What
is induction?
What would justify a person in using it?
Does Hume show that no one is justified in using it?
Greg Detre
@ 11.30 on Thursday, 8 February 2001
Lucy Allais, History of Philosophy IV
As I walk around inside my mind, amidst the �great, booming, buzzing confusion�[1], banging my shins against furniture and watching the motion of the celestial bodies, David Hume points out that these regularities upon which my life is based cannot be rationally justified. Now, I look around with trepidation, wondering at every moment whether the laws of gravity will cease to hold when I am in a lift, and whether my opponent is going to thrash me in this evening�s pool Cuppers match by turning my na� assumption about the predictable motion of the balls against me. He points out that there is no argument by which I might know that the laws of nature, especially of cause and effect, will hold true in the future just because they have always held to my knowledge in the past.
In order to do this, he has to first draw a distinction between what he sees as the two methods of acquiring understanding: relations of ideas, and matters of fact. This distinction could be seen in terms of the a priori, reason-based approach vs the a posteriori, experience-based approach. Relations of ideas helps us in our logical and mathematical enquiries, and allows us to deduce demonstratively necessary truths, but cannot help us in the world of the senses, where we rely on moral and empirical knowledge about matters of fact.
By �matters of fact� then, he is referring to whenever we think we know about something (or someone), understand its reasons, or can explain or predict their behaviour. This understanding is based upon our inescapable, internal causal model of the world, based on a faith in the uniformity (and accessibility) of the laws of nature. That is to say, our talk of causality is intuited from regularities in the constant conjunction of� events. At the root of all our knowledge about the world is our Custom, the inductive custom, to assume that because things have been a certain way in the past, they will continue to be in the future. In Hume�s words, �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�. Every time an event A precedes an event B, our expectation that this will occur in the future approaches an even greater certainty. �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.� Here, Hume is demonstrating a different use of induction, i.e. that because the properties of an object (which he terms �secret powers�) give rise to its fitting into our causal schema in a certain way, another object that resembles the first will behave similarly.
The problem with this inductive principle is that, although it has proved very successful in our dealings with the world, we cannot deduce that the world should and will continue to be inductible. The inductive principle is based wholly on experience, and no chain of reasoning can demonstrate a priori why things should necessarily follow the particular causal relationships we have come to expect them to. Any evidence from experience (including scientific evidence) which supports or explains the causal relations, itself begs the same question, i.e. it too assumes that the future will resemble the past. It certainly seems that it must be the case that induction is non-rational since peasants, infants and animals are all perfectly able to see causal connections in everything around them. And if I ask you to show me the chain of reasoning that you maintain affirms this connection, and you hesitate or ramble intricately, then this cannot be the same argument that all babes and �brute beasts� are so easily and intuitively able to employ.
The inductive principle operates very differently to deduction. Deduction demonstrates necessary truths � on the basis of a syllogism or a single instance, we can deduce that the angles in all triangles will add up to 180�, for instance. The denial of a deductive truth implies a contradiction. Testing hundreds of triangles will not increase our certainty, and if we were to find an exception, we would seek to account for it by an error in our reasoning. In contrast, our certainty about an inductive truth grows with every new instance we find that supports it.
Russell considers the problem of induction in terms of the uniformity of nature. In exceptional-seeming cases like the sun not rising tomorrow, science maintains the ultimate assumption that any general rules which do admit exceptions will eventually yield to general rules which have no exceptions. On this basis, we have been able to objectify our individual, internal models of the world mathematically, giving greater power and accuracy to our inductive truths, though without granting them any greater epistemological weight. He also considers the argument that whenever we have asked this question before, the future has become the past, and has always resembled the distant past. But of course, just because past futures have resembled past pasts, we are still no more certain that they will necessarily resemble all future futures. Russell also notes that we should strictly speak in terms of �fresh instances� rather than just the future, since uniformity has to be universal in time and space.
