24‐hour period) that there ever have been and ever will be.
The limitations of human experience, however (the fact that we can’t experience every single day), justify us in forming only the less strong ‘some’ sentence:
The sun has risen on every day (every 24‐hour period) that humans have recorded their experience of such things.
This weaker formulation, of course, enters only the limited claim that the sun has risen on a small portion of the total number of days that have ever been and ever will be; it makes no claim at all about the rest.
But here’s the catch. From this weaker ‘some’ sentence, one cannot construct a well‐formed deductive argument of the kind that allows the conclusion to follow with the kind of certainty characteristic of deduction. In reasoning about matters of fact, one would like to reach conclusions with the certainty of deduction. Unfortunately, induction will not allow it. There’s also another more complex problem lurking here that’s perplexed philosophers: induction seems viciously circular. It seems in fact to assume the very thing it’s trying to prove. Consider the following.
Assuming the uniformity of nature?
Put at its simplest, the problem of induction can be boiled down to the problem of justifying our belief in the uniformity of nature or even reality across space and time. If nature is uniform and regular in its behaviour, then what’s been observed past and present (i.e. premises of an induction) is a sure guide to the so far unobserved past, present, and future (i.e. the conclusion of an induction).
The only basis, however, for believing that nature is uniform is the observed past and present. We can’t then, it seems, go beyond observed events without assuming the very thing we need to prove – that is, that unobserved parts of the world operate in the same way as the parts we observe. In short, inductively proving that some bit of the world is like other bits requires already assuming that uniformities of that sort hold.
Induction undertakes to prove the world to be uniform in specific ways; but inductive inference already assumes that the world is relevantly uniform.
We can infer inductively that the sun will rise tomorrow on the basis of what it’s done in the past (i.e. that the future will resemble the past) only if we already assume that the future will resemble the past. Eighteenth‐century Scot David Hume has remained an important philosopher in part precisely for his analysis of this problem.
Believing, therefore, that the sun may possibly not rise tomorrow is, strictly speaking, not illogical, since the conclusion that it must rise tomorrow does not inexorably follow from past observations.
A deeper complexity
Acknowledging the relative weakness of inductive inferences (compared to those of deduction), good reasoners qualify the conclusions reached through it by maintaining that they follow not with necessity but only with probability (i.e. it’s just highly probably that the sun will rise tomorrow). But does this fully resolve the problem? Can even this weaker, more qualified formulation be justified? Can we, for example, really justify the claim that, on the basis of uniform and extensive past observation, it is more probable than not that the sun will rise tomorrow?
The problem is that there is no deductive argument to ground even this qualified claim. To deduce this conclusion successfully we would need the premise ‘what has happened up until now is more likely to happen tomorrow’. But this premise is subject to just the same problem as the stronger claim that ‘what has happened up until now must happen tomorrow’. Like its stronger counterpart, the weaker premise bases its claim about the future only on what has happened up until now, and such a basis can be justified only if we already accept the uniformity (or at least probable continuity) of nature. But again, the uniformity (or continuity) of nature is just what’s in question.
A groundless ground?
Despite these problems, it seems that we can’t do without inductive generalisations and inductive reasoning generally. They are (or at least have been so far!) simply too useful to refuse. Inductive generalisations compose the basis of much of our scientific rationality, and they allow us to think about matters concerning which deduction must remain silent. In short, we simply can’t afford to reject the premise that ‘what we have so far observed is our best guide to what is true of what we haven’t observed’, even though this premise cannot itself be justified without presuming itself.
There is, however, a price to pay. We must accept that engaging in inductive generalisation requires that we hold an indispensable belief which itself, however, must remain in an important way unjustified. As Hume puts it: ‘All our experimental conclusions proceed upon the supposition that the future will be conformable to the past. To endeavour, therefore, the proof of this last supposition by probable arguments … must be evidently going in a circle, and taking that for granted, which is the very point in question’ (Enquiry Concerning Human Understanding, 4.19). Can we accept reasoning and sciences that are ultimately groundless?
SEE ALSO
1 1.1 Arguments, premises, and conclusions
2 1.2 Deduction
3 1.7 Fallacies
4 2.4 Analogies
5 5.5 Hume’s fork
READING
Francis Bacon (1620). Novum Organum
David Hume (1739). A Treatise of Human Nature, Bk 1, Part 3, Section 6
D.C. Stove (1986/2001). The Rationality of Induction
* Colin Howson (2003). Hume’s Problem: Induction and the Justification of Belief
1.4 Validity and soundness
In his book, The Unnatural Nature of Science, the eminent British biologist Lewis Wolpert (b. 1929) argued that the one thing that unites almost all of the sciences is that they often fly in the face of common sense. Philosophy, however, may exceed even the (other?) sciences on this point. Its theories, conclusions, and terms can at times be extraordinarily counterintuitive and contrary to ordinary ways of thinking, doing and speaking.
Take, for example, the word ‘valid’. In everyday speech, people talk about someone ‘making a valid point’ or ‘having a valid opinion’. In philosophical speech, however, the word ‘valid’ is reserved exclusively for arguments. More surprisingly, a valid argument can look like this:
1 All blocks of cheese are more intelligent than any philosophy student.
2 Meg the cat is a block of cheese.
3 Therefore, Meg the cat is more intelligent than any philosophy student.
All utter nonsense, you may think, but from a strictly logical point of view this is a perfect example of a valid argument. How can that be so?
Defining validity
Validity is a property of well‐formed deductive arguments, which, to recap, are defined
