In the context of discussion of Hume’s famous “problem of induction,” induction is typically characterized as reasoning from what we have observed to what we have not observed. For example, we reason inductively in this sense when we infer from the fact that bread has nourished us in the past that it will also nourish us in the future. (There are, of course, other ways to characterize induction, but we can ignore them for the purposes of this post.)
Hume asks how we can be rationally justified in reasoning this way, and his answer is that we cannot be. For there are, he says, only two sorts of purported justifications that could be given, and neither of them works. The first would justify induction in terms of what Hume calls the “relations of ideas.” The proposition that all bachelors are unmarried is a stock example of something true by virtue of the relations of ideas. It is a necessary truth insofar as the idea of being a bachelor logically entails the idea of being unmarried. Justifying induction in these terms would involve showing, for example, that there is a similar logical relationship, and thus a necessary connection, between the idea of bread and the idea of being nourishing to us.
But there is, Hume argues, no such connection. For it is at least conceivable that bread could fail to nourish us, in a way it is not conceivable that a bachelor could be married. In general, it is conceivable with respect to any cause that its usual effect might fail to follow upon it. Hence we cannot reason on the basis of the relations of ideas to the conclusion that causes that we have not observed will operate like those we have observed.
The other way induction might purportedly be justified would be in terms of “matters of fact.” The proposition that many bachelors go to singles bars is true, not because the idea of being a bachelor logically entails the idea of going to a singles bar, but rather because it simply happens to be a contingent empirical fact that many bachelors do this. To justify induction in terms of “matters of fact” would involve arguing that as a matter of contingent empirical fact, induction has been a reliable way of reasoning, so that we have grounds to trust it in the future.
But the trouble with this attempt to justify induction is that it is circular. To infer from the fact that many observed bachelors have gone to singles bars the conclusion that many unobserved bachelors will do so too presupposes the reliability of induction. To infer from the fact that induction has been reliable in observed cases the conclusion that it will be reliable in future cases also presupposes the reliability of induction – where its reliability is, in this case, exactly what such an argument is supposed to be showing.
In summary, Hume’s argument against the possibility of justifying induction goes as follows:
1. Induction could be rationally justified only in terms of either the relations of ideas or matters of fact.
2. But it cannot be justified in terms of the relations of ideas, since for any cause and any effect it is conceivable that the one could in the future exist without the other.
3. And it cannot be justified in terms of matters of fact, since such a purported justification would presuppose the reliability of induction and thus beg the question.
4. So induction cannot be rationally justified.
As David Stove once said of Plato’s Theory of Forms, the sequel to Hume’s argument has been centuries of rapturous applause among philosophers. Stove didn’t mean it as a compliment; he was mocking something he took to be overrated. The mockery is in my view not justified in Plato’s case, but it would have been justified had the barb been directed instead at Hume’s overrated argument. For what we have here is one of many instances of Hume’s application of general philosophical presuppositions which we know to be highly problematic at best and demonstrably false at worst.
First, the initial premise of Hume’s argument is an application of Hume’s Fork, the principle that all knowable propositions concern either relations of ideas or matters of fact. But Hume’s Fork – which is itself neither true by virtue of the relations of its constituent ideas, nor true by virtue of empirically ascertainable facts – is notoriously self-refuting. It is as metaphysical a principle as any Hume was trying to undermine with it, and its very promulgation presupposes that there is a third epistemic point of view additional to the two Hume was willing to recognize. In that case, though, Hume’s celebrated “problem of induction” cannot even get out of the starting gate. Its entire force depends on a dichotomy that is demonstrably false.
Nor can the Humean plausibly salvage the argument by softening Hume’s Fork so as to avoid the self-refutation problem. For the softening can take one of three forms. The Humean could liberalize the principle by admitting that there is after all a third category in addition to “relations of ideas” and “matters of fact”; or he could maintain this dichotomy while liberalizing the notion of “relations of ideas” in such a way that Hume’s Fork itself will come out true by virtue of the relations of ideas; or he could maintain the dichotomy while liberalizing the notion of “matters of fact” in such a way that Hume’s Fork will come out true by virtue of matters of fact.
Whether and how any of these strategies could be developed in a plausible way is another question. But the point for present purposes is that, however that might go, if he is going to salvage Hume’s problem of induction, the Humean will have to soften Hume’s Fork in such a way that it will vindicate Hume’ Fork itself without also vindicating induction at the same time. In particular, the Humean will have to acknowledge a third category of knowable propositions in addition to relations of ideas and matters of fact while at the same time showing that induction isn’t justifiable in terms of this third category. Or he will have to liberalize the notion of “relations of ideas” while at the same time showing that induction isn’t justifiable in terms of this new, liberalized notion. Or he will have to liberalize the notion of matters of fact while at the same time showing that induction isn’t justifiable in terms of thatnew, liberalized notion.
