The problem with the FreeThinking Argument Against Naturalism

0. Introduction

Tim Stratton is an apologist who runs the website FreeThinkingMinistries. He has an argument he calls the Free Thinking Argument Against Naturalism (FAAN). It works like this: ‘thinking freely’ requires libertarian freewill, and this requires having a soul, and this requires that God exists, and if God exists naturalism is false. Here is how he puts it in his article ‘The FreeThinking Argument in a Nutshell‘:

  1. If naturalism is true, the immaterial human soul does not exist.
  2. If the soul does not exist, libertarian free will does not exist.
  3. If libertarian free will does not exist, rationality and knowledge do not exist.
  4. Rationality and knowledge exist.
  5. Therefore, libertarian free will exists.
  6. Therefore, the soul exists.
  7. Therefore, naturalism is false.
  8. The best explanation for the existence of the soul is God.

In this post, I will set out a quick problem with this argument.

  1. Justification

The main problem, as I see it, is with premise 3. Here is what Stratton says about this:

“…it logically follows that if naturalism is true, then atheists — or anyone else for that matter — cannot possess knowledge. Knowledge is defined as “justified true belief.” One can happen to have true beliefs; however, if they do not possess warrant or justification for a specific belief, their belief does not qualify as a knowledge claim. If one cannot freely infer the best explanation, then one has no justification that their belief really is the best explanation. Without justification, knowledge goes down the drain. All we are left with is question-begging assumptions (a logical fallacy).”

Stratton uses ‘justified true belief’ as the definition of knowledge, which seems a bit out of date with how contemporary epistemology thinks about it, but let’s pass over that and just play along.

Given that he says that on naturalism “[o]ne can happen to have true beliefs”, he seems to be conceding that true beliefs are possible on naturalism, but that having justification for true beliefs is not. So the question becomes: what is it about naturalism that rules out justification? However, all he says about why we would not be able to have justification on naturalism is that:

“If one cannot freely infer the best explanation, then one has no justification that their belief really is the best explanation.”

What is going on here?

2. Determinism

Let’s play along with the idea that on naturalism, “all that exists is causally determined via the laws of nature and the initial conditions of the big bang”. It doesn’t seem to be required to me. After all, the laws of physics could be indeterministic. Naturalism (plausibly) says that there are no non-natural causes, but doesn’t say that every state is determined by the initial state of the universe. Perhaps, as quantum theory seems to suggest, the laws of physics are indeterministic, and the evolution of the world is chancy. That might be correct, or it might be incorrect. Stipulating naturalism doesn’t on its own seem to settle this question though. But let’s just grant it anyway, just to see where it goes.

The question is: on naturalism, and determinism, if I have a true belief, can I have justification for that true belief? Stratton is saying ‘no’, and his reason seems to be that this is because I “cannot freely infer the best explanation”.

But why should I have to freely infer anything? I don’t think freedom, of the type he is suggesting, is required at all. Here is how that could work.

Suppose that strict determinism is true, such that “people are nothing more than material mechanisms bound by the laws of chemistry and physics”, “bags of chemicals on bones,” or “meat robots”, certainly not possessing a soul or libertarian free will. If so, then each of our beliefs will have been caused to be in our mind (or in our brain) by some antecedent state of affairs, which was itself caused, etc etc, in a chain going back to the initial state of the universe. It is logically possible that I could have believed otherwise than I do, but really there was never any physical possibility that I was going to.

3. The Counterexample

Let us suppose that in this situation, I have the belief:

A) Tim Stratton is the author of the FAAN

It is a true belief (presumably). But can I have justification for it if naturalism and determinism are true? Let us suppose also that I have the further two true beliefs as well:

B) There are various articles and YouTube videos by Tim Stratton in which he presents the FAAN, and in which claims to be the author of the argument.

C) Nobody would make an easily detectable false claim to authorship of an argument in so many articles and YouTube videos.

Nothing about naturalism or determinism prevents me from having these two beliefs. Perhaps they have to be merely brain states on naturalism, rather than ‘mental states’ (supposing that phrase to mean something other than brain states). Let’s suppose that as well for the sake of the argument.

It seems to me that nothing Stratton has said so far rules out the possibility that the brain states associated with me having beliefs B and C are part of the causal story involved in me having the belief A. It may be that something about the chemical reactions happening in the brain when I entertain both B and C causes me to have this belief A.

The question then would be: why my having beliefs B and C doesn’t count as justification for believing that A? In other words, why isn’t it a justification of my belief that Stratton authored the FAAN that I also believe that he has said it many times in articles and videos, and that people generally don’t pretend to have authored arguments like that?

This seems like a perfectly coherent situation. I actually do have the belief that he is the author of the argument for more or less those very reasons. I’ve never met him; I didn’t see him write the argument; I wasn’t with him when he first thought of it. I go off the evidence I have (the articles and videos) along with my assessment of how likely they are to be reliable (based on the thought that people generally don’t completely make up authorship of arguments like that). I didn’t freely pick any of those beliefs. Reading his articles caused me to believe that he says he authored them in the articles. My experience with people also caused me to come to believe people don’t generally make up easily detectable falsehoods. On the basis of those (let’s suppose: caused by those) I came to believe he authored the argument. This seems perfectly coherent. But if so, then I can have ‘rationality and knowledge’ without libertarian free will, and thus premise 3 is false.

3. Conclusion

If Stratton thinks that this cannot be a justification, for some reason, then he has not spelled it out that I know of. Nor do I understand how that would go. To show that such a situation cannot be an instance of a justified belief, he would have to show that such a situation is impossible (cannot happen), or that it is possible but cannot count as a justification. To me it obviously can happen even granting naturalism and determinism. All it requires is the holding of true beliefs (which Stratton explicitly allows in that situation) and that beliefs can be causally related to one another. But I supposed for the argument that beliefs are simply brain states, which are physical states, and the sorts of things that “bags of chemicals on bones” or “meat robots” could have. Obviously, they could be causally related; physical states can be causally related, brain states included.

Given all that in the counterexample, I have a true belief, A, and I have relevant beliefs, B and C, and it is on the basis of having those beliefs that I believe A. The thing that is important about whether B and C count as justifying belief A is how relevant they are to A, but not about whether they are casually related to my having belief A or not. The causal question seems irrelevant, so long as they are of the right type, and I believe A because I believe them. Both of those conditions are met here, so it counts as an instance of justification. Thus, the argument is unsound.

There are many other ways one could argue against FAAN, but I wanted to present this one. It is not my argument, but comes from Peter Van Inwagen, in his paper ‘C. S. Lewis’ Argument Against Naturalism‘. In reality, Stratton’s argument at this point is just a rehashed version of Lewis’ argument, and fails for the same reasons.


More on the potential / actual infinite part 1.2

0. Introduction

This is just a short post, as I am currently in the middle of working on the second (and hopefully third) longer posts in this series. I just want to get a point down on paper (as it were) for reference’s sake.

In a footnote to his book on the Kalam, Craig considers what I called ‘Cantor’s intuition’ (also known as ‘Cantor’s thesis’ or the ‘domain principle’), which is the thesis that the potential infinite entails an actual infinite. Craig claims that this thesis is refuted in a paper by W D Hart. That paper is called ‘The Potential Infinite‘ (Proceedings of the Aristotelian Society, New Series, Vol. 76 (1975 – 1976), pp. 247-264). It is true that Hart takes the hierarchy of sets to be a potential infinity without being an actual infinity, and that this is a rebuttal of the thesis. He says:

“We can take this as evidence that the existence of an actual infinity is not implied by there being potentially infinitely many F’s. This is a strong rebuttal of Cantor’s thesis” (p. 263)

This is more or less how I argued in the previous post. Not every potential infinite presupposes an actual infinite.

However, our question was less general (and more specific) than whether Cantor’s thesis is true in its widest scope. We were primarily interested in time, not sets. We wanted to know if the potentially infinite future presupposes an actually infinite future. And it is worth noting that Hart does touch on this in the paper – the paper that Craig cites as support for rebutting Cantor’s thesis, which is crucial to his defence against Morriston’s attack. What Hart says about this is interesting, and I just want to explain that here.

