A Strongly Differing Opinion on Proof-Theoretic Semantics?

Abstract

Responding to an invitation from Peter Schroeder-Heister, the paper reacts to some criticisms of 'model theory' voiced among proof theorists interested in prooftheoretic semantics. It argues that the criticisms are poorly targeted: they conflate model theory with model-theoretic semantics and with the model-theoretic definition of logical consequence, which are three largely unrelated areas of study. On defining the meanings of logical constants, and of natural language expressions in general, the paper lays out some methodological requirements that any satisfactory definitions would need to meet, for example about generalisability from one context of use to other contexts. On defining logical consequence, the paper argues that some points made recently by Schroeder-Heister and Kosta Došen are largely sound and probably uncontroversial if clearly stated, but their impact is blurred by some question-begging formulations.Keywords Proof-theoretic semantics · Model-theoretic semantics · Definition of logical consequence · Tarski It was very kind of Peter Schroeder-Heister to invite me to contribute to this meaty conference. He said:. . . you would fit very well into this meeting, even though (or perhaps because) you have opinions that strongly differ from [those] of the majority of people at the conference. Perhaps you can give a talk in defence of model theory, as far as the foundations of logic are concerned.(1) That's a fantastic invitation, and I went to the meeting resolved to disagree with as many people as possible.In the event it was not so easy. Partly there was serious research being done in proof theory, and I am not a proof theorist. Partly there were a good number of entirely sensible and friendly people. But also I often found it hard to see what the issues were. I think this was not entirely my fault. Straw men were being set up and W. Hodges (B)

Comments on an Opinion

“…6 and 7. In Wilfrid's remarks after (1.12) in [9], though at the end of the paragraph he admits that "a psychological analysis of 'making an inference' is not the right way to go", there are still psychologistic tones in his mentioning that "people can perform an act called making an inference". So I am afraid that the point Wilfrid ascribes to me with approval is not exactly mine.…”

“…Dummett's words are: "Frege's account, if it is to be reduced to a slogan, could be expressed in this way: that in the order of explanation the sense of a sentence is primary, but in the order of recognition the sense of a word is primary." ( [6], p. 4) In the penultimate paragraph of [9] Wilfrid says: "In the mainstream semantic and model-theoretic literature that I've seen, nobody talks about 'prior' notions or about one notion having 'primacy' over another. "…”