Essay On Pluralist Theory
In this introductory editorial we try to sketch the background of these discussions and explain how the articles in this collection contribute to them.
Many think of logic as a particular sub-discipline of mathematics that studies a certain class of abstract, formal structures.
As is well known, varying re-interpretations of the sentences of a language are used in order to cash out this idea.
Call an interpretation that makes a set of sentences true, a One can think of the re-interpretation of the sentences of the language as modeling all possible instances of an argument form.
Here is not the place, however, to discuss the various responses to the incompleteness results that proof-theorists have put forward.
The dominant model-theoretic tradition going back to Tarski starts from the idea that, in a valid argument, the conclusion is never false whenever the premisses are true.
While Carnap’s logical pluralism which is incorporated in is well known, a full appreciation of his explication of logical consequence is only just beginning.
We here thus concentrate on Gentzen’s and Tarski’s accounts.
An obvious solution to the conundrum is to insist that, despite the presence of the word ‘and’, the sentence does not express a conjunction.A further question about the status of logic is whether there is such a thing as correct logic to choose for our philosophical projects.This question perhaps arises regardless of whether logic can be, in the above sense, neutral with respect to every philosophical question, for different logics might place different constraints on our argumentation or on our theories.Is logic a neutral methodological framework within which we can develop and discuss our philosophical theories, or does the logic we chose as a framework already constrain the theories we try to develop in it?Of course, in order to be a useful framework, a logic should place constraints on our theory-building and argumentation (by requiring, for example, logical validity of our arguments and perhaps logical consistency of our theories), but it should not set constraints on our philosophical theories that beg the question regarding the problem that we are trying to find an answer to, or so one might think.The project of an explication of logical consequence has to accomplish two tasks: (i) it has to precisify the logical words by introducing technical terms in their place that behave in a more predictable way than their ordinary-language counterparts; (ii) it has to specify exactly what the logically valid argument forms are and what counts as an instance of such an argument form.1935 was a great year for the explication of logical consequence: Gerhard Gentzen published his “Untersuchungen über das logische Schliessen” Gentzen ().The two major traditions in logic, the proof-theoretic and the model-theoretic approach, go back to these pivotal works by Gentzen and Tarski, respectively.The starting point for the study of philosophical logic, however, is not purely mathematical interest.It rather takes wing from the observation that certain (ordinary language) arguments share two interesting features: on the one hand, their premisses necessitate their conclusion, and on the other hand, they share a certain structure.The articles in this volume discuss the status of logic.What is the status of logic vis-à-vis our philosophical aspirations and projects?