Stephan Molyneux and UPB

0. Introduction

Stephan Mulyneux is a YouTuber with a large following. He has been described as part of the ‘alt-right’, and defends a libertarian political view. He is also associated with the men’s rights movement. On his channel he has interviews on the main page with Paul Joseph Watson, Sargon of Akkad (or ‘Carl Benjamin’), Jordan Peterson and Katie Hopkins. I will leave you to draw your own conclusions about that.

In addition to riffing on things like politics, Molyneux also publishes books on ethics, such as this one: ‘Universally Preferable Behaviour: A Rational Proof of Secular Ethics‘.

There are lots of good analyses of this book, such as this one by philosopher Dan Shahar. I’m not going to provide anything like a long, detailed look at the book. What I am going to do is highlight one issue that jumped out at me as I casually read parts of it.

  1. Speech acts

Take the following quote, from page 25 of the book:

If I say, “I do not exist,” that is an example of an idea that is inconsistent with itself, since I must exist in order to utter the sentence.

There is something wrong with saying “I do not exist”. That is due to the fact that saying something is a type of action, something that you do. As such, it is the sort of thing that is located at a particular time and place, and is done by a particular person in a specific context. The conflict is between this set of background presuppositions (one of which is that the person doing the saying exists in a specific context) and the content of the sentence itself, which is a denial of the existence of the speaker of the sentence. That is the sense of contradiction here: the content of the sentence conflicts with one of the presuppositions of the sentence. Other examples might be things like

a) ‘You are not awake’, or

b) ‘You are not reading this’, etc.

These sentences also conflict with aspects of the context that we often do not state explicitly, i.e. presuppositions.

However, there is another way to think about these where the conflict seems not so pressing. Consider b). A few minutes prior to reading b) it was true that you were not reading the sentence. So there is nothing inherently contradictory about the idea of you not reading that sentence. The conflict only appears when you actually are reading it; there is only a conflict with the presupposition of action, not with the idea expressed by the sentence itself. And when I am not performing the action of reading the sentence, there is no conflict with the content of the sentence.

This is in contrast with sentences like ‘This is both an apple and not an apple’. In this case, the sentence is internally contradictory; it expresses both p and not-p explicitly. It doesn’t matter if you say it out loud, or if we merely consider the idea expressed by the sentence. The conflict is not between the content of the sentence and some aspect of the context of the saying of the sentence. And this makes it different to the other examples.

This brings us to Molyneux’s example. It is true that I must exist in order to utter the sentence “I do not exist” (indeed to utter any sentence). But, just as with b), there is nothing inherently inconsistent with the idea of me not existing. At some point I did not exist, and at some point I will not exist. Unfortunately for me, the idea of me not existing is not internally inconsistent. The only inconsistency is between the idea of me not existing on the one hand, and the concrete situation of me saying the sentence to you at a particular place and time on the other. Another way of saying the same thing: if uttered, then the content of the sentence is in conflict with an aspect of the context of use (i.e. my existence); but the content of the sentence itself, considered independently from any context, is not inconsistent (i.e. my non-existence is not itself an inconsistent idea).

Things are a little more complicated than that even. Not all contexts are created equal. Most of the time, if I say that I do not exist, then I run into trouble (because such a saying is an action that I do at some particular place and time). But I could leave such a statement in a will, or, like a suicide bomber, record a message only to be heard after my death (“If you are watching this, then I do not exist”, etc). The idea expressed in such a situation by that sentence is perfectly intelligible. As such, Molyneux’s sentence is only in conflict with aspects of what we might call ‘standard’ contexts of use. ‘Non-standard’ contexts like the reading of wills, or the playing back of messages intended to be heard after the speaker’s death, complicate the analysis. That they are intelligible though shows that they are not inconsistent.

The fact that Molyneux says that this is “an example of an idea that is inconsistent with itself”, rather than ‘an example of a speech act that is inconsistent with some aspect of its (normal) context of use’, shows that he is not sensitive to the idea of the presuppositions involved when making speech acts. (For some further reading around speech acts and the notion of linguistic presupposition, try these links: here and here.) 

2. Premise 6

This is interesting, because it sheds some light into Molyneux’s premise 4 and 6 of his argument. He wants to argue that these premises are true because their negation would involve some kind of inconsistency with something that they presuppose, such as the example of “I do not exist” above. Thus, without using the term (or being aware of it) he is offering a sort of ‘transcendental’ argument for some of his premises.

