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Full Idea
Gentzen argued that the inferential role of a logical constant constitutes its meaning.
Gist of Idea
The inferential role of a logical constant constitutes its meaning
Source
report of Gerhard Gentzen (works [1938]) by Robert Hanna - Rationality and Logic 5.3
Book Ref
Hanna,Robert: 'Rationality and Logic' [MIT 2006], p.63
A Reaction
Possibly inspired by Wittgenstein's theory of meaning as use? This idea was the target of Prior's famous connective 'tonk', which has the role of implying anything you like, proving sentences which are not logical consequences.
13832 | Natural deduction shows the heart of reasoning (and sequent calculus is just a tool) [Gentzen, by Hacking] |
10067 | Gentzen proved the consistency of arithmetic from assumptions beyond arithmetic [Gentzen, by Musgrave] |
11022 | Gentzen introduced a natural deduction calculus (NK) in 1934 [Gentzen, by Read] |
11065 | The inferential role of a logical constant constitutes its meaning [Gentzen, by Hanna] |
11023 | The logical connectives are 'defined' by their introduction rules [Gentzen] |
11213 | Each logical symbol has an 'introduction' rule to define it, and hence an 'elimination' rule [Gentzen] |