21 ideas
| 10807 | Mathematics reduces to set theory, which reduces, with some mereology, to the singleton function [Lewis] |
| Full Idea: It is generally accepted that mathematics reduces to set theory, and I argue that set theory in turn reduces, with some aid of mereology, to the theory of the singleton function. | |
| From: David Lewis (Mathematics is Megethology [1993], p.03) |
| 10809 | We can accept the null set, but not a null class, a class lacking members [Lewis] |
| Full Idea: In my usage of 'class', there is no such things as the null class. I don't mind calling some memberless thing - some individual - the null set. But that doesn't make it a memberless class. Rather, that makes it a 'set' that is not a class. | |
| From: David Lewis (Mathematics is Megethology [1993], p.05) | |
| A reaction: Lewis calls this usage 'idiosyncratic', but it strikes me as excellent. Set theorists can have their vital null class, and sensible people can be left to say, with Lewis, that classes of things must have members. |
| 10811 | The null set plays the role of last resort, for class abstracts and for existence [Lewis] |
| Full Idea: The null set serves two useful purposes. It is a denotation of last resort for class abstracts that denote no nonempty class. And it is an individual of last resort: we can count on its existence, and fearlessly build the hierarchy of sets from it. | |
| From: David Lewis (Mathematics is Megethology [1993], p.09) | |
| A reaction: This passage assuages my major reservation about the existence of the null set, but at the expense of confirming that it must be taken as an entirely fictional entity. |
| 10812 | The null set is not a little speck of sheer nothingness, a black hole in Reality [Lewis] |
| Full Idea: Should we accept the null set as a most extraordinary individual, a little speck of sheer nothingness, a sort of black hole in the fabric of Reality itself? Not that either, I think. | |
| From: David Lewis (Mathematics is Megethology [1993], p.09) | |
| A reaction: Correct! |
| 10813 | What on earth is the relationship between a singleton and an element? [Lewis] |
| Full Idea: A new student of set theory has just one thing, the element, and he has another single thing, the singleton, and not the slightest guidance about what one thing has to do with the other. | |
| From: David Lewis (Mathematics is Megethology [1993], p.12) |
| 10814 | Are all singletons exact intrinsic duplicates? [Lewis] |
| Full Idea: Are all singletons exact intrinsic duplicates? | |
| From: David Lewis (Mathematics is Megethology [1993], p.13) |
| 7548 | Classes, grouped by a convenient property, are logical constructions [Russell] |
| Full Idea: Classes or series of particulars, collected together on account of some property which makes it convenient to be able to speak of them as wholes, are what I call logical constructions or symbolic fictions. | |
| From: Bertrand Russell (The Ultimate Constituents of Matter [1915], p.125) | |
| A reaction: When does a construction become 'logical' instead of arbitrary? What is it about a property that makes it 'convenient'? At this point Russell seems to have built his ontology on classes, and the edifice was crumbling, thanks to Wittgenstein. |
| 10806 | Megethology is the result of adding plural quantification to mereology [Lewis] |
| Full Idea: Megethology is the result of adding plural quantification, as advocated by George Boolos, to the language of mereology. | |
| From: David Lewis (Mathematics is Megethology [1993], p.03) |
| 10816 | We can use mereology to simulate quantification over relations [Lewis] |
| Full Idea: We can simulate quantification over relations using megethology. Roughly, a quantifier over relations is a plural quantifier over things that encode ordered pairs by mereological means. | |
| From: David Lewis (Mathematics is Megethology [1993], p.18) | |
| A reaction: [He credits this idea to Burgess and Haven] The point is to avoid second-order logic, which quantifies over relations as ordered n-tuple sets. |
| 10808 | Mathematics is generalisations about singleton functions [Lewis] |
| Full Idea: We can take the theory of singleton functions, and hence set theory, and hence mathematics, to consist of generalisations about all singleton functions. | |
| From: David Lewis (Mathematics is Megethology [1993], p.03) | |
| A reaction: At first glance this sounds like a fancy version of the somewhat discredited Greek idea that mathematics is built on the concept of a 'unit'. |
| 10815 | We don't need 'abstract structures' to have structural truths about successor functions [Lewis] |
| Full Idea: We needn't believe in 'abstract structures' to have general structural truths about all successor functions. | |
| From: David Lewis (Mathematics is Megethology [1993], p.16) |
| 7545 | Visible things are physical and external, but only exist when viewed [Russell] |
| Full Idea: I believe that common sense is right in regarding what we see as physical and (in one of several possible senses) outside the mind, but is probably wrong in supposing that it continues to exist when we are no longer looking at it. | |
| From: Bertrand Russell (The Ultimate Constituents of Matter [1915], p.123) | |
| A reaction: This remark (in 1915) is a bit startling from a philosopher well known for his robustly realist stance. Just one of his phases! It seems very counterintuitive - that objects really exist externally, but only when viewed. Schrödinger's Cat? |
