Guest blogging is Lee Kelly in response to last night’s post by Gene Callahan on Karl Popper.
Yesterday, on his blog, Gene Callahan claimed that Popper did not solve the problem of induction. He produced familiar arguments claiming that Popper ‘sneaked induction in through the back door.’. These arguments, which have already been ably refuted by David Miller in his Critical Rationalism: A Restatement and Defence, are either logically flawed or radically misconstrue the position they suppose to be attacking. Contrary to these arguments, Popper’s solution to the problem of induction is not so much to be found in the act of falsification, but rather in the conjectural (unjustified and unjustifiable) character of our knowledge, especially our scientific knowledge.
I’ll break down my response into three separate counterarguments, each against a slightly different and more sophisticated manifestation of this kind of argument.
(1) A theory which is falsified by some observation-statement today is still falsified by it tomorrow, next week, a month later, and forever after. This is not induction. The falsifying relation is deductive and timeless–to say that it will continue to hold in the future is to be merely logically consistent.
A mathematician is not inducing when he concludes that ‘1 + 1 = 2’, which is true today, will continue to be true tomorrow. If there is no pretense of having derived the future from the past, then there is no attempted induction. The mathematician concludes that ‘1 + 1 = 2’ will continue to be true tomorrow because its negation is inconsistent–a deductive inference.
The falsifying relations between statements are analogous to the above equation. If a theory is falsified by some statement today, then it will continue to be falsified by it tomorrow. Whether we will continue to believe that the falsifying statement is true tomorrow is irrelevant to the logic of the situation.
(2) Gene equivocates between a theory’s falsity and its instrumental value. Past evidence, even falsification, does not imply anything about a theory’s future usefulness. Indeed, many falsified theories continue to have instrumental value within a limited domain, e.g. building bridges with Newtonian physics.
Indeed, we actually have falsifiable hypotheses about the instrumental value of different theories, and we regularly, by stress testing technology built with their aid, push the boundaries of their application.
(3) However, Gene is presumably hinting at a more specific issue: what about repeated instances of the same experiment? Just because an experiment falsified a theory today, it does not follow that repeating the same experiment will produce another falsification tomorrow. There are two sides to this argument that I wish to address.
(a) In practice, what counts as the ‘same experiment’ is a tricky matter. By assumption, our two experiments occur today and tomorrow, but tomorrow the earth will be in a slightly different position, it’ll be Saturday rather than Friday, the universe will have expanded some, and we will have used the restroom a few more times, and that is to name only a handful of facts we’re aware of. One experiment is only the same as another relative to higher-order hypotheses about which facts are relevant–those particular facts we want to replicate and those we are free to ignore. These higher-order hypotheses may themselves be mistaken, and so there is no guarantee we are, objectively, performing the ‘same experiment’ at all.
This is, of course, a classic argument against the utility of induction–what counts as two or more instances of the same observation depends on which facts we arbitrarily deem irrelevant to the situation. In principle, infinitely many different conclusions could be induced from the same set of observations–unaided induction has no power to select between competing interpretations.
In any case, this is not a problem for the logic of falsifiability, since it is entirely deductive. All the necessary assumptions are included in the premises. Of course, some of the premises of our argument may be false, such as the higher-order hypotheses mentioned before, but that is merely a reflection of our fallibility rather than the logic of falsifiability itself. This contrasts, for example, with unaided induction where, even if we assume different parties had the same observations, no particular conclusion follows.
(b) Putting such issues aside, let us assume, for the sake argument, that our experiment tomorrow really will be the same as today’s, i.e. all relevant facts to the experimental situation will hold constant. In this case, does it follow from our past falsifying observations that a theory will continue to be falsified by the same experiment in the future? Of course not, because induction is invalid.
Past observations, falsifying or otherwise, cannot inform us whether, or to what degree, the universe exhibits regular patterns. For example, as Popper argued, the universe may be intrinsically indeterminate and its fundamental laws only describable as probabilities. (In which case ‘an experimental test’ may actually involve many individual experiments to generate a comparable sequence of results.) Alternately, perhaps there are no stable regularities at all, deterministic or otherwise, and any apparent uniformity is mere illusion or fluke.
As I describe in this post on the Critical Rationalism Blog, falsifiability need not assume anything like the uniformity of nature. We search for regularities, but we don’t have to presuppose our own success in finding them.
Just as we may conjecture that a theory is true, without any pretense of having derived it from observation, so we can also conjecture that a theory falsified by an experiment will continue to be falsified by repeating the experiment in the future. Sometimes such conjectures are, in their turn, falsified, and we may be led to question other assumptions we had made about the experimental situation, even metaphysical ideas like determinism. So it is that science might progress, by conjecturing regularities about the universe (not assuming them), including regularities about the results of repeated experiments, and ruthlessly criticising them by any means at our disposal.
It may seem trivial, but the way to avoid induction is merely to argue validly. That is, we should not pretend, per impossibile, to logically derive our theories from observation. While observations, interpreted in the light of theories, may inspire a new conjecture, there is no logical inference from one to the other. Logic is best reserved for a critical role, i.e. to help select between competing conjectures, whether they’re inspired by particular observations or discovered after banging one’s head on the bathroom sink while trying to hang a clock. Even should an adequate theory of inductive inference be formulated, it would serve no purpose, because it betrays a preoccupation with where theories come from, or what justifies them, rather than their truth or falsity–it’s the genetic fallacy applied to epistemology.
Gene is right to say that ‘these arguments are well known in the literature, and considered decisive by almost all professionals in the philosophy of science, which is why there are only a handful of Popperians left in the field.’ But these arguments are also wrong, and radically misunderstand the position which they purport to refute. Moreover, the counterarguments I make here are not elusive, neither in Popper’s original works nor that of his students. To me, this all speaks very badly of professionals in the philosophy of science; it suggests that something is very rotten, either with the institutions or the prevailing assumptions of the professional philosophic community. That’s not an idea that I welcome, but the treatment, both intellectually and personally, that Popper and others like him have received is nothing short of scandalous.
The problem of induction is solved, and we’re still waiting for the professionals to catch up.