely contenders for the type of modality involved: epistemic modality, metaphysical modality, logical modality. I consider each in turn.

2.1 Epistemic Modality

Anderson and Welty are clearly not attempting to make an epistemological claim about the status of the laws of logic. They say they are not interested in exploring the epistemological connection between the laws of logic and God (“In this paper we do not propose to explore or contest those epistemological relationships”, p. 1), so I think it is safe to assume that when they say the laws of logic are necessary, they do not merely mean epistemologically necessary.

 

2.2 Metaphysical Modality

More likely, when Anderson and Welty say the laws of logic are necessary, they mean the laws of logic are metaphysically necessary. They are fairly explicit about this:

“…we will argue for a substantive metaphysical relationship between the laws of logic and the existence of God … In other words, we will argue that there are laws of logic because God exists; indeed, there are laws of logic only because God exists.” (p. 1)

Nonetheless, on this reading, I find the reasons they offer for thinking the laws of logic are necessary rather strange. They say,

“…we cannot imagine the possibility of the law of noncontradiction being false” (p. 6),

And in a footnote they say that they

“…rely on the widely-shared intuition that conceivability is a reliable guide to possibility” (ibid)

The suggestion then is that the reason for thinking that non-contradiction is metaphysically necessary because they cannot imagine true contradictions. I want to bring up three issues with this methodology:

  1. Conceivability is often a poor guide to metaphysical possibility
  2. The falsity of non-classical laws is conceivable
  3. The falsity of excluded middle is conceivable

2.2.1 Metaphysical modality and conceivability

Firstly, in contrast to their ‘widely-shared intuition’, conceivability seems to me to be a relatively poor guide to metaphysical possibility. Ever since Kripke’s celebrated examples of necessary a posteriori truths in Naming and Necessity, the epistemic and metaphysical modalities have been recognised to be properly distinct from one another. One could easily adapt those famous examples to show the independence of metaphysical possibility and conceivability.

For example, one might not be able to conceive of the morning star being identical to the evening star (if you were an ancient Babylonian astrologer, etc), but we now know that their identity is metaphysically necessary. Again, one might be able to conceive of the mind existing without the brain, but it is quite plausible their independence is metaphysically impossible. Kant famously thought Euclidian geometry was a synthetic a priori truth; one must presuppose Euclidean geometry to be true when we think about the world, which would make its falsity inconceivable. Yet our world is non-Euclidian. It took pioneering and brilliant mathematicians to imagine what geometry would be like in this case, but once their work has filtered down into mainstream educated society, this otherwise inconceivable metaphysical truth has become entirely conceivable.

A somewhat similar situation is now the case with non-contradiction. Graham Priest is a very widely respected, if controversial, logician and metaphysician who has argued for the thesis that there are true contradictions. One may disagree with his methodology and conclusions, and I am in no way asserting that dialethism is anywhere as near as well supported as non-euclidian geometry, but it seems odd to rule out all the work on dialethism and paraconsistent logic simply on the basis that one cannot conceive of it being true. It could quite easily be true regardless of your particular inability to conceive of it, as history seems to show.

To push this even further, it is worth noting that conceivability (like epistemic modality, and unlike metaphysical possibility) is agent-dependent, in the sense that what is, and is not, conceivable varies from agent to agent. I may be able to conceive of something you cannot. To take an example of an agent who cannot conceive of a thesis, and then to couple that with the claim that ‘conceivability is a reliable guide to possibility’, seems to be ad hoc. Had we started with someone else’s outlook (say Graham Priest’s), we would be using exactly the same argument to reach the opposite conclusion. The strength of the argument then would depend entirely on the choice of agent.

Anderson and Welty cannot conceive of true contradictions. But should we be consulting their notion of conceivability when trying to draw metaphysical conclusions? If we are going to use conceivability as a guide to metaphysical possibility, we had better make sure we pick an agent who’s idea of what his conceivable is suitable for the job. An agent who’s idea of what is conceivable differed radically from what is in fact metaphysically possible would be unsuitable for that purpose (a five year old child, for example). Ideally,  you would want an agent who’s idea of what is conceivable supervened perfectly on what is in fact metaphysically possible. The extent to which they differed, for some particular agent, is the extent to which conceivability, for that particular agent, is not a ‘reliable guide to (metaphysical) possibility’. Whether something is metaphysically possible could be determined by consulting whether it was conceivable for a given agent only on the assumption that what is conceivable for that agent supervenes on what is in fact metaphysically possible. But this means that what is relevant here is simply whether or not contradictions are in fact metaphysically possible, as this would itself determine whether it was conceivable for that agent; not the other way round. So we have been taken on a long and winding route, via the notion of conceivability, which ultimately is seen to be relevant only to the extent that is maps to metaphysical possibility, to get to this destination.

So, is Anderson and Welty’s inability to imagine what true contradictions would be like actually any kind of evidence that true contradictions are metaphysically impossible? The answer is: only if what they can conceive of matches perfectly (at least with respect to this issue) what is in fact metaphysically possible. We have to assume that they are right for the inference to be seen as valid. And we have been given no reason to think that this is the case. Until we are, we should draw no conclusions about what is metaphysically possible based on what they are able to conceive of. If they could produce some reason to think that what they can conceive of always tracks what is metaphysically possible, or at least successfully tracks what is metaphysically possible in this case, then we would have been given some reasonwe have been given no reason to buy the claim that true contradictions are metaphysically impossible.

There might be other reasons to think that contradictions are metaphysically impossible of course, but they are not mentioned in this paper. So the argument as stated has an unjustified premise, it seems to me.

2.2.2 Conceivability and non-classical laws

In the introduction to their paper, Anderson and Welty attempt to pre-empt a response about alternative laws of logic by saying that their argument is not dependent in any way on the  choice of these particular laws. They say:

Readers who favor other examples [of logical laws – AM] should substitute them at the appropriate points.”

I am not saying we should use any particular laws rather than the ones that they use here either. But I do want to point out that this part of the argument (about the laws being metaphysically necessary) does depend for its plausibility on the choice of laws, in contrast to the claim above. What we are being asked to accept is the inconceivability of the falsity of the laws of logic. I suggest that this far more likely to be considered true if we start with classical laws, than if we had substituted in other non-classical laws at the beginning. For example, would Anderson and Welty be prepared to defend that the falsity of the laws of quantum logic is also inconceivable? Or equally inconceivable as the falsity of the classical laws? The laws of quantum logic may well be true or false (at least from my perspective), and so their falsity is certainly conceivable to me.

Even if it turns out that they are big enthusiasts for quantum logic as well as for classical logic, finding each equally intuitive (which seems unlikely), there will surely be some far-out system of logic which has some law they find down-right implausible, for which its falsity is entirely conceivable to them. Then, their argument would not work if we substituted the laws from these logical systems instead.

This would mean that, to this extent then, their argument is only an argument for the sorts of logical systems they happen to find plausible. Thus, if a logic happens to be the one that God thinks, which also happens to be entirely implausible to Anderson and Welty (for which they find the falsity of its principles entirely conceivable), they would have failed to articulate an argument here which established a route from logic to God.

2.2.3 Excluded middle

The general argument for the laws of logic being metaphysically necessary is that their falsity is inconceivable. Here is Anderson and Welty:

Not only are the laws of logic truths, they are necessary truths. This is just to say that they are true propositions that could not have been false. The proposition that the Allies won the Second World War is a contingent truth; it could have been false, since it was at least possible for the Allies to lose the war. But the laws of logic are not contingent truths. While we can easily imagine the possibility of the Allies losing the war, and thus of the proposition that the Allies won the Second World War being false, we cannot imagine the possibility of the Law of Non-Contradiction being false. That is to say, we cannot imagine any possible circumstances in which a truth could also be a falsehood.” (p. 6, emphasis mine)

It is telling that Anderson and Welty use the law of non-contradiction as their example here, as it is admittedly rather difficult to get one’s head around the idea of it being false (none other than David Lewis famously claimed not to be able to do so).

However, this reasoning does not really work for the law of excluded middle. What we have to do to imagine that this is the case is to imagine that there is a proposition for which neither it nor its negation is true. Aristotle makes various comments in De Interpretione IX, which he (seems to) make an argument according to which statements about the future concerning contingent events, such as ‘Tomorrow there will be a sea battle’, should be considered neither true nor false. It follows from this that the law of excluded middle would be false, at least for future contingents such as this. There is controversy as to whether Aristotle was making this argument, with the issue being one of the longest logico-metaphysical debates in the history of philosophy (being discussed by Arabic logicians, medieval logicians, and modern logicians), and there is nothing like a consensus that Aristotle was correct in making this argument, if indeed he was actually making it. However, the thesis he was putting forward (that future contingents are neither true nor false) is clearly conceivable by a great many philosophers. Indeed, it is a textbook philosophical position.

So the argument was that the laws of logic are metaphysically necessary, and the support for this is that the falsity of the laws of logic is inconceivable. Yet, while it is perhaps true for the law of non-contradiction, this seems plainly false for the law of excluded middle. It is patently conceivable that it is false. Thus, the support for the laws of logic being metaphysically necessary only covers two of the three laws they themselves provide.

If we were to respond by dropping excluded middle just to get around this problem, that would be ad hoc. To respond to this, they should explain how the falsity of excluded middle is in fact inconceivable, or provide another reason for thinking that it is metaphysically necessary.

2.3 Possible worlds 

Anderson and Welty attempt to provide additional support for the metaphysical necessity of the laws of logic by asserting the laws of logic are true in all possible worlds. Again, leaning heavily on the notion of conceivability, they say:

[w]e cannot imagine a possible world in which the law of noncontradiction is false…Now you may insist that you can imagine a possible world—albeit a very chaotic and confusing world—in which the Law of Non-Contradiction is false. If so, we would simply invite you to reflect on whether you really can conceive of a possible world in which contradictions abound. What would that look like? Can you imagine an alternate reality in which, for example, trees both exist and do not exist?” (p. 6).

Firstly, for the law of non-contradiction to be false, there only has to be one true contradiction, and it is not required that contradictions ‘abound’. I think I could conceive of a possible world where there is a contradiction; and it might be the actual world. Perhaps the liar sentence (‘this sentence is false’) is an example. Maybe in the actual world everything else is classical apart from the liar sentence. If so I have conceived of a world in which the law of non-contradiction is false. This does not mean that ‘contradictions abound’, and we do no have to imagine trees both existing and not existing. I seem to have met their challenge.

Remember, I do not have to show that the liar sentence is in fact both true and false at the actual world. All I have to do is be able to conceive of a world in which the law of non-contradiction is false. It seems to me that, given the work of dialethists on this area, it is conceivable.

Perhaps sensing the need for further argument, they say that contradictory worlds cannot be conceived of, because possible worlds are by definition consistent:

The criterion of logical consistency—conformity to the law of noncontradiction—is surely the first criterion we apply when determining whether a world is possible or impossible. A world in which some proposition is both true and false, in which some fact both obtains and does not obtain, is by definition an impossible world. The notion of noncontradiction lies at the core of our understanding of possibility.” (p. 6 – 7)

This passage is quite hard to interpret. However, Anderson and Welty seem to argue in a circle. They seem to think non-contradiction is necessary because inconsistent possible worlds are inconceivable. But the only reason they give for thinking inconsistent worlds are inconceivable is, by definition, we use consistency as a sort of yard-stick to ‘determine’ whether a given world is indeed possible. Thus, laws of logic are necessary because they are true in all possible worlds, but laws of logic are true in all possible worlds because the laws of logic are necessary.

