Topics Logic

Question When did the definitions of induction and deduction change from reasoning from the universal to the particular (deduction) and particular to universal (induction), to this non-distinction of the strength of support the premises give to the conclusion? When did it happen and who did it?

Accepted:
February 13, 2009

Comments

I did it, last Tuesday.

But actually, I'm a bit puzzled. The distinction between deduction and induction never was a distinction between universal-to-particular and particular-to-universal. Consider: All dogs are mammals; all mammals are animals. So all dogs are animals. We haven't gone from universal to particular, but surely the reasoning is deductive. Or better: If Max is in Cincinnati, then so is Jennifer. But Max is in Cincinnati. So Jennifer is there too. A perfectly good deduction, but not a case of reasoning from universal to particular.

On the induction side, suppose that every egg I've eaten has given me hearburn. I'm about to eat an egg. So I infer that this particular egg will (probably) give me heartburn. This is inductive reasoning, but it doesn't go from particular to universal.

In a correct deductive argument, the conclusion follows from the premises. Put roughly, it's impossible for the premises to be true and the conclusion simultaneously false, but whether premises or conclusion are universal or particular is neither here nor there. When we reason inductively, however, we recognize, if we understand what we're up to, that even if our premises are true, it's at least possible that our conclusion is false. And so the question becomes: when and to what degree is it reasonable to accept the conclusion in cases like that? The answer, of course, will usually not be all or none.

So I guess I don't see why this is a non-distinction. Some conclusions follow from their premises and others don't. But when they don't, there are still patterns of inference that make it reasonable, given the premises, to accept the conclusion, or at least to think that it's likely.

I hadn't originally intended to attempt a reply to this one, simply because the history of this is something that I've never really looked at in detail. But I do have to take issue with something that Allen Stairs says: "The distinction between deduction and induction never was a distinction between universal-to-particular and particular-to-universal." Erm... that's precisely what it was. I've had a quick leaf through a few of the books I happen to have to hand, and it's quite clear that this was how folks like Bacon, Arnauld & Nicole, Leibniz, Newton, Berkeley, and many others, understood the distinction. Not to mention Aristotle. Or how about the following from John Stuart Mill's 1843 work, A System of Logic, Ratiocinative and Inductive:

"Although, therefore, all processes of thought in which the ultimate premises are particulars, whether we conclude from particulars to a general formula, or from particulars to other particulars according to that formula, are equally Inductive; we shall yet, conformably to usage, consider the name Induction as more peculiarly belonging to the process of establishing the general proposition, and the remaining operation, which is substantially that of interpreting the general proposition, we shall call by its usual name, Deduction." (book 2, ch. 3, sect. 7).

It is quite true that some inductive inferences -- such as Stairs's example with the eggs -- do yield particular conclusions. But one could quite reasonably suggest in such cases that the argument is actually enthymematic, and that it does tacitly involve a general principle after all. Each of these particular eggs has given me heartburn; therefore eggs in general give me heartburn; therefore this next one will do so. As Mill suggests, it's the first step in this argument, from several particulars up to the universal, that is the genuinely inductive one; while the second step, from that universal back down to a particular, is just a straightforward case of deduction.

I don't know when it was that things shifted, or who it was that shifted them. My suspicion is that folks like Frege and Russell will have had something to do with it, in the late-nineteenth and early-twentieth centuries. What their work showed was that there was actually a great deal more to logical demonstration than could be captured within the Aristotlelian syllogistic approach. Aristotelian syllogisms, even when (as in the case of the one that Stairs offers about dogs) they never quite arrive at full particularity, do at least tend to move from greater generality towards lesser generality. That, incidentally, is why the premises in a deduction are regarded as necessitating the conclusion: because the full content of the conclusion -- and usually quite a lot more besides -- is already present in the premises. An induction, by contrast, adds some genuinely new content in the move from premises to conclusion, and will for that very reason be fallible. But a lot of the entailments that modern logic allows seem to stay at precisely the same level of generality or particularity throughout. And yet they also seem to involve precisely the same kind of necessitation as one finds in the classical, syllogistic deductions. Consequently, the category of deductions has now been expanded to encompass these new forms alongside the classical ones, meaning that the classical definition of deduction is no longer so applicable. But still, I'm not so sure that the corresponding way of characterising induction has really gone away at all. Even now, it's not just any old probabilistic argument that gets called an "induction". That term is still reserved for the ones that proceed from particular instances to a general conclusion (or, via an implicit deduction from such a conclusion, back down to another particular instance).