26 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| 15941 | For intuitionists excluded middle is an outdated historical convention [Brouwer] |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! |
| 4986 | A weaker kind of reductionism than direct translation is the use of 'bridge laws' [Kirk,R] |
| Full Idea: If multiple realisability means that psychological terms cannot be translated into physics, one weaker kind of reductionism resorts to 'bridge laws' which link the theory to be reduced to the reducing theory. | |
| From: Robert Kirk (Mind and Body [2003], §3.8) | |
| A reaction: It seems to me that reduction is all-or-nothing, so there can't be a 'weaker' kind. If they are totally separate but linked by naturally necessary laws (e.g. low temperature and ice), they are supervenient, but not reducible to one another. |
| 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? |
| 5001 | Maybe we should see intentionality and consciousness as a single problem, not two [Kirk,R] |
| Full Idea: Many philosophers today have adopted the view that we can achieve an enormous simplification by reducing the two components of the mind-body problem - intentionality and consciousness - into one; ...consciousness is no more than representations. | |
| From: Robert Kirk (Mind and Body [2003], §8.4) | |
| A reaction: One would then see subjective experience and informational content as two consequences of a single mental activity. This strikes me as the correct route to go. We do, after all, learn BY experiencing. Hence concepts are tied in with qualia. |
| 4993 | If a bird captures a worm, we could say its behaviour is 'about' the worm [Kirk,R] |
| Full Idea: When a bird pulls a worm from the ground, then swallows it piece by piece, there is a sense in which its behaviour can be said to be about the worm. | |
| From: Robert Kirk (Mind and Body [2003], §5.4) | |
| A reaction: This is preparing the ground for a possible behaviourist account of intentionality. Reply: you could say rain is about puddles, or you could say we have adopted Dennett's 'intentional stance' to birds, but it tells us nothing about their psychology. |
| 5000 | Behaviourism says intentionality is an external relation; language of thought says it's internal [Kirk,R] |
| Full Idea: The conflict over whether intentionality is a matter of behavioural relations with the rest of the world, or of the internal states of the subject, is at its most dramatic in the contrast between behaviourism and the language of thought hypothesis. | |
| From: Robert Kirk (Mind and Body [2003], §7.10) | |
| A reaction: I just don't believe any behaviourist external account of intentionality, which ducks the question of how it all works. Personally I am more drawn to maps and models than to a language of thought. I plan my actions in an imagined space-time world. |
| 4982 | Dualism implies some brain events with no physical cause, and others with no physical effect [Kirk,R] |
| Full Idea: If the mind causes brain events, then they are not caused by other brain events, and such causal gaps should be detectable by scientists; there should also be a gap of brain-events which cause no other brain events, because they are causing mind events. | |
| From: Robert Kirk (Mind and Body [2003], §2.5) | |
| A reaction: This is the double causation problem which Spinoza had spotted (Idea 4862). Expressed this way, it seems a screamingly large problem for dualism. We should be able to discover some VERY strange physical activity in the brain. |
| 4991 | Behaviourism seems a good theory for intentional states, but bad for phenomenal ones [Kirk,R] |
| Full Idea: For many kinds of mental states, notably intentional ones such as beliefs and desires, behaviourism is appealing, ..but for sensations and experiences such as pain, it seems grossly implausible. | |
| From: Robert Kirk (Mind and Body [2003], §5.1) | |
| A reaction: The theory does indeed make a bit more sense for intentional states, but it still strikes me as nonsense that there is no more to my belief that 'Whales live in the Atlantic' than a disposition to say something. WHY do I say this something? |
| 4994 | Behaviourism offers a good alternative to simplistic unitary accounts of mental relationships [Kirk,R] |
| Full Idea: There is a temptation to think that 'aboutness', and the 'contents' of thoughts, and the relation of 'reference', are single and unitary relationships, but behaviourism offers an alternative approach. | |
| From: Robert Kirk (Mind and Body [2003], §5.5) | |
| A reaction: Personally I wouldn't touch behaviourism with a barge-pole (as it ducks the question of WHY certain behaviour occurs), but a warning against simplistic accounts of intentional states is good. I am sure there cannot be a single neat theory of refererence. |
