Popper’s Logic of Scientific Discovery
A deservedly well-regarded tour-de force tackling the problem of the nature of knowledge and of its growth by considering the best examples: in science. The keys are the exercise of critical faculties, not being dogmatically reliant on any one method, and testing theories.
His recommended approach is based on falsification: one ignores as meaningless theories that cannot in principle be falsified, but looks for critiques and data that seems most likely to be diagnostic between candidate theories, or to falsify the one theory that one has.
He is critical of induction and probability. Instead of regarded induction as indicating that a theory is true with some probability one has regard to ‘the degree of corroboration’. Instead of acting on what one believes to be ‘true’, one acts on what has been adequately corroborated. Popper focusses on critiquing the work of others, but his approach seems reasonably compatible with those of Kant and Keynes. Popper, like them, notes that there could be processes that are neither deterministic nor random (in the sense of total absence of regulation), and hence there is non-probabilistic ‘objective’ uncertainty, and emphasises at length the non-probabilistic nature of scientific uncertainty.
He develops an example of a possible measure of ‘degree of corroboration’ that conflates Keynes’ likelihoods and conventional priors, and discusses the problems of priors at length. He explains the advantages over Keynes’ ‘weights of evidence’ but on the other hand, in my view:
- One often wants to compute degree of corroboration incrementally, which i practice would mean keeping track of the likelihood and then treating the degree of corroboration as a kind of change of scale. In which case, why not use likelihood or weight of evidence directly?
- The main advantage that Popper highlights in viii of 10.1 of appendix ix. But the odd behaviour here is due to the use of a definition of likelihood that (as Jack Good showed)is inappropriate for imprecise hypotheses.
The preface (1959) is full of important observations such as:
- That reflexivity is at the root of logical paradoxes.
- That formal languages that are applicable to the growth of scientific knowledge cannot both be precise.
The text is also dotted with helpful insights, such as pointing out that the existence of causes or off statistical stability should never be taken for granted. We may act – pragmatically – as if we are making these assumptions, but we should always critique them and – where appropriate – test them.
KR Popper Realism and the aim of Science 1982 (the first volume of the postscript)
This gives Popper’s propensity interpretation of probability and clarifies the concepts of induction and falsifiability.
KR Popper The Open Universe: an argument for indeterminism 1982 (second volume)
This argues that rationality is limited in respect of the prediction of the growth of human knowledge.
KR Popper Quantum Theory and the schism in Physics 1982
Popper conjectures that the problems of interpretation of quantum mechanics can be traced to problems of the interpretation of the calculus of probability, and develops his propensity theory.
- Kant’s Critique of Pure Reason
- Keynes’ Treatise on Probability
- Good’s Good Thinking, which links Keynes to Popper