  1. Lack of clarity of potential infinite

First, note that part of the point of Hart’s paper is to clarify the notion of the potential infinite, which he thinks is far less clear than that of the actual infinite. As he notes:

“Cantor’s achievement was to bring the actual infinite out of the philosophical shadows into the scientific light. Can we do for the potential infinite what Dedekind and Cantor did for the actual infinite? That is my topic.” (p. 248)

Clearly, for Hart, the notion of the potential infinite is not settled mathematical cannon, unlike the notion of the actual infinite. It is an open question, one which is ‘his topic’, as to how it is to be understood in a formal sense. And although it is his project to look at this question, he does not settle it in this paper. He goes on:

“I do not claim to have analysed the potential infinite adequately. Instead, I shall explore two natural approaches that have been mentioned in the literature. I reach no decisive conclusion on the merits of either, but perhaps the explorations can turn up intuitions which are at least candidates for the eventual material adequacy conditions in terms of which a genuine analysis of the potential infinite should be judged. Such, at any rate, is my hope.” (ibid)

So the notion is problematic for Hart. There is no non-controversial definition of it which can be supposed that all mathematicians agree on. This is the problematic area he is working on, and he doesn’t claim to have settled the question. I just want to make that clear. When Craig appeals to the notion of the potential infinite, he is appealing to something that is not settled within the mathematical and philosophical literature. Of course, the paper was written almost 40 years ago, but it is contemporaneous with Craig’s book, and there is still considerable discussion of this topic today (see, for example, Dahl (2017)).

The simple point is just that the distinction between the potential and actual infinite is contentious in the academic literature, and the notion of the potential infinite is seen as problematic in particular by Hart.

Anyway, let’s move on to when Hart addresses an idea similar to Craig’s, and see what he says about it.

2. The temporal model

Immediately after the passage quoted above, Hart goes on to touch on an idea very similar to Craig’s (he says he wants to mention it “if only to get it out of the way”):

“For all I know, the best theory of the potential infinite identifies it with a process in time conceived of as a series of moments isomorphic to the natural numbers.” (ibid)

This does seem to be like Craig’s view. Consider this from Taking Tense Seriously:

“…virtually all philosophers who espouse a tensed, or A-theory of time, hold that the series of successively ordered, isochronous events later than some denominated event is potentially infinite.”

The ‘series of successively ordered isochronous events’ fits this bill pretty closely. Remember that Craig distinguishes between the past and present, which are ‘real’, and the future which is not. Hart seems to encode this intuition in the following considerations:

“Such a process might (1) have one input given at a moment zero prior to any operation of the process; (2) for any output the process has actually already yielded at a moment t, the process can take that and only that output as an input at the next moment t+1, and; (3) the process never yields the same output at two different moments and never destroys its input (so that what it once yields exists ever after). For such a process, there is no moment at which it can have produced an infinity of outputs, but no matter how many outputs it has yielded at a given time, at some later time it can always yield more.” (Hart, The Potential Infinite, p. 248)

So this is like counting up from 0 starting now, and writing down each number you have counted on a bit of paper. As you do so, the process can always go on further, but at no point will you have written down an actual infinity of digits. Writing the numbers down on a bit of paper is an analogue of Craig’s idea that once something has happened – once it has gone from being future, to being present / past – it is ‘real’. So, this seems to be substantially like Craig’s idea of the potential infinite.

But, what does Hart say about such a proposal? He says the following:

“The trouble with such a sketch is that we have no settled theory of processes in which to imbed it, so we have no sharp way to establish whether it satisfies reasonable desiderata for potential infinities” (ibid, p. 249)

What he is saying is that this is too messy and vague to know how to evaluate it. It presupposes too much of which is unclear, about the nature of time and how processes work, for it to be a proposal from which we can apply any meaningful considerations. He goes on:

“For example, does it presuppose a completed actual infinity of moments? This question is central to an issue raised by a thesis of Cantor’s to be stated below” (ibid)

The “issue raised by a thesis of Cantor’s” is exactly that which we considered in the previous post, namely the thesis is that a potential infinite presupposes an actual infinite.

Hart is saying that one of the problems with a proposal such as the temporal one described here (which looks just like Craig’s) is that it is not clear whether Cantor’s thesis holds of it or not. That is to say, it is unclear whether a potential infinite conceived of in that way presupposes a corresponding actual infinite or not. Thus, Hart is decidedly unhelpful for Craig in what he says which is directly relevant to the point in dispute.

3. Conclusion

To sum up the point here, Craig wants to say that the endless future is merely potentially infinite, and not actually infinite. He addresses ‘Cantor’s thesis’, which is that a potential infinite presupposes an actual infinite. When he does so, he references Hart’s paper, saying that Hart rebuts the claim. True, Hart rebuts Cantor’s thesis by arguing that the hierarchy of sets is a counterexample, i.e. it is potentially but not actually infinite. But, crucially, when he addresses the temporal model that Craig endorses, he refuses to treat them the same way. He suggests that it is unclear whether such a temporal account of the potential infinite presupposes an actual infinite or not. And the issue is that such an account is too vague for clear formal considerations to be applied to it productively. So while the paper is an example of someone arguing that Cantor’s thesis is false, it is only the most general form of the thesis that is rejected. Whether it can be applied to the temporal case is definitely not rebutted in this paper.

More on the actual / potential infinite

0. Introduction

One of the premises of the Kalam Cosmological Argument (KCA) is that the universe began to exist. There are two types of defence for this premise; scientific and philosophical. In the latter category, there is one argument in particular that I want to focus on, which Craig calls the ‘argument from the impossibility of an actual infinite’.

The argument runs like this:

  1. An actual infinite cannot exist
  2. An infinite temporal regress of events is an actual infinite
  3. Therefore, an infinite temporal regress of events cannot exist

Craig holds that the past had a beginning, but also that the future has no end (presumably due to his beliefs about the afterlife). This invites the following objection, which has been made in the literature by Wes Morriston (here). We seem to be able to formulate a symmetrical argument which should conclude that the future has an end point:

  1. An actual infinite cannot exist
  2. An infinite temporal progress of events is an actual infinite
  3. Therefore, an infinite temporal progress of events cannot exist

(The term ‘progress’ is artificial used in this context, but it is clearly intended as the temporal mirror of the term ‘regress’)

The first argument says that the past must have a beginning, otherwise it would constitute an actual infinity. The second argument, the counter-argument, says the future must have an end, otherwise it would constitute an actual infinity.

Morriston has a thought experiment to illustrate his point. He asks us to imagine two angels, Gabriel and Uriel, who take turns saying praises to God forever. He makes the following remarks:

“It’s true, of course, that Gabriel and Uriel will never complete the series of praises. They will never arrive at a time at which they have said all of them. Indeed, they will never arrive at a time at which they have said infinitely many praises. At every stage in the future series of events as I am imagining it, they will have said only finitely many. But that makes not a particle of difference to the point I am about to make. If you ask, “How many distinct praises will be said?” the only sensible answer is, infinitely many.” (Morriston, Beginningless Past, Endless Future, and the Actual Infinite, p. 446)

To counter this, Craig argues that the endless future is best considered a merely potential infinity, (in contrast to the beginningless past, which is best considered as an actual infinity). As Craig says in his reply to Morriston, Taking Tense Seriously:

“So with respect to Morriston’s illustration of two angels who begin to praise God forever, an A-theorist will concur whole-heartedly with his statement, “If you ask, ‘How many praises will be said?’ the only sensible answer is, infinitely many”— that is to say, potentially infinitely many. If this answer is allowed the A-theorist, then Morriston’s allegedly parallel arguments collapse.”

Effectively, Craig is denying the second premise of our counter-argument. He is saying that an infinite temporal progress of events is not an actual infinity – it is merely a potential infinity.

In what follows I want to look at three types of response to this. This post will constitute the first part, and in subsequent posts I will address the second and third points.

Firstly, I will spell out an intuition that many people have, according to which the existence of a potential infinity entails a corresponding actual infinity. We will call this ‘Cantor’s Intuition’ for reasons we will get into below. If Cantor’s Intuition was correct, then Craig’s response would be defused. For then we could “concur whole-heartedly with his statement” that the future is potentially infinite, and insist that it is also actually infinite. According to this line of thinking, the potential and actual infinite are not mutually exclusive.

Secondly, I want to look at a different strategy. Perhaps the future is not actually infinite, and the second premise of the counter-argument is false. But the thought is that maybe this leaves open the door to denying the second premise of the original argument. That is, if the infinite progress of events is a merely potential infinity, maybe the infinite regress of events is a merely potential infinity as well. Craig is very dismissive of this view, but I think it is worth exploring.

Lastly, I want to look at why Craig thinks there is an asymmetry here at all. Here it seems that considerations about the philosophy of mathematics are completely irrelevant, and all that is doing the heavy lifting is considerations about the philosophy of time. Of course, all but the most fanatical would concede that time is in some sense asymmetric. Yet, this can be cashed out in lots of different ways. Do any of those ways of understanding the asymmetry do the work that Craig needs?

