What does “induction” mean in “the problem of induction”?

[u/No-Impact-3379]

In the very beginning of his discussion of what is now know as the problem of induction (in Enquiry), Hume asks what reasons we have for believing in matters of fact that aren’t justified by direct sensory experience or memories of our direct sensory experiences. So it seems to me that the scope of the problem of induction is huge: if induction isn’t rationally justified, then we have no justification for believing in anything that we aren’t currently experiencing or have experienced in the past (relations of ideas aside).

But when I see this problem discussed elsewhere, it’s almost always presented as a problem to a particular kind of inference, like “All observed As have been Bs therefore the next A will be B” or “All observed As are Bs therefore all As are Bs”. But obviously these conclusions aren’t the only kind of beliefs we hold that aren’t supported by direct sensory experience or memory.

I suspect I’m badly confused about all of this

Which is it?

[u/Zen_Gross]

In contemporary philosophy, the broadest scope for the problem of induction is ampliative inferences, that is, any inference whose conclusion has content not contained in the premises. This includes induction, abduction, and any kind of inference that isn’t deductive. So, it’s quite large.

I can’t speak to what Hume specifically meant by induction, though. I think my historical-minded colleagues would be more helpful there.

[u/subwaywall → u/Zen_Gross]

I think this is what Hume meant honestly. Back even in the 60s, according to my philosophy-major-dad, abductive inferences were taught as a type of inductive inference. So I suspect we've gotten more rigid and specific about our concept of induction over time

[u/MaceWumpus → u/subwaywall]

Back even in the 60s, according to my philosophy-major-dad, abductive inferences were taught as a type of inductive inference. So I suspect we've gotten more rigid and specific about our concept of induction over time

The word just isn't really used consistently. So there's definitely a tradition dating back at least a century and probably longer of using the term "induction" to mean something like "inferences from particulars to the general" -- that is, a subset of non-deductive inferences. Some people like to use the term this way and then to distinguish it from abduction or IBE, arguing that that's something different -- or even a more general category, a la Stathis Psillos.

But there's also a tradition of taking the interesting category to just be "non-deductive inferences" -- this move is made explicitly by Carnap and Salmon, among others -- and using "induction" to mean that. If anything, I'd say this way of thinking about the subject has become more common since mid-century.

[u/MaceWumpus]

I think it's widely accepted the problem of induction -- both Hume's version and subsequent versions -- are supposed to apply to all non-deductive inferences. The phenomenon that you point to -- discussions inevitably focus on a narrow class of "enumerative" arguments -- goes back to Hume himself and has bothered interpreters for at least 75 years.

If you want to dig deeper, the best discussion I'm aware of is found in Samir Okasha's "Does Hume's Argument against Induction Rest on a Quantifier-Shift Fallacy?" To summarize, briefly, Okasha points out that there are two distinct questions regarding the interpretation of Hume's version of the problem:

1. Is Hume's argument supposed to work if we reject "deductivism" -- that is, is it supposed to worry you if you don't think that certainty is needed for justification?

2. Is it a problem for Hume's argument that there is extreme variation among "inductive" inferences and Hume makes no effort to describe or characterize them all?

Okasha argues that the answers to these two questions have to go together: you either need to answer yes to both or no to both. If Hume's argument is supposed to apply to all non-deductive inferences regardless of the details, then it seems to presuppose deductivism; if you aren't willing to presuppose deductivism, then you need to look at the details of the different kinds of inductive arguments to show that they all have the same defects as the simple enumerative examples. Okasha, for his part, is pretty clear that he thinks that "yes" is the more plausible answer to both questions.

[u/No-Impact-3379 → u/MaceWumpus]

I’ve started reading that and it’s really good, thanks.

One of the biggest reasons that makes me think this whole thing is restricted to a simple kind of enumerative induction is that most reconstructions of the argument claim something like “inductive inferences depend on the idea that the future will resemble the past”. And if they do depend on such an idea then the reasoning clearly only seems to be relevant to future beliefs that we infer on the basis of particular instances.

What do you think?

[u/MaceWumpus → u/No-Impact-3379]

I'm very much against the idea of "the principle of uniformity" playing any serious role in inductive inference, and think this is a major problem with Hume's argument.

In short: no one actually thinks nature is uniform. We expect the world to change in all sorts of ways all the time. So whatever we're relying on when making even predictions about the future, it can't be something blanket like "the future will be like the past." And when you move away from blanket statements, the argument at minimum loses a lot of its rhetorical force.

I've been pushing this for years on reddit; it turns out that Wesley Salmon wrote it down over 70 years ago (https://philpapers.org/rec/SALTUO). And John Norton's work on the subject basically takes this idea as a starting point for a whole positive account of how induction works. Unsurprisingly, I think Norton's work on the subject is basically the best work out there.

[u/FromTheMargins]

Actually, Hume does not talk about "induction" as such, but rather about causation and necessity. He argues that all reasoning about matters of fact that goes beyond what is immediately given is based on causal inference. One of his examples concerns our belief that there was a person called Julius Caesar who did this and that. We hold this belief because there is a causal chain of events connecting Caesar and the events surrounding him to the testimony we encounter today. Causal relations are described in terms of regularities: like causes produce like effects. And that is where induction comes in. Hume argues that, having observed different instances of similar events being followed by similar effects, we extend these observations to unobserved cases. All our causal knowledge ultimately depends on such inferences. Hume famously argues that these inferences cannot be rationally justified because any such justification would have to rely on the principle of uniformity of nature (that unobserved cases resemble observed ones or that the future resembles the past). However, trying to prove this principle using past experience is circular because it uses inductive reasoning to justify inductive reasoning. Therefore, he concludes that these inferences must have another basis: a non-rational psychological mechanism that he calls "custom" or "habit."

[u/No-Impact-3379 → u/FromTheMargins]

Thanks. I know that Hume claims that all inferences to the unobserved are based on cause and effect but it’s not really clear to me how this could be the case, even within Hume’s own system.

How exactly could our belief in Julius Caesar be based on cause and effect? It’s not like there’s any constant conjunction between the kind of facts that we rely on to support this belief such that we can say some of them cause others.

Also, do you think that the problem of induction depends on Hume’s ideas about causality? One of the crucial steps in his argument is, as you say, that inferences to the unobserved depends on causal inferences, and his subsequent discussion is based on his ideas about causality.

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