Proof-theoretic Semantics and Paradoxes

(Logic & Philosophy of Mathematics, English)

roof-theoretic semantics is an approach to the semantics of (logical) expressions which is based on the concept of proof. As such, proof-theoretic semantics is opposed to the standard semantical approach, namely model theory, i.e. truth-conditional semantics. As it is not based on the notion of truth, the truth tables are not considered to give the meaning of logical constants, but instead -- following Gentzen's remarks on his proof system of natural deduction -- the introduction and/or elimination steps are taken to be meaning-giving for logical constants. Thus, proofs are not only considered to be technical devices but to be actually important from a semantical point of view.

What I want to analyze in this talk is how proof-theoretic semantics can be used to cope with logical paradoxes like the Liar paradox. Traditional proof-theoretic semantics was not developed to handle paradoxes so that changes are needed if that is the aim. For our framework it is useful to consider Tennant's proof-theoretic analysis of paradoxes, namely that they yield a non-normalizing derivation of a contradiction. Next, the choice of the right proof-theoretic representation is important in this context, i.e. whether one works in a natural deduction framework or with the sequent calculus. While the former is the traditional one used in proof-theoretic semantics, there are arguments that the latter is more suitable for dealing with paradoxes. It is then possible to work in a paraconsistent system which does not give rise to the ''dangerous'' derivations of contradictions without the possibility to normalize them.

Chair: Stefan Forster

Time: 14:00-14:30, 15 September 2017 (Friday)

Location: HS E.002

Sara Ayhan

(Ruhr University Bochum, Germany)

I am studying in the Master of Arts Philosophy program at the Ruhr University Bochum. I obtained the degree of 1st state exam in philosophy, English and history in 2015 with a thesis about Donald Davidson's conception of truth. During these studies I spent a semester abroad at the University of Adelaide, South Australia. Currently, I am working on my Master's thesis about proof-theoretic semantics.

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