8 ideas
| 21855 | Only in the 1780s did it become acceptable to read Spinoza [Lord] |
| Full Idea: It was not until the 1780s that it became acceptable to read the works of Spinoza, and even then it was not without a frisson of danger. | |
| From: Beth Lord (Spinoza's Ethics [2010], Intro 'Who?') | |
| A reaction: Hence we hear of Wordsworth and Coleridge reading him with excitement. So did Kant read him? |
| 1489 | Modern philosophy tends to be a theory-constructing extension of science, but there is also problem-solving [Nagel] |
| Full Idea: Philosophy is now dominated by a spirit of theory construction which sees philosophy as continuous with science, but the other problem-centred style is still in existence and it is important to keep it alive. | |
| From: Thomas Nagel (The Philosophical Culture [1995], §6) |
| 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. |
| 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. |
| 21866 | Hobbes and Spinoza use 'conatus' to denote all endeavour for advantage in nature [Lord] |
| Full Idea: 'Conatus' [translated as 'striving' by Curley] is used by early modern philosophers, including Thomas Hobbes (a major influence of Spinoza), to express the notion of a thing's endeavour for what is advantageous to it. It drives all things in nature. | |
| From: Beth Lord (Spinoza's Ethics [2010], p.88) | |
| A reaction: I think it is important to connect conatus to Nietzsche's talk of a plurality of 'drives', which are an expression of the universal will to power (which is seen even in the interactions of chemistry). Conatus is also in Leibniz. |