The Meaning of Tonk

Màster en Filosofia Analítica (APhil), Facultat Filosofía, Universitat de Barcelona, Curs: 2021-2022, Director/Tutor: José MartínezThe present article follows on a line of research proposed by Ripley in his 2015 article ‘Anything goes’, where he proposes a conception of logical consequence bearing the peculiar characteristic of discarding the cut rule entirely, and transitivity with it. This is, of course, a bold step to take, given transitivity’s usefulness. It still bears some fruitful advantages for an inferential theory of meaning nonetheless, as it allows entrance into the inferential realm of meaning to many previously problematic entities -such as connectives like Prior’s infamous tonk. As the title of Ripley’s article suggests, it seems that in this interpretation of the turnstile (almost) anything goes. But how exactly does it go, we may ask ourselves. And indeed, this shall be the question we will try to sketch an answer for presently. What exactly could the meaning of tonk be in a framework which accounts for it, i.e. Ripley’s? We believe Ripley’s intuition to be mainly right, and that connectives like tonk do indeed possess a meaning, so we will try to delve deeper into what the meaning of these faulty connectives could be about. We will also briefly consider a side issue, which has to do with the fact that, even if everything goes, it does not seem to be the case that everything goes in the same way. Indeed, thanks to the many responses to Prior’s article numerous differences have been spotted between regular, ‘healthy’ connectives like conjunction and problematic ones like tonk

What are acceptable reductions? Perspectives from proof-theoretic semantics and type theory

It has been argued that reduction procedures are closely connected to the question about identity of proofs and that accepting certain reductions would lead to a trivialization of identity of proofs in the sense that every derivation of the same conclusion would have to be identified. In this paper it will be shown that the question, which reductions we accept in our system, is not only important if we see them as generating a theory of proof identity but is also decisive for the more general question whether a proof has meaningful content. There are certain reductions which would not only force us to identify proofs of different arbitrary formulas but which would render derivations in a system allowing them meaningless. To exclude such cases, a minimal criterion is proposed which reductions have to fulfill to be acceptable

Anything Goes

This paper consider Prior's connective Tonk from a particular bilateralist perspective. I show that there is a natural perspective from which we can see Tonk and its ilk as perfectly well-defined pieces of vocabulary; there is no need for restrictions to bar things like Tonk

Tonk and the model-theoretic conception of meaning

En este trabajo retomo la discusión en torno a la conectiva tonk y reseño brevemente las respuestas que se han ofrecido al desafío que ella plantea. Discuto críticamente el supuesto generalizado de que tonk representa un problema únicamente para el inferencialismo lógico; exploro y propongo contrapartes de tonk para aquellas teorías semánticas que dan cuenta del significado de las expresiones lógicas en términos de condiciones de verdad. In this paper I recall de discussion around tonk and summarize the answers that have been offered to it. I critically discuss the idea that tonk is a problem exclusive for an inferentilst approach to the meaning of logical constants and explore what would tonk look like for a truth-conditional approach.

What are acceptable reductions? Perspectives from proof-theoretic semantics and type theory

It has been argued that reduction procedures are closely connected to the question about identity of proofs and that accepting certain reductions would lead to a trivialization of identity of proofs in the sense that every derivation of the same conclusion would have to be identified. In this paper it will be shown that the question, which reductions we accept in our system, is not only important if we see them as generating a theory of proof identity but is also decisive for the more general question whether a proof has meaningful content. There are certain reductions which would not only force us to identify proofs of different arbitrary formulas but which would render derivations in a system allowing them meaningless. To exclude such cases, a minimal criterion is proposed which reductions have to fulfill to be acceptable

Reasoning with Attitude:Foundations and Applications of Inferential Expressivism

Certain combinations of sounds or signs on paper are meaningful. What makes it the case that, unlike most combinations of sounds answers to these questions are based on the idea that words stand for something, but it is difficult to say what words such as good, if, or probable stand for. This book advances novel answers based on the idea that words get their meaning from the way they are used to express states of mind and what follows from them. It articulates a precise version of this idea, at a time when the shortcomings of the traditional answers are hotly discussed

Replacing truth

Kevin Scharp proposes an original account of the nature and logic of truth, on which truth is an inconsistent concept that should be replaced for certain theoretical purposes. He argues that truth is best understood as an inconsistent concept; develops an axiomatic theory of truth; and offers a new kind of possible-worlds semantics for this theory