Tag: induction

The asymmetry between verifiability and falsifiability

Again, the attempt might be made to turn against me my own criticism of the inductivist criterion of demarcation; for it might seem that objections can be raised against falsifiability as a criterion of demarcation similar to those which I my­self raised against verifiability.

This attack would not disturb me. My proposal is based upon an asymmetry between verifiability and falsifiability; an asymmetry which results from the logical form of universal statements. For these are never derivable from singular statements, but can be contradicted by singular statements. Consequently it is possible by means of purely deductive inferences (with the help of the modus tollens of classical logic) to argue from the truth of singular statements to the falsity of universal statements. Such an argument to the falsity of universal statements is the only strictly deductive kind of inference that proceeds, as it were, in the ‘inductive direction’; that is, from singular to univeral statements. [19]

Liberating science from authority

Empiricism never did achieve its aim of liberating science from authority. It denied the legitimacy of traditional author­ities, and that was salutary. But unfortunately it did this by setting up two other false authorities: sensory experience and whatever fictitios process of ‘derivation’, such as induction, one imagines is used to extract theories from experience.

The misconception that knowledge needs authority to be genuine or reliable dates back to antiquity, and it still prevails. To this day, most courses in the philosophy of knowledge teach that knowledge is some form of justified, true belief, where ‘justified’ means designated as true (or at least ‘probable’) by reference to some authoritative source or touch­stone of knowledge. Thus ‘how do we know … ?’ is transformed into ‘by what authority do we claim … ?’ The latter question is a chimera that may well have wasted more philosophers’ time and effort than any other idea. It converts the quest for truth into a quest for certainty (a feeling) or for endorsement (a social status). This misconception is called justificationism.

The opposing position – namely the recognition that there are no authoritative sources of knowledge, nor any reliable means of justifying ideas as being true or probable – is called fallibilism. To believers in the justified-true-belief theory of knowledge, this recognition is the occasion for despair or cynicism, because to them it means that knowledge is un­attainable. But to those of us for whom creating knowledge means understanding better what is really there, and how it really behaves and why, fallibilism is part of the very means by which this is achieved. Fallibilists expect even their best und most fundamental explanations to contain misconceptions in addition to truth, and so they are predisposed to try to change them for the better. In contrast, the logic of justificationism is to seek (and typically, to believe that one has found) ways of securing ideas against change. Moreover, the logic of fallibilism is that one not only seeks to correct the misconceptions of the past, but hopes in the future to find and change mistaken ideas that no one today questions or finds problematic. So it is fallibilism, not mere rejection of authority, that is essential for the initiation of unlimited know­ledge growth – the beginning of infinity. [8-9]

An explanatory gap

An analogous gap exists in Popperian epistemology. Its critics wonder why the scientific method works, or what justifies our reliance on the best scientific theories. This leads them to hanker after a principle of induction or something of the sort (though, as crypto-inductivists, they usually realize that such a principle would not explain or justify anything either). For Popperians to reply that there is no such thing as justification, or that it is never rational to rely on theories, is to provide no explanation. Popper even said that ‘no theory of knowledge should attempt to explain why we are success­ful in our attempts to explain things’ (Objective Knowledge p. 23). But, once we understand that the growth of human knowledge is a physical process, we see that it cannot be illegitimate to try to explain how and why it occurs. Episte­mology is a theory of (emergent) physics. It is a factual theory about the circumstances under which a certain physical quantity (knowledge) will or will not grow. The bare assertions of this theory are largely accepted. But we cannot possibly find an explanation of why they are true solely within the theory of knowledge per se. In that narrow sense, Popper was right. The explanation must involve quantum physics, the Turing principle and, as Popper himself stressed, the theory of evolution. [341]

Corroboration and refutation

Well, Popperians might speak of a theory being the best available for use in practice, given a certain problem-situation. And the most important features of a problem-situation are: what theories and explanations are in contention, what arguments have been advanced, and what theories have been refuted. ‘Corroboration’ is not just the confirmation of the winning theory. It requires the experimental refutation of rival theories. Confirming instances in themselves have no significance. …