I think the direction of travel from possible worlds to possibilities is misguided. Anderson and Welty appear to be under the impression there is some metaphysically significant sense in which we can check possible worlds to see if they really are possible or not; as if possible worlds were conceptually prior to possibilities. The picture painted is that there is a sort of a priori rationalistic access we have to the set of possible worlds which we can consult in order to find out about what is really possible. This idea is actually warned against by Kripke in Naming and Necessity. There he argues against the identification of a prioricity and necessity:

I think people have thought that these two things [a prioricity and necessity – AM] must mean the same of these reasons: … if something not only happens to be true in the actual world but is also true in all possible worlds, then, of course, just by running through all the possible worlds in our heads, we ought to be able with enough effort to see, if a statement is necessary, that it is necessary, and thus know it a priori. But really this is not so obviously feasible at all.” (p. 38)

It also seems to fly in the face of Kripke’s famous telescope remark:

“One thinks, in this picture, of a possible world as if it were like a foreign country. … it seems to me not to be the right way of thinking about the possible worlds. A possible world isn’t a distant country that we are coming across, or viewing through a telescope.… A possible world is given by the descriptive conditions we associate with it” (Kripke,Naming and Necessity, p 43-44).

I think, apparently in contrast to A&W, possible worlds are just a way of cashing out our notion(s) of possibility. If we are thinking about what is logically possible (with classical logic in mind), then when constructing the possible worlds we make sure to get them consistent (to keep non-contradiction) and also maximal (to keep the law of excluded middle). So a truth assignment for a formula in classical propositional logic is a ‘possible world’, so long as the truth assignment covers all cases and gives each formula only one truth value.

However, different notions of logical consequence lead to different constructions of worlds. In intuitionist logic, where we want to have mathematical propositions for which there is no formal proof to be neither true nor false, the ‘possible worlds’ (or ‘constructions’) are not maximal. They may simply leave both p and not-p out altogether. Equally, for a dialetheist who believes there are true contradictions in the actual world, where both p and not-p are true, the notion of ‘possible world’ leaves out the notion of consistency (or, if you prefer, the dialetheist includes both possible worlds and ‘impossible worlds’ in his semantics). In the actual practice of formal and philosophical logic, one normally starts with a notion of logical consequence (or of ‘laws’) and then uses logical consequence to cash out what the appropriate semantic apparatus will be like. On this understanding (the usual understanding), one cannot use the fact that maximal and consistent possible worlds do not have contradictions to tell us which logical laws to accept as true, as we need an idea of which logical laws to accept prior to accepting anything about possible worlds. So the circularity of A&W’s reasoning here is completely avoidable. They just need to appreciate the role possible worlds semantics plays in philosophical logic. If they were able to see the restrictions they put on possible worlds (maximal, consistent, etc) are not mandatory, they would be able to more readily conceive of how a possible world could be inconsistent or non-maximal. Anderson and Welty appear to resemble the 17th century geometer who cannot imagine parallel lines ever meeting and concludes the meeting of parallel lines is metaphysically impossible. Thus, Anderson and Welty’s failure to imagine what non-classical worlds would be like seems to be a limitation on their part and should not be used as a support for their argument.

In sum, Anderson and Welty provide two reasons for thinking LOL are metaphysically necessary: (i) their falsity is inconceivable and (ii) they are true in every possible world. We have shown (i) provides flimsy support for their subconclusions and (ii) is based on several confusions concerning philosophical logic and possible worlds.

2.4 Logical Necessity

Finally, the claim could instead be read as saying the laws of logic are logically necessary truths. In some sense, one cannot deny the laws of logic are logically necessary truths, but this sense is trivial. Usually, the claim that p is logically necessary, with respect to a system S, simply means the truth of p does not violate any logical law of S. When p is an instance of a logical law of S, the claim becomes vacuous. If we said ‘p is chessessary’ means ‘the truth of p does not violate any of the laws of chess’, then, provided p is one of the laws of chess, obviously, p is chessessary. The claim, while true, is trivial. The necessary truth of laws of logic, if construed as logical necessity, is not a substantive claim, such as that associated with the necessary truth of the existence of platonic objects, or of God. Logical necessity is more like the way that statements about numbers depend on which number system you have in mind; is there a number between 1 and 2? No, if you mean ‘natural number’, yes if you mean a more complex notion of number. To ask ‘but is there really a number there?’ is arguably not a sensible question at all. If this is correct, then there may be no more to the notion of logical necessity than ‘necessary given system S’, and as such each logical law is true in its own system and (in general) is not in another system.

In sum, Anderson and Welty claim that the laws of logic are necessary truths. They do not seem to be making a claim about epistemological necessity; their arguments for a claim about metaphysical necessity are highly dubious; the claim that it is about logical necessity makes it vacuous. Thus, either this part of the argument is unsupported, or trivial.

3. Propositions are intentional

The most controversial aspect of Anderson and Welty’s argument is the move from the laws of logic being propositions, through them being intentional, to them being mental (or thoughts). In order to see what is at stake here, we need to be clear about both intentionality and propositions.

Anderson and Welty’s argument at this stage seems to be of the following form:

  1. All propositions are intentional.
  2. Everything intentional is mental.
  3. Therefore, all propositions are mental.

This little argument is clearly valid, so if the premises are also true, we would have to accept the conclusion.

I think there are reasons to doubt both premises. More specifically, there is reason to doubt that the arguments presented in Anderson and Welty’s paper support these premises.

3.1 Intentionality

The central idea behind intentionality is aboutness. Typical examples of intentional things are thoughts. So if I have a thought, it is always a thought which is about something, and it seems that there couldn’t be a thought which is not about anything. The typical philosophical authority referred to in this context is Brentano:

“Every mental phenomenon is characterized by what the Scholastics of the Middle Ages called the intentional (or mental) inexistence of an object, and what we might call, though not wholly unambiguously, reference to a content, direction towards an object (which is not to be understood here as meaning a thing), or immanent objectivity. In presentation something is presented, in judgement something is affirmed or denied, in love loved, in hate hated, in desire desired, and so on.” (Psychology from an empirical standpoint, Franz Brentano, 1874, p 68)

It has become customary to call the following claim ‘Brentano’s Thesis’:

x is intentional iff x is metnal

As this is a biconditional claim, it can be split into two conditionals:

  1. Everything intentional is mental
  2. Everything mental is intentional

It is standard for philosophers to argue that there are mental states which are non-intentional (Searle’s example is a vague an undirected feeling of anxiety), and thus that the second condition in Brentano’s thesis is false.

Anderson and Welty say that they are really concerned with the first of these conditions, and that

“…the argument is unaffected if it turns out that there are some non-intentional mental states” (p. 17)

What they need to do is show that there is nothing which is both intentional and non-mental. There seem to be counter-examples here though. Firstly, sentences of natural language seem to be intentional, in that they are about things. The sentence ‘Quine was a philosopher’ is about Quine. Yet that sentence is not itself mental. I can think about the sentence, of course, but the sentence itself is not mental.

The common response to this is to say that sentences are only derivatively intentional. On their own sentences are not about anything, but when read by a mind they become invested with meaning and this makes them about something. Sentences are just non-intentional  vehicles for communicating intentional thoughts. Anderson and Welty want to say that, while there may be instances of derivatively intentional phenomena (like sentences), anything which is inherently intentional is mental.

There are other approaches which hold that there are inherently intentional non-mental phenomena, such as that of Fred Dretske, according to which intentionality is best understood as the property of containing information. So an object is intentional if it contains some information. The content of the information is what makes the object about something else. So, an example is that there is no smoke without fire. In this sense, the smoke contains information about the presence of fire. Other examples stated on the Stanford page include:

A fingerprint carries information about the identity of the human being whose finger was imprinted. Spots on a human face carry information about a disease. The height of the column of mercury in a thermometer carries information about the temperature. A gas-gauge on the dashboard of a car carries information about the amount of fuel in the car tank. The position of a needle in a galvanometer carries information about the flow of electric current. A compass carries information about the location of the North pole.

All these objects are not mental, yet they carry information about things, and so are intentional in Dretske’s sense of the word. If this approach is correct, then Anderson and Welty’s inference is blocked (as there are things which are non-mental yet intentional), and with it the rest of the argument is blocked. You could not argue from the laws of logic being propositions, to them being intentional, to them being thoughts, to them being the thoughts of God. The jump from being intentional to being mental would be invalid if Dretske’s approach, or one like it, were correct.

There are problems with Dretske’s account of intentionality, as you would expect from a philosophical theory, but if Anderson and Welty want to advance the thesis that all intentional things are mental, they need to provide counter-arguments to proposals such as Dretske’s.

3.1.1 The mark of the mental

In fairness, Anderson and Welty do point to a paper by Tim Crane, about which they claim:

Following Brentano, Crane argues (against some contemporary philosophers of mind) that intentionality, properly understood, is not only a sufficient condition of the mental but also a necessary condition” (p. 17, footnote)

If this were right, then they would have some support for their claim that everything which is intentional is mental. However, I think they are using Crane to argue for a thesis that his paper does not support, and I will explain why I think this.

Crane’s main concern in his paper is to deal with intentionality being a necessary condition for being mental (i.e. that everything mental is intentional). The sufficiency claim (that everything intentional is mental), which is the only thing that Anderson and Welty are really concerned with for their argument, is only tangentially addressed by Crane in that paper. Crane’s motivation, as he explains, is to account for why Brentano would have asserted his thesis if there were so many seemingly obvious counter-examples to it:

If it is so obvious that Brentano’s thesis is false, why did Brentano propose it? If a moment’s reflection on one’s states of mind refutes the thesis that all mental states are intentional, then why would anyone (including Brentano, Husserl, Sartre and their followers) think otherwise? Did Brentano have a radically different inner life from the inner lives of contemporary philosophers? Or was the originator of phenomenology spectacularly inattentive to phenomenological facts, rather as Freud is supposed to have been a bad analyst? Or—surely more plausibly—did Brentano mean something different by ‘intentionality’ than what many contemporary philosophers mean?“(Crane, Intentionality as the mark of the mental, p. 2)

He says that he is not specifically interested in the historical and exegetical question of what Brentano and his followers actually said, but rather with the following question:

“…what would you have to believe about intentionality to believe that it is the mark of the mental?” (Crane, Intentionality as the mark of the mental, p. 2)

Thus, when Crane talks about ‘intentionality’, we should remember that he does not mean “what many contemporary philosophers mean” by the term. Rather, he has a specific aim in mind: to cash out what intentionality would be like if it was, by definition, the ‘mark of the mental’, i.e. not what intentionality is like, but what it would be like if Brentano’s thesis was true.

Most of the paper is directed at supposed examples of mental phenomena that are non-intentional, such as sense perception and undirected emotion. He gives an account of what it would mean to consider these as intentional. This effort is being addressed to defend the first part of Brentano’s thesis (that everything mental is intentional).

Although the focus of the paper is on the first part of Brentano’s thesis, Crane does directly confront the second part, i.e. the notion that everything intentional is mental:

I have been defending the claim that all mental phenomena exhibit intentionality. Now I want to return to the other part of Brentano’s thesis, the claim that intentionality is exclusive to the mental domain. This will give me the opportunity to air some speculations about why we should be interested in the idea of a mark of the mental.” (Crane, Intentionality as the mark of the mental, p. 14)

Crane addresses the Chisholm-Quine idea that sentences are intentional and non-mental phenomena. Chisholm (1957) proposed a criterion whereby we can tell if a sentence is intentional or not, which is basically if it is used in non-extensional (i.e. in intensional) contexts. Crane calls this the ‘linguistic criterion’. In response to this, Crane recommends that the position he is defending (intentionalism) should reject the linguistic criterion altogether. I will quote his reasons for recommending such a position in full:

“And given the way I have been proceeding in this paper, [the rejection of the linguistic criterion] should not be suprising. Intentionality, like consciousness, is one of the concepts which we use in an elucidation of what it is to have a mind. On this conception of intentionality, to consider the question of whether intentionality is present in some creature is of a piece with considering what it is like for that creature—that is, with a consideration of that creature’s mental life as a whole. To say this is not to reject by stipulation the idea that there are primitive forms of intentionality which are only remotely connected with conscious mental life—say, the intentionality of the information-processing which goes on in our brains. It is rather to emphasise the priority of intentionality as a phenomenological notion. So intentionalists will reject the linguistic criterion of intentionality precisely because the criterion will count phenomena as intentional which are clearly not mental.” (Crane, Intentionality as the mark of the mental, p. 15)

Thus we can see here that Crane rejects the criteria by which one says that some sentences are intentional, not because sentences are only ‘derivatively’ intentional, but “precisely because the criterion will count phenomena as intentional which are clearly not mentalUltimately, on Crane’s picture of intentionality, sentences are not intentional because they are not mental.

