9 ideas
| 6627 | Radical pragmatists abandon the notion of truth [Stich, by Lowe] |
| Full Idea: Some radical pragmatists, such as Stich, are ready to abandon the notion of truth. | |
| From: report of Stephen P. Stich (The Fragmentation of Reason [1990]) by E.J. Lowe - Introduction to the Philosophy of Mind Ch.3 n18 | |
| A reaction: Such a proposal strikes me as silly (unless the vacuum left by truth can be filled by something better than just the test of whether 'it works'). It currently strikes me that pragmatism has a sane wing (led by Peirce), and a mad wing. |
| 11022 | Gentzen introduced a natural deduction calculus (NK) in 1934 [Gentzen, by Read] |
| Full Idea: Gentzen introduced a natural deduction calculus (NK) in 1934. | |
| From: report of Gerhard Gentzen (works [1938]) by Stephen Read - Thinking About Logic Ch.8 |
| 11065 | The inferential role of a logical constant constitutes its meaning [Gentzen, by Hanna] |
| Full Idea: Gentzen argued that the inferential role of a logical constant constitutes its meaning. | |
| From: report of Gerhard Gentzen (works [1938]) by Robert Hanna - Rationality and Logic 5.3 | |
| 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. |
| 11023 | The logical connectives are 'defined' by their introduction rules [Gentzen] |
| Full Idea: The introduction rules represent, as it were, the 'definitions' of the symbols concerned, and the elimination rules are no more, in the final analysis, than the consequences of these definitions. | |
| From: Gerhard Gentzen (works [1938]), quoted by Stephen Read - Thinking About Logic Ch.8 | |
| A reaction: If an introduction-rule (or a truth table) were taken as fixed and beyond dispute, then it would have the status of a definition, since there would be nothing else to appeal to. So is there anything else to appeal to here? |
| 11213 | Each logical symbol has an 'introduction' rule to define it, and hence an 'elimination' rule [Gentzen] |
| Full Idea: To every logical symbol there belongs precisely one inference figure which 'introduces' the symbol ..and one which 'eliminates' it. The introductions represent the 'definitions' of the symbols concerned, and eliminations are consequences of these. | |
| From: Gerhard Gentzen (works [1938], II.5.13), quoted by Ian Rumfitt - "Yes" and "No" III | |
| A reaction: [1935 paper] This passage is famous, in laying down the basics of natural deduction systems of logic (ones using only rules, and avoiding axioms). Rumfitt questions whether Gentzen's account gives the sense of the connectives. |
| 13832 | Natural deduction shows the heart of reasoning (and sequent calculus is just a tool) [Gentzen, by Hacking] |
| Full Idea: Gentzen thought that his natural deduction gets at the heart of logical reasoning, and used the sequent calculus only as a convenient tool for proving his chief results. | |
| From: report of Gerhard Gentzen (Investigations into Logical Deduction [1935]) by Ian Hacking - What is Logic? §05 |
| 10067 | Gentzen proved the consistency of arithmetic from assumptions beyond arithmetic [Gentzen, by Musgrave] |
| Full Idea: Gentzen proved the consistency of arithmetic from assumptions which transcend arithmetic. | |
| From: report of Gerhard Gentzen (works [1938]) by Alan Musgrave - Logicism Revisited §5 | |
| A reaction: This does not contradict Gödel's famous result, but reinforces it. The interesting question is what assumptions Gentzen felt he had to make. |
| 4765 | Stich accepts eliminativism (labelled 'pragmatism') about rationality and normativity [Stich, by Engel] |
| Full Idea: Stich accepts a form of eliminativism (which he calls 'pragmatism') about rationality and normativity generally. | |
| From: report of Stephen P. Stich (The Fragmentation of Reason [1990]) by Pascal Engel - Truth §5.3 | |
| A reaction: This seems to be the correct position for a Humean empiricist connectionist. Presumably he has some good reasons for eliminating rationality. |
| 5954 | All inventions of the mind aim at pleasure, and those that don't are worthless [Metrodorus of Lamp., by Plutarch] |
| Full Idea: Metrodorus says that all the wonderful, ingenious and brilliant inventions of the mind have been contrived for the sake of pleasure of the flesh or for the sake of looking forward to it, and any accomplishment not leading to this end is worthless. | |
| From: report of Metrodorus (Lamp) (fragments/reports [c.291 BCE], Fr 6) by Plutarch - 74: Reply to Colotes §1125 | |
| A reaction: It is very hard to think of counterexamples! Would anyone bother to work out the theorems of number theory if they didn't enjoy doing it? Would any sensible person make great sacrifices if they didn't think that increased happiness would result? |