Is Hume right then in claiming that we as philosophers have no justification for our causal expectations? Well, we started by noting how well we can function in our world, and it seems nonsense to ask whether we are justified in employing a principle that is so clearly efficacious. But this is missing the point. Hume is a pragmatist, and recognises explicitly Nature�s wisdom in imbuing us with this automatic, non-rational mechanism for navigating our world. But, as rationalist philosophers, do we have any justification, i.e. by argument, for induction?
As mentioned above, any justification or argument for induction cannot itself rely on induction at any point, so it must be deductive, i.e. it must show that every inductively correct argument can be converted to a deductively valid one without reference to experience. Thus, Hume rejects the following argument that seems initially tempting:
(1) Past A-events have always been followed by B-events
(2) The future will resemble the past
�\
(3) If there is an A-event, there will be a B-event (or: present and future A-events will continue to be followed by B-events)
(2) is the premise doing the most work and is the one that Hume thinks we cannot accept without resorting to induction. On its own, (2) is not self-evident, and it is not demonstrable (its denial does not imply a contradiction), so the argument falls down.
This would seem to lead us to inductive scepticism, so we try and reject a premise, namely our assumption that �induction is rational only if it can be justified�. This is what Strawson opts to do, by arguing that �relying on induction is part of what it means to be rational, therefore induction is rational even if it cannot be justified�[2]. �It is an analytic proposition that is is reasonable to have a degree of belief in a statement which is proportional to the strength of the evidence in its favour; and it is an analytic proposition � that, other things being equal, the evidence for a generalisation is strong in proportion as the number of favourable instances, and the variety of circumstances in which they have been found, is great. So to ask whether it is reasonable to place reliance on inductive procedures is like asking whether it is reasonable to proportion the degree of one�s convictions on the strength of the evidence. Doing this is what �being reasonable� means in context.�[3]
This hinges on the statement that the strength of the evidence is proportional to the number of instances and variety of circumstances, which might be regarded as question-begging � for surely this �analytic� proposition is already �[making] a normative claim to the effect that inductive evidence is genuine or good evidence for a proposition�.
He also argues (the �ordinary language argument�) that to ask whether induction is a justified or justifiable procedure does not make sense. He is attacking our notion of what it means for something to be justified, or to require justification. By arguing that justification need not be deductive or demonstrative, he is effectively arguing that the force of the inductive principle is enough for it to be self-justifying. At one point, he appears to be arguing that �justification� as we use it in ordinary language always refers to an inductive justification, so it is no longer clear what the question means when we ask whether an inductive standard itself is reasonable, just as it makes little sense to ask whether the law is legal, for instance. It makes sense to ask about whether particulars fit in with the general principle, e.g. whether individual laws are legal, or whether a given belief is justified � but to ask whether the general principle from which we derive the reasonableness is itself reasonable � can this be reasonable? There is no higher standard by which to measure the reasonableness of inductive standards themselves.
Can we not simply reply to the ordinary language argument that philosophy, certainly analytic philosophy, is the business of seeking certain knowledge. Inductive justification is never wholly certain. Only deductive knowledge can be. Therefore, when a philosopher asks the question of whether or not a given approach is justified (other than circularly), he is clearly seeking some extraneous, deductive proof � as Hume clearly states. Yes, of course the principle of induction is reasonable, but it is not rational. After all, if it was only inductive proof that philosophy required, we would be back to natural philosophy, rather than rationalism, and metaphysics would boil down to physics, and there would be no difference in epistemic status between my opinion of what colour a pair of trousers is as opposed to an analytic proposition.
The entire discussion really ranges around the epistemic status of inductive truths. They seem to be somewhere in between deductive and purely empirical truths, since they rest securely and successfully on the internalist criteria of coherence and internal consistency in our world view. Indeed, it almost seems as though Hume prefers them to reason, insofar as they are not subject to error and are immediate and reliable. After all, what is there to elevate our reason above Custom other than the force, liveliness and steadiness of its conclusions?