Van Til on the Problem of Induction

Jon Stevens / December 21, 2018 / Presuppositional

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.

Van Til’s argument for Trinitarian Theism

Jon Stevens / December 8, 2018 / Presuppositional

We recently began looking at some presuppositional arguments from Van Til, as examined by James Anderson. One of Van Til’s more interesting arguments is one for the existence of a God that is not unitarian. Theoretically the same argument could be made for a God that exists in multiple persons of any number, not just 3. But for now, we will treat Christianity as the only worldview that has the requisite ontological commitments.

The argument is basically this: at the base level, reality is either fundamentally unity, diversity, or both. Reality being fundamentally unity or fundamentally diversity would undermine our knowledge of reality. Therefore if we are to know anything about reality, we must hold that reality is fundamentally both. Only Christianity presents a worldview under which this is true, so Christianity is true.

Here is Van Til:

As Christians, we hold that in this universe we deal with a derivative one and many, which can be brought into fruitful relation with one another because, back of both, we have in God the original One and Many. If we are to have coherence in our experience, there must be a correspondence of our experience to the eternally coherent experience of God. Human knowledge ultimately rests upon the internal coherence within the Godhead; our knowledge rests upon the ontological Trinity as its presupposition. (An Introduction to Systematic Theology, 23)

This is relatively easy to phrase in a more formal premise-conclusion form, so I won’t bother here. I am sure you can all reconstruct it.

What we must do now is justify the claim that under fundamental unity or under fundamental diversity, reality is not knowable.

Knowledge is impossible under diversity

Suppose that diversity is fundamental, and that every thing is distinct from every other thing. Knowledge therefore can only be had of individual things, and not categories. We can’t know things like “cats don’t like water” without all (or just most) cats having that property. But if there are no shared properties between objects, knowledge seems to be very difficult. We certainly want to affirm we have this kind of knowledge of classes and categories and groups, so we must deny that reality is fundamentally diverse.

Knowledge is impossible under unity

Under fundamental unity, where everything is at the base level the same kind of thing, knowledge seems impossible because there is nothing to differentiate one thing from another. We can only know that an object has a property A if there are some objects that do not have the property A. And perhaps more interestingly, if one knows something about an object, that it has a property A, it must be that we know it has a property A instead of property B. But under unity, there are no A and B, they are unified and identical. So between objects and within one object, knowledge depends on distinctions.

Isn’t it possible that fundamentally there are some things that are distinct and some that are similar?

Maybe. Suppose that this were the case, that fundamentally there are things of category A that are all the same and things of category B that are all the same (two kinds of monads) and they are entirely distinct from each other. We have distinction: Bs are not As. And we have unity. All As are As. This seems like it solves the problem of the unity/distinction tradeoff in the same way the Trinity does.

A possible monadology

Suppose that reality is fundamentally composed of monads, think of them like really small atoms for now. We cannot know one monad from another, other than by incidental properties like location or momentum (inasmuch as small objects have these). But these monads compose larger objects like chairs and cats. We can have knowledge about chairs and cats, they are real objects which share properties. They are unified and distinct in the right way. But they are composed of entirely unified monads. Where is the problem here? How would Van Til respond? I am not sure.

Conclusion

We are again seemingly left not totally convinced by Van Til. Maybe he is right that knowledge is impossible under fundamental unity and under fundamental diversity. But we don’t just know fundamentals, we know composites, and even if fundamentals are indistinguishable the composites aren’t.

More

Vern Poythress has done some interesting work expanding and explaining Van Til here, which I think is more promising than the work Van Til has done himself. But I am still not convinced that it is sufficient to demonstrate the existence of God.

Van Til on the Unity of Knowledge

Jon Stevens / December 3, 2018 / Presuppositional

In James Anderson’s 2005 paper, we are given an example of an argument that Van Til makes for the existence of God. Specifically, this is an argument that God is a necessary precondition for human beings to have any knowledge about anything. Van Til is hailed in Reformed circles as an excellent apologist, and his brand of presuppositionalist apologetics is very popular and is practised often at the exclusion of other schools of thought. However, I have noticed that very rarely does anyone ever actually present any of Van Til’s arguments. Perhaps today we shall see why. It seems to me that no-one actually reads Van Til, or at least tries to pull any arguments out of him.

Here are two relevant quotes from Van Til that Anderson gives us, which give us the argument we will examine now:

This modern view is based on the assumption that man is the ultimate reference point in his own predication. When, therefore, man cannot know everything, it follows that nothing can be known. All things being related, all things must be exhaustively known or nothing can be known. (An Introduction to Systematic Theology, 163)

Here too every non-Christian epistemology may be distinguished from Christian epistemology in that it is only Christian epistemology that does not set before itself the ideal of comprehensive knowledge for man. The reason for this is that it holds that comprehensive knowledge is found only in God. It is true that there must be comprehensive knowledge somewhere if there is to be any true knowledge anywhere but this comprehensive knowledge need not and cannot be in us; it must be in God (The Defense of the Faith, 41)

We, modern analytical thinkers, prefer to have arguments in a formal premise-conclusion style, so Anderson helpfully creates one:

If no one has comprehensive knowledge of the universe, then no one can have any knowledge of the universe.
Only God could have comprehensive knowledge of the universe.
We have some knowledge of the universe.
Therefore, God exists.

This argument is valid, and I think for the moment the atheist can grant premise 2. Any being which has comprehensive knowledge of the universe is probably worth being called God. The difficulty is of course with premise 1.

Van Til seems to have a justification like this in mind: we cannot know if there exists out there some fact which would demonstrate all of our previously held beliefs false. But knowing that, we cannot be justified in holding any of our beliefs. If we aren’t justified in holding our beliefs, we have no knowledge. So there must be some way of us being justified in believing that there is no such problematic unknown fact. And the only way for that to be the case is if God designed us with mental faculties which aim at truth in the right way, and intends for us to believe truth. Without God “holding our hand”, we can’t have any knowledge.

Unfortunately, I don’t think this is any good. The mere possibility that we might be wrong is not sufficient to remove justification. We “know” many things about which it is conceivably possible, however unlikely, that we might be wrong. Knowledge is not certain or proven true belief, but only a warranted true belief, and warrant doesn’t need to be certain.

One might attempt to justify the premise further, by using a kind of pessimistic meta-induction. For almost everything that almost all humans have ever believed, it turned out there was some fact out there which proved it wrong. So chances are, there is also some fact out there that proves us wrong. So it’s not only possible that we are wrong about everything we believe, it is now quite likely. And if that is the case, we probably don’t have knowledge.

But this goes too far. Because if that is the case, if theists attempt to make that rhetorical move, then it seems like God isn’t there holding our hand. In this case, God has not designed our mental faculties in the right way, because we are so often wrong. By attempting to prove that knowledge is impossible without God, we’ve also proven that it’s impossible with God.

Van Til has some more arguments that we will examine, but this was the simplest one. Have I missed something? Is the argument stronger than I make it out to be?