When it comes to propositions, it is actually quite controversial and non-standard to consider propositions to be mental (i.e. to be thoughts). Just like sentences, they are usually considered to be intentional (in the standard sense, in that they are about things) yet not mental. Anderson and Welty point to Crane as someone who has defended the thesis that everything intentional is mental. Yet, when we come to consider Crane’s special sense of intentionality, we see the author recommending that we should resist applying it to propositions just because we would end up classifying “phenomena as intentional which are clearly not mental“. Crane doesn’t deduce mentality from things that are otherwise obviously intentional; rather he ensures that everything intentional is mental by restricting the application of intentionality to only things which are obviously mental. It is a recommendation to change the meaning of intentional to get the desired result. If Anderson and  Welty want to say that the reason they have for claiming that propositions are mental is that they are intentional in Crane’s sense, then it is doubtful that this is true. It is doubtful that propositions are intentional in this sense precisely because they are not obviously mental. We could only use Crane’s sense of intentionality if we already thought that propositions were mental. Prima facie, it seems that are only as intentional as sentences, and if sentences are deemed non-intentional for Crane, then so should propositions. Thus, I see no benefit for Anderson and Welty for pointing us in the direction of Crane here.

 

4. Modal shift

Let’s say we grant that the laws of logic are (metaphysically/logically) necessary, and that they exist in every (metaphysically/logically) possible world. Let’s also grant that they are inherently intentional, and that they are therefore thoughts. What we would have established at this juncture is that there are some necessarily existing thoughts, which are constitutive of the laws of logic (and all other metaphysically necessary propositions). From this, Anderson and Welty draw the conclusion that this implies the presence of a divine mind:

But now an obvious question arises. Just whose thoughts are the laws of logic? There are no more thoughts without minds than there is smoke without fire … In any case, the laws of logic couldn’t be our thoughts—or the thoughts of any other contingent being for that matter—for as we’ve seen, the laws of logic exist necessarily if they exist at all. For any human person S, S might not have existed, along with S’s thoughts. The Law of Non-Contradiction, on the other hand, could not have failed to exist—otherwise it could have failed to be true. If the laws of logic are necessarily existent thoughts, they can only be the thoughts of a necessarily existent mind.” (p. 19)

So the inference from thoughts to a mind is as follows:

  1. There are no thoughts without minds.
  2. Necessarily there are thoughts.
  3. Therefore, necessarily there is a mind.

The scope of the necessity claim in the conclusion needs to be cashed out properly, for us to be able to judge whether the inference is valid. The precise logical form of the argument is not entirely clear to me, but here is my best shot:

  1. (∃x (Tx) → ∃y (My))    (If there is a thought, then there is a mind)
  2. (∃x (Tx))                     (Necessarily, there is a thought)
  3. (∃x (Mx))                   (Therefore, necessarily, there is a mind)

This argument follows, as it requires nothing but modus ponens, and the closure of necessity with respect to the theorems of propositional logic. The problem is that 3 is a de dicto necessity, where Anderson and Welty presumably want to have a de re necessity. They presumably want the conclusion to be that there is something that is a necessary mind (de re necessity), rather than it being necessary that there something which is a mind (de dicto necessity).

Here is an illustration of the difference between them. It is necessary that there is someone who is the oldest person alive. Say someone, let’s call them Raj, is the oldest person alive. It is not necessary of Raj that he is the oldest person, because he could die and the title of oldest person would pass to someone else. It is necessary that someone has the title (at least so long as there are people), but there is nobody of whom it is necessary that they have the title.

A&W want to say that there is a mind (God’s mind) of which it necessarily exists, which is a de re claim, and not just that it is necessary that some mind or other exists, which is a de dicto claim. The difference is between (∃x (Mx)) (‘It is necessary that there is a mind’), and (∃x (Mx)) (‘There is a necessary mind’).

If we change their argument to put the de re conclusion in that they want, it becomes the following:

  1. (∃x (Tx) → ∃y (Mx))
  2. (∃x (Tx))
  3. (∃x (Mx))

The problem is that 3 does not follow from 1 and 2. For an illustration of the counterexample (where premise 1 and 2 are true, but this de re reading of the conclusion is false), consider the following:

It may be that each possible world has its own unique mind, which thinks the laws of logic. This would mean that premise 1 is true, as whenever there is thought, there is a mind; and it would mean that premise 2 is true, as there is thought that exists in every possible world  (specifically, the laws of logic). However, on this model, no mind exists at more than one world; each logic-thinking mind is contingent. So, ‘(∃x (Mx))’ is true, in that at every world there is a mind, but ‘(∃x (Mx))’ is false, in that there isn’t a thing which is a mind in every world.

Anderson and Welty do anticipate this response:

It might be objected that the necessary existence of certain thoughts entails only that, necessarily, some minds exist. Presumably the objector envisages a scenario in which every possible world contains one or more contingent minds, and those minds necessarily produce certain thoughts (among which are the laws of logic). Since those thoughts are produced in every possible world, they enjoy necessary existence.” (p. 19, footnote 31)

This is essentially exactly the issue laid out above. They are saying that the inference to the de dicto conclusion might be seen as invalid, on the basis of a model in which there are multiple contingent minds. This is how my counter-example above worked; it involved each world having its own unique contingent mind.

They have two responses to such a move:

One problem with this suggestion is that thoughts belong essentially to the minds that produce them. Your thoughts necessarily belong to you. We could not have had your thoughts (except in the weaker sense that we could have thoughts with the same content as your thoughts, which presupposes a distinction between human thoughts and the content of those thoughts, e.g., propositions). Consequently, the thoughts of contingent minds must be themselves contingent. Another problem, less serious but still significant, is that this alternative scenario violates the principle of parsimony.” (p. 19-20, ibid)

To begin with we have the claim that “thoughts belong essentially to the minds that produce them“. So I have this particular thought about how lovely the weather is today. While you may also be thinking that the weather is lovely today, you are not literally having the same thought as me; rather you are having a different thought, even if it has the same content. Thus, this thought is had by me (and only me) in every world in which it exists. So being a thought of mine is an essential property of that thought. Because I am a contingent being, and do not exist in every possible world, it follows that there are worlds in which my particular thought about how lovely the weather is today also does not exist. Thus, given that thoughts are essentially of the minds that think them, contingent beings can only have contingent thoughts.

I am quite sympathetic to this response. It seems right to me that contingent beings can only have thoughts that are contingent too. While the content of my thought can be necessary, the thought itself cannot be. The counterexample above does seem to require there being contingent minds. Thus, in order for the thought to have the necessity required, the mind also has to be necessary.

However, while I find all this quite agreeable, there still seems to be a problem here, although I do find this quite hard to put into words completely clearly, and maybe it is something that could be cleared up with a little more detail on the ontology of how the laws of logic relate to God’s thoughts on A&W’s part. Anyway, here is how I see it.

The distinction between the thought and the content of the thought is that the former cannot be shared across minds (I cannot have the same thought as you), while the latter can be (I can have a thought with the same content as yours). This, it seems to me, generates a little problem for the divine conceptualist. It seems like the categories of thought and content are mutually exclusive; if I think of my coffee mug, then the thought is not the content of the thought. If I think about the thought I just had about the coffee mug, then my previous thought (about the mug) is the content of a new thought (about the thought about the mug). It seems unintelligible that one and the same thought could be the content of itself. Self-reflection, it seems, is hierarchical, not circular. Call this ‘the principle of the Distinctness of Thought from Content‘ (or PDTC). If PDTC is true, then it is impossible for a thought to be the content of itself.

Of course, there is the discussion in Metaphysics about God being thought that thinks thought. The idea is that God, the pure actuality, has to be thinking which has itself as it’s own object of thought. Aristotle seems to anticipate something like the PDTC, when he says the following:

“[God’s] Mind thinks itself, if it is that which is best; and its thinking is a thinking of thinking.

Yet it seems that knowledge and perception and opinion and understanding are always of something else, and only incidentally of themselves. And further, if to think is not the same as to be thought, in respect of which does goodness belong to thought? for the act of thinking and the object of thought have not the same essence.

The answer is that in some cases the knowledge is the object. In the productive sciences, if we disregard the matter, the substance, i.e. the essence, is the object; but in the speculative sciences the formula or the act of thinking is the object. Therefore since thought and the object of thought are not different in the case of things which contain no matter, they will be the same, and the act of thinking will be one with the object of thought.” (Aristotle, Metaphysics, book 12, 1074b-1075a)

So the claim is that the divine mind thinks itself. Then in the second paragraph the objection is posed that thoughts are always about something distinct from themselves. The ‘answer’ provided by Aristotle is that “in the speculative sciences the formula or the act of thinking is the object”. Logic certainly counts as an example of a speculative science (par excellence), and so it seems that Aristotle’s claim is that when God thinks about logic, his thought is identical to the object of the thought. If this is the case, Aristotle presents no argument for it (at least not that I know of). And it seems quite strange, if taken to be the claim that when one thinks about logic, the thought is the content of the thought. It seems quite clear that when I think of the laws of logic, they are the content of my thought, and not the thought itself.

Here is an argument for my claim:

  1. If p can be thought by a mind and a mind m’ , where m ≠ m’, then p is the content of their thought. (Contents of thoughts can be shared by minds)
  2. If t is a thought had by m, then t cannot be had by any mind m’, where m ≠ m’. (Thoughts cannot be shared by minds)
  3. Two people can both think of the law of non-contradiction.
  4. Therefore, the law of non-contradiction can be the content of thoughts. (from 1 + 3, modus ponens)
  5. Therefore, the law of non-contradiction cannot be a thought. (from 2 + 4, modus tollens)

The first two premises of this argument make the distinction between thought and contents of thoughts made by A&W above, and the third just says that two people can both think the LnC. It follows that the LnC cannot be a thought.

For the divine conceptualism of A&W, the law of non-contradiction is ultimately supposed to be God’s thought. So take the law of non-contradiction, ‘LnC’, and some thought had by God, T. If LnC = T, then (by the PDTC) it is not the content of T. But what is the content of T? What is God thinking about when he has the thought T which is the law of non-contradiction? The obvious answer would be that God is thinking about propositions, and how each proposition cannot be true along with its negation. But the problem with that is that it is the law of non-contradiction. That would make the LnC the content of T, and (if thoughts cannot be their own content) that would mean that T isn’t LnC. So when God thinks T, he must think about something other than the LnC.

 

But why is it then that T is LnC, if the content of T is something other than that propositions cannot be true with their negations? Nothing else is relevant! It seems incredible to consider that the content of T is (say) this coffee mug, while also insisting that T is the LnC. If the content of T, whatever it is, is not the mutual exclusivity of propositions and their negations, then it can only be arbitrarily connected with LnC. This makes it a mystery, ultimately, why it has anything to do with LnC, let alone being the LnC.

The question is: in virtue of what could a thought T, whose content is irrelevant to the LnC, be said to be the LnC?

There are three ways out of this problem, it seems to me.

One is to bite the bullet and say that God thinks something with completely arbitrary content, and this just is the LnC. It is a hard pill to swallow.

The next escape route would be to say that the LnC is in fact the content of T. This explains why it is that I can also think about LnC; both me and God think about the same thing. However, this option is rather like the horn of the Euthyphro dilemma that says that God likes good actions because they are good. If God has a thought which has LnC as its content, then the LnC is not to be associated with God’s thought any more than it is if I have a thought with the LnC as its content. The significance of God in the equation has been completely removed. It seems that the central claim of a divine conceptualist has been undermined if we take this route.