Premise 6 is clearer than premise 4, so I will quote that here:

Premise 6: Truth is better than falsehood

If I tell you that the world is flat, and you reply that the world is not flat, but round, then you are implicitly accepting the axiom that truth and falsehood both exist objectively, and that truth is better than falsehood.

If I tell you that I like chocolate ice cream, and you tell me that you like vanilla, it is impossible to “prove” that vanilla is objectively better than chocolate. The moment that you correct me with reference to objective facts, you are accepting that objective facts exist, and that objective truth is universally preferable to subjective error. (p. 35, emphasis mine)

Molyneux is saying that if we have a disagreement about something, then I am “implicitly accepting … that truth is better than falsehood”, and that “truth is universally preferable to subjective error”.

I think that Molyneux is saying that if you argue that p is true, you are showing a preference for truth over falsity. And whatever that means to ‘prefer truth over falsity’, you have to believe that p is true for your arguing that p is true to imply that you prefer truth over falsity. Yet, it can in fact be very reasonably questioned whether arguing that p is true implies that you even believe that p is true, let alone prefer truth over falsity.

Consider the phrase ‘for the sake of the argument’, or the synonymous Latin phrase ‘arguendo’. The function of these phrases is to indicate that something is being postulated provisionally, for the purposes of exploring the implications that come with it. Its function is to indicate explicitly that there is no presupposition that what is being argued for is true. Yet it is being argued for nonetheless.

Consider debate competitions, where the debaters are given topics that they have to come up with a good line of argument for. In such an activity, the purpose of the argument is to perfect the skill of arguing, not for pursuing the truth. It is rather like exercising in a gym, rather than playing a sport. One can become good at running without running any races. Similarly, one can meaningfully engage in debate without thereby presupposing that one believes in what one argues for (or presupposing that one ‘values truth’).

As a additional few examples, consider:

  • A lawyer who argues on behalf of her client because she gets paid to do so
  • A politician who argues what he believes his constituents want to hear
  • An internet troll who argues what she believes will irritate her audience the most
  • An undergraduate who argues what he believes will impress the girl he fancies

What these examples show is that the action of engaging in argument does not need to imply that the arguer believes the propositions for which they argue in favour. They could hold a mercenary-like attitude towards truth-telling, only ever saying what they believe will increase their power with those around them. Who is to say that this isn’t in fact the most common form of arguing?

All of these are examples where the person arguing need not also hold the attitude of ‘valuing truth over falsity’.

3. Conclusion

Unlike other cases of linguistic presupposition, Molyneux’s example isn’t a clear case where it has the presupposition he needs it to have for the transcendental argument to be plausible. Consider a plausible case from the Standford page on presupposition:

  1. The dude released this video before he went on a killing spree
  2. Therefore, the dude went on a killing spree

In contrast, Molyneux’s argument is something like this:

  1. You say (as part of an argument) that the world is not flat, but round
  2. Therefore, you believe that the world is not flat, but round

Or possibly:

  1. You make an argument
  2. Therefore, you value truth over falsity.

Yet, all of the examples of contexts given above show that this does not follow. Thus, the implicit transcendental argument contained in Molyneux’s argument here is invalid. Making an argument does not automatically validate the ‘universally preferable behaviour’ of valuing truth over falsity.



Successive addition

0. Introduction

One of the two philosophical arguments which is supposed to show that the history of the universe must be finite is the impossibility of forming an actual infinite by successive addition. I think this argument begs the question, because there is one premise which can only be true if we assume that the conclusion is true.

  1. The argument

The argument, which can be seen here, looks like this:

1. A collection formed by successive addition cannot be actually infinite.
2. The temporal series of past events is a collection formed by successive addition.
3. Therefore, the temporal series of past events cannot be actually infinite.

I am going to grant premise 2 for the sake of the argument, although I think it could be questioned. All that I want to focus on is premise 1. This premise, it seems to me, can only be regarded as true if we assume that the conclusion is true.

First, what is ‘successive addition’? It means nothing more than continually adding one over and over again, 1 + 1 + 1 …, which is itself akin to counting whole numbers one at a time, 1, 2, 3 … . The idea is that such a process can never lead to anything but a finite result, as Craig explains:

“…since any finite quantity plus another finite quantity is always a finite quantity, we shall never arrive at infinity even if we keep on adding forever. Infinity in this case serves merely as a limit which we never attain.”

2. The counterexample 

There is obviously a close connection between numbers and our concept of time. Exactly what that relationship is, doesn’t matter too much here. One thing that seems obvious though is that we routinely associate sequences of whole numbers with durations of time. Consider the convention which says that this year is 2019. What this means is that if there had been someone slowly counting off integers one per year since year 0, by now he would have counted up to the number 2019.