  1. Potential infinite implies actual infinite

The mathematical study of the infinite was revolutionised in the 19th century by the work of various mathematicians, but the primary figure is clearly Georg Cantor. He was the first to work out the mathematics of the infinite, and in particular gave a formal treatment of the actual infinite. He changed his mind quite a lot, but at one time in particular he held a view that I want to bring up here. In 1886, he wrote a letter to the mathematician Richard Dedekind, in which he made the following comments:

“… since there can be no doubt that we cannot do without the variable magnitudes in the sense of the potential infinite, then the necessity of the actual infinite can be proved as follows: In order for such variable magnitudes to be capable of evaluation in a mathematical investigation, their “range” of evaluation must be precisely known by means of a prior definition. But this “range” cannot itself be in turn something variable, for otherwise every fixed support for the investigation would give way; hence this “range” is a definite actually infinite set of values. Thus, every potential infinite, if it is to be employable in mathematics, presupposes an actual infinity.” (Quoted in ‘The Potential Infinite‘, by W D Hart, 1979)

Cantor’s Intuition seems to be that the following inference is valid:

x is a potential infinite; therefore, x is an actual infinite.

If Cantor’s Intuition is right, and the above inference is valid, then Craig’s argument does not work. The reason is that Craig is using the terms potential infinity and actual infinity as if they were mutually exclusive; that something can be one or other but not both. After all, he says that the endless future is potentially infinite as a rebuttal to Morriston’s claim that there are infinite future prayers. Clearly, Craig thinks this rebuttal rules out there being actually infinitely many future prayers.

But if Cantor is right, then something being potentially infinite means that it is also actually infinite. If so, then when Craig says that the endless future is potentially infinite, this would entail that it is also actually infinite. And that would completely undercut his reply to Morriston.

But is Cantor right?

2. A potential infinite that is not an actual infinite

Well, in some sense it seems that he was wrong. Not every potential infinity presupposes an actual infinity. Consider the hierarchy of sets. So, start with the empty set (the set with zero elements):

Then there is the set with one element; namely, it has the empty set as it’s sole element:


Then there is the set that contains two elements: the empty set, and the the set which contains the empty set:

{∅, {∅}}

The next level in the hierarchy contains the previous levels as distinct elements; levell 0 contains nothing, level 1 contains level 0, level 2 contains level 0 and level 1, etc. Clearly, we can go on elaborating this hierarchy forever, just constructing more sets in this way. But does this constitute a completed totality – an actual infinity?

There are good reasons for thinking not. Such a proposal seems to require that there is a ‘set of all sets’, and that seems incoherent. The reasoning is as follows. Suppose there was a set, V, which was the set of all sets. Well, why can’t we make another set, which has all the sets which are elements of V, as well as V, as it’s elements? Such a thing seems to be a set, and seems to employ just the process we have used at the lower levels. Yet it contains V, which we just postulated was the set of all sets. And that would mean that V is not the totality of all sets after all, but merely one more level of the hierarchy.

Such considerations seem to suggest that there cannot be a set of all sets, conceived of in this way. And if that is right, then the hierarchy of sets is potentially infinite, in that each set is finite but part of a never-ending hierarchy, where the notion of the completed totality is incoherent. Thus, along this way of thinking, we have an example of a potential infinite which is not an actual infinite. Such is the view of many people, including set theorists such as Ernst Zermelo, Kurt Gödel, and philosophers of mathematics such as Hilary Putnam, Charles Parsons, Geoffrey Hellman, and Oystein Linnebo.

And if this way of thinking is right, then Cantor was wrong here. Not every potential infinity implies an actual infinity.

3. A potential infinity that is also an actual infinity

Yet, things are not quite so straightforward. Although not every instance of a potential infinity presupposes an actual infinity; still, some might do. The hierarchy of sets is a particularly striking example where the idea of the completed infinity seems incoherent (for the reasons given above). However, the same sorts of considerations are not present in other cases.

For example, take the natural numbers. One can easily, and quite without contradiction, talk about the set of ‘all natural numbers’. This notion does not fall prey to the same worries as the set of all sets. Part of the achievement of Cantor was to elaborate the mathematical treatment of totalities such as the natural numbers. It is true that one could imagine counting forever, and such a process would increase without limit, always remaining finite and never being completed. Thus, it would be a potential infinity.

However, we can say things like “You will never have counted all the natural numbers” and when we use the phrase ‘all the natural numbers’ so we refer to a coherent concept. Even if we cannot reach the totality by counting, the concept of the totality itself does not seem incoherent in the same way as it does for the hierarchy of sets.

So in the case of the natural numbers, we have a potential infinity (instantiated by you trying to count them all), but we also have a completed infinity, which is the totality of numbers you are counting. And this is Cantor’s point. You can have a ‘variable magnitude’, which is the number you have counted (which is increasing over time), and there is the ‘range’ of numbers you are counting off, which does not increase and is an actual infinity. Thus, it seems like a potential infinity which presupposes an actual infinity.

Some people do disagree with this, of course. But such people are not merely saying that the concept of the actual infinity cannot be applied in the ‘real world’, as opposed to the mathematical world. Rather, such opposition requires disagreeing with Cantor that the actual infinity is a legitimate concept even in the mathematical realm. Carl Friedrich Gauss, for instance, strongly objected to the actual infinite even in mathematics. Such a position is called ‘finitism‘.

Craig, on the other hand, seems to have no principled objection to Cantorian treatments of the actual infinite in mathematics; he does not seem to be a finitist. If so, he should accept that sometimes there are potential infinities that are also actual infinities, such as the natural numbers.

4. Conclusion

Where does this leave us? I think we can say two things. Firstly, the following inference is invalid:

If x is a potential infinity, then x is an actual infinity.

It is invalid because the hierarchy of sets seems to be a plausible counterexample. However, unless one wants to take a very stern Gaussian position and banish the actual infinite even from mathematics, one must also concede that the following inference is also invalid:

If x is a potential infinity, then x is not an actual infinity

This seems invalid because the coherence of the totality of the natural numbers seems to be a counterexample.

This means that one cannot say that the angels prayers constitute an actual infinity merely because they constitute a potential infinity; but also one cannot say that they do not constitute an actual infinity merely because they constitute a potential infinity. Both sides can agree that they constitute a potential infinity, and this leaves open the question about whether they also constitute an actual infinity. In effect, the observation that they constitute a potential infinity is besides the point. The salient issue is about whether they constitute an actual infinity, and that is logically independent (assuming both of the above inferences are indeed invalid).

I think the lesson from this is that some potential infinities are also actual infinities, and some are not. The question becomes: which type is the future? The case we saw where something was potentially infinite but not actually infinite involved an incoherence involved in the notion of the totality. Is such a consideration present when it comes to the notion of the future?

One thing that seems plausibly problematic is the notion of the last time. One might think that the very notion of ‘a time’ implies that it has a past and a future. Such seemed to be Aristotle’s view:

“Now since time cannot exist and is unthinkable apart from the moment, and the moment a kind of middle-point, uniting as it does in itself both a beginning and an end, a beginning of future time and an end of past time, it follows that there must always be time: for the extremity of the last period of time that we take must be found in some moment, since time contains no point of contact for us except the moment. Therefore, since the moment is both a beginning and an end, there must always be time on both sides of it.” (Physics, book 6, part 1)

But such considerations shouldn’t sway us here. After all, the notion of number is similar in this respect. Just as we might think that for each moment of time there must be both past and future on either side of it, so too for each number there must be both higher and lower numbers on either side of it. The point is that we can conceive of the totality of natural numbers without thinking of there being a highest natural number. So, by analogy, even if there is no final time, this does itself stop us from conceiving of the totality of all future time.

We would be able to say that the future is potential and not actually infinite if there were some incoherence involved in thinking of the totality of future time, like there was with the totality of the hierarchy of sets. Yet, the cases seem dissimilar here. After all, what was causing the problem with the case of the sets was that the totality was itself a set. This meant that it could be fed into the iterative process that generated each preceding level in the hierarchy, generating a new level above it.

But such a move is not applicable to the notion of time. After all, the totality of time is not itself a time. Therefore, we need not suppose that the totality of time is itself followed by another time. If we did, then the case would be analogous to the set example. But it seems clearly to be distinct.

This does not establish that the case of time definitely is one that is both potentially infinite and actually infinite, but it does seem to show that if there is a reason it is not directly analogous to the hierarchy of sets example. Maybe there is an argument, but what is it?

