Underestimating the problem of induction
I'm going to talk about two of the biggest problems I can see with the presupposition lists. Attempts to establish a rational basis for inductive reasoning. Hum's writing on inductive inference draws our attention to the fact that inductive inferences are not rational; they arise from custom and habit.
One way to illustrate this is to think of whether the sun will rise tomorrow. Most of us agree that the sun is more likely to rise tomorrow than it is not to rise. Whichever way we explain our judgment about the likelihood of a sunrise, all our explanations depend on the assumption that the future will resemble the past in a fundamental way.
To give a more concrete example, we assume that the laws of physics we understand today won't be radically contradicted by how things behave tomorrow. But what are these assumptions based on? How can we know that the laws of physics that explain the sunrise will function in the same way tomorrow as they do today? It seems that we can't know these things, and it's not immediately obvious how we can even assign probabilities to them.
It can feel unsatisfying to think that our expectations about the future are inherently irrational. The presuppositionalist thinks that he has a way out. He believes that a God exists who has promised to maintain the uniformity of nature. We can take the uniformity of nature to mean that the future will resemble the past in some fundamental way.
There are at least two distinct problems with the solution, though, either of which invalidate it. They can be summarized as follows:
- We can't trust a God's promise without using induction. So if you're using God's word to justify induction, you're begging the question.
- Even if nature is uniform, this isn't enough to provide a rational justification for induction, as illustrated by the Black Swan example.
I'm going to explain the first problem in a bit more detail. According to the presupposition list, God has promised to maintain the uniformity of nature, which is needed if inductive inferences are ever going to turn out to be true. God is all-powerful, and his word is final, so that might seem to settle things.
But even if we ignore the so-called biblical evidence, which plainly shows that God often changes his mind and breaks his promises, it's not as simple as that. How do we know to trust someone's promise? In deciding about their trustworthiness, we take things into consideration about the one who's making the promise.
A particularly important consideration is whether the promise maker has broken or kept his promises in the past. To see that this applies even if we're considering a divine promise maker, think about how you'd react to a new promise from a God who had made many promises in the past and broken all of them. Even his most devout worshipper would be a fool to trust him.
So the presuppositionalist uses the ideas he has about how his God behaved in the past and comes to the conclusion that his God is very unlikely to break his promise about the uniformity of nature in the future. He's using induction: "God never lied to me in the past; God won't lie to me in the future."
But remember that induction is the very thing that the presuppositionalist wanted to justify in the first place. The presuppositionalist might protest that he's not really using induction to know that God won't lie. He might say that he knows God won't lie because it's not in God's nature to lie.
But all he's done is generate a different indu of justification: "God's nature was X in the past; therefore, God's nature will be X in the future." Whichever way he chooses to explain his trust in God's word, the presuppositionalist uses induction in his solution. He's assuming what he sets out to prove. This is a fallacy called begging the question.
Any defense of rational induction that depends on a God's promise falls into the same trap. The second problem is that even if we know that nature is uniform, we still haven't done anything to provide a rational basis for induction. It seems that the only way we could be certain that an inductive inference would turn out to be true is if the universe was uniform and we knew everything about it, and this is clearly not the case.
While there are things we don't know about the universe, we can never be sure our inductive inferences will turn out to be true. Perhaps the sun, according to some previously unknown feature of our uniform universe, will vanish before the sunrise we predicted has had a chance to happen.
"All swans we have seen are white; therefore, all swans are white." Induction in a uniform universe can and does give false results. GPA's example of the black swan illustrates this. So the uniformity of nature, while being necessary in order for us to gain any advantage from our habits of induction, is useless if you want to establish a rational basis for inductive reasoning.