Adapting this familiar idea, we can postulate that there is some metronomic person counting off whole integers one every minute. After three minutes he will have counted up to the number 3, after one hundred minutes he will have counted up to the number 100, etc.

Let’s make this very simple and intuitive idea slightly more formal. Let us think of a counting function for this person. It takes an input, x, and returns an output, y. The value of x will be some amount of time that has passed (three minutes, one hundred minutes, etc), and the value of y will be whatever number has been counted to (3, 100, etc).

This counting function is therefore akin to asking the question:

‘After x units of time have passed, which number have they counted to?’

The value of y will be the answer to the question.

When Craig says “any finite quantity plus another finite quantity is always a finite quantity”, we can cash this out in our function as saying something like:

If the value of x is finite, then the value of y is finite. 

No matter how much time has passed, so long as it is a finite amount of time, then the number that has been counted to must be merely some finite number.

However, what happens if the value of x is not finite (i.e. if it is transfinite)? Let’s suppose that the amount of time that has passed is greater than any finite amount, i.e. that an infinite amount of time has passed. Will the value of y still remain finite? Clearly, the answer here is no. After all the finite ordinal numbers comes the first transfinite ordinal number, ω. If the amount of time that has passed is greater than any finite amount, but less than any other transfinite amount, then the number that will have been counted to will be ω. That is, the function we have been using so far returns this value if we set the value of x to the right amount. But what this seems to say is that if you had been counting for an infinite amount of time, then the number you would have counted to would be greater than any finite number.

At no point have we specified that we are not using successive addition, i.e. counting. WE have explicitly said that this is what we are doing. All we have varied is how long we have been doing it for. The lesson seems to be that if you only count for a finite amount of time, then you cannot construct an actual infinite by successive addition, but if you do it for an actually infinite amount of time, then you can.

Thus, in order for premise 1 to be considered correct, we have to restrict the amount of time we spend counting to arbitrarily high finite amounts of time. If we place that restriction on, then the premise looks true. But if we take this restriction off, then the premise is false, as we just saw.

This means that whether the premise is true or false depends on whether we think that the value of x can be more than any finite number or not. And that just means whether the extent of past time can be infinite or not. If it can be, then we have enough time to have counted beyond any finite number. Yet, that is the very question we are supposed to be settling here. The conclusion of the argument is that the past is finite. Yet we need to suppose precisely this proposition in order to make the first premise true. Without it, the first premise is false.

Thus, the argument seems to simply beg the question here.

More on the FreeThinking Argument

0. Introduction

In the last post, I explained the ‘FreeThinking Argument Against Naturalism’ (FAAN). I criticised premise 3, which was that “If libertarian free will does not exist, rationality and knowledge do not exist”. In this post, I will look at a reply Stratton gave to an objection that is somewhat similar to mine, in a post he wrote called Robots and Rationality. In the end, nothing he says helps at all.

  1. Robots

Stratton says that some people object to premise 3 of his argument by saying that “computers seem to be rational and they do not possess libertarian free will”. Nevertheless, he thinks that he has a reply to this such that the “deductive conclusions of the Freethinking Argument remain unscathed”.

Right off the bat, Stratton begs the question against the view I outlined in the last post. Consider the very next line, in which he says:

“…simply by stating that computers are, or robots of the future could be, rational in a deterministic universe *assumes* that the determinist making this claim has, at least briefly, transcended their deterministic environment and freely inferred the best explanation (the one we ought to reach) via the process of rationality to correctly conclude that computers are, in fact, rational agents.”

But that’s wrong. The act of stating “computers seem to be rational and they do not possess libertarian free will” can be done in a deterministic universe, no problem. It doesn’t require ‘transcending the environment’. You could even make that statement in a deterministic, naturalistic universe, and have a justified true belief about it while you are doing it.

Here’s how. Assume internalism about justification, so that justifications are beliefs. That means that for me to have a justified true belief that p, the true belief needs to be supported by other beliefs, say q and r, which are the justifications for believing that p. There are two things we can also say about how the justifications need to be related to p. This is not the only way you could cash this out, but it will do for our purposes:

  • They have to be related to p in the ‘right sort of way’ (arbitrary beliefs cannot be justifications), and
  • It needs to be that my believing q and r is why I believe p (it’s no good for me to believe q and r, but believe p because the coin landed heads, etc).

