27 ideas
| 12452 | Our dislike of contradiction in logic is a matter of psychology, not mathematics [Brouwer] |
| Full Idea: Not to the mathematician, but to the psychologist, belongs the task of explaining why ...we are averse to so-called contradictory systems in which the negative as well as the positive of certain propositions are valid. | |
| From: Luitzen E.J. Brouwer (Intuitionism and Formalism [1912], p.79) | |
| A reaction: Was the turning point of Graham Priest's life the day he read this sentence? I don't agree. I take the principle of non-contradiction to be a highly generalised observation of how the world works (and Russell agrees with me). |
| 15941 | For intuitionists excluded middle is an outdated historical convention [Brouwer] |
| Full Idea: From the intuitionist standpoint the dogma of the universal validity of the principle of excluded third in mathematics can only be considered as a phenomenon of history of civilization, like the rationality of pi or rotation of the sky about the earth. | |
| From: Luitzen E.J. Brouwer (works [1930]), quoted by Shaughan Lavine - Understanding the Infinite VI.2 | |
| A reaction: [Brouwer 1952:510-11] |
| 18119 | Mathematics is a mental activity which does not use language [Brouwer, by Bostock] |
| Full Idea: Brouwer made the rather extraordinary claim that mathematics is a mental activity which uses no language. | |
| From: report of Luitzen E.J. Brouwer (Mathematics, Science and Language [1928]) by David Bostock - Philosophy of Mathematics 7.1 | |
| A reaction: Since I take language to have far less of a role in thought than is commonly believed, I don't think this idea is absurd. I would say that we don't use language much when we are talking! |
| 18247 | Brouwer saw reals as potential, not actual, and produced by a rule, or a choice [Brouwer, by Shapiro] |
| Full Idea: In his early writing, Brouwer took a real number to be a Cauchy sequence determined by a rule. Later he augmented rule-governed sequences with free-choice sequences, but even then the attitude is that Cauchy sequences are potential, not actual infinities. | |
| From: report of Luitzen E.J. Brouwer (works [1930]) by Stewart Shapiro - Philosophy of Mathematics 6.6 | |
| A reaction: This is the 'constructivist' view of numbers, as espoused by intuitionists like Brouwer. |
| 12451 | Scientific laws largely rest on the results of counting and measuring [Brouwer] |
| Full Idea: A large part of the natural laws introduced by science treat only of the mutual relations between the results of counting and measuring. | |
| From: Luitzen E.J. Brouwer (Intuitionism and Formalism [1912], p.77) | |
| A reaction: His point, I take it, is that the higher reaches of numbers have lost touch with the original point of the system. I now see the whole issue as just depending on conventions about the agreed extension of the word 'number'. |
| 18118 | Brouwer regards the application of mathematics to the world as somehow 'wicked' [Brouwer, by Bostock] |
| Full Idea: Brouwer regards as somehow 'wicked' the idea that mathematics can be applied to a non-mental subject matter, the physical world, and that it might develop in response to the needs which that application reveals. | |
| From: report of Luitzen E.J. Brouwer (Mathematics, Science and Language [1928]) by David Bostock - Philosophy of Mathematics 7.1 | |
| A reaction: The idea is that mathematics only concerns creations of the human mind. It presumably has no more application than, say, noughts-and-crosses. |
| 12454 | Intuitionists only accept denumerable sets [Brouwer] |
| Full Idea: The intuitionist recognises only the existence of denumerable sets. | |
| From: Luitzen E.J. Brouwer (Intuitionism and Formalism [1912], p.80) | |
| A reaction: That takes you up to omega, but not beyond, presumably because it then loses sight of the original intuition of 'bare two-oneness' (Idea 12453). I sympathise, but the word 'number' has shifted its meaning a lot these days. |
| 12453 | Neo-intuitionism abstracts from the reuniting of moments, to intuit bare two-oneness [Brouwer] |
| Full Idea: Neo-intuitionism sees the falling apart of moments, reunited while remaining separated in time, as the fundamental phenomenon of human intellect, passing by abstracting to mathematical thinking, the intuition of bare two-oneness. | |
| From: Luitzen E.J. Brouwer (Intuitionism and Formalism [1912], p.80) | |
| A reaction: [compressed] A famous and somewhat obscure idea. He goes on to say that this creates one and two, and all the finite ordinals. |
| 8728 | Intuitionist mathematics deduces by introspective construction, and rejects unknown truths [Brouwer] |
| Full Idea: Mathematics rigorously treated from the point of view of deducing theorems exclusively by means of introspective construction, is called intuitionistic mathematics. It deviates from classical mathematics, which believes in unknown truths. | |
| From: Luitzen E.J. Brouwer (Consciousness, Philosophy and Mathematics [1948]), quoted by Stewart Shapiro - Thinking About Mathematics 1.2 | |
