Hume's Fork and the problem of induction

Hume now draws the distinction that organises his whole theory of knowledge, often called Hume’s Fork. Every object of human reasoning falls into exactly one of two kinds (Enquiry IV):

• Relations of ideas — a priori, necessary, and demonstrative. Mathematics and logic. Their truth depends only on the ideas involved, discoverable “by the mere operation of thought.” To deny one is to assert a contradiction.
• Matters of fact — a posteriori and contingent. Truths about how the world happens to be. Their contrary is always possible: it can be distinctly conceived, and implies no contradiction. Known only through experience.

Now Hume asks the key question: when a matter of fact goes beyond what we presently observe or remember — beliefs about the unobserved, especially the future — what is our reasoning based on? His answer: always on cause and effect. You believe your absent friend is in France because you received a letter (effect) and infer its cause. All reasoning about unobserved matters of fact links a present impression to something else via causation.

And where does our knowledge of cause and effect come from? Never from reasoning a priori, Hume insists. Confronted with a wholly novel object, no amount of pure thought reveals its effects — Adam, however perfect his reason, could not deduce from the fluidity and transparency of water that it would drown him. We learn “A causes B” only by experiencing A and B together, repeatedly. Causal knowledge is entirely a posteriori.

Here is the trap Hume now springs — the problem of induction. Every inference from the observed to the unobserved has a hidden assumption: that the future will resemble the past, that nature is uniform. “Bread nourished me yesterday, so it will nourish me tomorrow” only follows if the course of nature stays constant. Call this the Uniformity Principle. Hume asks the simplest possible question: what justifies it?

Run it through the Fork. Could the Uniformity Principle be a relation of ideas, provable by pure reason? No: we can distinctly conceive the course of nature changing — a world where bread suddenly poisons, where the sun stays down. There is no contradiction in it. Whatever is conceivable is possible, so uniformity cannot be demonstrated a priori. The first prong fails.

Could it then be justified by experience — the second prong? This is where Hume shuts the door. Any argument from experience already presupposes uniformity. “It has always held before, so it will hold again” uses the past-to-future inference to prove the very principle that licenses the past-to-future inference. The reasoning is circular — it assumes what it set out to establish. So experience cannot justify uniformity without begging the question.

Both prongs of the Fork have failed. The conclusion is startling: our inductive inferences — the whole engine of science and daily life — have no rational foundation. Reason neither demonstrates nor experientially proves that the future will resemble the past. This is Hume’s skepticism about induction, and no one has produced an agreed answer to it in nearly three centuries.

So if reason does not carry us from past to future, what does? Hume’s answer is psychological, not logical: custom or habit. After seeing flame constantly conjoined with heat, the mind is simply determined by habit to expect heat on seeing flame. This propensity, produced by repetition, “is the great guide of human life.” We infer, and must infer — but we do so as creatures of habit, not as pure reasoners.