What does it mean for q and r to be related to p in the ‘right sort of way’? This is obviously a very complicated question to answer. We don’t have to settle it here though. Let’s just consider clear cases. The relationship between them just needs to be such that q and r provide significant support for p; they raise the probability, at least the subjective assessment of the probability, of p by the person with the beliefs. A very clear case of this would be if q and r logically entailed p. Other examples would be if q and r were raised the probability of p far above 0.5, to something like 0.9. We don’t need to worry here about exactly where the line is though, because we will consider just a clear example, one where we have logical entailment, because that is clearly a justification. And we only need one example to show that the principle that Stratton appeals to is false, after all. So here it is.

Assume I have two beliefs:

A) My laptop seems to be rational

B) My laptop does not have LFW

I could have those beliefs in a deterministic, naturalistic universe, no problem. These beliefs would be brain states that I have (on assumption). Let’s say that they deterministically cause me to have another brain state, which is:

C) (at least some) computers seem to be rational and they do not possess LFW

Because this belief is caused by the first two, it’s true that I only believe it because I believe the first two. Yet those two paradigmatically justify the third. They logically entail the third. Anyone who believes that their laptop seems to be rational and that it does not have LFW, is thereby justified in believing that (at least some) computers are rational and do not possess LFW.

So on this proposal, I believe C, it is true, and I possess beliefs, A and B, which significantly raise the probability of C (by logically entailing it), and the having of A and B is why I believe C. Thus, it meets the criteria I gave above for counting as a justification for the true belief that I have.

Now, obviously, Stratton would object here. He thinks that the criteria for justifications of p should be that they are beliefs, that are related to p in the right sort of way, you believe p because you have the justifications, and also that believing p was a freely chosen action. But what is the reason that we should accept this additional criteria?

2. Coercion

Assume that some agent A punches some other agent B in the face. Suppose also that A has a desire to hurt B. A natural answer to the question for why A punched B (i.e. what the reason was for A’s action) is that he desired to hurt B. The action could be regarded as free, and the reason is part of why he did the free action.

However, imagine that we learned subsequently that A was a Manchurian candidate, and had been brainwashed, or hypnotised, such that given a certain trigger (maybe by seeing a woman in a polka-dot dress), then he would instinctively take a swing at B. Now, we might think, his antecedent desire to hurt B cannot really be the reason why he punched B. Given that he was compelled to do it (we might say caused to do it), by seeing the woman in the dress, that really isn’t the reason at all. Because he was coerced to do it by the brainwashing, he was not doing it because of the reason he had (his antecedent desire to hurt B). This seems plausible. And if it is right, then being coerced (or being caused) is incompatible with doing something because of having a motivation (like a desire). This could be questioned, but let’s grant it, for the sake of the argument.

Stratton does not give this sort of argument, but you could imagine that it is the sort of thing he has in mind to support his claim that a belief cannot be justified unless it is freely chosen. There does seem to be an analogy here. If the reason for an action cannot be a desire unless it is free of coercion, then maybe the justification for a belief cannot be another belief unless it is free of causation. Maybe each has to be free for it to count.

Even though there is some plausibility to the analogy to begin with, I think it is easy to start to see that the two cases are really quite different. Even if we grant that coercion completely rules out freely acting due to motivations (desires), the case where I come to believe something without willing to believe it is far less clearly problematic.

Consider a case where someone really wants to believe, say, that their son is innocent of a murder. They may, nevertheless, come to believe that the son is guilty during the trial, where all the evidence is presented. We could describe this situation as her being compelled to believe that her son was guilty despite her firm will to not believe this. Of course, this is not a mandatory reading, and no doubt other ways of describing this situation could be given as well. The point is just that this description seems far less problematic than assuming that A was both a brainwashed Manchurian candidate, and also acted with a desire as his reason. Being compelled to believe p, because the evidence caused you to do so, doesn’t seem incompatible with believing p with justification in the same way. Thus, the analogy is clearly questionable.

Stratton did not offer the coercion analogy as an argument against my position. I offered it on his behalf, because I don’t think he has an argument. But to me the analogy is not plausible, because even if you grant the action case, the belief case doesn’t seem problematic in the same way. What’s true about reasons for actions is not necessarily the same as what’s true about justifications for beliefs. And because of that we would need to see an argument to the effect that the claim about beliefs is true, and not just an appeal to the action case.

3. Luck

Stratton makes the following comments a few lines later on, where he appeals to the notion of luck:

“…if determinists happen to luckily be right about determinism, then they did not come to this conclusion based on rational deliberation by weighing competing views and then freely choosing to adopt the best explanation from the rules of reason via properly functioning cognitive faculties. No, given determinism, they were forced by chemistry and physics to hold their conclusion whether it is true or not.” 

So the idea here is that I could believe that determinism is true, and be correct about that (I could be “right about determinism”), but that this is just a matter of luck. He is saying that, in general, on determinism, one could believe p simply because the causal history of the world happened to be such that I hold that belief. If so, then my holding the belief is unrelated to whether p is true, or what the justifications are for holding that p is true; it’s all a matter of what the causal history of the world is like and nothing more.

Three things.

Firstly, luck implies contingency. If an event is lucky, it has to be possible for it to have happened differently, or not at all. For it to be lucky that I won the lottery, it has to be actually possible that I could have lost. If I rigged the lottery so that it had to show my ticket number, then my winning is no longer a matter of luck. But on determinism, all events are necessary, because they couldn’t have happened differently. So while things might look as if they were lucky (in the sense that the rigged lottery result might look lucky), they weren’t really. And if so, then no belief that I hold is lucky.

In order to have lucky events on determinism, then we need contingency. The only way to get that is if the initial conditions of the universe are themselves contingent. But if the initial conditions themselves could have been different, then, since all subsequent events depend on that contingent event, it makes all events contingent, because for each event it could have gone differently. That is, the initial conditions could have been different, leading to the event being different. And if that is all that is required for an event to be considered as ‘lucky’, then all events are lucky, even on determinism. And that means that even if I was caused to believe that p, and p was true, and I was caused to believe it on the basis of justifications, this would still be lucky. The question then is if luck is cashed out like this, just how this undermines the claim that p is a justified true belief. It seems that it doesn’t.

Secondly, putting it in terms of the belief being ‘unrelated to the truth of p’ seems to beg the question against the view I have been defending here. It could be the case that the causal history of the world also includes me having the right types of beliefs, the sorts of beliefs that count as justifiers for p (such as ones which logically entail, or raise the probability a great deal that p is true), and these would be directly related to why I believe that p is true (they are part of the cause of me believing that p is true). If that is right, then it isn’t the case that my holding the belief is unrelated to whether p is true, even if it is lucky (in the sense described above).

Thirdly, Stratton says:

“…given determinism, they were forced by chemistry and physics to hold their conclusion whether it is true or not”

It seems to me that all this is saying is that on the determinist picture, it is possible to believe something false. But I could construct a parody of this, and say:

‘Given LFW, they freely choose to believe their conclusion, whether it is true or not’

After all, you could freely choose to believe something false. That shows that it is also possible on Stratton’ view to believe something false. And that means that regardless of whether the view is determined or freely chosen, it is possible for the belief to be false. So whether you are caused to believe p, whether it is true or false, or freely choose to believe p, whether it is true or false, we are in the same position.

Again, this shows how irrelevant it is to bring up the freeness of the belief. What is important is the justification for the belief. If the justifications are there, then the belief can be JTB, regardless of whether it is determined or freely chosen.

4. Liars

Stratton makes anther appeal:

“If you have reason to suspect a certain man is a liar, why should you believe this individual when he tells you that he is not a liar? Similarly, if we have reason to suspect we cannot freely think to infer the best explanation, why assume these specific thoughts (which are suspected of being unreliable) are reliable regarding computers?”

Thinking that someone is a liar is reason to not trust what they say to you. Fair enough. The problem now is that trusting someone who is a liar, which means someone with a track record of often lying, is not relevantly analogous to thinking that the inferences made by someone is determined are not reliable. It would be, of course, if you considered someone who was determined and who had a track record of making incorrect inferences. But then, the track record is doing all the work, and the determinism is doing none of the work. I wouldn’t trust someone with LFW who had the same track record of lying either.

The problem here is that even if you “have reason to suspect we cannot freely think to infer the best explanation”, that isn’t itself reason to conclude that they are “suspected of being unreliable”. That is, even if you have reason to think that we cannot freely infer the best explanation, that doesn’t on its own mean we cannot infer the best explanation.

What matters is if the process of belief formation takes into account the justifications for holding the belief. Whether it is a determined process or one that involves a free choice is irrelevant.

For example, think of a robot which is equipped with a mechanism that analyses a target at a firing range and processes the information it receives in such a way that it reliably hits a bullseye nine times out of ten. Even though its mechanism is deterministic, that doesn’t mean it is unreliable.

Compare the robot with a free individual, with LFW, who also hits the target nine times out of ten. The reliability of their shooting is something you evaluate by looking at their record of success, and by examining the process by which they came to hit the target. If everything else is equal (they hit the same number of targets, and the internal mechanism of the robot is relevantly similar to the way the person’s eye and brain allow them to determine where to aim the gun), then the freedom itself doesn’t play any role in our assessment of which one is more reliable.

Yet, Stratton makes the assumption that the lack of freedom is a reason to doubt reliability. He says that “if we have reason to suspect we cannot freely think to infer the best explanation” then we have reason to suspect that they cannot infer the best explanation. This seems to me to be false. A sufficiently advanced robot could reliably draw the right inferences yet not have LFW.

5. Self-refutation

Stratton says:

“…the naturalist who states that he freely thinks determinism is true is similar to one arguing that language does not exist, by using English to express that thought.”

But here, surely, the problem is that anyone who states that he (LFW-) freely thinks determinism is true is uttering a contradiction. They are saying both that they believe they are free (in the LFW sense) and the determinism is true, and surely they cannot both be true. Making such a statement would be contradictory.

But, as should be clear by now, the determinist need not make such a statement. Rather than saying that they freely think that determinism is true, they should say that their belief that determinism is true is also determined. When said like that, there is no hint of self-refutation here.

He goes on:

“Until naturalists demonstrate exactly how a determined conclusion, which cannot be otherwise and is caused by nothing but physics and chemistry, can be rationally inferred and affirmed, then the rest of their argument has no teeth in its bite as it is incoherent and built upon unproven assumptions.”

I hope that by now the general idea of how this would work is clear. What has to be made explicit is that beliefs can be caused, but so long as they are caused by other beliefs (brain states, if you like), then they can still stand in the same relation to justifiers as they do on any other JTB view. So the question of ‘Why do you believe that (at least some) computers seem to be rational and they do not possess LFW?’ is answered by saying ‘Because I believe that my computer is rational and it does not have LFW’. That answer is true, even though there is also a story we could tell about how some bit of brain chemistry lead to some other bit. If those bits of brain chemistry are beliefs, then both ways of talking are true.

This is a familiar line. Why did the allies win world war two? Because Hitler overreached by invading Russia. That’s true. But, of course, there is a much more detailed story involving the precise movements of every regiment across the whole of the world. There is another story that involves the movement of all the atoms across the whole world too. All three of these are true. The fact that the much more detailed story about atoms is true doesn’t mean the others are not. It doesn’t mean the others are reducible to the story about atoms either (maybe they are, but maybe they aren’t).

The same sort of thing is going on here. There is a story about what happens at a chemical level in my brain, and another one about what beliefs I believe on the basis of other beliefs. If naturalism is true, beliefs are something like brain states. If determinism is true, then they can cause other brain states to exist. So long as this causal chemical set of reactions is correlated reliably with inferring the best explanations, then it is as good as the LFW account.

But are they correlated in that way? Well, not by default. The actions we engage in train them up. Learning to speak, going to school, reading philosophy, etc. These sorts of things  make us better at inferring the right things from our beliefs. But that can be told as a chemical causal story too. When I study I am causing my brain to make more reliable connections more often. The pathways in my brain become intrenched in certain ways, leading to me more often getting it right. Not always, but often enough to count as being rational (rationality comes in degrees, after all). Nothing about this requires LFW. All of those actions can be deterministically caused.

6. Conclusion

Stratton ends with this:

“If all is ultimately determined by nature, then all thoughts — including what humans think about the rationality of computers — cannot be otherwise. We are simply left assuming that our thoughts (which we are not responsible for) regarding computers are good, the best, or true. We do not have a genuine ability to think otherwise or really consider competing hypotheses at all.”

Firstly, note that now he is insisting that on determinism, our thoughts cannot be otherwise. If that’s right, then they should not be regarded as being lucky, or unlucky.

But regardless of that, he says that in that situation, we “are simply left assuming that our thoughts … regarding computers are good, the best, or true.” But as I showed here, we are not left in that situation. I could come to that conclusion because I also have other beliefs, which are relevant to that conclusion. He is saying that if we are determined, then we are left with nothing but assumptions. He is saying that if we are determined, then we cannot think about competing hypotheses and weigh options against each other. This is clearly incorrect. All we cannot do if we are determined is freely do those things. What we can do, if we are determined, is do those things.

Thus, the third premise of his argument fails. Nothing he says in his Robots and Rationality article helps, at all.

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.