Van Til on the Problem of Induction

The third argument from Van Til that we will examine is the argument from induction. Van Til argues (rightly) that we must be able to use induction in order to be able to reason about the world. That is, we have to be able to reason from our past experiences as individuals and as a society and infer the future. But to reason this way, we must assume that reality has a kind of uniformity or intelligibility. And according to Van Til, the only way we can know this is through theism.

 

Does Christianity offer a solution to induction?

The first step in evaluating Van TIl’s argument is discussing whether Christianity can actually justify induction as we use it. I am not currently aware of any serious arguments that induction is impossible under Christianity, and I think it’s reasonably clear that under Christianity we can perform induction. How do we know that reality is regular or predictable in the right kind of way? Because the God of order and knowledge created not only a world that is ordered and knowable, but also our minds. And since He created our minds intending that they would know the world, we can know the world through induction.

It’s true that some argue that under sceptical theism, we cannot do induction. We may discuss this more when we discuss solutions to the evidential problem of evil, but it doesn’t apply to theism in general.

 

Secular justifications of induction

In order for Van Til’s argument to succeed, it must not only be the case that theism allows for induction, but that there is no coherent secular response to the problem as well. Many attempts have been made at secular answers to this problem, we will have a brief look at some of them here.

 

Popper: Falsification, Not Induction

Karl Popper has famously argued that inductive reasoning ought not to be performed in the manner that is normally considered here. Instead of looking for observations to confirm or verify our hypothesis, we should instead look for observations that falsify the hypothesis. And if we don’t find any, we don’t consider the hypothesis true, we just consider it to be not yet falsified.

This approach is perhaps the dominant approach in philosophy of science and indeed in the practice of science. However, I think it is somewhat difficult to swallow. We end up not really believing that things are “true”, instead we believe they are “not yet proven false”. But that’s simply not how we reason about the world, we do think it is true that our various inductive hypotheses are correct. We do think it is true that the sun will rise tomorrow because we have observed it doing so in the past. So while here we do have a coherent way of reasoning, it doesn’t save our normal, everyday reasoning using induction. Therefore this is not a good enough response to the problem of induction

 

Law of Large Numbers

This is another, less popular (though I think stronger) response to the problem of induction. Helpfully explained by this Reddit comment (the whole /r/askphilosophy subreddit is pretty great by the way), we can justify induction essentially a priori using some mathematics. However, it is not without its issues as well. I will quote the SEP:

The more problematic step in the argument is the final step, which takes us from the claim that samples match their populations with high probability to the claim that having seen a particular sample frequency, the population from which the sample is drawn has frequency close to the sample frequency with high probability. The problem here is a subtle shift in what is meant by “high probability”, which has formed the basis of a common misreading of Bernouilli’s theorem. Hacking (1975: 156–59) puts the point in the following terms. Bernouilli’s theorem licenses the claim that much more often than not, a small interval around the sample frequency will include the true population frequency. In other words, it is highly probable in the sense of “usually right” to say that the sample matches its population. But this does not imply that the proposition that a small interval around the sample will contain the true population frequency is highly probable in the sense of “credible on each occasion of use”. This would mean that for any given sample, it is highly credible that the sample matches its population. It is quite compatible with the claim that it is “usually right” that the sample matches its population to say that there are some samples which do not match their populations at all. Thus one cannot conclude from Bernouilli’s theorem that for any given sample frequency, we should assign high probability to the proposition that a small interval around the sample frequency will contain the true population frequency. But this is exactly the slide that Williams makes in the final step of his argument. Maher (1996) argues in a similar fashion that the last step of the Williams-Stove argument is fallacious. In fact, if one wants to draw conclusions about the probability of the population frequency given the sample frequency, the proper way to do so is by using the Bayesian method described in the previous section. But, as we there saw, this requires the assignment of prior probabilities, and this explains why many people have thought that the combinatorial solution somehow illicitly presupposed an assumption like the principle of indifference. The Williams-Stove argument does not in fact give us an alternative way of inverting the probabilities which somehow bypasses all the issues that Bayesians have faced.

In simpler terms, it has been objected that this response to the problem of induction incorrectly assumes that the sample distribution matches the population distribution. That is, it incorrectly assumes that what we have observed is representative of some sort of universal law. Which is in fact precisely the thing that we are trying to prove. Presumably, the proponents of this solution would argue that in general, we assume that a sample is drawn randomly unless we have any reason to suspect otherwise unless we can demonstrate a bias. But that’s not necessarily true, often sampling measures come under scrutiny and must demonstrate their random methodology.