| A reaction: Clearly intuitionist mathematics is a close cousin of logical positivism and the verification principle. This view would be anathema to Frege, because it is psychological. Personally I believe in the existence of unknown truths, big time! |
| 10117 | Intuitonists in mathematics worried about unjustified assertion, as well as contradiction [Brouwer, by George/Velleman] |
| Full Idea: The concern of mathematical intuitionists was that the use of certain forms of inference generates, not contradiction, but unjustified assertions. | |
| From: report of Luitzen E.J. Brouwer (Intuitionism and Formalism [1912]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.6 | |
| A reaction: This seems to be the real origin of the verificationist idea in the theory of meaning. It is a hugely revolutionary idea - that ideas are not only ruled out of court by contradiction, but that there are other criteria which should also be met. |
| 20289 | Ethics is universalisable - it must involve an impartial and universal view of things [Singer] |
| Full Idea: A distinguishng feature of ethics is that ethical judgements are universalisable. Ethics requires us to go beyond our own personal point of view to a standpoint like that of the impartial spectator who takes a universal point of view. | |
| From: Peter Singer (Practical Ethics [1979], 10) | |
| A reaction: I'm thinking that ethical agents are more 'situated' than that. Suppose a finance minister stole billions in tax and gave it to a poor country. Good from the universal angle, perhaps, but a shocking betrayal of his own community. |
| 20286 | Following an inner voice for morality is irresponsible in a rational agent [Singer] |
| Full Idea: When following conscience means doing as one's 'internal voice' prompts one to do, to follow one's conscience it so abdicate one's responsibility as a rational agent. | |
| From: Peter Singer (Practical Ethics [1979], 09) | |
| A reaction: Seems dead right. An inner voice is far more likely to be your culture and upbringing than to be an absolute moral truth. It may not be entirely wrong, though, to behave as your culture requires. |
| 20282 | The sanctity of a human life depends either on being of our species, or on being a person [Singer] |
| Full Idea: The doctrine of the sanctity of human life has two separate claims, one that there is a special value in the life of a member of our species, and the other that there is a special value in the life of a person. | |
| From: Peter Singer (Practical Ethics [1979], 04) |
| 20278 | 'Marginal utility' says something is more useful if it is in short supply [Singer] |
| Full Idea: The economic principle of marginal utility states that for a given individual a set amount of something is more useful when the individual has little of it than when he has a lot. | |
| From: Peter Singer (Practical Ethics [1979], 02) | |
| A reaction: But individuals may very a lot on this one. 'He can't get enough of X'. I may be desperate to buy 10,000 books, but you may consider such a need ridiculous, so who decides? |
| 20281 | Why should I do anything for posterity? What has posterity ever done for me? [Singer] |
| Full Idea: Most striking is the impact of the contract model on our attitude to future generations. 'Why should I do anything for posterity? What has posterity ever done for me?' would be the view we ought to take. | |
| From: Peter Singer (Practical Ethics [1979], 03) | |
| A reaction: I should bury my mobile phone for future archaeologists, because it will be more valuable then than it is now. Singer cites the disposal of nuclear waste as an instance. |
| 20276 | Conflict of rules might be avoided by greater complexity, or by a hierarchy of rules [Singer] |
| Full Idea: Those who think ethics is a system of rules can rescue their position by finding more complicated and more specific rules which do not conflict, or by ranking the rules in some hierarchical structure to resolve conflicts. | |
| From: Peter Singer (Practical Ethics [1979], 01) | |
| A reaction: The problem is that clear-cut rules seem to produce conflicts. I would have thought that more specific rules would increase that problem. Safety is in generality. |
| 20290 | Psychopaths may just be bored, because they cannot participate in normal emotional life [Singer] |
| Full Idea: Maybe psychopaths are bored because their emotional poverty means that they cannot take interest in, or gain satisfaction from, what for others are the most important things in life: love, family, success in business or professional life, etc. | |
| From: Peter Singer (Practical Ethics [1979], 10) | |
| A reaction: [he cites Hervey Cleckley for this] Maybe boredom is a symptom of some human inadequacy, but it might sometimes be a mark of superiority. It drives people to both creation and destruction. Quite a good account of criminal behaviour. |
| 7073 | I am a creative nothing, out of which I myself create everything [Stirner] |