Good luck with all that. Until one of these strategies is actually developed, we don’t really have a Humean “problem of induction.”
That’s just one problem. Another is that Hume’s second premise depends on the principle that conceivability is a guide to real possibility. Now, contemporary philosophers never tire of pointing out how problematic this principle is when Cartesians deploy it in arguments for their brand of dualism. The Cartesian says that we can clearly conceive, without contradiction, of minds existing in the absence of bodies, and concludes from this that it is therefore possible in principle for minds to exist apart from bodies. But how, the critic responds, can we rule out the possibility that this seems conceivable only because of a deficiency in our grasp of the mind? Someone with only a vague understanding of what a Euclidean triangle is might think it possible for such a triangle to have angles that add up to something other than 180 degrees. When he acquires a better grasp he will realize that this is not in fact possible. Perhaps, the critic suggests, a more penetrating grasp of the nature of the mind would reveal that it cannot really exist apart from matter.
But the same sort of objection can be raised against Hume (and, in my view, with greater justice). Perhaps if we had a complete grasp of the nature of bread and the nature of the human body, we would see that it is not in fact possible for bread to fail to be nourishing to us. If so, then we would be justified in judging that bread will nourish us in the future just as it has in the past.
Now, the reason Hume is so confident that this is not the case is because of what commentators call his copy principle, viz. the thesis that an idea is just a faint copy of an impression. I have an impressionof red when I am looking at a certain apple. When the apple is not present I can call to mind what that color looked like, and this mental image is (Hume claims) my idea of red. More complex ideas are made up of combinations of simpler ones of this sort. My idea of bread, for example, is just a combination of the idea of a certain color, the idea of a certain shape, the idea of a certain texture, and so forth. Thus understood, it seems plausible to say that there is nothing in my idea of bread that entails that it will be nourishing in all cases.
But this account of our ideas is ludicrous. It reflects the imagist thesis that a concept is essentially a kind of mental image, and imagism is demonstrably false. We have a great many concepts that are clearly not identifiable with mental images. For example, the concept of triangularity is not identifiable with any mental image. Any triangle you can imagine will always be of a certain specific color – black, red, green, or whatever – whereas the concept triangularityapplies to all triangles whatever their color. Any triangle you can imagine will be a right triangle, or an equilateral triangle, or in some other way have features that don’t apply to all triangles, whereas the concept triangularity does apply to all triangles. And so forth. This is just the beginning ofthe problems with imagism. (Here’s a fun exercise: Try to identify the mental image that the concept mental imagemight be identified with.)
Then there is the assumption that all necessity is logicalnecessity, viz. the sort of necessity exhibited by the relations between concepts. Aristotelians and other non-Humean philosophers would deny this. They hold that there is a deeper, metaphysical kind of necessity that exists in things themselves and not merely in our concepts of things. Logical necessity, on this view, is an echo of this deeper sort of necessity. And the echo might not ring out very strongly in a mind that has too superficial an acquaintance with all the relevant facts. Hence, suppose that, given the nature of bread and given the nature of a healthy human body, it cannot possibly be the case that bread will fail to nourish such a body. It may still turn out that a given person might conceive of a scenario wherein bread fails to be nourishing, not because such a failure is really possible, but rather merely because that person’s intellect has not attained a sufficiently penetrating grasp of the natures of bread and of the body.
For the non-Humean, then, it is simply not the case that all propositions are either necessary but mere conceptual truths (“relations of ideas”), or empirical but merely contingent truths (“matters of fact”). There are also truths which are empirical but nevertheless necessary. That bread will nourish the body could be a necessary truth even if we can know that it is true (if it is in fact true) only by empirical investigation of the natures of bread and of the body.
Naturally, the Humean will disagree with all of this, but the point is that, unless he offers an independent argument against these alternative ways of understanding the nature of concepts, necessary truth, etc., he will not have given us any non-question-begging reason to believe that there is a “problem of induction.”
The real problem, then, is not the problem of justifying induction. The real problem is justifying the claim that there is a “problem of induction” that remains once we have put aside the false or otherwise problematic philosophical assumptions that Hume himself deployed when arguing that induction cannot be justified.