I think this solution is stronger than the previous one, however.

Perhaps in the future, we will consider more solutions to the problem of induction, but here I have presented the most common one and one that I think is quite interesting.

Saturday Links 15/12/2018

Honeymoon Reading

I have just returned from my honeymoon, and so of course the first question anyone has for me is: what did you read while you were away?

So here is a list:

 

I am sure my wife had a great time.

Charles Taylor’s A Secular Age

Many of you will have noticed that I reference the book A Secular Age by Charles Taylor quite regularly. Outside of scripture, no other book has been more influential in shaping my thinking about the Western world. Where we are, how we got here, what it means, and where we’re going.

If for some reason you don’t feel like spending 4 months digging through this 900 page tome, then there is an alternative that I haven’t read myself, but some of my friends recommend. From James Smith, the author of You Are What you Love, it is a summary of Taylor, containing many of his most important ideas, and it seems to attempt to make them explicitly and directly relevant to the Christian apologist. I also believe that Smith is Reformed, which always wins points in my book.

If those are too hard (and I strongly encourage you to take one of those two options, even as audiobooks or something) then I have found a reasonably good series of YouTube videos, they seem to be recordings of a philosophy class at a university discussing the book. They are not an alternative, but they may be helpful.

Common Objections to the LCA

In our previous three posts here, here, and here, we have gone through a brief summary of Leibniz’ Cosmological Argument. And of course, many objections are likely to arise, mostly from misunderstandings of the argument. Here I would like to briefly respond to some of those common objections.

What if the universe had no beginning?

You’ve got this argument confused with another argument. My argument says nothing about the universe as a whole, and only needs one contingent object to succeed. My argument also says nothing about anything “beginning”. This argument would work just fine if the universe had no beginning.

What explains God?

The way we have used the word “God” is by meaning “The non-contingent object”. But given our definition for contingent, this means “The object that does explain itself”. So if you ask “What explains God?”, you are asking “What explains the thing that explains itself?”. The answer is obvious: God does.

How do you know there are contingent things?

Consider a simple fact: things fall down. The first scientists asked: why do things fall down? They needed an explanation. The fact that things fell down wasn’t self-explanatory. And they found an answer, coming up with a theory of gravity. But then again: why do things have mass? The fact that things have mass requires and demands an explanation. It is contingent. And we built the Large Hadron Collider looking for that explanation.

You’re just defining God into existence!

What I am doing is inferring the existence of something by looking at the effects it has. For example, I might look at a clock and infer the existence of a motor behind the arms, because it is making those arms move. Am I defining the motor into existence by doing this? No I am not.

This only proves a deist God, not the Christian God!
True, this is not a sufficient argument for Christianity. It gets us to theism, but we need further arguments to get to Christianity. But it’s a step in the right direction, ruling out atheism.

This is a God of the gaps argument!

What I am doing is inferring the existence of something by looking at the effects it has. A God of the gaps argument goes something like “We can’t explain this thing, therefore God did it”. I am not doing that at all. Instead, what I’m doing is arguing that God is the only possible explanation for something. Suppose I have a car that works. Am I right in inferring the existence of a motor inside the car? Is that a motor of the gaps argument? No.

Believing the PSR commits us to denying libertarian free will/accepting necessitarianism

This doesn’t bother me much, since I am a Calvinist and therefore a compatibilist, and I am a modal necessitarian. However I do need to maintain that God is totally free, so I have to engage with it to some degree. A good argument can be found here, it is reasonably well explained and I will not reproduce it.

We should only believe things we can test, how did you test this?
I reject the claim that we must test every claim. I only think we should test scientific claims. If you can test this, go ahead, but I think it is fundamentally impossible. Just like it’s fundamentally impossible to test whether the square root of two is irrational. But that doesn’t mean the proofs that the square root of two is irrational fail, nor does it mean that Leibniz’ cosmological argument fails. The simple fact is that logic works, and we can use deductive logic to work out truths from true premises. If you think my premises are false, or my arguments for why they are true fail, then feel free to tell me why. But if you think my premises are true, then you must accept the conclusion, it’s the result of simple and easy to follow logic.

The necessary thing is the universe/big bang/laws of physics

That’s a reasonable suspicion when we get up to (4), but falls flat after (5). We not only prove that there is a necessary object, but we prove that it has all the properties we normally think of God as having. And none of the suggestions above for the necessary object have these properties.  We cannot merely attach the description “necessary” to whatever we please, we must discuss what properties the necessary thing must have.

