Hume’s fork
Hume starts the section from which this extract is taken with the bold claim that all the objects of human reason can be divided between relations of ideas and matters of fact. This distinction, generally known as ‘Hume’s Fork’ sets up the contrast that will be important between the status of knowledge claims that can be arrived at through deductive demonstration and those for which a merely inductive warrant can be provided. It is worth noting briefly two features that characterize the distinction.
1. Truths that comprise relations of ideas do not depend on, or presuppose, any existence claims. Thus the claim that the square of the hypotenuse is equal to the sum of the squares of the other two sides is a truth that is independent of whether there are any right-angled triangles in the universe.
2. The negation of truths that comprise relations of ideas produces claims that could not have been true and cannot be ‘distinctly conceived by the mind’. By contrast, the negation of matters of fact could have been true and thus can be so conceived. This amounts to saying that relations of ideas express necessary rather than just contingent truths.
Three kinds of truth
A distinction of this sort has been influential throughout empiricist philosophy. Consider the three binary distinctions:
1. epistemological: a priori versus a posteriori
2. metaphysical: necessary versus contingent
3. semantic: analytic versus synthetic.
One appealing assumption has been that these different ways of sorting truths all sort them into the same sets. Thus all truths that can be known a priori (that is, without experience) are necessarily true and their truth is fixed by the concepts used to frame them (they are analytically true in virtue of their meaning). Equally, all truths that require experience to be known, and are thus a posteriori, are also contingent and synthetic (i.e. their truth requires both a contribution from their meaning and from the world).
There are also prima facie plausible arguments for the alignment of these distinctions. For example, if a truth is a priori then one does not need to know which possible world one inhabits in order to know its truth. (Experience teaches us which of the many possible worlds we actually live in.) This suggests in turn that it must be a necessary truth (one that holds in all possible worlds). Furthermore it seems plausible that it must be analytic, because its truth clearly does not require a worldly contribution and thus must be fixed entirely by its meaning.
(Despite these arguments, the neat alignment of truths has also come under attack. The Prussian philosopher Immanuel Kant (1724–1804) argued that there were synthetic truths which could be known a priori including mathematics. In this century, the American philosopher W.V.O. Quine (1908–2000) attacked the assumption that the distinctions are well founded clear-cut distinctions of kind and the logician Saul Kripke (1940–) argued that some a posteriori truths are, nevertheless, necessary (such as that water is H2O). For now all that matters is noting that drawing the distinction allows Hume to focus the issue of the foundations of matters of fact. (If the distinctions do not align or are not even firm this will not solve the general problem Hume raises for justifying empirical knowledge. It merely changes the form it takes because there ceases to be a clear contrast between fallible a posteriori reasoning and the supposedly certain a priori and deductive reasoning.))
Knowledge by induction versus knowledge through the testimony of the senses
Having drawn the distinction between relations of ideas and matters of fact, Hume then focuses his attention on the status of knowledge of matters of fact. In fact, the focus is narrower still: on knowledge of what lies ‘beyond the present testimony of our senses, or the record of our memory’ (p. 26). Thus he does not here investigate the status of direct observational knowledge of particular matters of fact—knowledge made available by my opening our eyes to the world—or even our memory of such particular facts. On the one hand, this sets up an implicit contrast between observation and induction. The latter appears less reliable than the former. And indeed, as we will see later, induction in general will never have a stronger justification than observation in general because inductive inferences take observations as their premisses. On further reflection, however, the concepts used to frame observation reports are typically laden with theory. They can in individual cases thus be overturned on the basis of enough inductive counter-evidence.
Hume suggests that such reasoning is founded on the relation of cause and effect. It is this relation that underpins reasoning beyond our direct observations and binds unobserved facts to observed facts. ‘Were there nothing to bind them together, the inference would be entirely precarious.’ (p. 27). However, Hume goes on to question what grounds our knowledge of cause–effect relations. He argues that this cannot be a piece of a priori reasoning and is instead based on our experience. Hume argues both that cause–effect relations concern separate events and thus no amount of inspection of the cause-event can yield knowledge of what effect it will lead to and also that the negation of cause–effect relations does not produce any logical contradiction or a state of affairs that cannot be distinctly conceived. Having cleared the ground in this way, Hume goes on to discuss how experience rather than a priori demonstration can ground our knowledge of cause–effect relations.
