If we replaced ‘and’ by ‘unless’, ‘until’, or ‘only if’, we would typically not be prepared to judge the argument to be valid.
Let us call these words on which the validity of an argument forms hangs “”. While we want to hold on to the thought that the schema above describes a valid argument form, ordinary language does hold felicitous counterexamples: we would not usually take ‘You keep making a racket and you will not get any dessert’ to entail either of its conjuncts.
In fact, an utterance of this sentence would typically be designed to ensure that neither of the conjuncts—in particular, the first—turns out to be true, while the conjunction itself would be uttered in sincere belief of its truth.
An obvious solution to the conundrum is to insist that, despite the presence of the word ‘and’, the sentence does not express a conjunction.
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.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.Carnap took all of his technical apparatus to be , and his account of consequence no doubt has a decidedly syntactic feel.Many of the techniques and notions Carnap uses may be seen to fall into the remit of semantics, however, when viewed through Tarskian goggles.Sometimes (and in particular in the motivating introductory chapters of logic textbooks) it seems that this comprises the main role of logic in philosophy.Such a view somewhat overshadows the analytical role of logic as a theory of logical consequence mentioned above.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.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.