# The PTS-Network

A Home for Proof-Theoretic Semanticists

Proof-Theoretic Semantics - An Origin Story and the Aims of this Network

Proof-theoretic semantics (PTS) is an approach to the meaning of (logical) expressions which is based on the concept of proof. The idea of PTS is to give the meaning of logical connectives in terms of the rules of inference or proof conditions governing their use. Thus, since in PTS meaning is based on how we use expressions in proofs and how we draw inferences - so on fundamentally human activities - PTS is an anti-realist approach, i.e., meaning is not considered to be some entity existing independently of us. Furthermore, PTS is counted among inferentialism or inferential role semantics, which can be seen as the broader view that the meaning of linguistic expressions is determined by how the expressions are used in inferences. Thus, PTS very broadly also belongs to the tradition based on the slogan ‘meaning is use’ going back to Wittgenstein’s famous remarks in his “Philosophical Investigations”.

Usually, the roots of the idea of PTS are ascribed to Gerhard Gentzen due to his frequently cited remarks concerning his calculus of Natural Deduction:

The introductions represent, as it were, the ‘definitions’ of the symbols concerned, and the eliminations are no more, in the final analysis, than the consequences of these definitions.

(Gerhard Gentzen, Investigations into Logical Deduction, 1964[1935], p. 295)

This idea has been picked up and further developed in the second half of the 20th century by - among others – Franz von Kutschera, Dag Prawitz, Per Martin-Löf, Georg Kreisel and Michael Dummett in a field they called general proof theory. Their motivation was – in opposition to David Hilbert’s understanding of proof theory – to generate a new appreciation of proofs, namely not as mere tools but as objects which are worth to be studied in their own right. On such a view it is, e.g., not only an interesting question what can be proved, but rather how something can be proved. The term proof-theoretic semantics, though, was only coined at a conference in 1991 by Peter Schroeder-Heister in order to express a particular focus in this overarching field.

Since these beginnings the field of PTS has grown and developed in different directions and it is our aim to offer with this network a joint base for all these different approaches and to facilitate communication and exchange between researchers interested in PTS. With our website we want to update the community about news related to PTS, like upcoming events or recently published papers in the field.

You are welcome to join our network as an official member or – independently of that – just subscribe to our mailing list if you want to be kept posted about the current news in PTS.

## Related Associations and Sites

AILA (Italian Association of Logic and its Applications) - ailalogica

SILFS (Italian Society of Logic and Philosophy of Sciences) - silfs

Symposia on Proof-Theoretic Semantics - pts-symposium

The Proof Society - proofsociety