Hume’s problem of induction
Section iv, part II contains the sceptical discussion of induction. Hume begins by asking, on the assumption (for which he has just argued) that the foundation of our knowledge of matters of fact (aside from the case of direct perception) is knowledge of cause–effect relations, what underpins that relation? His answer is experience. This seems like a good answer and in everyday contexts would mark the end point of inquiry. But Hume, like a good philosopher, then asks a further question: ‘what is the foundation of all conclusions from experience?’ (p. 32). He suggests that he will argue that our knowledge of matters of fact is not founded on reasoning from past experience.
Taking as his example the connection between the sensible or observational properties of bread and its ‘secret power’ to provide nourishment, Hume argues that experience can play only a direct role in establishing that there has been such a connection in particular cases in the past, but questions how experience can underpin the extension of a more general connection ‘to future times, and to other objects’.
These two propositions are far from being the same, I have found that such an object has always been attended with such an effect, and I foresee, that other objects, which are, in appearance similar, will be attended with similar effects. I shall allow, if you please, that the one proposition may justly be inferred from the other: I know, in fact, that it always is inferred. But if you insist that the inference is made by a chain of reasoning, I desire you to produce that reasoning. (p. 34)
Hume goes on to argue that inductive inferences cannot be demonstrative because their negations make good sense. The course of nature could (logically possibly) change. Thus a deductive defence of induction appears to be unconvincing because too strong. But on the other hand inductive defences of induction also appear hopeless because they are circular. Hume suggests that empirical reasoning: proceed[s] upon the supposition that the future will be conformable to the past. To endeavour, therefore, the proof of this last supposition by probable arguments, or arguments regarding existence [ie inductive arguments about matters of fact], must be evidently going in a circle, and taking that for granted, which is the very point in question. (pp. 35–36).
The problem in a nutshell
So stepping back from the details of Hume’s argument we can set out the problem as follows. Suppose that the premiss is that all bread previously tested has been nourishing and the conclusion is that all future bread will be nourishing. Hume’s challenge is to explain what form of inference justifies the conclusion. The natural suggestion is that experience grounds the rule of inference as well as the premiss (in this case that all bread previous tested has been nourishing). It does this because of the more general piece of direct experiential knowledge that correlations between (in this case) sensible qualities and secret powers have held over time. This general experiential finding is then used to ground the inference from past to future in the specific bread case.
But as Hume points out: using experience to ground the rule itself presupposes that very rule as an inference. Why should the fact that such correlations have held in the past support the claim that they will hold in the future unless an inductive inference is justified here as well? Hume (1975) says:
When a man says, I have found, in all past instances, such sensible qualities conjoined with such secret powers: And when he says, Similar sensible qualities will always be conjoined with similar secret powers, he is not guilty of a tautology, nor are these propositions in any respect the same. You say that the one proposition is an inference from the other. But you must confess that the inference is not intuitive; neither is it demonstrative: Of what nature is it then? To say it is experimental, is begging the question. For all inferences from experience suppose, as their foundation, that the future will resemble the past . . . It is impossible, therefore, that any arguments from experience can prove this resemblance of the past to the future; since all these arguments are founded on the supposition of that resemblance. (pp. 36–37)
Inductive justification of induction
This passage suggests the following alternatives. For experience to yield a principle that will underpin reasoning from observed to unobserved cases we need an argument of the following sort.
Premiss 1: Correlations have held in the past (observed cases)
Conclusion: Correlations will hold in the future (unobserved cases)
Now by itself this argument is neither demonstrative nor deductive (it is not a valid argument). If experience of the stability of past correlations is to warrant the claim that they will continue to be stable, it does this in virtue of an inductive inference. But that was the very rule that this argument was supposed to justify rather than presuppose.
Deductive justification of induction
On the other hand, Hume suggests that such arguments presuppose that the future will resemble the past. Now putting aside the details of how it resembles it, if this were true, inductive arguments would be successful. But how is this fact supposed to help justify those arguments? The obvious answer is that if this is introduced as a second premiss, the argument becomes a valid demonstrative argument.
Premiss 1: Correlations have held in the past (observed cases)
Premiss 2: The future resembles the past (unobserved resemble observed cases)
Conclusion: Correlations will hold in the future (unobserved cases)
But if it is to underwrite a true conclusion, this valid argument requires the truth of the second premiss, which is, as Hume points out, not a necessary truth or a truth that can be arrived at demonstratively. It requires a further inductive argument to justify it. So in either case, there appears to be no non-circular argument for inductive reasoning from experience.
Can we escape the problem?