The only other escape route I can see here is to deny that LnC cannot be both T and the content of T. Perhaps when it comes to God’s thoughts, they can be both thought and content together. So the LnC is the content of God’s thought (i.e. he is thinking about how propositions and their negations cannot both be true) and that this thought is the law itself. It may seem unintelligible for us humans to have such a thought, but maybe this is how God thinks.

The problem with this route, it seems to me, is that it undermines the analogy between divine thoughts and mere human thoughts. When the divine conceptualist says that laws of logic are divine thoughts, we take it that the claim is saying that they are thoughts that are at least a somewhat similar to human thoughts. This seems to be required for the argument from propositions being intentional in section 3 (above). Propositions don’t seem to be mental on their face, but the idea is that they are because they are intentional, and everything intentional is mental. This last claim is undermined significantly if the extension of ‘mental’ includes things which are significantly unlike human thoughts. To the extent then that we have to broaden the category of thoughts to include the seemingly unintelligible idea of a thought being at once its own content, the universal claim is also undermined. Consider the claim spelled out in full:

“Everything intentional is mental, and and under the term ‘mental’ I include things which are very unlike human thoughts because they have properties which are unintelligible if applied to human thoughts (such as a human thought which is its own content)”

Where we have arrived at, is a destination where the central claim of the divine conceptualist is that the laws of logic are to be associated with some aspect of God, which in some sense resembles human thoughts, but that in another sense is nothing like human thoughts. Saying that the laws of logic are thoughts at all on this picture seems quite a difficult thing to maintain.

5. Conclusion

It seems to me that there are quite a few problems with the argument presented in The Lord of Non-Contradiction. Some of them are quite subtle, like the final one concerning the precise relationship between the laws and the thoughts of God, and it is entirely possible that they could be cleared up. Some of them are quite technical, such as the details of how possible worlds are cashed out in the metaphysics of modality, and A&W could be forgiven for not realising them. Some of them, I suggest, are quite a lot more serious, such as the inference from intentionality to mentality. I don’t see this being fixed up with a little revision or by spelling something out a bit more clearly. It is utterly foundational to the argument and it seems to me that it is just fallacious.

Accounting for logic – again

0. Introduction

In this post I will be looking at a blog entry on the BibleThumpingWingnut website, entitled ‘Christianity and Logic’. The entry is written by Tim Shaughnessy, and takes a Clarkian angle. Shaughnessy’s argument is basically that Christianity can provide an ‘epistemological foundation’ for logic, using Scripture as a sort of axiomatic basis for logic, and that ‘the unbeliever’ cannot provide such a foundation, or ‘account’, for logic. If this is the first time you are encountering this Clarkian view, have a look at this article by Clark. I have written on this topic before, and I think that many of those points are directly relevant here.

For instance, here I argue that there is no binary choice between Christianity and non-Christianity; there are different versions of Christianity, different monotheistic religions, different versions of theism, and different versions of atheism. This version of Christianity is just one tiny dot on a huge intellectual landscape. To argue by elimination that this version Christianity is correct, means you have to eliminate a possibly infinite variety of systems. Pitting (this version of) Christianity against ‘the unbelieving worldview’ is already to commit the fallacy of false dichotomy. We might want to call this version of it the ‘Bahnsen fallacy’, in honour of its main witness.

More specifically with regards to the broadly Clarkian idea of deriving logical principles from the Scriptures, I have argued here that this is incoherent. Derivation requires a logical framework, which is constituted in part by logical principles (or axioms); derivation is a logical notion, and thus presupposes logical principles.

There are some new points which seem to be worth raising however, given the particular presentation by Shaughnessy, and so I will be exploring those ideas here.

  1. ‘What is logic?’ 

Shaughnessy’s view of logic seems to be entirely gained from the study of Clark, in that he is the only author cited (rather than, say, Aristotle or Frege) on the topic of what logic is. This is unfortunate, because it seems that  Shaughnessy is unaware of the controversy surrounding the topic. So, we see him state that logic is “the correct process of reasoning which is based on universally fixed rules of thought”. This idea, that logic is about laws of thought, is a historically significant idea, coming to prominence in the 18th and 19th centuries, but it has never been a universal consensus among logicians and philosophers. These days it is not widely represented among practising logicians and philosophers at all (see this for a quick overview). The reason for this is that in the contemporary setting logic has a much broader extension, and can cover systems which deviate wildly from how we might realistically model thought (which is the preserve of logicians and computer scientists working in artificial intelligence). Logic, thought of broadly as concerning valid inference for various types of argument forms, is not considered to be tied in any special manner to how we think. There may be a logic to how we think, but logic is not just how we think. Never-the-less, Shaughnessy makes no mention of this, and simply asserts that logic has this 18th century relation to cognition.

His out-of-date description of logic becomes confounded with outright misunderstandings when he spells out what he considers to be the three laws of thought. It is utterly standard, when going down this non-modern view, to list the three laws of thought as: ‘the law of identity’, ‘the law of non-contradiction’ and ‘the law of excluded middle’. What is odd is the way these are cashed out by Shaughnessy. For instance, the law of non-contradiction is cashed out as “A is not non-A”, and the law of excluded middle is cashed out as “A is either B or non-B”. It seems to me that there is a failure of Shaughnessy to distinguish clearly between different aspects of vocabulary. There is a fundamental difference between logical vocabulary that refers to things directly (like ‘Alex’, ‘London’, ‘your favourite type of ice cream’, etc) and those which express facts (‘Alex is in London’, ‘vanilla is your favourite type of ice cream’, etc). The first are called ‘terms’, and the latter are called ‘propositions’. Propositions can be thought of as made up of terms standing in certain relations to one another. Crucially, propositions are given truth-values, true or false; terms are not. So, ‘Alex’ isn’t true or false; but ‘Alex is in London’ is either true or false. In Shaughnessy’s expression of the law of non-contradiction, we have a letter ‘A’, which seems to be a term, as it is something we are predicating something to, but then the predicate we are ascribing to it is that it is “not non-A”. The problem is that we have a negation fixing to a term, ‘non-A’. As I have pointed out before, negation is a propositional operator, and its function is to switch the truth-value of the proposition is prefixes from true to false (or vice versa). If we prefix it to a referring term, like ‘A’, then (because terms don’t have truth values), the resultant operation is undefined.

The conventional way to express the law of non-contradiction is with a propositional variable, ‘p’, which ranges over all propositions, as follows:

¬(p ∧ ¬p)    (‘it is not the case that both p and not-p’)

If you want to express this using propositions where the relation of terms is explicit (i.e. in a first-order manner), then it would be as follows, where ‘Px’ is a predicate and ‘a’ is a term:

¬(Pa ∧ ¬(Pa))   (‘it is not the case that a both is and is not P’)

The same problem infects “A is either B or non-B”. The correct way to express this is just that for every proposition, either it is true, or it’s negation is true:

p ∨ ¬p     (‘either p or not-p‘)

It is bizarre to say that either ‘A is B or non-B’. There is no predicate ‘non-B’; rather, either B applies or it doesn’t. Take the proposition that I am 6 feet tall. Either I am 6′ or I am not. In the second case I don’t have a property, called non-6′. What would this property be? Every height other than 6′? I am not 6′, but I am also not every height other than 6′. I just am 5’11”. So the way Shaughnessy expresses excluded middle is also confused.

And it’s not like stating non-contradiction and excluded middle is extremely complicated; all it involves is: ‘p or not-p’, and ‘not both p and not-p’. He hasn’t simplified them for a non-specialist audience – he has just misrepresented them.

So we have an out-of-date view of logic, coupled with a technically incorrect presentation of the principles under discussion. It’s not a great start to an article about the nature of logic.

1.1 Logic in the Bible?

Perhaps Shaughnessy’s misrepresentation of the basic laws of thought is more understandable when we see where he is going with all of this. The ultimate point he will be driving at is that these laws are found in the Bible. Various snippets of the Bible are then presented as evidence of this, but because they don’t really fit that well with the laws when expressed properly, he has written them in such a way that the claim that they are found in the Bible becomes (slightly) easier to swallow. Here is what he has to say about it:

The law of non-contradiction (A is not non–A) is an expression of the eternal character and nature of God, “for he cannot deny [contradict] himself” (2 Tim. 2:13). The law of identity (A is A) is expressed in God’s name, “I AM WHO I AM” (Exodus 3:14), and the law of the excluded middle (A is either B or non-B) is expressed in Christ’s own words, “He who is not with Me is against Me” (Luke 11:23).

Let’s take these one at a time. It is hard to take them seriously, but I will try.

1.1.1 Non-Contradiction

In the book of Timothy, it is said that God cannot contradict himself. I say that this is completely irrelevant to the principle of non-contradiction. There is a difference between saying things, and things being true (or false). The law of non-contradiction is about the latter, not the former. It isn’t a rule which says ‘thou shalt not contradict thy self’. It says that there is no proposition for which both it and its negation are true. It doesn’t proscribe what you can or cannot say at all.

For example, I can contradict myself, and sometimes do. Does this mean I broke the law of non-contradiction when I did so? No, of course not. Imagine I say ‘It is sunny now, at 14:07’, and then a few minutes later, ‘It was not sunny then, at 14:07’. The two sentences I uttered were expressing (from different times) that it was and was not sunny at 14:07. Obviously, it would be a contradiction if both of these were true, as p and not-p would both be true (exactly what the law of non-contradiction forbids). But were they both true? That would mean that it was both sunny and not sunny at the same time. Conventionally thinking, this is impossible. Therefore, while I contradicted myself, I didn’t break the law of non-contradiction. I expressed a true proposition, and then when I uttered the negation of that proposition what I said was false (or vice versa). Contradicting yourself isn’t a case of breaking the law of non-contradiction.

Back to the Biblical example, God cannot contradict himself. So what? The law of non-contradiction is true even though people can contradict themselves. An example of a being, even an infinite one, who cannot contradict themselves, is not an example of the law of non-contradiction. To think that it is, is to mix up the idea of saying two contradictory things with two contradictory propositions both being true.

1.1.2 Identity

Shaughnessy does manage to state the law of identity correctly, which is that (for all referring terms) A = A. Everything is identical to itself. According to the example given, the law of identity is expressed in “I am who I am”, which is the answer God gives to Moses in the book of Exodus. It has always baffled me as to why this has been seen as a profound thing for God to say here. God tells Moses to go to the Pharaoh and bring the Israelites out of Egypt. Moses basically says, ‘who am I to do that?’ God says that he will be with Moses, but Moses wants a bit more reassurance for some reason:

Moses said to God, “Suppose I go to the Israelites and say to them, ‘The God of your fathers has sent me to you,’ and they ask me, ‘What is his name?’ Then what shall I tell them?”

God said to Moses, “I am who I am. This is what you are to say to the Israelites: ‘I am has sent me to you.’” (Exodus, 3: 13-14)

One of my favourite comedy series ‘Knowing Me, Knowing You’, staring Steve Coogan, features a pathetic TV chat show host, called Alan Partridge. In episode 2, he is interviewing an agony aunt called Dannielle, played by Minnie Driver, who is listing the things she likes in men:

Dannielle: Power is attractive. Sensitivity. Sense of humour. I like a man who knows who he is.

Alan: I’m Alan Partridge.

If you think that the law of identity is expressed by Exodus 3:14, then you should also hold that it is expressed in this little bit of Alan Partridge script.

I’m just going to leave that there.

1.1.3 Excluded Middle

In the last example, Jesus saying “He who is not with Me is against Me” is an example of someone expressing something stronger than the law of excluded middle. The logical law of excluded middle says that for every proposition, p, either it or its negation is true. There are two propositions being considered in the saying above, put together in the form of a disjunction. The two propositions are:

‘x is with Jesus’

‘x is against Jesus’

The combined disjunction is universal, in that it applies to everyone:

For all x: either x is with Jesus or x is against Jesus.

