For a précis, see this Note1.
Write-up2 (as at 13/07/2020 13:23:31): Popper - Merits of Improbability
- This note provides my analysis of "Popper (Karl) - Corroboration: The Merits of Improbability". I must have written it as an undergraduate at Birkbeck, probably around 2002.
- It starts off with the text I originally wrote – which is a very detailed analysis. I wrote these analyses in that way to force myself to focus on the detail of the argument. Sometimes they are longer than the original paper. I doubt they are of any value to anyone other than me, but may provide a different “take” on the paper or chapter under review and may help someone to understand what’s going on.
- I’ve left this text substantially as it was, but may add further notes below to discuss some of the issues raised insofar as they impact on my research into Personal Identity.
- Popper denies that his theory of preference is for the “more probable” hypothesis. On the contrary, he claims to have shown that the testability of a theory rises with its information content, and therefore with its improbability (in the sense, he says, of the calculus of probability). The preferred hypothesis will therefore most often be the least probable. However, Popper rejects the notion – proposed by Harsanyi (see Philosophy 35, 1960) – that he adopts an “improbability criterion for the choice of scientific hypotheses”. Not only has he no “criterion”, but also often he cannot prefer the more improbable hypothesis on account of it having been proved empirically false. Even so, Popper has been thought perverse, yet he claims his argument is simple – “content = improbability” – and has even been espoused by such as Rudolf Carnap who promote inductivism and a probabilistic theory of induction3.
- Popper had originally introduced the term “degree of corroboration” to show that probabilistic theories of preference (or induction) are absurd. This term isn’t a mathematical “straw man” to be knocked down, but is “defined” with respect to a certain theory as
- an evaluation report at a certain time of the state of critical discussion, showing the way it solves its problems,
- its degree of testability,
- the severity of the tests it has undergone and (4) the way it has withstood these tests.
- Degree of corroboration thus evaluates past performance and is essentially comparative – one theory may be better corroborated than another up to time t. While it may lead us to prefer some theories to others, it says nothing about future performance or about the “reliability” of a theory. This evaluation would not be affected even should Popper’s or an alternative formulation of degree of corroboration be capable of quantification. Popper claimed that Lakatos believes that quantification of Popper’s theory would make it into a probabilistic theory of induction, making reference to The Problem of Inductive Logic, but now admits that he’d misunderstood the passage4.
- The purpose of Popper’s introduction of formulae as definitions of degree of corroboration was to show that in many cases the more improbable hypothesis is preferable and to show clearly in which cases it does and doesn’t hold. He claims to be able to show that preferability cannot be a probability in the mathematical sense. One can still call the more preferable theory the more probable, but mustn’t be misled by terms.
- In summary, we can often say – in Popper’s terms defined above – that one theory is preferable to, or better corroborated than, another. But, obviously, the degree of corroboration at a certain time says nothing about the future, being (in my words) just a “state of the art” report.
- Popper has to emphasise the provisional nature of the degree of corroboration, because some have misunderstood him as using corroboration as an index of the future performance of a theory. Popper quoted from LSD5 to the effect that he advocates, instead of talking of the probability of a hypothesis, that we should try to assess the tests it has withstood and assess how far it has proved its fitness to survive – how far it has been corroborated. People had thought that “prove its fitness to survive” meant fitness to withstand future tests.
- Popper denies having mixed the Darwinian metaphor. No one thinks species that have survived in the past will on that account survive in the future. All species that failed to survive some time t had survived up to t.
- Popper now turns to the degree of corroboration of a statement s that follows logically from a theory T, but is logically much weaker6 than the theory T to which it belongs. Since s will have less information content that T, s and the system S of all statements that can de deduced from s, will be less testable and corroborable than T. However, Popper thinks that because T has been well tested, its high corroboration applies to all it entails, and consequently s, attains a higher degree of corroboration than it ever could apart from T.
- Popper relates this to the thought that degree of corroboration is a means of stating preference with respect to truth. If we prefer T with respect to its claims to truth, we must logically prefer all its consequences, which are true if T is, even if they are less easy to test separately.
- Consequently, Popper claims, the degree of corroboration of statement s “The sun rises in Rome once every 24 hours”, itself not very well testable7, has risen following the corroboration of Newton’s theory and the description of the earth as a rotating planet, both of which are well testable and, if true, imply the truth of s. A statement s that is derivable from a well-tested theory T has, regarded as a part of T, the degree of corroboration of T. However, if it’s not derivable from T, but jointly from two theories T1 and T2, it will qua part of these theories, have the same degree of corroboration as the less well tested8 of T1 and T2. This is despite the possibility of s on its own having a very low degree of corroboration.
- The main difference between Popper’s and the inductivist’s approaches is that Popper stresses negative arguments, whereas the inductivist stresses “positive instances” from which (quoting Carl Hempel), “non-demonstrable inferences” can be drawn which are hoped to guarantee the “reliability” of the conclusions of these inferences. Popper’s view is that all that can be positive in scientific knowledge is so only insofar as certain theories are preferred to others in the light of critical discussions (including attempted refutations & empirical tests) up to a certain time.
- These negative methods, all that can be said to be positive, clarify many points such as explaining what’s meant by positive or supporting instances of a law.
Footnote 3: Footnote 4: Footnote 5: Footnote 6:
- This is the write-up as it was when this Abstract was last output, with text as at the timestamp indicated (13/07/2020 13:23:31).
- Link to Latest Write-Up Note.
- What’s this supposed to mean?
- Is this really less testable than these theories Popper suggests?
- This requires a proof. I suspect it of being too optimistic.
Text Colour Conventions (see disclaimer)
- Blue: Text by me; © Theo Todman, 2020