Did Hume argue against partial support of a statement?

Question

From what I have read, Hume argued that induction cannot be justified. But did he also argue that probabilistic justification isn’t a thing? For example, most of us usually have a notion of a proposition being weakly or strongly supported by relevant past instances using induction or some form of analogical reasoning. Did Hume argue that all of this is unjustified?

Answer 1

Hume argues two things. Firstly, that inductive inferences are not demonstrations. This is usually understood to mean they are not a priori knowable or they are not deductively certain. This is because from any given series of observations, no contradiction arises from supposing that the next observation will be different.

Secondly, he argues that we do not have rational grounds for claiming that some prediction of the future is probable, based on past observations. It may be that Hume is not using the term 'probable' in a modern sense. He is talking about reasoning based upon considerations of fact. He claims that any such reasoning assumes a principle of uniformity, i.e. that future observations conform to those of the past. Hume says that making this assumption is circular, because it begs the question at issue.

One way to express this circularity might be to say the following:

1. I have rational justification for expecting future observations of X provided:
2. I have made past observations of X, and
3. The future conforms to the past.

But then 3 is just an assumption. How do we justify 3 itself? If we substitute 3 into position X we have:

4. I have rational justification for expecting that observations of the future conform to the past, provided:
5. I have made past observations that the future conforms to the past, and
6. The future conforms to the past.

This definitely appears to be circular. It makes the justification for 3 depend on the assumption that it is in fact true.

There have been a huge number of proposed responses to this argument. The SEP article on the problem of induction contains a survey.

Hume's own proposal is that our expectation of the future conforming to the past is a mental habit that results from our constant experience of such conjunctions. This is not a rational justification, but a fact about how human beings think and reason. Depending on how you understand Hume's philosophy you might consider this to be a form of skepticism or of naturalism or some combination of both.