Göran Sundholm

Bolzano reduced inferential validity of the inference (from premise judgements to conclusion judgment) to the holding of logical consequence between the propositions (in themselves) that serve as contents of the respective judgements. This explicit reduction of inferential validity among judgements to logical consequence among propositions (or, alternatively, to logical truth of certain implicational propositions) has been largely taken over by current logical theory, say, by Wittgenstein’s Tractatus, by Hilbert and Ackermann, by Quine, and by Tarski also. Frege, though, stands out among those who did not adopt such an account. Under the Bolzano reduction also some blind inferences, with no epistemic support, are deemed valid, which is unacceptable. The Completeness Theorem reduces inferential validity to the logical truth of a certain well-formed formula, whence the unacceptable blindness phenomena are retained. Accordingly, the interest of the Completeness Theorem for logic, construed as the theory of inference, is nugatory.

The lecture spells out the difference between the validity of inference (-figure)s and validity applied to demonstrations (‘proof acts’). The latter notion is not an ordinary characterizing one; in Brentano's terminology it is a modifying one. A demonstration lacking validity is not a real demonstration, just as a false friend is no true friend. Throughout, the treatment makes crucial use of an epistemological perspective that is cast in the first person. Furthermore, the difference between (logical) consequence among propositions and the validity of inference from judgement to judgement is explained. Particular attention is paid to alleged issues of circularity in the definition of the validity of inference, and to the ‘explosion’ validity of inference from contradictory premisses. Drawing upon a version of the dialogical framework of Per Martin-Löf, namely, ‘When I say Therefore, I give others my permission to assert the conclusion’, while stressing also the importance of the first person perspective, both difficulties can be neutralized.

Inference versus consequence , an invited lecture at the LOGICA 1997 conference at Castle Liblice, was part of a series of articles for which I did research during a Stockholm sabbatical in the autumn of 1995. The article seems to have been fairly effective in getting its point across and addresses a topic highly germane to the Uppsala workshop. Owing to its appearance in the LOGICA Yearbook 1997 , Filosofia Publishers, Prague, 1998, it has been rather inaccessible. Accordingly it is republished here with only bibliographical changes and an afterword.

In his Grundgesetze, §32, Frege launched the idea that the meaning of a sentence is given by its truth condition, or, in his particular version, the condition under which it will be a name of the True. This, indeed, was only one of the many roles in which truth has to serve within the Fregean system. In particular, truth is an absolute notion in the sense that bivalence holds: every Gedanke is either true or false, in complete independence of any conative activity, whether by God or man. Thus various epistemological notions, such as the correctness of an assertion made, or judgement passed, are reducible to this absolute notion of truth: an assertion made through the utterance of a declarative sentence is correct when the proposition expressed by the sentence in question is true. Given this absolute status of truth it is not surprising that Frege is of the opinion that truth is a sui generis notion which has to be left unanalyzed and, indeed, which is indefinable.