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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 ().
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.
It is worth noting, however, that a year before, Carnap ().
Carnap’s work has been superseded by Tarski’s, of course.
Moreover, it seems that the first is the case because of the second.
Presumably since Aristotle, the study of philosophical logic is the attempt to develop a formal theory that describes what these structures or patterns are and explains why some of these patterns have the interesting property of having only valid arguments as their instances., and thus independent of the content or the subject matter of the argument.
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.
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.