Hume claimed that we do not make inductive inferences using reason. So I began by explaining what he meant by “reason” or “reasoning.”
I then identified the grand theme of Hume’s philosophy: underming the picture of humanity found in the doctrine that we are made in the image of God. Specifically, I claimed, Hume disagreed with this doctrine’s assumption that we could achieve ideal understanding of the world and ethics by developing our powers of reasoning.
Finally, I turned to the problem of induction. Induction is the process of reasoning from one set of observations to conclusions about things that haven’t been observed. We use induction when we make predictions about the future or offer explanations about the unobserved events that led up to the present. Hume’s problem of induction seems to show that we have no reason to draw these inferences.
Reasoning is a way of reaching a conclusion from some premises through thought. It is contrasted with experience or memory. I reach the conclusion that there is a cat in the room by seeing a cat, I reach the conclusion that I had a sandwich for lunch by remembering what I had for lunch, and I reach a conclusion about what will happen tomorrow by thinking about what happened in the past. Only this last way of reaching a conclusion counts as reasoning.
Hume asserted, without argument, that there are only two kinds of reasoning. One involves comparisons of ideas. For example, the idea of 1 is equivalent to the idea of 1. Or if ‘all men are mortal’ and ‘Socrates is a man,’ then ‘Socrates is mortal.’ The other involves matters of fact. For example, one billiard ball has always moved away from the one that strikes it in the past, therefore, this billiard ball will move away from that one when that one strikes this one. Everything about billiard balls in the previous sentence is a matter of fact, facts about billiard balls in the past and a predicted fact about billiard balls in the future.
Hume claimed that our reasoning about matters of fact moves from observations to conclusions about things that have not been observed. (Our examples usually involve predictions about the future. But we use induction to draw conclusions about things we don’t observe in the past and present as well.) He claimed that we need a principle to connect the observations to the conclusions. But we have no reason for believing in the principle that we need.
All the argumentative fire is concentrated on the principle. I called it the Uniformity Principle. It holds “that the future will resemble the past” (p. 24) or, “that the course of nature will continue uniformly the same.”** from An Abstract of A Treatise of Human Nature. It’s on p. 130 of our book. The challenge is to show that we have a reason to believe this principle.
Hume goes through each of the two kinds of reasoning and finds that neither measures up. The first won’t do because nothing about the idea of the past shows that the future must be the same: it could be different. But if we use the second, we’ll go in a circle. We need the principle to answer questions about why we can draw conclusions from past observations but we need to draw conclusions from past observations in order to answer questions about the principle.
That’s the problem of induction.