We could write this in first order logic as follows:

∀x (Wx ∨ Ax)

However, this isn’t a logical truth. There is no logical reason to stop someone being neither with nor against Jesus. The following is not a logical contradiction:

∃x (¬Wx ∧ ¬Ax)      (‘there is an x such that it is not with Jesus and it is not against Jesus’)

If Jesus had said ‘Either you are with me or not with me’, then he would have said something which would have been logically true (because of the law of excluded middle). It would have the following form:

∀x (Wx ∨ ¬Wx)

Therefore, when Jesus says that everyone is either with him or against him, something which goes beyond the law of excluded middle, and it is not a logical truth. Why this has been picked to be an instance of this law can only be put down to either the author not understanding what the law actually states, or being so determined to find something that fits the pattern that they wilfully ignore the fact that it doesn’t.

1.2 The problem

If we are thinking of the examples of someone not contradicting themselves, or of everyone being split into the ‘with’ or ‘against’ categories, then we have (at best) particular instantiations of these rules, but not examples of the rules. Consider the difference between:

a) A sign which said ‘do not step on the grass’.

b) Someone walking along the path next to the grass.

With regards to a), we would say that it had the rule, ‘do not step on the grass’, written on it. On the other hand, b) would just be an instance of the someone following the rule.

Finding Jesus saying ‘Either you are with me or you aren’t’ would be like finding someone walking next to the grass. Sure, it instantiates what the law of excluded middle is about, but it isn’t the rule. The rule is general. It says ‘nobody walk on the grass’, not just this guy in particular; excluded middle says ‘for all propositions, either p or not-p‘. The Bible nowhere makes generalised statements about language, reasoning or validity.

So the examples fail in that they aren’t actually instances of the rules (as the laws themselves are muddled by Shaughnessy), but they also fail because (even if we pretend that they do instantiate the rules) they aren’t examples of the rules. The Bible doesn’t have the law of excluded middle stated in it. It instantiates it, in that every proposition expressed in the Bible is either true or false, but that is not important at all. Every proposition expressed in any book is either true or false! Exactly the same goes for non-contradiction. There is nothing special about the Bible such that you can find the three rules of thought in it. If you want to see what a book looks like which explicitly has the rule of non-contradiction in it, read Aristotle’s Metaphysics, book IV, section 3:

“...the most certain principle of all is that regarding which it is impossible to be mistaken; for such a principle must be both the best known (for all men may be mistaken about things which they do not know), and non-hypothetical. For a principle which every one must have who understands anything that is, is not a hypothesis; and that which every one must know who knows anything, he must already have when he comes to a special study. Evidently then such a principle is the most certain of all; which principle this is, let us proceed to say. It is, the same attribute cannot at the same time belong and not belong to the same subject and in the same respect.

For Aristotle, the basic declarative sentence (the basic proposition) is the ascription of an attribute (or property) to a subject, and this is explored explicitly by him at great length. So ‘Alex is happy’ is this type of sentence. When he says “the same attribute cannot at the same time belong and not belong to the same subject and in the same respect”, this is simply to say that there cannot be any proposition, such as ‘Alex is happy’, for which it is true that ‘Alex is happy’ and it is also true that ‘Alex is not happy’, i.e. we cannot have both p and not-p. In contrast to the Bible then, Aristotle does not just give an instance of a sentence of the same form as the law of non-contradiction, like ‘it is not that Alex is both happy and not happy’ – he reflects on this and states the general proposition in its generalised form. It is explicit. With the case of the Bible, we have shoddy eisegesis going on, where Aristotelian principles are being read into a text that doesn’t have them.

So far, not great. Shaughnessy makes the following claim:

It is precisely because the laws of logic are embedded in Scripture that the Christian is able to establish from an epistemological standpoint that they are fixed and universal laws. Without this epistemological foundation, we cannot account for the laws of logic

Well, given what I’ve written above, it should be pretty obvious that I disagree with that. The laws of logic are not in the Bible. Given this, by his own standards, Shaughnessy doesn’t have an ‘epistemological foundation’ and ‘cannot account for’ these laws. Too bad.

2. An epistemological foundation for logic

Shaughnessy then presents the standard presuppositional line, the one we all knew was coming, where they brag about how great their ‘account’ of logic is, and how rubbish ‘the other account’ is.

The unbeliever cannot account for logic in his own worldview and therefore cannot account for his ability to think rationally. The challenge has been made many times to unbelievers to account for logic in their own worldview and it has always fallen short or gone unanswered. Never has an adequate response been given. In formal debates, the challenge is often ignored by the unbeliever, yet the challenge demands an answer because debates presuppose logic. The unbeliever is required to use logic in order to make his argument against Christianity consistent and intelligible, but only the Christian worldview can account for logic. He is therefore required to rob the Christian worldview in order to make his argument against Christianity intelligible.”

Ok, well we’ve all seen this over and over again. So I am going to meet the challenge head on, and provide a few different ‘accounts’ of logic, which could be ‘epistemological foundations’ for it.

First of all, what do we mean by and ‘epistemological foundation’ for something? Well, I take it to mean something in virtue of which we can come to know something. So, an epistemological foundation for x could be thought of an an answer to the question, ‘how is it that we are able to know about x?’

Given that, our question is: ‘How is it that we are able to know about logic (and in particular those logical laws)?’. In order to play the game right, I shall not appeal to God in any way, I will just go along with the idea that logical laws are things that have some kind of ontology capable of allowing reference to them, and I will just pretend that the three principles cited by Shaughnessy (identity, non-contradiction and excluded middle) really are ‘logical laws’, even though it is a clumsy and out-dated way to talk about logic. I will play the game anyway, just to be a good sport.

2.1 They are self-evident.

Here is the first way of answering that question: we are able to know about logical laws because they are self-evident truths. This just means that to think about them is to know that they are true. They don’t need anything else to support my knowledge of them, because they are self-evident. This is a really simple answer, and there isn’t much more to be said about it.

The response might be something like: “that’s rationalism! You are saying that all knowledge is rationally determined based on self-evident truths, like Spinoza!” Before we get into the standard disputes about rationalism and empiricism, I want to point out that I don’t need to also say that this is how I get knowledge generally. The question is about logical laws only. Maybe these are the only self-evident truths, and I gain knowledge about other parts of the world through empirical access, or mystical intuition, or because a ghost illuminates the right answer for me. Who cares? The point is that this plainly is an answer to the question ‘how could we know about logical laws?’. It doesn’t require a God of any type, so is available to an atheist (or a theist, or really anyone apart from those people who for some reason are committed to the view that there are no such things as self evident truths). They are pretty good candidates for self-evident truths if you ask me, and I would dispute the claim that there are candidates that are more plausible (is ‘cogito ergo sum’ more plausible as a self-evident truth than non-contradiction? They seem even, if anything). If anything is self evident, its the law of non-contradiction. So this view is plausible, at least on first blush.

If there is a secret cheat-card answer to this that presuppositionalist apologists have, I’ve never heard it. Remember the challenge: “The challenge has been made many times to unbelievers to account for logic in their own worldview and it has always fallen short or gone unanswered.” Well, that’s one account. Here is another one.

2.2 They are synthetic a priori knowledge

Here is my second proposal: we are able to know about logical laws because they are synthetic a priori truths. In the Critique of Pure Reason, Immanuel Kant summarises his views on this type of knowledge as follows:

“…if we remove our own subject or even only the subjective constitution of the senses in general, then all constitution, all relations of objects in space and time, indeed space and time themselves would disappear, and as appearances they cannot exist in themselves, but only in us. What may be the case with objects in themselves and abstracted from all this receptivity of our sensibility remains entirely unknown to us. We are acquainted with nothing except our way of perceiving them, which is peculiar to us, and which therefore does not necessarily pertain to every being, though to be sure it pertains to every human being.”

Synthetic a priori knowledge has the property that it is integral to how we see the world. It is subjective, in the sense that Kant explains above (that is, if we were to remove the subject, then it would also disappear), but it is also universal, in the sense that it applies to “every human being”. So, space and time may be known a priori, yet the knowledge is not simply analytic (i.e. true in virtue of the meaning of the words used), but synthetic (true because of more than just the meaning of the words used). What we know is the form of our intuition, which is a non-trivial fact about the way things are, but is also directly available to us, as subjects, a priori. We are programmed to see the world in a spatio-temporal way.

Kant has his own ways of demonstrating that this is the case, using transcendental arguments which inspired Van Til and should be familiar to all presuppositionalist apologists. Essentially you show that the contrary leads to a contradiction. So we have to see the world in terms of space and time, because the contrary view (where we do not see the world in such a way) leads to complete incoherence. Space and time are necessary presuppositions of the intelligibility of experience (a phrase presuppositionalists love to use). As such, we have transcendental proofs for them. Presuppositionalists, like the gang at BibleThumpingWingnut.com, should welcome this methodology, as it is basically the sophisticated version of the Van Tillian method they endorse themselves, only directed squarely at epistemological issues.

I say that we just point the synthetic a priori machinery at the laws of logic, and there we go, an epistemological foundation for the laws of logic. We know excluded middle, non-contradiction and identity as forms of intuition. Everyone has them (which explains their apparent universal character). If we try to conceive the world without them, we get incoherence (which shows their necessity).

On this view, we are not suggesting that these principles have metaphysical necessity. As good Kantians, we simply say that we cannot know about the numenal realm. But this should be perfectly acceptable to those presuppositionalists who throw the gauntlet of providing an epistemological foundation for the laws of logic. They are the ones, after all, who think that these principles are the ‘laws of thought’. On this reading of what they are, the Kantian line seems perfectly suited.

It would be really hard to imagine a presuppositionalist mounting a successful attack against this view, which didn’t also backfire and undermine their own transcendental arguments. You can’t have it both ways. If you are going to use transcendental arguments for God, I’m going to use them for what I want as well.

2.3 They are indispensable

Here is one last attempt. How do we know about the laws of logic? Well, they are indispensable to our best theories of science, so it is reasonable to believe in them. This is a version of the Quine-Putnam indispensability argument for the existence of mathematical entities. Here is how I see the argument going:

  1. We are justified to believe in all the entities that are indispensable to our best scientific theories.
  2. Laws of logic are indispensable to our best scientific theories.
  3. Therefore, we are justified to believe in the laws of logic.

I’m not personally that convinced by premise 2, but presumably Shaughnessy and all those who throw down the presup gauntlet are. Premise 1 says that we have justification to believe in those things which are indispensable to our best theories, and I think this is going to be accepted by most people. We believe in viruses because our best science tells us that they exist. It is reasonable to hold the belief in viruses on this basis.

This argument doesn’t say that we have conclusively established that the laws of logic exist, but it provides justification. Presuming a broadly fallibilist idea of justification (as most contemporary professional epistemologists do), then even though the indispensability argument doesn’t ensure the laws of logic exist, it provides sufficient support for the belief that they do to be justified. So it allows us to have justified belief in the laws of logic existing. If that belief is also true, then we know that they exist. Thus, this is an explanation of how we come to know (as in ‘justified true belief’) that the laws of logic exist. Thus, it is an answer to how we can have knowledge of them, and ultimately part of an epistemic foundation, and an ‘account’, of them.

3. Conclusion

So, above are three distinct views about the epistemological foundations of logic. None of them required God, or Jesus, or Reformed theology at all. No doubt, they will continue, over at BibleThumpingWingnut.com, to claim that “The challenge has been made many times to unbelievers to account for logic in their own worldview and it has always fallen short or gone unanswered. Never has an adequate response been given“. In reality though, for those of us who have spent a long time doing philosophy seriously, these claims are easily countered. I’m not saying I have all the answers; I’m saying that they don’t. I don’t know what the ‘right answer’ is about the nature of logic, or how epistemology and logic fit together. It is an incredibly complicated area. As with philosophy, it may be something we will ultimately never answer. It may be that for some reason the question itself doesn’t make sense, but that this realisation doesn’t come for many generations yet. Maybe the answer was given in some obscure scroll, now long forgotten by history. All these possibilities remain. But to claim that there is only one answer to this sort of question is silly. I have thought up the three examples here by referencing well-known ideas in philosophy. I could have easily plundered the great works of philosophy to find dozens more (such as platonism, structuralism, formalism, intuitionism, plenitudinous platonism, etc, etc). Don’t be fooled into thinking that in such a rich and complicated area of philosophy as this, that there are any easy answers.

The “Matt Slick Fallacy Fallacy” Fallacy

Introduction

Recently, a friend of mine sent me a link to a website where a person called A.J. Kitt had written a blog post about my ‘Matt Slick Fallacy’ article. I suggest that if you haven’t read it, then you stop and read it now, as it is important to understand my points (and it is not very long).

In it, Kitt makes some rather scathing remarks, such as:

“…sorry, Malpass. You blew it

and

“…if Dr. Alex Malpass feels his credibility has been undermined, well… he should. Perhaps next time he’ll check his argument before he puts it out there“.

In this post, I will look at Kitt’s claims and see how they relate to my original post. Kitt explains his general point as follows:

“…his claim only works by severely altering or misunderstanding what should have been the presumed qualities and relationships of Slick’s argument

While this isn’t specific about what ‘qualities and relationships’ it is that I got wrong, it is clear that the idea has something to to with me representing the spirit of the argument incorrectly. If so, then it would be like saying I argued against a straw-man. Obviously, I don’t want that to be the case, as it would mean that I didn’t address Slick’s actual argument, so let’s look closely at what Kitt has to say about what I said, and how it may have gone wrong.

False substitution fallacy

Kitt says that I make ‘false substitutions’ in my arguments, and it seems that this is the root of my problems, in his view. Kitt doesn’t provide any non-controversial examples of what he means by a ‘false substitution’, but I presume he means something like the following. A ‘false substitution’ fallacy would be where someone claims that an argument, A, is invalid, but the demonstration of that claim addresses a different argument, B, which is arrived at by substituting some term from A for a different term.

For example, imagine your debate partner makes the following argument:

1)    “All A’s are B; x is an A; thus, x is a B”.

You might be determined to argue against this point, and thus try to argue that 1 is invalid. You would commit the ‘false substitution’ fallacy if you then claimed that what your debate partner said was wrong (i.e. that 1 is invalid), but then by way of substantiating this claim proceeded to demonstrate that the following argument is invalid instead of 1:

2)     Some A’s are B; x is an A; thus, x is a B”.

Correctly showing that 2 is invalid does nothing to show whether 1 is invalid. If you responded by making this type of move, your debate partner might call false substitution fallacy on you. Kitt’s charge is that I am making this sort of fallacy when I argue against Slick.

So I had said that Slick’s argument suffers from the ‘false dilemma’ fallacy (the ‘Matt Slick Fallacy’). Kitt responds that my argument suffers from the ‘false substitution’ fallacy (the ‘Matt Slick Fallacy Fallacy’), and thus that Slick’s argument is rescued. If Kitt is wrong about this, then his argument itself will be fallacious in some way (which would make it the ‘Matt Slick Fallacy Fallacy Fallacy’). Let’s look in more detail at what he says.

Cause and existence

Kitt says about me:

“…he correctly identifies that either God or not-God did it“.

But then, apparently, it all goes wrong when I use my toast example. It is here where I make “the magical substitution”:

He says, since neither the existence of toast nor the lack of the existence of toast has anything to do with the existence of logic, the God/not-God argument is flawed. Worded that way, did you notice the problem?

Actually, no, I didn’t. Helpfully, Kitt goes on:

Malpass substituted existence for cause. With the substitution, he’s right. Whether God exists or not, as well as with whether toast exists or not, doesn’t necessarily say anything about the existence of logic (or anything else).” [emphasis mine]

So, according to Kitt, I was right to point out that ‘Whether God exists or not … doesn’t necessarily say anything about the existence of logic (or anything else)’. Ok, great. To that extent then, it seems we are in agreement! But then comes the following:

But without that substitution… the toast analogy supports Slick. Toast, or something-other-than-toast, definitely caused logic. In this case, I’m pretty sure logic didn’t happen because toast did it. Therefor, it is logical to assert that something-other-than-toast did. Soooo… sorry, Malpass. You blew it.” [emphasis mine]

Here is where Kitt obviously feels on his strongest ground, where I ‘blew it’. So let’s see what he is saying as clearly as possible. Kitt is saying that I inserted the word ‘existence’ into an argument which originally used the word ’cause’ (“Malpass substituted existence for cause”). When I was addressing the issue in terms of existence, what I said was “right” (“With the substitution, he’s right.”), but if I had addressed the argument in terms of cause, my point would not hold (“But without that substitution… the toast analogy supports Slick. Toast, or something-other-than-toast, definitely caused logic”).

It would be helpful to see both arguments next to each other so we could see clearly the difference between them. Kitt doesn’t provide any quote of mine, or Slick’s, to show the two arguments side-by-side (as I did with the ‘all’ and ‘some’ example above). All he has said directly about the toast analogy so far is this:

And the analogy could have been accurate – but it wasn’t; just take a look. Simply (according to Malpass): ‘God or not-God accounts for logic’ is the same as: ‘toast or not-toast accounts for logic’

I don’t see the words ‘existence’ or ’cause’ there, which you would expect to see, given the charge that I fallaciously substituted in one for the other.

And if you think about it, it’s quite hard to come up with a plausible version of how that would go, where one word could be substituted for the other to make two premises which are plausible candidates for what I and Slick said. There are three obvious conditions for the pair of premises to count:

Slick)                  One must be a premise of Matt Slick’s version of his argument.

Malpass)            One must be a premise of my version of Slick’s argument.

Substitution)     The premise from Malpass) must be the premise from Slick), but with ‘existence’ swapped in for ’cause’.

Here is a candidate:

3)    ‘The existence of God accounts for the laws of logic’

4)    ‘The cause of God accounts for the laws of logic’

4 is the result of substituting ‘existence’ for ’cause’, so the Substitution condition is fulfilled. 3 is a fair enough reading of what I said, so the Malpass condition is fulfilled. However, I think 4 would be a very unfair reading of Matt Slick’s argument, so the Slick condition would not be fulfilled. Slick’s view is that God doesn’t have a cause, and certainly not one that itself accounts for logic. He thinks God accounts for logic, not that the cause of God accounts for logic. This candidate fulfils Malpass and Substitution, but not Slick. So this cannot be the substitution that Kitt is talking about. Here is another candidate:

5) ‘God is the cause of logic’

6) ‘God is the existence of logic’

I think 5 would be a slightly different point to what Slick was saying, so it is not clear that it fulfils the Slick condition. But even if it were a perfect characterisation of Slick, it is clear that 6 (i.e. the result of substituting ‘existence’ for ’cause’ in 5) doesn’t even make sense grammatically. When I said there were problems with Slick’s argument, it wasn’t because I pretended that one of the premises of his argument was ‘God is the existence of logic’. It would be a very unfair reading of what I was saying in my original post. Thus, this definitely does not fulfil the Malpass condition.

I am genuinely at a loss for an proposition which is something I said, and is a version of what Matt Slick said but with the word ‘existence’ put in place of the word ’cause’. Even a candidate that just fulfils the Slick and Substitution conditions while remaining grammatically well-formed is difficult to think of, as 6 shows.

If Kitt is trying to argue that I was guilty of the ‘false substitution’ fallacy (by making a straw-man argument out of Matt Slick’s argument that used the word ‘existence’ in place of the word ’cause’), then he needs to substantiate this by providing both of those two arguments. He does not do that, and, for the reasons outlined above, I don’t really see how that specific charge can be substantiated.

Can and does

Kitt makes a further claim that I make a false substitution:

And then he does it again. Malpass switches out “does” for “can.” “Does” creates a mutually exclusive dichotomy: either God or not-God does account for choose-your-thing. But swapping in “can,” on the other hand, fails. Malpass correctly states that just because not-God cannot do yadda-yadda doesn’t prove that God can. But that’s not what Slick said. Slick still stands. Sooo… sorry, Malpass. You blew it twice.”

Kitt’s claim is that 7 is a dichotomy, but 8 is not:

7) God or not-God does account for x

8) God or not-God can account for x

Kitt gives no reason for thinking that this is true; he must assume that it is so obvious as to not need any argument. No examples from ordinary language are given where swapping ‘does’ for ‘can’ switches between a dichotomy and a normal disjunction. Nothing at all is provided to back up the point. So we have to guess why he thinks it is true.

I say that it is not true. Take any sentence that has the word ‘does’ and which is a dichotomy, substitute in the word ‘can’, and the result will remain a dichotomy. Here is an example:

‘Superman does fly or it is not the case that superman does fly’

This is a dichotomy, as it is of the form ‘A or not-A’. Now substitute in the word ‘can’ for ‘does’:

‘Superman can fly or it is not the case that superman can fly’.

This remains of the form ‘A or not-A’, and thus remains a dichotomy. Substituting in ‘does’ for ‘can’ in a dichotomy doesn’t make any difference to whether it is a dichotomy. So, in fact Kitt blew it.

Kitt’s real mistake, though, is in thinking that either of 7 or 8 is a dichotomy. In reality, neither are (more on this below), and the substitution of ‘does’ for ‘can’ makes no relevant difference to them (or course, it makes a modal difference to talk about what something can do rather than what it does do, but this is not relevant here). The both remain contingent disjunctions.

One last thing on this, before I move on to my main point. He says that when I talk about ‘existence’ rather than ’cause’, and when I talk about ‘can’ instead of ‘does’, I am not talking in the same terms as Slick does, as if I have erected a straw-man and torn that down instead of Slick’s actual argument. Of course, it is possible that I have addressed a different argument to what Slick originally intended, but is it the case that the straw-man I have created is one which uses those substitutions? Did I superimpose ‘existence’, where Slick talked about ’cause’, and did I superimpose ‘can’, where Slick talked about ‘does’?

Here is what I said in my article. In three places I present Slick’s argument. Firstly, and informally, I put it like this:

1. Either God, or not-God.

2. Not-God cannot account for the laws of logic.

3. Therefore God can account for the laws of logic.

Then I make things a bit more clear in ‘reconstruction 1’ (which I say is guilty of false dichotomy):

1. Either God can account for the laws of logic, or not-God can account for the laws of logic.

2. Not-God cannot account for the laws of logic.

3. Therefore, God can.

Finally, I present the argument in such a way that it avoids false dichotomy (‘reconstruction 2’):

1. Either God can account for the laws of logic, or it is not the case that God can account for the laws of logic.

2. It is not the case that (it is not the case that God can account for the laws of logic).

3. Therefore, God can account for the laws of logic.

I don’t actually use the word ‘exists’, but it is not a wild reinterpretation to put it in, such as: ‘Either the existence of God can account for the laws of logic, or it is not the case that the existence of God can account for the laws of logic’. I do use the word ‘can’. So Kitt is correct at least that my version of Slick’s argument uses ‘existence’ and ‘can’. Does Slick use ’cause’ and ‘does’ though?

Here is how Slick puts his TAG argument on his website (https://carm.org/transcendental-argument), and I have highlighted a few key terms:

1.If we have only two possible options by which we can explain something and one of those options is removed, by default the other option is verified since it is impossible to negate both of the only two exist options.

2. God either exists or does not exist.  There is no third option.

3. If the no-god position, atheism, clearly fails to account for Logical Absolutes from its perspective, then it is negated, and the other option is verified.

4. Atheism cannot account for the necessary preconditions for intelligibility, namely, the existence of logical absolutes.  Therefore, it is invalidated as a viable option for accounting for them and the only other option, God exists, is validated.

The word ’cause’ doesn’t appear at all, and the words ‘exist’ and ‘does not exist’ appear in the relevant places. The word ‘does’ doesn’t appear at all, and the words ‘can’ and ‘cannot’ appear in the relevant places. So far, with respect to the use of ’cause/existence’ and ‘can/does’, Slick and my presentation of Slick are in agreement. Kitt’s claim was that I falsely substituted in ‘existence’ for ’cause’, but so far both Slick and I use ‘existence’ and not ’cause’. So far, Kitt’s point seems completely baseless.

In my article that Kitt was responding to, I quoted a short monologue from Slick’s radio show. Just to make sure I didn’t cherry-pick the above presentation of the argument because it suited my point, let’s make sure that the actual version of the argument I used as a foil originally didn’t use ’cause’ or ‘does’. Here is what Slick said on his radio show:

“If you only have two possibilities to account for something … if one of them is negated the other is necessarily validated as being true … So we have ‘God and not-God’, so that’s called a true dichotomy, God either exists, or it is not the case that God exists, we have the thing and the negation of the thing. So now we have a true disjunctive syllogism … We have, for example, the transcendental laws of logic … Can the no-God position account for the transcendental laws of logic? And the ultimate answer is no it cannot. So therefore because it cannot, the other position is automatically necessarily validated as being true. Because, you cannot negate both options out of the only two possibilities; that’s logically impossible.”

Once again, ‘existence’ and ‘can’ are the relevant terms. ‘Cause’ and ‘does’ are not mentioned.  I conclude, given the examination of Slick’s actual arguments, that I have not substituted in terms falsely, but have actually used the terms Slick used. Given that Kitt insists on talking about arguments which use ’cause’ and ‘does’, it is Kitt who has made false substitutions. It is ironic that Kitt has accused me of doing something, when it is himself who is guilty of doing precisely that. Kitt doesn’t directly quote me or Slick in his article, so one could be forgiven if they just read his article for thinking that his assessment was correct. Once we compare what I put with what Slick put, like actually side-by-side comparing them, we see that Kitt’s claims are baseless. This adds a further irony, as Kitt’s explicitly said:

“…if Dr. Alex Malpass feels his credibility has been undermined, well… he should. Perhaps next time he’ll check his argument before he puts it out there.”

It seems that in actual fact, Kitt has been rather sloppy with his claims about my and Slick’s arguments, and failed to check whether the claims were themselves correct before he put it ‘out there’ for other people to critique. Perhaps next time he will check his argument first.

False dichotomy

At the end of all this, there is really only one fallacy, and it is the Matt Slick Fallacy (false dichotomy). Kitt just makes the same fallacy again. Here it is in all it’s glory:

Toast, or something-other-than-toast, definitely caused logic.

I say that with this claim, Kitt demonstrates that he does not understand my argument at all, and in fact has just walked straight into the problem that Slick was facing. It may be my fault that he didn’t understand my argument (maybe my words were not sufficiently clear), but it is his own fault for not being able to see this for himself. His reasoning seems to be that the claim that ‘toast or some other thing caused logic’ is logically true. He says as much quite clearly:

Either:

A. ‘God caused it’ or

B. ‘Something other than God caused it’. 

That – A OR B – is a logically true statement.

The disjunction (‘A or B’) is not a tautology (i.e. true independently of the content of A and B) – it is not a “logically true statement”. ‘A or not-A’ would be a tautology, but Either: A. ‘God caused it’ or B. ‘Something other than God caused it’ is not an instance of ‘A or not-A’. It isn’t an instance of any other tautology either. Trying to palm it off as a dichotomy is the textbook definition of the false dichotomy fallacy. Sorry, Kitt, but it’s true.

Think about it like this: could the following pair both be true?

9) ‘Either a caused b, or something other than a caused b

10) ‘Nothing caused b

The answer is: no. If nothing caused b (if 10 is true), then ‘either a caused b, or something other than a caused b‘ (i.e. 9) has to be false. For a Christian (and presumably Kitt is a Christian), this should be obvious. Is it logically true that ‘either a caused God, or something other than a caused God’? The traditional understanding is that God is uncaused. Nothing caused God to exist. But if it were a logical truth that ‘either a caused b, or something other than a caused b‘ then it would entail, logically, that God had a cause. If Kitt is right, then God had a cause.

Causing logic

While that claim of mine (that the proposition ‘something accounts for logic’ is assumed and not argued for) is well rehearsed on this blog, I want to focus on the particular issue Kitt feels is his strongest point; the idea that logic was caused. I think this idea is incoherent. It is quite hard to make this point perfectly clear, but here goes.

Firstly, it is not clear to me that saying ‘logic exists’ is the most helpful way of speaking. There is a wide range of positions on the nature of logic, but straightforwardly ascribing existence to logic is not uncontroversial. Physical objects, like tables and chairs, are the sort of paradigm examples of existing things. Obviously, some philosophers (platonists, etc) have claimed that abstract objects exist. However, these same philosophers also claim that these existing abstract objects are outside the usual causal chains that physical objects are in. The number 17, for example, is generally regarded by platonists to be an eternally existing abstract object, but also causally inert; nothing causes it to exist, and it causes nothing to exist. It has no causal relationships with anything. So this platonistic account of abstract objects, which sanctions the locution ‘abstract object x exists’, doesn’t sanction, ‘y caused abstract object x to exist’. So this cannot be what Kitt means when he says that logic was caused to exist. I think we are owed some sort of explanation of what Kitt has in mind for what he means by logic existing when it is caused to be, but we get nothing of the sort.

Perhaps he may simply want to say that God made the logical principles true, regardless of whether they exist or not as abstract objects. So one might ask ‘why is the law of non-contradiction true’, to which Kitt’s answer would (perhaps) be ‘because God caused it to be true’. This way of talking side-steps the platonistic talk of abstract objects existing. While this is somewhat more attractive as an option therefore, it also suffers from what I consider to be a fundamental incoherence.

The situation is sort of similar to a well-known difficulty for the idea that God caused time to exist. The creation of something is a change. And you cannot have change without time. But the creation of time is a change, specifically the change from time not existing to time existing. This change presupposes that time exists; the time ‘before’ time started to exist, the time and ‘after’ it started to exist. So the creation of time can only take place if time already exists. Thus, there is an incoherence in the idea of the ‘creation of time’. Our notion of creation cannot be applied to the notion of time, without becoming incoherent. In other words, creation presupposes time. You cannot make sense of creation outside of time.

Now consider the claim that God created logic. What was it like before God created logic? You couldn’t use logical inferences, and there would be no logical truths. So it wouldn’t be that ‘Socrates is mortal’ followed from ‘all men are mortal’ and ‘Socrates is a man’. It wouldn’t be that ‘Either Socrates is a man or it is not the case that Socrates is a man’ is true.

One might be tempted to bite the bullet and say ‘well, yeah, before God created logic, stuff was crazy like that’. But I think that even this is not available. If you deny logic altogether, then there is no room for the notion of causation to operate; too much has been taken away for the ascription of causation to mean anything. Here are a few, often admittedly difficult to understand, examples of what it might mean for logic to not exist, and how this makes causation, and indeed everything, impossible.

Trivialism

Maybe you think that when logic didn’t exist all contradictions were true; call this view ‘trivialism’. God existed and didn’t exist; Monday was Tuesday; I was you; up was down, etc. Well, this is equivalent to saying that everything was true and false; every proposition and its negation is true. But now we have an axiom, which we could call the ‘triviality’ axiom:

Triviality)                        ∀p: p & ¬p

(alternatively: ∀p: Tp & Fp)

This says, for all propositions, p, ‘both p and its negation are true’. Alternatively, it says that for all propositions, p, ‘p is both true and false’. It looks like we have a logical principle after all, and we might think that before logic there was in fact a type of logic (a bit like with the time example above). But the logic case is more curious than this. Because, if all contradictions are true, Triviality itself would also be false; the negation of Triviality would be true:

Not-Triviality)             ¬(∀p: p & ¬p)

But, because of Triviality (which says that for every proposition, both it and its negation are true), both Triviality and Not-Triviality are true:

Triviality.2)                    (∀p: p & ¬p) & ¬(∀p: p & ¬p)

But, because of TrivialityTriviality.2 (which says that both Triviality and Not-Triviality are true) would also be false:

Not-triviality.2)        ¬((∀p: p & ¬p) & ¬(∀p: p & ¬p))

But, because of Triviality, both Triviality.2 and Not-Triviality.2 hold:

Triviality.3)                  ((∀p: p & ¬p) & ¬(∀p: p & ¬p)) & (¬(∀p: p & ¬p) & ¬(∀p: p & ¬p))

This is obviously a never ending regress, as from Triviality.3)Not-triviality.3) could be generated, ad infinitum. If you want to say that what it ‘was like before God had made logic’ is a state where ‘all contradictions were true’ (i.e. trivialism) then you necessarily run into this regress.

The significance of the regress is that it, on trivialism, you cannot talk about what it was like before logic was created, because you would immediately have to contradict yourself, whatever you said. But, making a claim, of any description, is to convey that (at least one) proposition is true and not it’s negation. It is a necessary condition for making a claim, that you convey that (at least one) proposition is true and not it’s negation. For example, if I say ‘It is sunny’, I am communicating the fact that the proposition ‘It is sunny’ is true, and the negation, ‘It is not sunny’, is false. But according to Trivialism, before logic was caused, you could not pick one side out of any pair, p & ¬p, to be true rather than the other, because for every such pair both members are true (and false).

Usually, when something is caused to happen, like when I caused my wine glass to break by knocking it on the floor, a proposition became true (‘the glass is broken’), which was previously not true. So, before God caused logic, when all contradictions were true, it was true that he had ‘not already caused logic’. But if it was true that ‘God has not already caused logic’, then (by Triviality) it was also true that he had already caused logic (because everything is both true and false). So saying that God caused logic, on trivialism, is not to say that he made it true that ‘God caused logic’ (which is how we usually understand causation), because that was already true (and already false). Thus it is impossible to see how, on trivialism, causation as we usually understand it could be employed before logic.

The response might be that: ‘God caused logic’, doesn’t mean that God made something true; rather, that he made something false.  When God caused logic, he didn’t make it true that true that ‘Logic exists’ (because it was already true) – rather, God made it false that ‘Logic does not exist’. Effectively, we mean that he changed one option out of every mutually exclusive disjunction from being true to being false; as if he ‘ironed out’ the contradictoriness from the world. So if ‘p & ¬p’ were true before God caused logic, then by causing logic, he made it false that (say) ‘¬p’. Call this act of making consistency out of inconsistency ‘consistecising’. So ‘God caused logic’ is to say that God ‘consistecised’ all the contradictions, thereby making the principle of non-contradiction true.

It looks like we have we found a way of describing what stuff was like before God caused logic, and what it means to cause logic in such a setting. Before God caused logic, every contradiction was true, but then by causing logic, God made one member from each pair false and not also true (i.e. he consistecised the contradictions).

Well, ask yourself: before God caused logic (i.e. when all contradictions were true) had he already consistecised all the contradictions (i.e. had he already made all the contradictions not contradictory)? The answer, according to Triviality is yes and no; it was true that God had already consistecised all the contradictions, and it was false that he had consistecised all the contradictions. So we cannot say that God causing logic was that he made it false that ‘God has not consistecised all the contradictions’, because this was already false (and already true). We are back to the very same problem of having to state something was made true (‘God consistecised all the contradictions’), which is already true (according to Trivialism); stating that something was made false (‘God has not consistecised all the contradictions’) runs into the same problem, as everything is already false (and true) according to Trivialism.

This makes the idea that ‘all contradictions were true’ an infinitely problematic notion, and an environment in which we can make no sense out of causation.

Nihilism

Trivialism may not be what one means by ‘what it is like before God caused logic’ though. Here is another try:

Nihilism)                        ∀p: ¬(p ∨ ¬p)

(alternatively: ∀p: Fp)

This says that for all propositions, p, ‘neither p nor not-p is true’; or for all propositions, p, ‘p is false’. Nihilism says that nothing is true (in contrast to trivialism which said that everything was true). Perhaps this is what is meant by ‘before God caused logic’.

But could God cause logic to exist if Nihilism were true? Well, if he could, then it would be true that he could. But, by Nihilism, it is false that he could cause logic to exist (because everything is false). So if Nihilism were true, it would be false that God could cause logic. Does God even exist in this situation? No! Otherwise the proposition ‘God exists’ would be true, violating Nihilism! So, if this is what we mean by ‘what it was like before God caused logic’, we would have to say that God couldn’t cause logic, and didn’t even exist, before he caused logic.

But it gets worse. Is Nihilism even true in such an environment? No, it has to be false as well (because every proposition is false). If everything was false, then it would be false that everything was false. Everything wouldn’t be false. So it would be the case that everything was false, and it is false that everything is false. But even that would be false.  It would not be that (everything was false, and everything was not false). Nor would that be the case…

Again we are stuck in a never ending regress. Plus we would have to say that it is false that God could cause logic, and false that God existed, before he caused logic. In what way can we make sense of causation in such a situation? It cannot be normal causation, or anything like it.

It is conceivable that a reply could be made, along the lines of ‘but you are using logic to try to describe what it was like before logic, and you can’t do that’. In response, I say that I am showing that you cannot say anything about what it was like before logic. Specifically, you cannot talk about God, or God causing anything, before logic. The claim, that God caused logic, is precisely the sort of thing you cannot say.

The point is that ‘causing logic to exist’ isn’t like causing a table or a chair to exist. It is not even on the same level as causing the physical universe in total to exist. Saying that there was a point where logic didn’t exist, where logical principles were not true, and that logical inferences were not valid, etc, is just to say something that doesn’t make any sense. Trying to have your cake, by insisting on a time where logic doesn’t apply, but eating it too, by having things coherent enough to have causation remain meaningful, or even for God to exist, is impossible. Saying that God caused logic is incoherent. Saying that it is definitely true that something caused logic, and that this is a logical truth, is just false.

Conclusion

A.J. Kitt tried to defend Matt Slick’s argument against my critique, but his criticisms were hard to make sense of and unsubstantiated, like with the charge that I substituted ‘existence’ for ’cause’. I can see no evidence of Slick using a ‘God caused logic’ argument, and even if he does, I was responding legitimately to an argument where he doesn’t. And if we look at the claim that God, or anything, ’caused’ logic, it seems incoherent. Causation requires logic, just like it requires time. It makes no sense to say of either logic or time that they were caused or created, as causation and creation are temporal notions that are defined in such a way that presupposes that logical notions apply. To put the case in the presuppositional terminology that Slick enjoys; logic is a necessary precondition for the intelligibility of anything, including the idea of causation or the existence of God. Remove logic altogether and everything becomes impossible.

Logic 101

Sigh.

Two weeks in a row Matt Slick, Andrew Rappaport and the rest on BTWN have tried to save face after I explained my critique of their argument. Seeing as they are still just as confused as before I went on (and possibly more so), I have decided to spell out a few more issues here. They say it is an issue of wording. In reality, it is an issue of logic. As demonstrated already, they don’t get this because they don’t understand logic.

So, the first version of the argument has the first premise as this:

1) ‘Either god or not-god accounts for logic’.

This is how Slick actually said it, word-for-word, at various times on BTWN, in debates with people, on his radio show, etc. It is also a horrible train-wreck of a sentence. So what is wrong with this sentence? The problem is the placement of the ‘not’. Negation is a ‘truth-functional monadic operator’. What this means in more plain terms is just that it prefixes individual formulas (which is what makes it monadic), and the new formula it makes when it has been applied has a truth-value which is a product of the truth-value of the original proposition (which is what makes it truth-functional). So, an example will help. Here is a proposition:

2) Washington was the first president of America.

If we want to negate this proposition, we stick a ‘not’ in front of it as follows:

3) Not-(Washington was the first president of America).

The way negation works is by making the new formula have the opposite truth-value to the original one. Say 2) is true, then 3) (the negation of 2) is false. Also, say 2) is false, then 3) is true. Negation toggles between truth-values.

We can say 3) a little more perspicuously as

4) It is not the case that (Washington was the first president of America).

This means the same as 3).

In English, the grammar is messy and not logically regimented, meaning that we often express the same thing by having the negation in the middle of the sentence rather than at the start, as follows:

5) Washington was not the first president of America.

However, this is just a difference of wording, and 3), 4) and 5) all express exactly the same proposition. In propositional logic, if we set p = ‘Washington was the first president of America’, then we would write all three of these formally as follows:

6) ~(p)

In first-order logic, where we have terms for names and simple properties, we would express it differently. We would have a term for the name ‘Washington’, say ‘w’, and a term for the property ‘…was the first president of America’, say ‘F’. So we would write 2) as follows:

7) Fw

With the negation being:

8) ~(Fw)

Now, to return to Slick’s first premise, the negation does not prefix a proposition, but rather just a term in a proposition. It says that ‘not-god’ accounts for logic. But, as we have just seen, negation prefixes propositions not names. It is as if Slick’s premise would be written in first-order logic as

9) Ag or A~(g)

(where ‘g’ is ‘God’ and ‘A’ is ‘…accounts for logic’).

But because the negation is prefixing not the proposition ‘Ag’ but the name ‘g’ inside the proposition, it makes no sense. It is not a well-formed formula, and so cannot be given a truth-value. It is like the way ‘President first the was America Washington’ is just nonsense, and so neither true nor false. So if we take Slick literally, and phrase the argument exactly as he does, then the first premise isn’t really a premise at all, but a meaningless string of words.

If I said ‘either Bob broke into my house, or not-Bob broke into my house’, you would think I had difficulty talking properly. ‘Not-Bob’ isn’t a person, and obviously he didn’t break into my house. Phrasing it as not-Bob is literally meaningless.

To make it a well-formed formula, the closest thing would be:

10) Ag or ~(Ag)

But now we have a dichotomy as the first premise, and if we use disjunctive syllogism we are going to be inevitably back to triviality (as I literally proved in my original post). Let’s quickly give the argument both ways just in case anyone is still unsure how it goes:

Pr1. Ag or ~(Ag)

Pr2. ~(Ag)                  (i.e. negating the first option)

Con. ~(Ag)                  (i.e. concluding the second option)

 

Pr1. Ag or ~(Ag)

Pr2. ~~(Ag)                  (i.e. negating the second option)

Con. Ag                        (i.e. concluding the first option)

So Slick doesn’t want to repair his train wreck of a sentence, 1), into 10), because it is check-mate for the argument if he does that. No debate. Game over.

So it looks like the choice is between a meaningless first premise (i.e. 9) and a trivial argument (i.e. if we use 10). Well, we can read 1) a little differently, a little more charitably. There is another reading of 1) which is not meaningless. So go back to the example of me saying the following:

11) Either Bob broke into my house, or not-Bob broke into my house.

Instead of reading this as ‘Either Bob broke into my house, or it is not the case that he broke into my house (which would make the subsequent argument trivial again), we could read it as follows:

12) Either Bob broke into my house, or someone else broke into my house.

Now, we can express this perfectly well in first order logic, using quantifiers. These are devices which use variables (rather than names). So one quantifier is called the ‘existential’ quantifier, ‘∃’. To say ‘something is red’, we would use the variable ‘x’ and the predicate ‘R’ for ‘…is red’ and the existential quantifier as follows:

13) ∃x(Rx)

This says ‘There is a thing x such that x is red’, or more colloquially ‘something is red’. So when someone says 12, the implicit assumption is that someone broke into the house, and either it was Bob, or it wasn’t Bob. We can express this as follows:

14) ∃x(Bx) and ((x = b) or ~(x = b))

It says ‘there is a thing x such that x broke into my house, and that thing x is either identical to Bob, or it is not identical to Bob’. More colloquially, ‘either Bob broke into my house or someone else did’. Stating it this way excludes the idea that nobody broke into the house, and presumably you would only say 12) if you knew that someone had broken in.

So we could read Slick’s first premise more charitably along those lines, and build in explicitly the claim that something accounts for logic to the premise, and than say that either that thing is identical to god or it is not identical to god, as follows:

15) ∃x(Ax) and ((x = g) or ~(x = g))

This says ‘there is something that accounts for logic, and that thing is either identical to god, or it is not identical to god’. More colloquially, ‘either  god accounts for logic, or something else does’.

So, it looks like we have made some progress towards finding a more charitable way to cash out the logical form of the first premise. 15) is well-formed, so not meaningless, and it doesn’t lead to triviality the same way as 10) did. So, is this the desired destination for Slick’s argument form? I say no. Here’s why.

There is good reason for thinking that nothing accounts for logic, which would make 15), though elegantly formed, false. Here is Aristotle, in the Metaphysics (book IV, section 4) discussing whether the law of non-contradiction can be demonstrated:

“But we have now posited that it is impossible for anything at the same time to be and not to be, and by this means have shown that this is the most indisputable of all principles.-Some indeed demand that even this shall be demonstrated, but this they do through want of education, for not to know of what things one should demand demonstration, and of what one should not, argues want of education. For it is impossible that there should be demonstration of absolutely everything (there would be an infinite regress, so that there would still be no demonstration); but if there are things of which one should not demand demonstration, these persons could not say what principle they maintain to be more self-evident than the present one.”

This much debated passage seems to be suggesting that non-contradiction cannot be demonstrated from some other foundation, because it is the foundation for demonstration itself. Some things, he suggests, must be the end of demonstration and explanation, lest there be an infinite regress of explanation. If so, then it seems that we may have some reason to suppose that no ‘account’ of this principle of logic can be given. Here is another philosopher, David Lewis, making a similar point:

“Maybe some truths just do have true negations [i.e. maybe non-contradiction doesn’t hold].  … The reason we should reject this proposal is simple. No truth does have, and no truth could have, a true negation. Nothing is, and nothing could be, literally both true and false. This we know for certain, and a priori, and without any exception for especially perplexing subject matters … That may seem dogmatic. And it is: I am affirming the very thesis that Routley and Priest [i.e. philosophers who deny non-contradiction] have called into question and-contrary to the rules of debate-I decline to defend it. Further, I concede that it is indefensible against their challenge. They have called so much into question that I have no foothold on undisputed ground. So much the worse for the demand that philosophers always must be ready to defend their theses under the rules of debate.” (Lewis, Logic for Equivocators, (1998), p 434 – 435).

Lewis, probably the most influential analytic philosopher of the late 20th Century, and no stranger to defending controversial theses adeptly, simply offers no argument in support of non-contradiction. He seems to be implying that the very call to account for it is impossible to answer.

Now, obviously, Aristotle and Lewis can be wrong. I disagree with both about different things (future contingents and realism about possible worlds, respectively), so just citing them as authorities is not a way of establishing the thesis they argue for. However, what this does is highlight the difficulties associated with establishing 15), as it requires explicitly what Aristotle and David Lewis are very insistent cannot be granted; a reason for thinking that non-contradiction holds, or an ‘account’ of non-contradiction.

So this does not say that 15) is false. But it does show that it would be almost impossible to establish it. Matt Slick, an admittedly learned theologian, who has had no training in philosophy or logic, would have to solve a puzzle that has literally been too difficult for the greatest philosophers and logicians in history to solve: how to justify non-contradiction.

With these considerations in mind, we can see how Herculean the task would be to justify the premise. Possibly something accounts for logic, but how do you show that? How do you show that it is not just a brute given foundation?

One thing is clear: Slick’s original way of pumping up the intuition that 1) is true is to cite the fact that either god exists or it is not the case that he exists. But this dichotomy is not the same premise, and could be true even when 15) is false. So it is no help. The fallacy of begging the question, that I accused him of before, was not just that he gave a premise that was a potentially dubitable disjunction instead of a dichotomy; it was that he offered the dichotomy as justification for the premise. That is the essence of the false dichotomy, and now it is clear what the task is for justifying 15), it is obvious that it will not work again.

There is nowhere for this argument to go. It is over, even if they claim that it isn’t. Even if they claim that I was making a point about ‘wording’, or that I was drunk (which I wasn’t), or any other ad hominem. The task is too great to be overcome by Slick, and if it is too difficult for Aristotle or David Lewis, I am not holding my breath that anyone will be able to justify 15) either.