| Full Idea: I am not nothing in the sense of emptiness, but I am the creative nothing, the nothing out of which I myself as creator create everything. | |
| From: Max Stirner (The Ego and Its Own [1844]), quoted by Simon Critchley - Continental Philosophy - V. Short Intro Ch.2 | |
| A reaction: This appears to be the germ of the entire existentialist view, which gives a helpful gloss on the concept of 'nothing' - as the motivation for human creation, the vacuum in the mind that has to be filled. Call it 'creative boredom'. |
| 20288 | You can't condemn violent revolution without assessing the evils it prevents [Singer] |
| Full Idea: It would be one-sided to say that violent revolution is always absolutely wrong, without taking account of the evils that the revolutionaries are trying to stop. | |
| From: Peter Singer (Practical Ethics [1979], 09) | |
| A reaction: This seems like common sense, but there are plenty of right-wing authoritarians who would claim that stable authority has priority over all social wrongs. I think that view is mistaken. But the problem is, how to know the future? |
| 21997 | In Marxism the state will be superseded [Singer] |
| Full Idea: It is a famous Marxist doctrine that the state will be superseded. | |
| From: Peter Singer (Marx [1980], 9) | |
| A reaction: Why is that final state communism rather than anarchism? |
| 20287 | If 49% of the population can be wrong, so can 51% [Singer] |
| Full Idea: The case for majority rule should not be overstated. No sensible democrat would claim that the majority is always right. If 49% of the population can be wrong, so can 51%. | |
| From: Peter Singer (Practical Ethics [1979], 09) | |
| A reaction: Well said! We can't possibly put a figure on when the majority become right. In the recent Brexit referendum hardly anyone seemed to understand the issues very well, so none of us have a clue about who was right. |
| 21993 | Materialist history says we are subject to incomprehensible forces [Singer] |
| Full Idea: The materialist conception of history tells us that human beings are totally subject to forces they do not understand and control. | |
| From: Peter Singer (Marx [1980], 6) | |
| A reaction: How does Marx know the forces? An exceptionally influential idea, because it is a modern commonplace that we have very little control over our own lives (apart from right wingers asserting that 'you can have anything if you really really want it'). |
| 20277 | Equality of interests is a minimal principle, not implying equal treatment [Singer] |
| Full Idea: Equal consideration of interests is a minimal principle of equality in the sense that it does not dictate equal treatment. | |
| From: Peter Singer (Practical Ethics [1979], 02) | |
| A reaction: Do those convicted of serious crime retain equal interests? Should a huge group of people sacrifice all of their interests, because of the powerful interests of one person? |
| 20279 | Equality of opportunity unfairly rewards those lucky enough to have great ability [Singer] |
| Full Idea: Equality of opportunity is not an attractive ideal. It rewards the lucky, who inherit those abilities that allow them to pursue interesting and lucrative careers. | |
| From: Peter Singer (Practical Ethics [1979], 02) | |
| A reaction: He makes it sound like cheating. Singer has a highly individualistic view, but society as a whole needs the development of talent, wherever it can be found. |
| 20285 | If a right entails having the relevant desire, many creatures might have no right to life [Singer] |
| Full Idea: If to have a right one must have the ability to desire that to which one has a right, then to have a right to life one must be able to desire one's own continued existence. | |
| From: Peter Singer (Practical Ethics [1979], 07) | |
| A reaction: The unborn, small infants, and persons in comas may well lack the relevant desire (at least consciously - arguably even a plant has a non-conscious 'desire' or drive for life). The idea that a right entails a conscious desire seems daft. |
| 20284 | Why should a potential person have the rights of an actual person? [Singer] |
| Full Idea: A prince may be a potential king, but he does not have the rights of a king. Why should a potential person have the rights of a person? | |
| From: Peter Singer (Practical Ethics [1979], 06) | |
| A reaction: But the prince is probably accorded special rights, merely on the grounds that he is the potential king. An unborn potential king is always considered as special. |
| 20283 | Killing a chimp is worse than killing a human too defective to be a person [Singer] |
| Full Idea: It seems that killing a chimpanzee is worse than the killing of a gravely defective human who is not a person. ...[p.103] the effects on relatives of the defective human will sometimes constitute additional indirect reasons against killing the human. | |
| From: Peter Singer (Practical Ethics [1979], 05) | |
| A reaction: Singer's most notorious idea. Perhaps we should all carry cards (perhaps combined with donor cards) saying how many people will care if we die. |