22 ideas
| 11064 | Classes can be reduced to propositional functions [Russell, by Hanna] |
| Full Idea: Russell held that classes can be reduced to propositional functions. | |
| From: report of Bertrand Russell (Mathematical logic and theory of types [1908]) by Robert Hanna - Rationality and Logic 2.4 | |
| A reaction: The exact nature of a propositional function is disputed amongst Russell scholars (though it is roughly an open sentence of the form 'x is red'). |
| 6407 | The class of classes which lack self-membership leads to a contradiction [Russell, by Grayling] |
| Full Idea: The class of teaspoons isn't a teaspoon, so isn't a member of itself; but the class of non-teaspoons is a member of itself. The class of all classes which are not members of themselves is a member of itself if it isn't a member of itself! Paradox. | |
| From: report of Bertrand Russell (Mathematical logic and theory of types [1908]) by A.C. Grayling - Russell Ch.2 | |
| A reaction: A very compressed version of Russell's famous paradox, often known as the 'barber' paradox. Russell developed his Theory of Types in an attempt to counter the paradox. Frege's response was to despair of his own theory. |
| 10418 | Type theory seems an extreme reaction, since self-exemplification is often innocuous [Swoyer on Russell] |
| Full Idea: Russell's reaction to his paradox (by creating his theory of types) seems extreme, because many cases of self-exemplification are innocuous. The property of being a property is itself a property. | |
| From: comment on Bertrand Russell (Mathematical logic and theory of types [1908]) by Chris Swoyer - Properties 7.5 | |
| A reaction: Perhaps it is not enough that 'many cases' are innocuous. We are starting from philosophy of mathematics, where precision is essentially. General views about properties come later. |
| 10047 | Russell's improvements blocked mathematics as well as paradoxes, and needed further axioms [Russell, by Musgrave] |
| Full Idea: Unfortunately, Russell's new logic, as well as preventing the deduction of paradoxes, also prevented the deduction of mathematics, so he supplemented it with additional axioms, of Infinity, of Choice, and of Reducibility. | |
| From: report of Bertrand Russell (Mathematical logic and theory of types [1908]) by Alan Musgrave - Logicism Revisited §2 | |
| A reaction: The first axiom seems to be an empirical hypothesis, and the second has turned out to be independent of logic and set theory. |
| 23478 | Type theory means that features shared by different levels cannot be expressed [Morris,M on Russell] |
| Full Idea: Russell's theory of types avoided the paradoxes, but it had the result that features common to different levels of the hierarchy become uncapturable (since any attempt to capture them would involve a predicate which disobeyed the hierarchy restrictions). | |
| From: comment on Bertrand Russell (Mathematical logic and theory of types [1908]) by Michael Morris - Guidebook to Wittgenstein's Tractatus 2H |
| 21718 | Ramified types can be defended as a system of intensional logic, with a 'no class' view of sets [Russell, by Linsky,B] |
| Full Idea: A defence of the ramified theory of types comes in seeing it as a system of intensional logic which includes the 'no class' account of sets, and indeed the whole development of mathematics, as just a part. | |
| From: report of Bertrand Russell (Mathematical logic and theory of types [1908]) by Bernard Linsky - Russell's Metaphysical Logic 6.1 | |
| A reaction: So Linsky's basic project is to save logicism, by resting on intensional logic (rather than extensional logic and set theory). I'm not aware that Linsky has acquired followers for this. Maybe Crispin Wright has commented? |
| 18126 | A set does not exist unless at least one of its specifications is predicative [Russell, by Bostock] |
| Full Idea: The idea is that the same set may well have different canonical specifications, i.e. there may be different ways of stating its membership conditions, and so long as one of these is predicative all is well. If none are, the supposed set does not exist. | |
| From: report of Bertrand Russell (Mathematical logic and theory of types [1908]) by David Bostock - Philosophy of Mathematics 8.1 |
| 18128 | Russell is a conceptualist here, saying some abstracta only exist because definitions create them [Russell, by Bostock] |
| Full Idea: It is a conceptualist approach that Russell is relying on. ...The view is that some abstract objects ...exist only because they are definable. It is the definition that would (if permitted) somehow bring them into existence. | |
| From: report of Bertrand Russell (Mathematical logic and theory of types [1908]) by David Bostock - Philosophy of Mathematics 8.1 | |
| A reaction: I'm suddenly thinking that predicativism is rather interesting. Being of an anti-platonist persuasion about abstract 'objects', I take some story about how we generate them to be needed. Psychological abstraction seems right, but a bit vague. |
| 18124 | Vicious Circle says if it is expressed using the whole collection, it can't be in the collection [Russell, by Bostock] |
| Full Idea: The Vicious Circle Principle says, roughly, that whatever involves, or presupposes, or is only definable in terms of, all of a collection cannot itself be one of the collection. | |
| From: report of Bertrand Russell (Mathematical logic and theory of types [1908], p.63,75) by David Bostock - Philosophy of Mathematics 8.1 | |
| A reaction: This is Bostock's paraphrase of Russell, because Russell never quite puts it clearly. The response is the requirement to be 'predicative'. Bostock emphasises that it mainly concerns definitions. The Principle 'always leads to hierarchies'. |
| 20657 | There are 23 core brain functions, with known circuit, transmitters, genes and behaviour [Watson] |
| Full Idea: In 2014 the National Institutes of Mental Health published a list of 23 core brain functions and their associated neural circuitry, neurotransmitters and genes, and the behaviour and emotions that go with them. | |
| From: Peter Watson (Convergence [2016], 16 'Physics') | |