The PSR is almost true, there’s only one brute fact: The BCCF

This is a common objection. We can get all the benefits of the PSR, without being forced into accepting God. But it has some unfortunate implications. Consider a weakened PSR: every fact possibly has an explanation. It turns out that this is sufficient to prove God. Suppose the BCCF is possibly explained. If it is explained, it’s explained by a necessary God (as we have already shown). So possibly a necessary God exists. But by S5 modal logic, this means God exists. So the objection is no good. Instead, the objector has to say that necessarily the BCCF has no explanation. Now first, it seems to me that if a fact necessarily has a property, that fact is necessarily true. But further, it is a hard burden to take onto yourself to say that the BCCF is necessarily unexplained. The one who claims that it is necessarily unexplained must give a coherent and non-arbitrary reason why it is necessarily unexplained. No such reason has yet appeared.

LCA Point 5: The Necessary Object is God

This is our third post in a series on Leibniz’ Cosmological Argument. You can find the first post here and the second here. The full argument is:

(1)               Every contingent fact has an explanation.

(2)               There is a contingent fact that includes all other contingent facts.

(3)               Therefore, there is an explanation of this fact.

(4)               This explanation must involve a necessary object.

(5)               This necessary object is God.

Today we will be examining…

(5)               This necessary object is God.

This is much like the first point, in that it’s not obvious and requires some argumentation. First, let’s talk about what it means to be a necessary object. A necessary object is an object that explains its own existence. It does not “depend” on any other object to exist. Using the possible world terminology we introduced last post, a necessary object is an object that exists in every possible world. 

So what properties can we deduce about the necessary object? Well it’s clearly not material, as material objects depend on matter to exist and are contingent. In fact, it’s not composite at all, since composite objects depend on their components to exist. So the necessary object must be entirely simple.

Whatever necessarily exists must always exist, since the fact that it necessarily exists is true no matter what time period you are in. So the necessary object is everlasting.

The necessary object must be unchangeable. Suppose that the necessary object were to change. That change must either be caused by the necessary object itself, or something else. It cannot be caused by something else, because that would make the state of the necessary object contingent on that thing that caused it. So if it changes, it must cause that change itself. If something changes itself, either part of it changes another part, or the whole changes the whole. Since the object in question has no parts, the whole necessary object must change the whole necessary object. But if this were the case, it would have already been the thing it was going to change into. So it cannot change.

The necessary object must also be omnipresent. The necessary object is free from any contingent properties, or any arbitrary properties, in virtue of necessity and simplicity. However existing at a particular physical location is a contingent property, since the existence of that physical location is contingent. Therefore the necessary object has does not exist at any particular physical location. This is omnipresence: present in equal measure at all places and at all times.

Now Leibniz presents an argument that the necessary object has understanding, a will, and power. He argues that it has understanding, as it can survey all possible worlds it can create. It has a will, as it selected one possible world. And it has power, as it actually created that world.

Is this argument reasonable? Consider first the understanding argument. Can the necessary object survey all possible worlds? A possible world is a world that could exist. If such a world contains any contingent objects, then the necessary object must exist. And if it doesn’t contain any contingent objects, and only the necessary object, then the necessary object must still exist.

Our necessary object explains all contingent objects. That means it must in some way contain information about those objects. And it contains information not only about contingent objects that exist, but also all possible contingent objects, since it would also explain them. And clearly it contains information of itself, since everything does. This kind of containing information is understanding.

Does it have a will? Of all the possible worlds, it chose one. Is simply choosing one possibility out of many having a will? Probably not, since my computer also does this and does not have a will. Instead, it seems more reasonable to say that having a will, or maybe a free will, is choosing an option apart from any outside compulsion. My computer chooses what it was programmed to choose, and so doesn’t have a will in this sense. But the necessary object is not compelled by anything external to it, and its choice comes entirely from within. So it seems it has a will.

And power? This one is more clear: it did in some sense create the world. It chose this possible world, and actualised it over other possible worlds. That is power.


Since the understanding, will, and power are directed towards all possibilities, they are infinite. The necessary being understands all possibilities, can will to create any of them, and has the power to carry out that will, whatever it may be.

And since choosing is to judge that the thing you choose is the best thing among the alternatives, and since the necessary object has full knowledge (knowledge of all possible worlds), it judges which is actually the best among infinitely many alternatives. This means that it is in a sense infinitely good.

