A note on a Kuhnian-Lakatosian reading of the debate between realism and constructivism in logic

I suggest a programmatic interpretation of the opposition between realism and constructivism in logic via Kuhn’s and Lakatos’ theories for the historical and conceptual development of science. I claim that realism forms a Kuhnian paradigm constituted by a semantic side, given by Tarskian model-theory, and a foundational side, given by axiomatic set-theory. Constructivism is seen as a more flexible Lakatosian research programme, instantiated by a number of theories. More specifically, I consider Prawitz’s proof-theoretic semantics, for the semantic side, and Martin-Löf’s type theory, for the foundational side. The reading presupposes a preliminary discussion of the question whether it makes sense to speak of logical revolutions, which is in turn just a special case of the broader question whether revolutions do occur in mathematics.