| 10810 | I say that absolutely any things can have a mereological fusion [Lewis] |
| Full Idea: I accept the principle of Unrestricted Composition: whenever there are some things, no matter how many or how unrelated or how disparate in character they may be, they have a mereological fusion. ...The trout-turkey is part fish and part fowl. | |
| From: David Lewis (Mathematics is Megethology [1993], p.07) | |
| A reaction: This nicely ducks the question of when things form natural wholes and when they don't, but I would have thought that that might be one of the central issues of metaphysicals, so I think I'll give Lewis's principle a miss. |
| 7549 | If my body literally lost its mind, the object seen when I see a flash would still exist [Russell] |
| Full Idea: My meaning may be made plainer by saying that if my body could remain in exactly the same state in which it is, though my mind had ceased to exist, precisely that object which I now see when I see a flash would exist, though I should not see it. | |
| From: Bertrand Russell (The Ultimate Constituents of Matter [1915], p.126) | |
| A reaction: Zombies, 70 years before Robert Kirk! Sense-data are physical. It is interesting to see a philosopher as committed to empiricism, anti-spiritualism and the priority of science as this, still presenting an essentially dualist picture of perception. |
| 7553 | Sense-data are purely physical [Russell] |
| Full Idea: Sense-data are purely physical, and all that is mental in connection with them is our awareness of them. | |
| From: Bertrand Russell (The Ultimate Constituents of Matter [1915], p.138) | |
| A reaction: Once this account of sense-data becomes fully clear, it also becomes apparent what a dualist theory it is. The mind is a cinema, I am the audience, and sense-data are the screen. There has to be a big logical gap between viewer and screen. |
| 7546 | A man is a succession of momentary men, bound by continuity and causation [Russell] |
| Full Idea: The real man, I believe, however the police may swear to his identity, is really a series of momentary men, each different one from the other, and bound together, not by a numerical identity, but by continuity and certain instrinsic causal laws. | |
| From: Bertrand Russell (The Ultimate Constituents of Matter [1915], p.124) | |
| A reaction: This seems to be in the tradition of Locke and Parfit, and also follows the temporal-slices idea of physical objects. Personally I take a more physical view of things, and think the police are probably more reliable than Bertrand Russell. |
| 7550 | We could probably, in principle, infer minds from brains, and brains from minds [Russell] |
| Full Idea: It seems not improbable that if we had sufficient knowledge we could infer the state of a man's mind from the state of his brain, or the state of his brain from the state of his mind. | |
| From: Bertrand Russell (The Ultimate Constituents of Matter [1915], p.131) | |
| A reaction: This strikes me as being a very good summary of the claim that mind is reducible to brain, which is the essence of physicalism. Had he been born a little later, Russell would have taken a harder line with physicalism. |
| 22489 | 'Good' is an attributive adjective like 'large', not predicative like 'red' [Geach, by Foot] |
| Full Idea: Geach puts 'good' in the class of attributive adjectives, such as 'large' and 'small', contrasting such adjectives with 'predicative' adjectives such as 'red'. | |
| From: report of Peter Geach (Good and Evil [1956]) by Philippa Foot - Natural Goodness Intro | |
| A reaction: [In Analysis 17, and 'Theories of Ethics' ed Foot] Thus any object can simply be red, but something can only be large or small 'for a rat' or 'for a car'. Hence nothing is just good, but always a good so-and-so. This is Aristotelian, and Foot loves it. |
| 7551 | Matter is a logical construction [Russell] |
| Full Idea: We must regard matter as a logical construction. | |
| From: Bertrand Russell (The Ultimate Constituents of Matter [1915], p.132) | |
| A reaction: A logical construction is a fancy way of saying a best explanation (but with Ockham's Razor hanging over it). A key component missing from Russell's account is that we can directly experience matter, because we are made of it. |
| 7547 | Matter requires a division into time-corpuscles as well as space-corpuscles [Russell] |
| Full Idea: A true theory of matter requires a division of things into time-corpuscles as well as space-corpuscles. | |
| From: Bertrand Russell (The Ultimate Constituents of Matter [1915], p.125) | |
| A reaction: The division of matter in space seems decidable by physicists, but the division in time seems a bit arbitrary (unless it is quanta of time?). Russell focuses on observable qualities, but are there also intrinsic qualities? |
| 7552 | Six dimensions are needed for a particular, three within its own space, and three to locate that space [Russell] |
| Full Idea: The world of particulars is a six-dimensional space, where six co-ordinates will be required to assign the position of any particular, three to assign its position in its own space, and three to assign the position of its space among the other spaces. | |
| From: Bertrand Russell (The Ultimate Constituents of Matter [1915], p.134) | |
| A reaction: Not a proposal that has caught on. One might connect the idea with the notion of 'frames of reference' in Einstein's Special Theory. Inside a frame of reference, three co-ordinates are needed; but where is the frame of reference? |