Another argument can be made for a more general agency of the necessary object. As far as we understand explanations, there are three types: scientific, conceptual, and agential. The necessary object is clearly not a scientific explanation, since it cannot be material, due to simplicity. Further, science only explains things in terms of contingent things, or at least it has in every case we know of.

Nor is it a conceptual explanation. Among the contingent things we find substances, the stuff that other things are made from. Dualists will argue that the soul is a different kind of substance to matter, for example. Matter/energy is the substance that physical objects are made of. But the activity of a substance cannot be conceptually explained by the activity of something other than that substance. A conceptual explanation can tell us why things behave the way they do, in terms of what they are. But a conceptual explanation cannot give an account of why they are in the first place. So a conceptual explanation is insufficient for the big contingent fact.

So the only option remains is an agential explanation: an explanation in terms of some agent. So the necessary thing must be an agent in some sense.

We can also demonstrate uniqueness: every property the necessary object has must be a property it necessarily has, by a similar argument to the simplicity argument above. So if there are two necessary objects, they have the same properties. But two objects with identical properties are actually just one object. So there is only one necessary object.

At this point, we have proven that there exists a necessary object, which has infinite knowledge, infinite power, is infinitely good, is simple, eternal, unique, immutable etc. I know no name we could give this object other than “God”. And of course we have not yet arrived at Christianity. But I claim that after proving that this God exists, we may go looking for it in the world.

We find this: there exists a religious tradition spanning thousands of years who claim to worship something with all of these properties. They record centuries of interactions with this thing, who behaves exactly as we’d expect God to behave, including giving and fulfilling prophecy. And in the end we see the man Jesus who comes claiming to be God come in the flesh, who behaves as we’d expect God to behave, with a supremely good moral character, who fulfills prophecy given over the last few thousand years. I believe Him.

My Thoughts on Jordan Peterson

Jordan Peterson has recently become an influential figure in modern culture, especially among young men, especially those young men who have previously found themselves at odds with feminism, progressive culture, etc. I think much of this admiration is misplaced, and that there are good criticisms to make of Peterson. However I think it’s also important to understand what it is that’s drawing people to him.

I find myself in two communities here. First I am part of the community of conservative young men. Men who have strong criticism of modern culture, who feel that the direction of progress is wrong, who feel like people have become soft, weak, shallow and thoughtless. A group of people who have grown up in a world lacking direction, purpose, or meaning. A world which is hostile to the nature of young men.

Second, on the outskirts of the academic philosophy community, engaging with it as an amateur and autodidact. Here, Peterson is widely considered to be a moron, who thinks he has engaged with important issues but has thoroughly missed the point.

I think these second people are right. Peterson is a psychologist, who was unknown until he started a controversy about the use of transgender pronouns. This was picked up by the alt-right, who used Peterson as a figurehead for their own opposition to transgenderism. He also fuels their rage against “post-modernism”, which I think both they and Peterson misunderstand, and “cultural Marxism”, which isn’t a real thing at all. In fact, Marx would be thoroughly modernist, not post-modern. But I don’t want to get into those things here, instead, I’ll just encourage anyone reading this to research modernism, post-modernism, and Marxism yourself. I am indeed thoroughly opposed to post-modern thought and to Marxism, but I doubt most of Peterson’s fans understand these topics. I do not think Peterson does either. This is why academics do not like Peterson in general.

But most of the people who like Peterson do so for reasons unrelated to his philosophical positions. Young men have grown up in a world of coddling, victim-mentality, and weakness. As a young man, I’ve felt this too. We are encouraged to have a weak will, to blame others when we fail, we’ve been told: “believe in yourself and you can do anything, because you’re unique like a snowflake”. We live in a culture that glorifies narcissism, fragility, and an external locus of control. A culture that raises what C.S. Lewis calls “Men without chests”. 

Peterson has been adopted as the intellectual of the right-wing movement because he speaks against this. He tells young men to grow up and take responsibility. To grow a backbone, to do hard things because you know they’re right, to act with honour and integrity. To not worry about your rights being violated (since rights exist to protect weak and vulnerable) and instead worry about your own competence (since the competent never need to refer to their rights). Some people are weak and vulnerable and should be protected, but you should do whatever you can to take yourself out of that category. Virtue requires a strong will.

Peterson is right about these things. Young men especially should grow a backbone, accept responsibility, and forge themselves into strong, honourable, skilled men. This is what appeals to young men. They fundamentally know this is right.

But this isn’t a good reason to revere Peterson. Many have said this before, many have said it better, and many have said it without bringing in misunderstandings of philosophical and literary narratives, or without Peterson’s rather strange metaphysical background.

Further reading: