Abstract
Abstract Lakatos’s analysis of progress and degeneration in the Methodology of Scientific Research Programmes is well-known. Less known, however, are his thoughts on degeneration in Proofs and Refutations. I propose and motivate two new criteria for degeneration based on the discussion in Proofs and Refutations – superfluity and authoritarianism. I show how these criteria augment the account in Methodology of Scientific Research Programmes, providing a generalized Lakatosian account of progress and degeneration. I then apply this generalized account to a key transition point in the history of entropy – the transition to an information-theoretic interpretation of entropy – by assessing Jaynes’s 1957 paper on information theory and statistical mechanics.
Highlights
Lakatos (1976/2015) argued in Proofs and Refutations (P&R) that the comprehension of mathematical concepts must be accompanied with a clear understanding of how and why these concepts came into existence
The stated motivations for his paper (Jaynes 1957, p. 261) suggest preliminary grounds for concern about superfluity. Jaynes claims that his primary motivations are (i) bringing in new mathematical machinery to statistical mechanics, and (ii) the notion that information theory is “felt by many people to be of great significance for statistical mechanics”, “the exact way in which it should be applied has remained obscure.”
In this paper we suggest a reinterpretation of statistical mechanics which accomplishes this, so that information theory can be applied to the problem of justification of statistical mechanics. (Jaynes 1957, p. 621)
Summary
Lakatos (1976/2015) argued in Proofs and Refutations (P&R) that the comprehension of mathematical concepts must be accompanied with a clear understanding of how and why these concepts came into existence. Deductivist style tears the proof-generated definitions off their ‘proof-ancestors’, presents them out of the blue, in an artificial and authoritarian way It hides the global counterexamples which led to their discovery. This tells us how a mathematical theory or concept ought to grow, from a rough primitive conjecture to a proof-generated concept (and beyond), through the use of heuristics like employing counterexamples, discovering hidden lemmas, and so on. While Lakatos paints a clear picture as to how mathematical theories grow, he is much less explicit about degeneration This is curious because the term “degeneration” seems to bear significant normative weight in Lakatos’s appraisal of research methodologies. My goal here is to remedy this situation by explicating Lakatos’s account of degeneration in terms of two distinct criteria
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