1 hr 18 min

Do Modus Ponens and Tollens Really Leak? Remarks from a Linguistic Semanticist MCMP – Metaphysics and Philosophy of Language

    • Philosophy

Dietmar Zaefferer (LMU) gives a talk at the MCMP Colloquium (15 May, 2014) titled "Do Modus Ponens and Tollens Really Leak? Remarks from a Linguistic Semanticist". Abstract: Despite considerable progress in formal logic and semantics conditional constructions continue to be a hotly debated topic. One reason for this difficulty of achieving a consensus could be that the problem is simply too hard to be solvable at the current state of the art, so McGee might still be right with his 1985 conjecture: „It may be that it is not possible to give a satisfactory logic of conditionals. This is not to say that it is not possible to give a linguistic account of how we use conditionals, but only to say that such an account would not give rise to a tractable theory of logical consequence.“ (McGee 1985:471) Another reason could be lack of cross-disciplinary communication: This paper looks at logicians’ discussions of counterexamples to MP an MT from the point of view of a linguist and endeavors to show at least that some of them are fallacious, and at most that a considerable amount of problems in this domain is due to insufficient care in formalization, i.e. in semantic analysis. Assume that the miniature archipelago Twin Islands, consisting of Westland and Eastland, is rarely visited, and that at present Jeff and Jane are the only visitors. Assume further that Jane is on Westland. Then the following propositions seem to be true: (P1) Jeff is not the only visitor. non q; (P2) If Jeff is on Eastland, then Jeff is the only visitor. if p then q. Application of modus tollens should lead us to the truth of: (C1) Jeff is not on Eastland. non p.However, intuitively, this does not seem to follow. So this appears to be a counterexample to modus tollens. But it isn’t. It’s easy to see why: Visitor is a relational noun. Jeff is a visitor can only be the case if there is a location Jeff is a visitor of. Uncovering the hidden parameter makes the counterexample disappear: (P1) Jeff is not the only visitor (of Twin Islands). non q; (P2) If Jeff is on Eastland, then Jeff is the only visitor (of Eastland). if p then r. Since q and r are different, there is no way of applying MT. This seems to be an easy exercise from Semantics 101, but I will argue that recent counterexamples to MT (Yalcin 2012) and MP (Kolodny&MacFarlane 2010) are subject to analogous criticism. If there is time I will also comment on the consequences of these considerations for the restrictor – operator view debate (Gillies 2010). All in all, the direction of impact of these remarks is to argue, pace McGee, that it is not only possible to give a linguistic account of how we use conditionals, but also that such an account could arguably give rise to a tractable theory of logical consequence.

Dietmar Zaefferer (LMU) gives a talk at the MCMP Colloquium (15 May, 2014) titled "Do Modus Ponens and Tollens Really Leak? Remarks from a Linguistic Semanticist". Abstract: Despite considerable progress in formal logic and semantics conditional constructions continue to be a hotly debated topic. One reason for this difficulty of achieving a consensus could be that the problem is simply too hard to be solvable at the current state of the art, so McGee might still be right with his 1985 conjecture: „It may be that it is not possible to give a satisfactory logic of conditionals. This is not to say that it is not possible to give a linguistic account of how we use conditionals, but only to say that such an account would not give rise to a tractable theory of logical consequence.“ (McGee 1985:471) Another reason could be lack of cross-disciplinary communication: This paper looks at logicians’ discussions of counterexamples to MP an MT from the point of view of a linguist and endeavors to show at least that some of them are fallacious, and at most that a considerable amount of problems in this domain is due to insufficient care in formalization, i.e. in semantic analysis. Assume that the miniature archipelago Twin Islands, consisting of Westland and Eastland, is rarely visited, and that at present Jeff and Jane are the only visitors. Assume further that Jane is on Westland. Then the following propositions seem to be true: (P1) Jeff is not the only visitor. non q; (P2) If Jeff is on Eastland, then Jeff is the only visitor. if p then q. Application of modus tollens should lead us to the truth of: (C1) Jeff is not on Eastland. non p.However, intuitively, this does not seem to follow. So this appears to be a counterexample to modus tollens. But it isn’t. It’s easy to see why: Visitor is a relational noun. Jeff is a visitor can only be the case if there is a location Jeff is a visitor of. Uncovering the hidden parameter makes the counterexample disappear: (P1) Jeff is not the only visitor (of Twin Islands). non q; (P2) If Jeff is on Eastland, then Jeff is the only visitor (of Eastland). if p then r. Since q and r are different, there is no way of applying MT. This seems to be an easy exercise from Semantics 101, but I will argue that recent counterexamples to MT (Yalcin 2012) and MP (Kolodny&MacFarlane 2010) are subject to analogous criticism. If there is time I will also comment on the consequences of these considerations for the restrictor – operator view debate (Gillies 2010). All in all, the direction of impact of these remarks is to argue, pace McGee, that it is not only possible to give a linguistic account of how we use conditionals, but also that such an account could arguably give rise to a tractable theory of logical consequence.

1 hr 18 min

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