| 4992 | In 'holistic' behaviourism we say a mental state is a complex of many dispositions [Kirk,R] |
| Full Idea: There is a non-reductive version of behaviourism ( which we can call 'global' or 'holistic') which says there is no more to having mental states than having a complex of certain kinds of behavioural dispositions. | |
| From: Robert Kirk (Mind and Body [2003], §5.2) | |
| A reaction: This is designed to meet a standard objection to behaviourism - that there is no straight correlation between what I think and how I behave. The present theory is obviously untestable, because a full 'complex' of human dispositions is never repeated. |
| 4990 | The inverted spectrum idea is often regarded as an objection to behaviourism [Kirk,R] |
| Full Idea: The inverted spectrum idea is often regarded as an objection to behaviourism. | |
| From: Robert Kirk (Mind and Body [2003], §4.5) | |
| A reaction: Thus, my behaviour at traffic lights should be identical, even if I have a lifelong inversion of red and green. A good objection. Note that physicalists can believe in inverted qualia as well a dualists, as long as the brain states are also inverted. |
| 4984 | All meaningful psychological statements can be translated into physics [Kirk,R] |
| Full Idea: All psychological statements which are meaningful, that is to say, which are in principle verifiable, are translatable into propositions which do not involve psychological concepts, but only the concepts of physics. | |
| From: Robert Kirk (Mind and Body [2003], §3.8) | |
| A reaction: This shows how eliminativist behaviourism arises out of logical positivism (by only allowing what is verifiable). The simplest objection: we can't verify the mental states of others, because they are private, but they are still the best explanation. |
| 4998 | Instead of representation by sentences, it can be by a distribution of connectionist strengths [Kirk,R] |
| Full Idea: In a connectionist system, information is represented not by sentences but by the total distribution of connection strengths. | |
| From: Robert Kirk (Mind and Body [2003], §7.6) | |
| A reaction: Neither sentences (of a language of thought) NOR connection strengths strike me as very plausible ways for a brain to represent things. It must be something to do with connections, but it must also be to do with neurons, or we get bizarre counterexamples. |
| 4985 | If mental states are multiply realisable, they could not be translated into physical terms [Kirk,R] |
| Full Idea: If psychological states are multiply realisable it is hard to see how they could possibly be translated into physical terms. | |
| From: Robert Kirk (Mind and Body [2003], §3.8) | |
| A reaction: Reductive funtionalism would do it. A writing iimplement is physical and multiply realisable. Personally I prefer the strategy of saying mental states are NOT multiply realisable. If frog brains differ from ours, they probably don't feel pain like us. |
| 4997 | It seems unlikely that most concepts are innate, if a theory must be understood to grasp them [Kirk,R] |
| Full Idea: It is widely accepted that for many concepts, if not all, grasping the concept requires grasping some theory, ...which makes difficulties for the view that concepts are not learned: for 'radical concept nativism', as Fodor calls it. | |
| From: Robert Kirk (Mind and Body [2003], §7.3) | |
| A reaction: Not a problem for traditional rationalist theories, where the whole theory can be innate along with the concept, but a big objection to modern more cautious non-holistic views (such as Fodor's). Does a bird have a concept AND theory of a nest? |
| 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. |
| 4999 | For behaviourists language is just a special kind of behaviour [Kirk,R] |
| Full Idea: Behaviourists regard the use of language as just a special kind of behaviour. | |
| From: Robert Kirk (Mind and Body [2003], §7.9) | |
| A reaction: This is not an intuitively obvious view of language. We behave, and then we talk about behaviour. Performative utterances (like promising) have an obvious behavioural aspect, as do violent threats, but not highly theoretical language (such as maths). |
| 4995 | Behaviourists doubt whether reference is a single type of relation [Kirk,R] |
| Full Idea: To most behaviourists it seems misguided to expect there to be a single relation that connects referring expressions with their referents. | |
| From: Robert Kirk (Mind and Body [2003], §5.5) | |
| A reaction: You don't need to be a behaviourist to feel this doubt. Think about names of real people, names of fictional people, reference to misunderstood items, or imagined items, or reference in dreams, or to mathematical objects, or negations etc. |