Do Modus Ponens and Tollens Really Leak? Remarks from a Linguistic Semanticist

Do Modus Ponens and Tollens Really Leak? Remarks from a Linguistic Semanticist

Released Friday, 19th April 2019
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Do Modus Ponens and Tollens Really Leak? Remarks from a Linguistic Semanticist

Do Modus Ponens and Tollens Really Leak? Remarks from a Linguistic Semanticist

Do Modus Ponens and Tollens Really Leak? Remarks from a Linguistic Semanticist

Do Modus Ponens and Tollens Really Leak? Remarks from a Linguistic Semanticist

Friday, 19th April 2019
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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.

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Mathematical Philosophy - the application of logical and mathematical methods in philosophy - is about to experience a tremendous boom in various areas of philosophy. At the new Munich Center for Mathematical Philosophy, which is funded mostly by the German Alexander von Humboldt Foundation, philosophical research will be carried out mathematically, that is, by means of methods that are very close to those used by the scientists.The purpose of doing philosophy in this way is not to reduce philosophy to mathematics or to natural science in any sense; rather mathematics is applied in order to derive philosophical conclusions from philosophical assumptions, just as in physics mathematical methods are used to derive physical predictions from physical laws.Nor is the idea of mathematical philosophy to dismiss any of the ancient questions of philosophy as irrelevant or senseless: although modern mathematical philosophy owes a lot to the heritage of the Vienna and Berlin Circles of Logical Empiricism, unlike the Logical Empiricists most mathematical philosophers today are driven by the same traditional questions about truth, knowledge, rationality, the nature of objects, morality, and the like, which were driving the classical philosophers, and no area of traditional philosophy is taken to be intrinsically misguided or confused anymore. It is just that some of the traditional questions of philosophy can be made much clearer and much more precise in logical-mathematical terms, for some of these questions answers can be given by means of mathematical proofs or models, and on this basis new and more concrete philosophical questions emerge. This may then lead to philosophical progress, and ultimately that is the goal of the Center.

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