(This is part of an ongoing series on logic and theories of judgment in modern philosophy)
In an earlier post I discussed Kant on the normativity of Logic. In this post I want to examine whether Hume can allow for a non-psychological notion of logical consequence.
The worry is rather simple–indeed, call this the “simple argument”.
- Hume denies that there are necessary connections between distinct existences (I.iii.vi.1).
- The notion of logical consequence requires that there be a necessary connection between distinct propositions.
- So, according to Hume, there could not be such necessary connections between propositions.
- Hence, the cannot be any form of genuine logical consequence.
Hume is notorious for his attack on probability, inductive consequence and inductive knowledge.
But if the above simple argument is correct then, according to Hume, there is no deductive consequence either.
This should bring into doubt much of Hume’s argument against inductive knowledge. Part of that (already obscure) argument depends on his claim that “there can be no demonstrative argument” (I.iii.vi.5) for proving the basic assumption of inductive knowledge, that the future will be like the past, or that what we have not experienced will resemble what we have experienced in the relevant manner. But, if the conclusion of the simple argument above is true then how can demonstrative argument be so much as even possible for Hume?
This is also going to create problems for Hume’s views on inference because what justifies transitioning from one belief or knowledge state to another is not going to be appeal to a notion of logical consequence. Instead it will have to be something like reliable (in the sense of truth-preserving) association. And reliable association could become unreliable at any moment. So while demonstrative reasoning has been useful in the past, who knows what it will do for us tomorrow?
Perhaps Hume might also appeal to his version of analyticity–viz. relations between ideas? This would still be a psychologistic conception of consequence, governed by Hume’s laws of association (resemblance, contiguity, and causation). Which is to say, that it wouldn’t be a real conception of consequence at all. We would just have following, not following from.
So I’m curious what others think here. Is this the right way to think about Hume?
Perhaps what I’ve said here is obvious, but I find the topic remarkably under discussed in the literature.
Moreover, the lack of an account of logical consequence also spells trouble for Hume’s distinction between relations of ideas and matters of fact. For example, take the clichéd judgment that all bachelors are unmarried men. This is supposedly a relation between ideas, and the judgment is true in virtue of this relation, rather than as a matter of fact.
For example, one does not have to go and take a poll of the various bachelors in one’s neighborhood to see whether they are married. But, if the simple argument is correct, then it cannot be a consequence of the content of the idea<bachelor> that the judgment “all bachelors are unmarried” is true, because there are no logical consequences. So it is actually a bit difficult to see how it really is true. Moreover, on Hume’s theory, maybe tomorrow things will be such that not all bachelors are unmarried.
There may yet be substantive ways of distinguishing relations of ideas form matters of fact, and most plausibly, these differences will be epistemic. But philosophers who have attempted to link a priori truth to necessity will find no comfort in Hume. For Hume, our whole system of reasoning is shot through with contingency.
In future posts I’ll discuss other conceptions of consequence in the modern era, especially in the influential Port Royal logic and in Kant’s logic.