My thought is that the time example is more like the natural numbers than the sets. Talk of the totality seems coherent. Thus, it seems entirely possible, at least conceptually, that the future is both a potential infinity and an actual infinity. And if that is right, then Craig’s reply is kind of impotent. Yes, potentially infinitely many praises will be said. But also, there is an actual infinity of praises yet to be said. The former point does not itself rule out, or in, the latter. Clearly, more needs to be said (though, hopefully not infinitely more).

Rasmussen’s New Argument for a Necessary Being

0. Introduction

Josh Rasmussen is a philosopher at Azuza Pacific University. He recently sent me a copy of a paper entitled ‘A New Argument for a Necessary Being‘ in which he lays out an ingenious cosmological argument. I have a response to it, which I will outline here.

  1. The argument

 Here is the argument:

  1. Normally, for any intrinsic property p that (i) can begin to be exemplified and (ii) can be exemplified by something that has a cause, there can be a cause of p’s beginning to be exemplified.
  2. The property c of being a contingent concrete particular is an intrinsic property.
  3. Property c can begin to be exemplified.
  4. Property c can be exemplified by something that has a cause.
  5. Therefore, there can be a cause of c’s beginning to be exemplified (1–4).
  6. If 5, then there is a necessary being.
  7. Therefore, there is a necessary being.

Part of the cleverness of this argument is how weak the premises are. This means that they are easier to motivate and harder to object to. Premise 1, for example, is a defeasible rule of thumb. It isn’t ruling out there being objects that don’t satisfy it; as Rasmussen explicitly says, his argument

“…allows for the possibility of uncaused natural objects” (p. 4)

The modesty of its presuppositions is a strength.

In some respects, this argument is similar to the modal ontological argument. That too has very modest premises. One supposedly only has to grant that it is possible that God exists to get that he necessarily exists, to the conclusion that he actually exists.

However, I have an objection. My objection is similar to the objection to the modal ontological argument, whereby one says that it is possible that God does not exist, from which it follows that he necessarily does not exist, and so actually does not exist.

I will essentially present a new version of premise 4, from which we get a new version of premise 5, from which we get the conclusion that there is no necessary being. I will argue that my new version of premise 4 is explicitly allowed because of the weakness of Rasmussen’s premises, and that the only way to avoid it would require tightening it up, which loses the distinctive appeal and novelty of his approach. In addition, my new version of premise 4 is a core doctrine of Christianity, and as such Christians cannot simply deny it in favour of Rasmussen’s premie (in fact, they must find a way to block one of the premises of my argument or deny its validity, else it would rule out Christianity from being true).

Before we come to that, we need to understand Rasmussen’s argument in more detail. He provides a useful summary of premise 1 as follows:

 “…any beginning of an exemplification of an intrinsic property can have a cause…” (p. 2)

As a defeasible rule of thumb, this is quite plausible. Rasmussen provides an a priori type of justification and an abductive justification. The a priori justification is as follows:

“…imagine an arbitrary, unexemplified intrinsic property i . Suddenly, something changes. Snap! Property ibecomes exemplified. At this point, you may wonder why isuddenly became exemplified. Your mind might thus be inclined to think that i ’s exemplification canhave a causal explanation (especially if ican have caused instances). I suspect that some philosophers who come to the table as sceptics of a necessary being will have this intuition.” (p. 2 – 3)

The abductive justification runs as follows:

“…when a scientist creates a new piece of technology, a new type of thing begins to exist, and the scientist thereby causes one or more intrinsic properties to begin to be exemplified. As another example, we can imagine hydrogen and oxygen atoms coming together to form the first water molecule, thereby causing the property of being waterto become exemplified. In general, when we consider a new type of object, we can coherently imagine a cause of the exemplification of the new intrinsic properties instantiated by that object. Thus, we might infer (1) as a plausible explanation of these cases of apparent causability.” (p. 3)

Thus, we can see the sorts of things that Rasmussen has in mind as being examples of what premise 1 is about. We can grant this for the purposes of my argument. It is not supposed to be a universal principle, and might have exceptional cases which are counterexamples to it, but:

If someone has reason to doubt (1) based upon certain exceptional cases, she could still accept (1) as a general rule of thumb. (p. 3)

I have no need to dispute this here.

Premise 2 just says that the property of being a contingent concrete particular is an example of an intrinsic property. The notion of being an intrinsic, as opposed to extrinsic property roughly means that the property is held of an object without relation to any other objects. It is an intrinsic property of me that I am 5’10”, but it is an extrinsic property of me that I am taller than my friend Joe, etc. It is tricky to spell this distinction out perfectly, and Rasmussen offers a simple sufficient (but not necessary) condition for being intrinsic, namely:

“p is intrinsic if one who grasps p does not thereby grasp any external”

We can grant this for the purposes of my response. We can also grant that being a contingent concrete particular is an intrinsic property.

Premise 3 says that the property of being a contingent concrete particular, i.e. c, can begin to be exemplified. The premise doesn’t say that it actually did begin to be exemplified, only that it is possible for it to be so. Rasmussen says as an example:

“…we can imagine a beginning to the existence of contingent bits of matter as they explode out of an initial singularity.” (p. 4)

Thus, in a broad sense, it is possible for contingent concrete things to have an origin point. We can grant this for now as well.

Premise 4, according to Rasmussen, says:

there can be a contingent concrete particular that has a cause. (p. 4)

In defence of this, Rasmussen says:

“Take me, for example: I am a contingent concrete particular and my existence was caused some time ago.”

That seems very reasonable. I won’t directly challenge this premise, but it is at this point that my argument will kick in (more on that in a moment). Before we get to that, let’s just see how Rasmussen ties these considerations together into a whole.

Premises 2, 3 and 4 establish that c is intrinsic, can begin to be exemplified, and can have caused instances. This means that it is the sort of property that premise 1 applies to; it is the sort of property according to which

“there can be a cause of [c]’s beginning to be exemplified” (p. 1)

But because c is the property of being a contingent concrete particular, this means that:

“…there can be a cause of a beginning of contingency” (p. 5)

This is premise 5, and it follows from premises 1 – 4.

The move to premise 6 is my favourite bit of the argument, and I think the most ingenious. So far, all we have established is that it is possible that there is a cause for the beginning of contingency. We have not established that there is a beginning of contingency, or that there is a cause; just that such a cause of a beginning is possible.

From this, Rasmussen says, it follows that a necessary being exists. Here is how he gets there.

First, suppose that no necessary being exists. If that is the case, then, Rasmussen says, there couldn’t be a necessary being. This is the familiar inference used in the modal ontological argument; necessary beings exist at all possible worlds, so if there is even one at which they don’t exist, they exist at none at all. But if it is not possible for a necessary being to exist, it is not possible for a necessary being to be to cause the beginning of contingency either. So if there is no necessary being, then it must be possible for a contingent thing to cause the beginning of contingency (for it to remain possible at all, as premise 5 states). But this is incoherent, and thus impossible. Rasmussen explains:

This is because c —the property of being a contingent concrete particular— would already have to be exemplified if a contingent concrete particular were to cause c to begin to be exemplified in the first place. In other words, the exemplification of contingency would be ‘prior to’ the exemplification of contingency, which is impossible. (p. 5)

Rasmussen concludes this section with the following:

Thus, if there is no necessary being, then it is not possible for anything to cause a beginning of contingency, which contradicts (5). Therefore, if there is no necessary being, then (5) is not true. This result is the contrapositive of (6). Therefore, (6) is true.
From (1)–(6), it follows that there is a necessary being. (p. 5)

Now, I must say, I think this is a brilliant bit of reasoning. It is ingenious and original. I really like it.

But I still think I have a problem for it.

2. Counter-argument

My response to this argument is not really to reject any of the premises or the inference to the conclusion. The type of response I am giving is a sort of stale-mate response, rather than a defeating response. I think that we have just as good a reason to think that the negation of the conclusion is true, and I have an argument which is almost exactly the same as Rasmussen’s. In this respect, it mimics a familiar response to Plantinga’s modal ontological argument. That argument can be stated as follows:

  1. It is possible that a necessary being exists
  2. Therefore, a necessary being actually exists

The response to this is to simply postulate an alternative argument, with premises that are just as plausible, but with the opposite conclusion:

  1. It is possible that no necessary being exists
  2. Therefore, no necessary being actually exists

The question then becomes which of the two premises is more plausible. Each premise is equally plausible. Without a way of deciding between the premises which does not beg the question, the argument ends in a stalemate. Plantinga seems to accept this stalemate, because he is merely interested in establishing the rationality, rather than the truth, of the conclusion:

“[modal ontological arguments] cannot, perhaps, be said to prove or establish their conclusion. But since it is rational to accept their central premise, they do show that it is rational to accept that conclusion” (Plantinga 1974, 221)

If my argument works, Rasmussen would be pushed into accepting merely this sort of less ambitious defence, or he would have to tighten up the premises and thus lose the attractiveness of them.

Here is my counter-argument:

  1. Normally, for any intrinsic property p that (i) can begin to be exemplified and (ii) can be exemplified by something that has a cause, there can be a cause of p’s beginning to be exemplified.
  2. The property c of being a contingent concrete particular is an intrinsic property.
  3. Property c can begin to be exemplified.
  4. Property c can be exemplified by something WITHOUT a cause.
  5. Therefore, there can be NO cause of c’s beginning to be exemplified (i.e. it is possible that there is no cause of c’s beginning to be exemplified).
  6. If 5, then there is NO necessary being.
  7. Therefore, there is NO necessary being.

The argument is the same up to premise 4. The new version of premise 4 mimics the form of Rasmussen’s fourth premise, but simply says that c can be exemplified by something without a cause. As we saw above, Rasmussen is explicit that his argument allows for “the possibility of uncaused natural objects”. This seems enough to buy us my new premise 4; after all we only need the possibility, not the actuality of such objects for this premise to work. We will come back to what reasons we might have to thinking that premise 4 is true, but for now, let’s see what affect this has on the argument if we were to grant it.

One way of the new premise 4 being satisfied is by there being a first contingent thing that just pops into existence uncaused. Let’s say that a teapot pops into existence uncaused, and thus exemplifies property c. Thus, property c is exemplified by something which itself has no cause. In this scenario, premise 5 is true, because the teapot is the first (and indeed only) contingent concrete particular. Thus, it is a case of c beginning to be exemplified without any prior cause. Again, we are not saying that this scenario is true; just that it is possible that it is true.

This scenario doesn’t directly rule out a necessary being, but it does indirectly. We might think that there may be a necessary being who exists necessarily, and a teapot spontaneously pops into existence, as it were, next to her; or it may be that there is no necessary being at all (and, indeed nothing at all) and then a teapot just pops into existence on its own. Either seems possible.

But, as the familiar modal ontological argument reasoning goes, if the second scenario is even possible, then the first one isn’t. So if it is possible that the teapot pops into existence on its own, then there necessarily isn’t a necessary being. And remember, the premise

“…does not assert that this is actually the case—only that it is broadly logically possible for this [scenario] to be the case”

The test of broad logical possibility that Rasmussen uses throughout the paper was just whether we can imagine it. Recall, he said in defence of premise 3:

 “…we can imagine a beginning to the existence of contingent bits of matter as they explode  out of an initial singularity.”

If that establishes the possibility that premise 3 needs, then my being able to imagine the teapot popping into being on its own establishes my new premise 4.

But what about Rasmussen’s ingenious bit at the end of his paper, where he seemed to rule out this scenario? Didn’t he establish that “it is not possible for a contingent concrete particular to cause a beginning of contingency without circularity”?

Well, we can actually grant that he did. My counter-argument doesn’t require that the teapot causes c to become exemplified. As Rasmussen said, premise 1 is a rule of thumb, and not an exceptionalness principle. The teapot coming into existence is a case of an uncaused thing beginning to exist, and of c being exemplified without cause. Thus, we do not get caught in the trap that Rasmussen lays. We are simply explaining one way that new premise 5 is satisfied, which is that c begins to be exemplified by something uncaused, and it is one of those rare cases that premise 1 does not rule out. The very modesty of Rasmussen’s argument allows for this sort of case to pop up (in the broad logical sense).

So, if it is possible that the teapot pops into existence with no cause, then there is no necessary being (via the modal ontological argument inference). As new premise 5 states, such a thing is possible; therefore there is no necessary being.

3. Justifying new premise 4

The strategy I am employing here ends up with a stalemate, or at least that is the intention. Rasmussen’s premise 4 leads to the conclusion that God (or at least a necessary being) exists, and my new premise 4 leads to the conclusion that no necessary being exists.

One response would be to suggest that Rasmussen’s premise 4 is more plausible than my premise 4. If so, that might tip the balance in favour of his conclusion. In the case of the modal ontological argument, the thought was that no non-question-begging reasons could be brought forward that favoured one argument over the other. But perhaps there are decent reasons for thinking that the original premise is more plausible than the new one. We have already seen Rasmussen’s reason for thinking that his premise is true, which are pretty straightforward, and don’t seem remotely question-begging. His own existence as a contingent concrete particular was all that seemed to be needed.

Why think that the new premise 4 is correct though? We already saw that nothing in Rasmussen’s argument ruled it out. The modesty of the premises, which is one of its great strengths, also means there is more room for premises like mine though. The mere possibility of uncaused contingent concrete particulars is all I need, and they seem compatible with his argument. To rule them out, he would have to tighten up the premises, which would be to surrender some of the distinctiveness of his approach, and would mean that his premises would be harder to justify. But that could be done in principle. He could also take Plantinga’s route, and fall back on his argument merely establishing the rationality of belief in a necessary being rather than establishing the truth of the claim. Something has to give though, it seems to me.

However, I have one further problems related to this, specifically relating to Christianity.

Christian theism seems particularly invested in the scenario I used to satisfy premise 4 not being merely possible, but being the actual world. On Christian theism, it isn’t just that a contingent concrete particular can be exemplified by something without cause; it is the central doctrine of the religion this happened. Jesus came to earth and took on a human form. As part of the trinity, Jesus is an uncaused necessary being; what happened when he took on human form was that he exemplified a contingent concrete particular. Thus, Christianity seems invariably committed to the truth of my new premise 4.

So, while it is true that someone could tighten up the argument to avoid my counterexample, it doesn’t seem possible for a Christian.

Richard Carrier not getting an ought from an is

0. Introduction

In the book The End of Christianity, Richard Carrier has a chapter called Moral Facts Naturally Exist, in which he claims to be able to “dispense” with the is-ought problem. I don’t think he does this. I’m not going to look at the whole piece here, because it is quite long, but I intend to come back to it later. I’m just going to look at a few remarks he makes about the ‘is-ought’ problem.

  1. The argument

Characteristically, he is quite ambitious:

It’s often declared a priori that “you can’t get an ‘ought’ from an ‘is’,” and that therefore science can’t possibly discover moral facts. This is sometimes called a “naturalistic fallacy.” But calling this a fallacy is itself a fallacy. Indeed, it’s not merely illogical, it’s demonstrably false. We get an “ought” from an “is” all the time.

Given this primer, I am expecting to see the demonstration of how to get an’ ought’ from an ‘is’. That is, I am expecting to see a valid argument, with true premises that are purely descriptive that has a conclusion which contains the word ‘ought’.

Yet, this is not what we get. Here is what we get:

For example, “If you want your car to run well, then you ought to change its oil with sufficient regularity.” This entails an imperative statement (“you ought to change your car’s oil with sufficient regularity”), which is factually true independent of human opinion or belief. That is, regardless of what I think or feel or believe, if I want my car to run well, I still have to change its oil with sufficient regularity

Now hold on a minute. Let’s break this down into the relevant bits. Firstly we have a conditional statement:

  1. If you want your car to run well, then you ought to change its oil with sufficient regularity.

We also have an expression of the consequent of this conditional:

2.  You ought to change your car’s oil with sufficient regularity

Yet, contrary to Carrier’s claim, 1 does not entail 2 (if you disagree, please tell me the inference rule used). To make it entail 2, we would have to add in a premise, 1a, about what you want:

1. If you want your car to run well, then you ought to change its oil with sufficient regularity
1a. You want your car to run well
2. Therefore, you ought to change its oil with sufficient regularity (1, 2, modus ponens)

Together, 1 and 1a jointly entail 2 (via MP), but on its own 1 does not entail 2.

Carrier says that 2 is “factually true independent of human opinion or belief”, but it doesn’t follow from 1 unless we have the premise, 1a, which explicitly references what people want. We can, of course, assert that 2 is true independently of human opinion or belief if we like, but we have not shown that it is derived from 1. Asserting that 2 is true surely cannot be held to be an example of deriving an ‘ought’ from an ‘is’; it would be just an assertion of an ‘ought’.

Indeed, Carrier changes scope in the very next sentence, from 2 being what is independent of human opinion of belief, to 1 being independent of human belief:

“That is, regardless of what I think or feel or believe, if I want my car to run well, I still have to change its oil with sufficient regularity”

Clearly, he is now saying that the conditional statement is what is true independently of what people feel or believe. In the previous sentence, he is making a different claim, namely that the consequent is what is independent of what people feel or believe.

