19 ideas
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. |
20653 | Six reduction levels: groups, lives, cells, molecules, atoms, particles [Putnam/Oppenheim, by Watson] |
Full Idea: There are six 'reductive levels' in science: social groups, (multicellular) living things, cells, molecules, atoms, and elementary particles. | |
From: report of H.Putnam/P.Oppenheim (Unity of Science as a Working Hypothesis [1958]) by Peter Watson - Convergence 10 'Intro' | |
A reaction: I have the impression that fields are seen as more fundamental that elementary particles. What is the status of the 'laws' that are supposed to govern these things? What is the status of space and time within this picture? |
7352 | Jesus said learning was unnecessary, and only the spirit of the Law was needed [Jesus, by Johnson,P] |
Full Idea: Jesus was a learned Jew who said that learning was not necessary, who took the spirit and not the letter as the essence of the Law. | |
From: report of Jesus (reports [c.32]) by Paul Johnson - The History of the Jews Pt II | |
A reaction: This seems to me the perfect opposite of Socrates's intellectualism, offering the essence of morality as 'purity of heart', rather than careful thought about virtue or principles. On the whole I am with Socrates, but the idea is interesting. |
6289 | Love your enemies [Jesus] |
Full Idea: Love your enemies. | |
From: Jesus (reports [c.32]), quoted by St Matthew - 01: Gospel of St Matthew 05.44 | |
A reaction: The germ of this idea had been around for several hundred years, but this very forceful statement is perhaps Jesus' most distinctive contribution to moral thought. It has the same clarion call as the Stoic demand for pure virtue. What about deserving? |
6292 | Love thy neighbour as thyself [Jesus] |
Full Idea: Love thy neighbour as thyself. | |
From: Jesus (reports [c.32]), quoted by St Matthew - 01: Gospel of St Matthew 19.19 | |
A reaction: It would be stronger and better to say 'Love your neighbour, even if you don't love yourself'. Self-loathing and vicious hatred often go together. For once Jesus does not attach an instant heavenly reward to obedience of the command. |
5356 | Treat others as you would have them treat you [Jesus] |
Full Idea: All things whatsoever ye would that men should do to you, so ye even so to them: for this is the law and the prophets. | |
From: Jesus (reports [c.32]), quoted by St Matthew - 01: Gospel of St Matthew 07.12 | |
A reaction: A problem which probably didn't occur to Jesus and the prophets is that of masochists. Personally I like buying philosophy books, but most people have no such desire. The Rule needs restricting to the basics of pleasure and pain. |
6286 | Blessed are the merciful: for they shall obtain mercy [Jesus] |
Full Idea: Blessed are the merciful: for they shall obtain mercy. | |
From: Jesus (reports [c.32]), quoted by St Matthew - 01: Gospel of St Matthew 05.07 | |
A reaction: This appears to be a straightforward application of social contract morality, with God playing the role of Hobbes' absolute monarch. It highlights the uncomfortable fact at the heart of Christian morality, that the motivation for altruism is selfish. |
6290 | Except ye become as little children, ye shall not enter heaven [Jesus] |
Full Idea: Except ye be converted, and become as little children, ye shall not enter into the kingdom of heaven. | |
From: Jesus (reports [c.32]), quoted by St Matthew - 01: Gospel of St Matthew 18.03 | |
A reaction: The appeal of such purity of heart is undeniable, but essentially I dislike this remark. It is the opponent of education, reason, autonomy, responsibility, democracy and maturity. It confirms the view that religion is the opium of the people. |
6287 | If you lust after a woman, you have committed adultery [Jesus] |
Full Idea: Whosoever look on a woman to lust after her hath committed adultery with her already in his heart. | |
From: Jesus (reports [c.32]), quoted by St Matthew - 01: Gospel of St Matthew 05.28 | |
A reaction: Compare Democritus, Idea 503. Literally this idea seems absurd, but it is also at the heart of Greek virtue theory. Aristotle (Idea 34) defines virtue as an activity 'of the soul', not an action in the world. Excellence has become purity of soul. |
6285 | Blessed are the meek; for they shall inherit the earth [Jesus] |
Full Idea: Blessed are the meek; for they shall inherit the earth. | |
From: Jesus (reports [c.32]), quoted by St Matthew - 01: Gospel of St Matthew 05.05 | |
A reaction: If they are truly meek, why would they want to inherit the earth? This is the classic statement of Nietzsche's 'inversion of values', where the qualities of a good slave are elevated above those of the greatest human beings. |
6288 | Don't resist evil, but turn the other cheek [Jesus] |
Full Idea: Ye have heard it said, An eye for an eye, and a tooth for a tooth; But I say unto you, That ye resist not evil, but whosoever shall smite thee on thy right cheek, turn to him the other also. | |
From: Jesus (reports [c.32]), quoted by St Matthew - 01: Gospel of St Matthew 05.38-9 | |
A reaction: Compare Socrates, Idea 346. The viciousness of many Hollywood movies is that they set up a character as thoroughly evil so that we can have the pleasure of watching him pulverised. On the whole, Jesus gives bad advice. 'Doormats' in game theory. |
6293 | It is almost impossible for the rich to go to heaven [Jesus] |
Full Idea: It is easier for a camel to go through the eye of a needle, than for a rich man to enter into the kingdom of God. | |
From: Jesus (reports [c.32]), quoted by St Matthew - 01: Gospel of St Matthew 19.24 | |
A reaction: Aristotle and others (Margaret Thatcher) have observed that you cannot practise charity if you are poor. Jesus implies that the human race should remain in poverty. No wonder autocratic medieval rulers taught Christianity to peasants. Cf. Matt 25.30. |
6291 | No one is good except God [Jesus] |
Full Idea: Why callest thou me good? There is none good but one, that is, God. | |
From: Jesus (reports [c.32]), quoted by St Matthew - 01: Gospel of St Matthew 19.17 | |
A reaction: This remark raises the problem that if God is good, there must be some separate moral standard by which he can be judged good. What is that standard? It is related to the problem of whether Plato's Form of the Beautiful is itself beautiful. |
7351 | Jesus turned the ideas of Hillel into a theology reduced to its moral elements [Jesus, by Johnson,P] |
Full Idea: Jesus was a member of the school of Hillel the Elder, and may have sat under him. He repeated some of the sayings of Hillel, ...and turned his ideas into a moral theology, stripping the law of all but its moral and ethical elements. | |
From: report of Jesus (reports [c.32]) by Paul Johnson - The History of the Jews Pt II | |
A reaction: The crucial move, it seems to me, is to strip Judaism of its complexity, and reduce it to very simple moral maxims, which means that ordinary illiterate people no longer need priests to understand and follow it. Jesus was, above all, a great teacher. |