89 research outputs found
The Completeness of Carnap's Predicate Logic
The paper first proves the completeness of the (non-modal) first-order predicate logic presented in Carnapâs 1946 article âModalities and quantificationâ. By contrast the modal logic defined by the semantics Carnap produces is unaxiomatisable. One can though adapt Carnapâs semantics so that a standard completeness proof for a Carnapian version of predicate S5 turns out to be available./
To Teach Modal Logic: An Opinionated Survey
I aim to promote an alternative agenda for teaching modal logic chiefly
inspired by the relationships between modal logic and philosophy. The guiding
idea for this proposal is a reappraisal of the interest of modal logic in
philosophy, which do not stem mainly from mathematical issues, but which is
motivated by central problems of philosophy and language. I will point out some
themes to start elaborating a guide for a more comprehensive approach to teach
modal logic, and consider the contributions of dual-process theories in
cognitive science, in order to explore a pedagogical framework for the proposed
point of view.Comment: Proceedings of the Fourth International Conference on Tools for
Teaching Logic (TTL2015), Rennes, France, June 9-12, 2015. Editors: M.
Antonia Huertas, Jo\~ao Marcos, Mar\'ia Manzano, Sophie Pinchinat,
Fran\c{c}ois Schwarzentrube
The Completeness of Carnap's Predicate Logic
The paper first proves the completeness of the (non-modal) first-order predicate logic presented in Carnapâs 1946 article âModalities and quantificationâ. By contrast the modal logic defined by the semantics Carnap produces is unaxiomatisable. One can though adapt Carnapâs semantics so that a standard completeness proof for a Carnapian version of predicate S5 turns out to be available./
Ideal Reasoners donât Believe in Zombies
The negative zombie argument concludes that physicalism is false from the premises that p â§ÂŹq is ideally negatively conceivable and that what is ideally negatively conceivable is possible, where p is the conjunction of the fundamental physical truths and laws and q is a phenomenal truth (Chalmers 2002; 2010). A sentence Ï is ideally negatively conceivable iff Ï is not ruled out a priori on ideal rational reflection. In this paper, I argue that the negative zombie argument is neither a priori nor conclusive. First, I argue that the premises of the argument are true only if there exists an adequate finite ideal reasoner R that believes â(p ⧠q) on the basis of not believing pâq on a priori basis. Roughly, a finite reasoner is a reasoner with cognitive limitations (e.g. finite memory). I argue that R is finite only if R reasons nonmonotonically and only approach ideal reflection at the limit of a reasoning sequence. This would render the argument nonconclusive. Finally, I argue that, for some q, R does not believe â(p ⧠q) on the basis of not believing pâq on a priori basis (e.g. for q =âsomething is consciousâ). This would render the choice of an adequate q dependent on empirical information (and the argument a posteriori). I conclude that the negative zombie argument (and, maybe, all zombie arguments) is neither a priori nor conclusive
A Modal Translational Semantics in Priorâs âSymbolism and Analogyâ
This paper explores a modal semantics Arthur Prior developed in his 1957 lecture, âSymbolism and Analogy.â Priorâs semantics employs a translational scheme where certain modal axioms are translated as sentences in an easily understood language. Using Priorâs semantics, we show that one can distinguish between modal logics like D, M, T, S4, and S5 without recourse to possible worlds. Finally, given the current conception of what a semantics ought to be, we consider whether Priorâs modal semantics is indeed a semantics
First degree formulas in quantified S5
This note provides a proof that the formula L(Ex)( Fx & ~LFx) is not equivalent to any first degree formula in the context of the quantified version of the modal logic S5. This solves a problem posed by Max Cresswell
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