But even if the conditional (i.e. 1) is true independently of what people feel or believe, this does not mean that the consequent of the conditional (i.e. 2) is true independently of what people feel or believe. You can’t derive ‘q’ merely from ‘if p, then q’. And you can’t derive ‘q is independent of what people feel or believe’ from ‘(if p then q) is independent of what people feel or believe’.

But perhaps his claim is just that we can derive 2 from 1 and 1a. If so, he is right. And I also think that 1 and 1a are both true. I’m not disputing the logical form of that argument, or either premise. So that argument is both valid and has true premises. Great!

So, what’s the problem? Well, premise 1 has an ‘ought’ in it. So this is not an example of an argument which has an ‘ought’ in the conclusion, but no ‘ought’ in the premises. We are not getting an ‘ought’ from an ‘is’. We are getting an ‘ought’ from an ‘ought’ and an ‘is’. That is not what was advertised.

2. Diagnosis

What is going on here is that we often express the relationship between A and B, where A is something we want and B is the ‘optimal’ way of getting A, by saying that we ‘ought’ to do B. For example, most will happily nod along to the following:

If you want to go to university, and if studying hard for your exams is the optimal way to ensure going to university, then you ought to study hard for your exams. 

But, if you stop to think about it, the relationship between the antecedent and the consequent is not one of logical entailment. That is, the following is logically invalid:

  1. You want to go to university, and studying hard for your exams is the optimal way to ensure going to university
  2. Therefore, you ought to study hard for your exams.

I admit that this argument sounds valid. It sounds valid, and it has a descriptive premise with a normative conclusion. Contrary to what I’m claiming, many people will think that this is a way to derive an ‘ought’ from an ‘is’.

Regardless of how it seems, strictly speaking it isn’t valid. In reality it is an enthymeme, or an argument in which one premise is implicit. For example, if I say “x is a horse, therefore x is an animal”, we will hear this as valid, but only because the premise “if x is a horse, then x is an animal” is implicit. In formal logic though, we need to state all our assumptions. In the ‘is/ought’ problem, this is also true.

What is implicit in our case is the following premise:

1a. If you want A, and B is the optimal way of realising A, then you ought to do B.

We might have this in our background knowledge, as an implicit assumption, but if we are talking about logical validity (as indeed we are here), then we need to make these explicit. Once we add this new premise in, we can substitute terms from 1 to 1a to get:

1b. If you want to go to university, and if studying hard for your exams is the optimal way to ensure going to university, then you ought to study hard for your exams.

Now, 2 follows from 1 and 1b via modus ponens. That is, the following is valid:

1. You want to go to university, and studying hard for your exams is the optimal way to ensure going to university
1a. If you want A, and B is the optimal way of realising A, then you ought to do B.
1b. Therefore, if you want to go to university, and if studying hard for your exams is the optimal way to ensure going to university, then you ought to study hard for your exams (1, 1a, substitution)
2. Therefore, you ought to study hard for your exams. (1b, 1, modus ponens)

This argument is now formally valid, and the premises are true. But again, we have needed to insert a premise, 1a, which is not purely descriptive – it contains an ‘ought’ in it. Once again, we are not deriving an ‘ought’ from an ‘is’, but are deriving an ‘ought’ from an ‘ought’ and an ‘is’. In addition, 1a does not seem to be something that is empirically discoverable. It looks like a kind of conceptual truth. It doesn’t look like something that science discovered though. Yet it is needed to get to the conclusion.

Carrier says that:

There are countless true imperative facts like this that science can discover and verify, and that science often has discovered and verified, from “If you want to save the life of a patient on whom you are performing surgery, you ought to sterilize your instruments” to “If you want to build an enduring bridge, you ought not to employ brittle concrete.”

I think that what science discovers is something purely descriptive, such as that sterilising your instruments is (part of) the optimal way of performing surgery on patients without them dying. What we discovered is that people much more frequently die if we perform surgery on them with unsterilised instruments. Presumably, we want to ensure that people don’t die when we perform surgery on them. That means we have the thing desired, and (let’s say) an empirically discovered fact about the optimal way to realise that desire. But as we saw above, unless we insert a premise which links what we desire, the optimal way of realising it, and what we ‘ought’ to do, we cannot derive anything about what we ought to do. And that generalised principle, even if it is true, isn’t something science discovered.

His examples only get the varnish of looking valid by smuggling in the premise which mentions ‘ought’. Thus, all of his examples seem to fall foul of the same problem, and none of them are examples of getting an ‘ought’ from an ‘is’.

3. A deeper problem

But, let’s say that we agree that there are basic hypothetical normative facts about the world of the form “if you want to do x, then you ought to do y”. As I mentioned in a previous post, some of these are clearly not moral. Perhaps it is true that if you want to torture someone, you ‘ought’ to kidnap them and tie them up in your basement. Perhaps that is the optimal way of realising your desire to torture someone. A central moral intuition is that, regardless of this empirically discoverable fact about how best to realise your desire, you ought not do that. Some things are wrong, and some things are good, regardless of what we desire. Some things, like torturing innocent people, are wrong even if you are a sadist with a desire to do it; and some things, like helping old ladies across the road (or whatever) are good even if you are selfish and don’t want to do it. Someone who believes that all morality is reducible to hypothetical norms has a very hard time explaining these sorts of situations, where bad things are in line with our desires and good things in conflict with our desires.

I suspect that Carrier wants to say that people with such sadistic (etc) views are irrational somehow, but this seems like an article of faith. Why can’t there be an internally coherent belief set in which someone desires to torture innocent people? Maybe he has a response to this, but I haven’t read enough of his work to know.

Even if there are true hypothetical norms, I think these cannot be the whole story about morality. What we need in addition to these are categorical norms. Carrier’s attempt to say everything we need to about morality purely in terms of hypothetical norms seems to me to be wide of the mark, because it cannot make room in principle for immoral desires, or for moral things that go against our desires.

4. Conclusion

I intend to come back to this essay of Carrier’s, because it has many other seemingly interesting things going on in it. To sum this up, I think he fails to show how to derive an ‘ought’ from an ‘is’, and even if we give him the hypothetical norms he wants, these can never be enough to capture all moral truths.

Molinism and the Grounding Objection, Part 2

0. Introduction

In part 1, I outlined an objection to Craig’s suggestion that Molinist counterfactuals are easily known, which I called the ‘epistemic objection’. Here I will respond to a different claim that Craig makes in his paper.

Craig argues that the truth-maker principle is dubious, and states various counter-examples to it. He also suggests that even if we grant the truth-maker principle, Molinist counterfactuals can be given certain types of truth-makers anyway.

I think this is wrong. ‘Counterfactuals of creaturely freedom’ are just an instance of a type of counterfactual, which in turn fits into a wider family of counterfactuals. The overall analysis of this family of concepts shows us a different reason for rejecting Molinist counterfactuals being true.

  1. Truth-making

The dialectic works as follows.  Molinism is the position that some ‘counterfactuals of creaturely freedom’ are true, and as such are known by God. The ‘grounding objection’ is that Molinist counterfactualshave no truth-makers, and that this means that they must be regarded as being either truth-valueless or uniformly false. If so, then there are no such truths for God to know.

Part of the response to the grounding objection is to point out that it presupposes the more general principle of truth-making, according to which all true propositions are made true by something. Typical candidates for truth-makers are such things as ‘facts’ or ‘obtaining states of affairs’, etc. While such a view might initially seem plausible, it is a matter of serious dispute amongst philosophers.

For instance, Craig offers several examples of sentences which are difficult to fit in to various naive sorts of truth-maker theory, such as the theory that all true propositions are made true by some obtaining states of affairs. Consider the following proposition:

“Dinosaurs are extinct today.”

What truth-maker makes this proposition true? The relevant state of affairs, of ‘dinosaurs existing’, is absent. So, one might argue, the proposition is not made true by a state of affairs obtaining, but rather it is made true by a state of affairs not obtaining. If so, then it is an exception to the truth-maker principle, which is that all true propositions are made true by states of affairs obtaining. The proposition would be true, but without a truth-maker. And as Craig goes on to say:

“If there can be true statements without any truth–makers of those statements, how do we know that counterfactual statements cannot be true without truth–makers?”

It seems that the onus is on the anti-Molinist to defend the thesis of ‘truth-maker maximalism’, that there are no exceptions at all to the truth-maker principle, if that is to include Molinist counterfactuals. For if there are exceptions to the truth-maker principle, such as the one above, then maybe Molinist counterfactuals are exceptions as well.

We can think of the argument like this, where M is ‘Molinism is true’, G is ‘the grounding objection is successful’, T is ‘the truth-maker theory is true’.

