The former expectation does not seem very realistic. Albeit anecdotally, in my experience, most people I’ve surveyed over the years (many of them very intelligent and well educated individuals) have little or no familiarity with David Hume, let alone with any particular argument he championed. Even among those who took an introductory philosophy course back in junior college, few seem to remember much of anything about Hume.
The latter expectation, or rather hope, strikes me as rather devious and scheming. The problem of induction neatly lends itself as a ready gateway to a god-of-the-gaps style apologetic.
One’s initial reaction to the problem of induction may have a lot to do with how it is presented in the first place. Ostensibly, Hume sought to produce an actual argument which draws a clear conclusion, namely one which makes an assessment of induction bringing its reliability into serious question. In the apologist’s hands, however, the actual guts of Hume’s argument tend to remain obscure while its conclusion, taken more or less for granted, is positioned as an interrogatory device.
James Anderson’s own encapsulation of the problem of induction provides an example of what we may expect from apologists. In his seminal paper Secular Responses to the Problem of Induction, Anderson offers the following summary:
The basic problem can be summarised as follows. Suppose that we observe a large number of objects with characteristic A, noting that all of them also possess characteristic B. It is natural for us to conclude that, in all probability, all objects with A also possess B — including those objects with A that have yet to be observed (or cannot be observed). The question posed by Hume is: What rational justification is there for making this inference? More generally, what reason do we have to believe that our conclusions about observed instances may be extended (even with probability) to include unobserved instances? The same basic question is most frequently framed in temporal terms: What reason do we have to think that we can draw reliable conclusions about future (unobserved) instances on the basis of past (observed) instances?
Now while the intention of positioning the problem of induction as essentially a question which screams out for an answer is apparently to lay a heavy burden on non-Christians and thus gum up any position they may affirm or objection they may raise against theism, the question itself can in fact be easily dispatched: we can rationally justify drawing general inferences from limited samples presented in our experience by an application of the axioms, the primacy of existence and the objective theory of concepts. Since no actual argument is given here, we solve the basic problem as it is summarized not by presenting a refutation (again, there’s no argument to rebut), but by providing a direct answer to the question which informs that summary. And hopefully my answer would generate a deeper discussion of the conceptual nature of induction and the reasons why it vindicates the rational alternative to the theistic paradigm defended by the apologist.
Contrast Anderson’s summary above with Leah Henderson’s reconstruction of Hume’s own case for his skeptical conclusion, found in the Stanford Encyclopedia of Philosophy:
Hume’s argument concerns specific inductive inferences such as:All observed instances of A have been B.
The next instance of A will be B.Let us call this “inference I”. Inferences which fall under this type of schema are now often referred to as cases of “simple enumerative induction”. Hume’s own example is:All observed instances of bread (of a particular appearance) have been nourishing.
The next instance of bread (of that appearance) will be nourishing.Hume’s argument then proceeds as follows (premises are labeled as P, and subconclusions and conclusions as C):
- P1. There are only two kinds of arguments: demonstrative and probable (Hume’s fork).
- P2. Inference I presupposes the Uniformity Principle (UP).
- P3. A demonstrative argument establishes a conclusion whose negation is a contradiction.
- P4. The negation of the UP is not a contradiction.
- C1. There is no demonstrative argument for the UP (by P3 and P4).
- P5. Any probable argument for UP presupposes UP.
- P6. An argument for a principle may not presuppose the same principle (Non-circularity).
- C2. There is no probable argument for the UP (by P5 and P6).
- C3. There is no argument for the UP (by P1, C1 and C2).
- P7. If there is no argument for the UP, there is no chain of reasoning from the premises to the conclusion of any inference that presupposes the UP.
- C4. There is no chain of reasoning from the premises to the conclusion of inference I (by P2, C3 and P7).
- P8. If there is no chain of reasoning from the premises to the conclusion of inference I, the inference is not justified.
- C5. Inference I is not justified (by C4 and P8).
Of course, one could spend quite a while picking apart Henderson’s rendition of Hume’s case against the reliability of induction. I won’t do that here, but I will offer a couple of objections.