Under inductivism, observation was supposed to be primary. One imagined a mass of past observations from which the theory was supposed to be induced, and observations also constituted the evidence which somehow justified the theory. In the Popperian picture of scientific progress, it is not observations but problems, controversies, theories and criticism that are primary. Experiments are designed and performed only to resolve controversies. Therefore only experimental results that actually do refute a theory – and not just any theory, it must have been a genuine contender in a rational controversy – constitute ‘corroboration’. And so it is only those experiments that provide evidence for the reliability of the winning theory. …

And even then, the ‘reliability’ that corroboration confers is not absolute but only relative to the other contending theories. That is, we expect the strategy of relying on corroborated theories to select the best theories from those that are proposed. That is a sufficient basis for action. We do not need (and could not validly get) any assurance about how good even the best proposed course of action will be. Furthermore, we may always be mistaken, but so what? We cannot use theories that have yet to be proposed; nor can we correct errors that we cannot yet see. [148-9]

Ever since Galileo

I have described Galileo’s new conception of our relationship with external reality as a great methodological discovery. It gave us a new, reliable form of reasoning involving observational evidence. That is indeed one aspect of his dis­covery: scientific reasoning is reliable, not in the sense that it certifies that any particular theory will survive unchanged, even until tomorrow, but in the sense that we are right to rely on it. For we are right to seek solutions to problems rather than sources of ultimate justification. Observational evidence is indeed evidence, not in the sense that any theory can be deduced, induced or in any other way inferred from it, but in the sense that it can constitute a genuine reason for preferring one theory to another.

But there is another side to Galileo’s discovery which is much less often appreciated. The reliability of scientific reason­ing is not just an attribute of us: of our knowledge and our relationship with reality. It is also a new fact about physical reality itself, a fact which Galileo expressed in the phrase ‘the Book of Nature is written in mathematical symbols’. As I have said, it is impossible literally to ‘read’ any shred of a theory in nature: that is the inductivist mistake. But what is genuinely out there is evidence, or, more precisely, a reality that will respond with evidence if we interact appropriately with it. Given a shred of a theory, or rather, shreds of several rival theories, the evidence is available out there to enable us to distinguish between them. Anyone can search for it, find it and improve upon it if they take the trouble. They do not need authorization, or initiation, or holy texts. They need only be looking in the right way – with fertile problems and promising theories in mind. This open accessibility, not only of evidence but of the whole mechanism of knowledge acquisition, is a key attribute of Galileo’s conception of reality. [94]

The power of logic

Most people think that the purpose of an argument is to justify its conclusion — and to thereby establish its certainty — and that the problem with inductive arguments is that they fail to establish their conclusions with objective certainty since their conclusions may be false even if all of their premises are true. But this entirely confuses the issue, and it has even enabled inductivists to take the high ground in the debate, arguing that objective certainty is an impossible dream, and that inductive arguments are not, as a consequence, at fault for failing to achieve it.

But if the uncertainty of their conclusions were the problem with inductive arguments, then we would also have a similar problem with deductive arguments. For the premises of a deductive argument may be false. And the conclusion of a deductive argument may be false as well.

Contrary to what most people think, logical arguments cannot establish the truth, let alone the certainty, of their con­clusions. And so contrary to what most people think, the problem with inductive arguments has nothing to do with the uncertainty of their conclusions.

The best that a logical argument can do is test the truth of a statement. But it can do this only by showing that its falsity is inconsistent with the truth of other statements that can only be tested and never proved. Our so-called ‘proof’ methods are really techniques for testing consistency. And the demonstration that a ‘conclusion’ follows from a ‘premise’ shows only that the falsity of the ‘conclusion’ is inconsistent with the truth of the ‘premise.’

That is all that is involved.

But so long as we regard contradictions as unacceptable, it is really quite a lot.

The inconsistency that marks a valid deductive argument — the inconsistency, that is, between the truth of is premises and the falsity of its conclusion — cannot force us to accept the truth of any belief. But it can force us, if we want to avoid contradicting ourselves, to reexamine our beliefs, and to choose between the truth of some beliefs and the falsity of others — because the falsity of the conclusion of a valid argument is inconsistent with the truth of its premises. …

And this is just another way of saying that what we call a proof actually presents us with the choice between accepting its conclusion and rejecting its premises. …

We construct logical arguments in order to persuade others of our beliefs. But the best we can do is to clarify a choice that they have to make. Inductive arguments, however, cannot even do this. [86-7]