  1. If G, then ~M
  2. G
  3. Therefore, ~M     (1, 2, modus ponens)

However, Craig’s reply is:

  1. If G, then T
  2. ~T
  3. Therefore, ~G       (via 1, 2, modus tollens)

So, Craig’s argument is designed to block the second premise of the first premise. Craig’s argument here does not prove that Molinism is true, but if successful would remove one of the reasons people have for thinking that Molinism is false.

2. Truth-making on the cheap

But Craig plays a stronger hand than this. He suggests that there are plausible truth-makers for Molinist counterfactuals, although these are not the types that anti-Molinists typically demand.

Anti-Molinists typically want counterfactual truth-makers to be things that actually exist. Yet, if we think of the counterfactual involving Louis and the bike (see my previous post), it seems that the real, actually existing, version of Louis lacks any properties that entail whether he would have freely stolen it rather than not stolen it. Modally speaking, he was just free to do either. No investigation into any of Louis’ actual properties will ever reveal which one it would have been though. Therefore, the facts about the actual Louis underdetermine whether he would have freely chosen to steal the bike or not.

In response to this though, Craig proposes a different theory. According to this theory, Molinist counterfactuals do have truth-makers, but they are not categorical (or descriptive) properties of actually existing objects. Rather, they are a different type of property, namely modal properties. The distinction between modal properties and categorical properties is fairly easy to draw, and is done so quite nicely in the first two pages of this book by Joe Melia. Categorical properties include things like the size, shape, position, and velocity of every object that there is (insofar as modern physics allows for such properties, I guess). So, a categorical fact would be that Louis is 5’10”, and is currently in his living room watching his TV. Suppose we could specify as precisely as we liked, and include exactly which colour each pixel is on his screen, and exactly which cells in his brain are currently generating his experience, etc. The thought would be that we could extend this description of Louis out from his living room and include the properties of everything else that exists, starting with his house, the street he lives on, his city, the country, the planet, the galaxy and including the whole universe.

It would be tempting to think that such a description covered everything. Yet there is reason to think that an important class of truths would have been left out of such a description. Sure, Louis is currently sitting down. But, he could have been standing up. This is a modal fact, and describes not just how things are, but introduces how things could be; it is not just categorical, but modal.

If there are modal facts, in addition to categorical facts, then Craig could use them as the truth-makers for his counterfactuals.

In order to motivate this option, Craig favourably endorses a strategy employed in the philosophy of time, concerning tense.

There are theories of propositions according to which they have tense. We call such theories A-theories. Something very similar to the grounding objection could be pressed to A-theories, and Craig is impressed with one way that A-theorists can respond to the objection.

Take the view that there are tensed propositions, such as ‘There was snow yesterday’. A truth-maker theorist might want to say that this proposition is made true by some presently obtaining state of affairs, i.e. present-tensed fact (such as the presence of snow on the ground right now, etc). The problem is that there are various future- or past-tensed propositions for which no such presently obtaining truth-maker exists (i.e. for which no corresponding present-tensed fact exists). Take the tensed proposition ‘There was snow exactly 100 years ago today’. It is doubtful that anything about the current state of affairs determines whether there was snow exactly 100 years ago today or not. Either option is possible, for all the present facts about today determine. Thus, not all future- or past-tensed facts have presently obtaining truth-makers.

The idea here is that future-tensed propositions, like “It will be that p”, are made true by future-tensed facts. If we allow that there currently are facts of the form ‘p will be made true’, then these could be the truth-makers for future-tensed propositions. Craig quotes Freddoso:

“…there are now adequate metaphysical grounds for the truth of a future–tense proposition Fp just in case there will be at some future time adequate metaphysical grounds for the truth of its present–tense counterpart p”

Freddoso is pointing out that there may be no present-tensed obtaining states of affairs that could ground the future-tensed truth, but if we allow for future tensed states of affairs (or future-tensed facts), such as “there will be at some future time adequate metaphysical grounds for the truth of its present–tense counterpart p“, then we do have a presently obtaining state of affairs to play the role of truth-maker. The idea is that future-tensed truths require future-tensed truth makers. And it is this sort of idea that Craig is going to endorse when we come to the case of counterfactuals.

So, on Craig’s proposal, a counterfactual is not made true by any categorical states of affairs, but by modal states of affairs. This is explained by Flint, according to which:

“It would be the case (if c were true) that z” is now grounded iff “z is grounded” would be the case (if c were true).

We can ground the truth of “Louis would have stolen the bike had he been tempted” with the modal fact, that ‘Louis would have stolen the bike had he been tempted’. As Craig puts it himself:

“For my part, I should say that if true counterfactuals of creaturely freedom have truth–makers, then the most obvious and plausible candidates are the facts or states of affairs disclosed by the disquotation principle. Thus, what makes it true that “If I were rich, I would buy a Mercedes,” is the fact that if I were rich I would buy a Mercedes. Just as there are tensed facts about the past or future which now exist, even though the objects and events they are about do not, so there are counterfactuals which actually exist, even though the objects and events they are about do not.”

So, in summary, Craig is adopting a strategy commonly appealed to in the philosophy of time. A certain type of truth-maker (namely present-tensed facts, or purely categorical facts) is not suitable for grounding a certain type of proposition (namely future tensed propositions, or counterfactuals of creaturely freedom), and in each case a different type of truth-maker is proposed (future-tensed facts, or modal facts).

3. Objection

It has taken a while to explain Craig’s move, and it will take just as long to explain the objection. I suggest that the anti-Molinist need not posit truth-maker maximalism; nor need they posit that all truths have merely categorical truth-makers. Maybe there are truths that are not grounded in anything, such as ‘This sentence is true’. Maybe that is true but not grounded in anything. Who knows? Maybe there are tensed facts, such as that Matt Damon will be the first man on Mars. Who knows? I don’t need to rule either of those out.

Why not? Well, because I can phrase the objection in a more specific way. Consider a fair coin, with heads on one side and tails on the other, and also a rigged coin, with heads on both sides. It seems true to say of the fair coin that it could land heads, and that it could land tails. Also, it seems false to say of the fair coin that it would (necessarily) land heads, or that it would (necessarily) land tails. Things are obviously different for the rigged coin. It is true to say that it will necessarily land heads, and false to say that it even could land tails. As such, the two coins have a different set of modal properties. The modal facts about the coins is different. But ask yourself why that is. The obvious candidate answer is that they have different categorical properties. The fair coin has different things on each side, and the rigged coin has the same thing on each side. Clearly, the categorical facts explain the modal facts; and as such the categorical facts explain the modal facts. This all seems very straightforward.

But what this means is that there are various counterfactuals which, even if they are made true by modal facts, are ultimately explained by categorical facts. Here is one:

A) ‘Had I flipped the rigged coin, it necessarily-would have landed heads’.

A) is true, and let us suppose (for the sake of the argument) that what makes it true is the modal fact had I flipped the rigged coin, it necessarily-would have landed heads (to make it in line with what Craig proposes).

My conjecture, which seems pretty obvious, is that the modal fact that makes A) true is explained by (and hence grounded in) the categorical facts about the coin, and in particular about it having heads on both sides.

Consider the following pair:

B) ‘Had I flipped the fair coin, it might have landed heads’

C) ‘Had I flipped the fair coin, it might have landed tails’

Clearly, B) and C) are. Even if this is because they are made true by modal facts, it is still the case that these modal facts themselves are going to be explained (among other things) by the categorical fact that the fair coin has heads on one side and tails on the other.

I say “among other things” because no doubt there will be some modality involved in the description of the situation. The coins need to be flipped in the right circumstances, for example. If flipped in the vacuum of space, the will just spin off forever and not land at all, etc. So we would have to say something like “in normal circumstances”, and this would involve a specification of the laws of physics acting on the coins. Laws themselves have irreducibly modal aspects to them, one might think, and if so then our description is not purely categorical.

That might be true, but it doesn’t matter even if it is. All I need is that, at least in part, the modal facts are explained via reference to categorical properties (such as the actual properties of the coins). This is my conjecture, and I think it is correct.

What does it mean to deny it though? Well, remember that the coins have associated with them different counterfactuals. We can think of this as the ‘modal profile’ for the coins. The fair coin has both B) and C) in its profile, but the rigged coin only has B), for example. The question is what explains this difference in profile. My conjecture is essentially that part of the explanation involves reference to categorical facts, and cannot be purely modal. The cost of denying my conjecture is that the explanation of why the rigged coin has a different modal profile to the fair coin becomes inexplicable. The rigged coin just has different modal facts associated with it; end of explanation. Yet, we all clearly see that there is a deeper explanation which involves the categorical facts about the coin and what is on its faces. So the cost of denying my conjecture is that you end up making something clearly explicable into a mystery. This is clearly a theoretical cost, and needless.

