A common response going back to Putnam (1957) and Morton (1973), is to claim that sides who agree on enough logical principles involving some connective or quantifier are indeed using the same connective or quantifier. The obvious difficulty with this idea is spelling out what counts as "enough" agreement. Recently, some inferentialists have tried to do just that (Restall 2002, 2014; Paoli 2013, 2014; Dicher 2016). They are often called minimalists, following Hjortland's (2014) terminology. Minimalists draw a boundary roughly along the line between the operational and structural rules of sequent calculi: operational rules confer meaning, structural rules don't. Therefore, disagreements about logic that can be seen as disagreements about structural rules need not involve a change of language.
In this talk I will argue that current minimalist proposals lead to untenable views about which connectives are identical, or have the same meaning. I will also argue that the importance of the ‘change of language’ issue has been exaggerated. In many cases, I think, there is likely no fact of the matter as to whether different logics share their stock of operators, but there can still be substantial disagreement between partisans of each of them."
The fourth session of the Proof-Theoretic Semantics Seminar Series is coming up!
A common response going back to Putnam (1957) and Morton (1973), is to claim that sides who agree on enough logical principles involving some connective or quantifier are indeed using the same connective or quantifier. The obvious difficulty with this idea is spelling out what counts as "enough" agreement. Recently, some inferentialists have tried to do just that (Restall 2002, 2014; Paoli 2013, 2014; Dicher 2016). They are often called minimalists, following Hjortland's (2014) terminology. Minimalists draw a boundary roughly along the line between the operational and structural rules of sequent calculi: operational rules confer meaning, structural rules don't. Therefore, disagreements about logic that can be seen as disagreements about structural rules need not involve a change of language.
In this talk I will argue that current minimalist proposals lead to untenable views about which connectives are identical, or have the same meaning. I will also argue that the importance of the ‘change of language’ issue has been exaggerated. In many cases, I think, there is likely no fact of the matter as to whether different logics share their stock of operators, but there can still be substantial disagreement between partisans of each of them."