| A reaction: They were interested in the functions behind mental health, but I am interested in the functions behind our belief systems, which might produce a different focus. Sub-functions, perhaps. |
| 20656 | Traditional ideas of the mind were weakened in the 1950s by mind-influencing drugs [Watson] |
| Full Idea: One development in particular in the 1950s helped to discredit the traditional concept of the mind. This was medical drugs that influenced the workings of the brain. | |
| From: Peter Watson (Convergence [2016], 16 'Intro') | |
| A reaction: This explains Ryle's 1949 book, and the Australian physicalists emerging in the late 1950s. Philosophers don't grasp how their subject is responsive to other areas of human knowledge. Of course, opium had always done this. |
| 20655 | Humans have been hunter-gatherers for 99.5% of their existence [Watson] |
| Full Idea: Anthropology shows that the hunter-gathering lifestyle has occupied 99.5 per cent of the time humans have been on earth. | |
| From: Peter Watson (Convergence [2016], 13 'Emergence') | |
| A reaction: If you are trying to understand humanity, you ignore this fact at your peril. Even agriculture is only a tiny part of our history, and that only disappeared as a major human activity (in many nations) in the last hundred years. |
| 20650 | The Uncertainty Principle implies that cause and effect can't be measured [Watson] |
| Full Idea: The Uncertainty Principle implied that in the subatomic world cause and effect could never be measured. | |
| From: Peter Watson (Convergence [2016], 05 'Against') | |
| A reaction: The fact that it can't be measured does not, presumably, entail that it doesn't exist. Physicists seem to ignore causation, rather than denying it. Can causation be real if it only exists at the macro-level, as an emergent phenomenon? |
| 20649 | The interference of light through two slits confirmed that it is waves [Watson] |
| Full Idea: Thomas Young in 1803 confirmed the idea of Huyghens that light is waves, showing how light passing through two slits produces an interference pattern that resembles water waves sluicing through two slits. | |
| From: Peter Watson (Convergence [2016], 04 'Conception') | |
| A reaction: The great puzzle emerges when it also turns out to be quantised particles. |
| 20661 | Electrons rotate in hyrogen atoms 10^13 times per second [Watson] |
| Full Idea: In the hydrogen atom the electron rotates some 10,000 billion times per second. | |
| From: Peter Watson (Convergence [2016], 18 'Evolutionary') | |
| A reaction: That's an awful lot. Is it at the speed of light? |
| 20647 | Quantum theory explains why nature is made up of units, such as elements [Watson] |
| Full Idea: Planck's quantum idea explained so much, including the observation that the chemical world is made up of discrete units - the elements. Discrete elements implied fundamental units of matter that were themselves discrete (as Dalton had said). | |
| From: Peter Watson (Convergence [2016], 4 'Intro') | |
| A reaction: The atomic theory was only finally confirmed by Einstein in 1905. This idea implies that the very lowest level of all must have distinct building blocks, but so far we have got down to 'fields', which seem to be a sort of 'foam'. |
| 20654 | Only four particles are needed for matter: up and down quark, electron, electron-neutrino [Watson] |
| Full Idea: We need twelve particles in the master equation of the standard model, but it is necessary to have only four to build a universe (up and down quarks, the electron and the electron neutrino (or lepton). The existence of the others is 'a bit of a mystery'. | |
| From: Peter Watson (Convergence [2016], 11 'First Three') |
| 20651 | The shape of molecules is important, as well as the atoms and their bonds [Watson] |
| Full Idea: Pauling showed that the architecture - the shape of molecules was relevant (as well as the bonds). This meant that molecules were just as important as atoms in the understanding of matter. Molecules were not just the sum of their parts. | |
| From: Peter Watson (Convergence [2016], 05 'Three') | |
| A reaction: If Aristotle struggled to understand matter, then so should modern philosophers. This involves thermodynamics and chemistry, as well as quantum theory. |
| 20652 | In 1828 the animal substance urea was manufactured from inorganic ingredients [Watson] |
| Full Idea: In 1828 Wöhler, in an iconic experiment, had manufactured an organic substance, urea, hitherto the product solely of animals, out of inorganic materials, and without any interventions of vital force. | |
| From: Peter Watson (Convergence [2016], 06 'Inorganic') | |
| A reaction: For reductionists like me, the gradual explanation of life in inorganic terms is the great role model of explanation. I take it for granted that the human mind will go the same way, despite partisan resistance from a lot of philosophers. |
| 20658 | Information is physical, and living can be seen as replicating and preserving information [Watson] |
| Full Idea: In passing information, physical changes take place, and information is thus physical. On this account, the act of living can be seen as replicating and preserving the information that a living body is comprised of. | |
| From: Peter Watson (Convergence [2016], 17 'Dreams') | |
| A reaction: [He emphasises 'the act' of living, rather than a life] |
| 16713 | Philosophers are the forefathers of heretics [Tertullian] |
| Full Idea: Philosophers are the forefathers of heretics. | |
| From: Tertullian (works [c.200]), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 20.2 |
| 6610 | I believe because it is absurd [Tertullian] |
| Full Idea: I believe because it is absurd ('Credo quia absurdum est'). | |
| From: Tertullian (works [c.200]), quoted by Robert Fogelin - Walking the Tightrope of Reason n4.2 | |
| A reaction: This seems to be a rather desperate remark, in response to what must have been rather good hostile arguments. No one would abandon the support of reason if it was easy to acquire. You can't deny its engaging romantic defiance, though. |