Yet, a Molinist has to make such a move. This is because if we introduce Molinist counterfactuals into the picture, then we have to suppose that our fair coin has in its modal profile a counterfactual proposition of the following form:

D) ‘Had I flipped the fair coin, it just would have landed tails’

This proposition doesn’t express either that the coin had to land heads, nor that it merely could have done; rather it expresses the idea that God knows which way it would have contingently landed if you had flipped it.

When it comes to these counterfactuals, Craig supposes that we can have a purely modal truth-maker for it. The proposition ‘Had I flipped the fair coin, it just would have landed tails’ can be made true merely by the modal fact that had I flipped the fair coin, it just would have landed tails.

But now consider the two things side by side. On the one hand, we have strong ‘would’ and mere ‘might’ counterfactuals, and these seem to require reference to categorical facts, even if they have modal truth-makers. On the other hand, we have Molinist counterfactuals, which Craig supposes can have purely modal truth-makers. Given that they are clearly in the same family of expressions, it is puzzling as to why they have such different types of semantics. Why does one have to have categorical aspects to it’s grounding while the other does not?

We might try to align them to avoid this weird asymmetry. We could either try to introduce some categorical facts into the explanation of the Molinist truth-maker, or we could try to remove the categorical facts from the explanation of the other counterfactual’s truth maker. Well, as I argued above, if we remove reference to the categorical facts about the coin from the explanation of the truth-makers for the first type of counterfactuals, then we made an explanation into a mystery. As such the latter option is a non-starter. As such, to align the analysis of counterfactuals, we need to introduce something categorical into the explanation of the Molinist counterfactuals. But what could this be? There is clearly nothing categorical, nothing purely descriptive, about the fair coin which determines that it would land heads rather than tails on any given flip. This is really the heart of the grounding objection. Up to the point of being flipped, the world where the fair coin lands heads is utterly identical to the world where it lands tails. As such there cannot be any purely categorical fact that tells between heads and tails.

But this leaves us with a weird asymmetry. The analysis of would and might counterfactuals takes one form, but the analysis of Molinist counterfactuals has to take another. Why is the analysis symmetric? Is there anything that accounts for it? I think there isn’t. There is no principled reason why Molinist counterfactuals have such a different type of semantics from all the other types of counterfactual. But the fact that they appear on their own, untethered from the satisfying and explanatory semantics that their cousins enjoy, makes Molinist counterfactuals look suspect. They look like gerrymadered creations. It is not just that they have to have modal facts, but they also have to have a different type of analysis of their own.

Let me make the point sharply before stopping.

Here is the analysis of a might counterfactual:

Propositions B) and C) are both true of the fair coin. Why is that the case? Well, let’s say that they have modal truth-makers which make those propositions true, i.e. which give them their modal profile. What accounts for the difference in modal profile between the rigged and fair coin? Well, this is accounted for by a deeper description, at least partially involving categorical facts about the actually existing coins themselves.

Here is an analysis of a Molinist counterfactual:

Proposition D) is true of the fair coin (at some particular time). Why is that the case? Well, let’s say that it has a modal truth-maker which makes that proposition true. What explains why D) is true right now of this fair coin, but that two minutes later, if flipped again, it would have happened to have landed tails? Well, all Craig can say is that it has a different modal truth-maker two minutes late. But why is this the case? There is no reason; the analysis ends here. Nothing categorical can be wheeled in to explain it, and all we have is a sort of brute fact.

When put like this, the two analyses seem very different, and the onus is on the Molinist to either realign their analyses or to find some non ad hoc way of accounting for the difference. I think it is obvious that they cannot be realigned (as we went through the options above), and given the closeness of the propositions grammatically, any explanation of why their analysis is so different is bound to be ad hoc. Maybe God wants them to have different analyses, for example, is not going to cut it.

4. Conclusion

The conclusion is that counterfactuals, even if they have modal truth-makers at some level, are tethered to categorical facts about how things actually are. It is because Molinist counterfactuals cannot be tethered to reality in this way, and can only be supported by purely modal facts, that we can see that they are just a philosopher’s fantasy. This is the real grounding objection, in my opinion. I’m not proving that they are a philosopher’s fantasy, but I am bringing out how much strain they put on the analysis, and what a big semantic problem they have. Craig makes it seem like it is an effortless move to make, but by making the move he breaks from the clear and obvious way we analyse all other counterfacuals. The complaint is that the difference in analysis can only be justified by special pleading. Counterfactuals are analysed like this, says me. That’s true of the others, but not when it comes to these ones, says Craig. But why are they treated differently? That is the question I need to hear an answer to, and I don’t think there is one, apart from ‘because if they are then my theory works’, which is the definition of ad hoc.

Sam Harris not getting an ought from an is

Sam Harris recently made a series of Tweets which, he claimed, showed how to get an ‘ought’ from an ‘is’. Here they are:

  1. Let’s assume that there are no ought’s or should’s in this universe. There is only what *is*—the totality of actual (and possible) facts.
  2. Among the myriad things that exist are conscious minds, susceptible to a vast range of actual (and possible) experiences
  3. Unfortunately, many experiences suck. And they don’t just suck as a matter of cultural convention or personal bias—they really and truly suck. (If you doubt this, place your hand on a hot stove and report back.)
  4. Conscious minds are natural phenomena. Consequently, if we were to learn everything there is to know about physics, chemistry, biology, psychology, economics, etc., we would know everything there is to know about making our corner of the universe suck less.
  5. If we *should* to do anything in this life, we should avoid what really and truly sucks. (If you consider this question-begging, consult your stove, as above.)
  6. Of course, we can be confused or mistaken about experience. Something can suck for a while, only to reveal new experiences which don’t suck at all. On these occasions we say, “At first that sucked, but it was worth it!”
  7. We can also be selfish and shortsighted. Many solutions to our problems are zero-sum (my gain will be your loss). But *better* solutions aren’t. (By what measure of “better”? Fewer things suck.)
  8. So what is morality? What *ought* sentient beings like ourselves do? Understand how the world works (facts), so that we can avoid what sucks (values).

The whole thing boils down to premise 5. He says that we ought avoid things that ‘suck’. By ‘suck’ he basically means things that are painful (as his example of the stove indicates). So premise 5 basically just says: we ought to avoid pain. That is assuming an ought coming from an is: we ought not do things that cause pain (that ‘suck’).

The only thing he says to justify this is “If you consider this question-begging, consult your stove, as above”. But all ‘consulting the stove’ would do is remind us how painful the experience was. It wouldn’t, on its own, show us that we ‘ought’ not do it.

What Harris is relying on is the fact that we don’t want to have the experience of pain that touching the stove provides. The idea is that there is a hypothetical norm of the following form:

If you don’t want to feel pain, you ought not put your hand on the stove.

Harris is relying on the fact that we all don’t like feeling pain, and so the antecedent condition applies universally. But still, it is a hypothetical norm, not an unconditional (or ‘categorical’) norm.

What difference does that make?

Well, it isn’t really an example of getting an ought from an is; at least, not in any morally significant sense anyway. That’s because hypothetical norms are just the best ways of realising your desires. If you desire x, you *ought* to do y, when y is the optimal way of realising x. They can be morally significant things, like if you want to make the world a better place, you ought to give to charity, etc. But they can also be morally neutral: if you want to get your car fixed, you ought to take it to a mechanic; if you want to loose weight, you ought to take more exercise. They can also be immoral: if you want to murder your neighbour, you ought hit him over the head with this rock.

Morality, on the other hand, is usually thought of as being unconditional, or ‘categorical’. Take my last example. Sure, hitting your neighbour is an efficient way of murdering him. But we generally think that we simply ought not murder people at all. Even if I want to, I ought not do it. The ‘is-ought’ issue is about how to derive these sorts of ‘oughts’ from mere ‘is’s.

So the mismatch is that he is asserting a categorical normative statement (“we should avoid what really and truly sucks”), and he is offering only a hypothetical norm as it’s justification (which is that if you don’t want to experience things that suck, you ought not do things that will produce experiences that suck).

Hypothetical norms can’t justify categorical norms though, because the former require you to have a particular desire, whereas categorical norms are independent of what you desire; hypothetical norms only apply to you if you have a certain desire, but categorical norms apply to you regardless of whether you do.

Its a bit like saying ‘Everything is A’, but justifying that with the statement ‘Everything which is B is A’. Even if we agree with the latter, that cannot justify believing the former.