One way would be to challenge premise P4: “The negation of the UP is not a contradiction.” Rather, it strikes me that if one were to affirm the negation of the Uniformity Principle, he would be essentially saying that it nature is not uniform. Is it the case, then, that nature is not uniform uniformly? To negate the Uniformity Principle would itself be a general statement about nature as such, and thus imply a uniformity to the negation itself as an act as well as to what is being negated. I don’t see how that would not be self-contradictory.
Another approach to challenging this premise would involve examining its conceptual roots. We can point out, for example, that categorizing a statement as a negation would require forming the concept ‘negation’ in the first place. But to form the concept ‘negation’ would imply the sharing of across-the-board similarities among all units subsumed by the concept ‘negation’; i.e., to have any stable meaning itself, the concept ‘negation’ would include only those instances which share the essential feature(s) which distinguishes a negation from anything else. But this implies uniformity as a precondition necessary to forming the concept as such. In other words, the concept ‘negation’ would have no uniform meaning across instances of its use unless nature itself were uniform, indeed unless the UP obtained independently already as an underlying precondition. This in turn tells us that a negation of the UP would necessarily commit the fallacy of the stolen concept, which is a type of self-contradiction. So the argument as framed here contains a defective premise – namely a premise which cannot be accepted as true.
Another way to challenge the argument would consist of an investigation into the argument’s premises and desired conclusions for their own reliance on induction, the very mechanism whose reliability the argument aims to undermine. If one were to claim that mathematics is unreliable and that he could demonstrate this by means of a mathematic proof, we should rightly dismiss his claim for relying on what he expressly sets out to repudiate. Similarly, if one argues for the conclusion that inductive inferences cannot be accepted as reliable and yet his argument to this effect contains premises which were drawn by means of inductive inferences, should we also not likewise consider that case suspect?
The argument as reconstituted in the SEP seems rife with such instances. For example, consider premise P2: “Inference I presupposes the Uniformity Principle (UP).” While the premise is cast in the singular and thus appears to be about one specific premise, it is in fact intended to represent all inferences of “simple enumerative induction,” as the quoted portion makes clear. Thus the premise in fact affirms a general statement, presumably including both observed as well as unobserved instances of “simple enumerative induction.” But how then can one know that premise P2 is generally true without applying induction? It certainly does not denote a fundamental fact whose truth is perceptually self-evident. Rather, the premise seems to rely on the very faculty which the argument aims to discredit.
Likewise consider premise P5: “Any probable argument for UP presupposes UP.” This too affirms a scope of general proportions, as if to say “all probable arguments for UP presuppose UP.” But how would one know this without using induction? Indeed, while often we are told that inductive conclusions can only be accepted as probable, the conclusion that “all probable arguments for UP presuppose UP” is not only a general statement, and thus smacks of one drawn inductively, it also seems to be affirmed as a certainty to which there can be no exception.
If arguments against the reliability of induction are themselves defective (indeed, any argument which seeks to establish a general conclusion about all instances of induction would itself seem unable to get off the ground without induction being reliable in the first place), then there may be a reason why apologists prefer simply to cast the problem of induction as a series of questions instead of presenting an argument to begin with.
Going back to Anderson’s summary quoted above, who else caught the phrase “more generally” opening the fifth sentence of the paragraph? If the problem here constitutes a call to argue for a justification which applies “generally,” doesn’t the very way the problem is so framed thus invite one to enlisting an inductive process in order to justify induction? Apologists who raise the problem of induction often seem eagerly ready to pounce on all responses to the problem of induction as defective by virtue of arguing in a circle. “You’re assuming what the Hume’s argument calls into question!” they will retort. Thus you’re guilty of begging the question.
To top it off, apologists seem to think that the problem of induction can be solved by affirming some variant of theism. This strikes me as rather unself-aware. For it is by means of induction that we can infer knowledge from things observed to things unobserved, and the problem of induction is raised to call such inferences into question. We can’t know, we’re told, about things we cannot observe by reference to what we can and do observe. And yet, this problem, we are also told, is averted by asserting the reality of something allegedly existing in a realm which we can never observe. We cannot perceive – and thus cannot observe – a supernatural being which allegedly wished the universe into being and which allegedly “sustains” all the order we do observe in our experience. So it seems that the very objection that we cannot justify induction because we cannot know beyond what we can immediately observe, would rule out the “solution” which apologists themselves propose as their answer to Hume’s problem, for the very same reason they raise it.
I’m glad these aren’t my problems!
by Dawson Bethrick