20 ideas
| 19433 | The universe is infinitely varied, so the Buridan's Ass dilemma could never happen [Leibniz] |
| Full Idea: The Buridan's Ass case of perfect equilibrium is chimerical. ...The universe has no centre and its parts are infinitely varied; thus it will never happen that all will be perfectly equal and will strike equally from one side or the other. | |
| From: Gottfried Leibniz (Letters to Coste [1707], 1707) | |
| A reaction: Can the great Leibniz have missed the point? Surely all that matters is that the ass cannot distinguish the two options - not that they actually are identical in every detail? If the ass is short-sighted, that should be easy to set up. |
| 15544 | If what is actual might have been impossible, we need S4 modal logic [Armstrong, by Lewis] |
| Full Idea: Armstrong says what is actual (namely a certain roster of universals) might have been impossible. Hence his modal logic is S4, without the 'Brouwersche Axiom'. | |
| From: report of David M. Armstrong (A Theory of Universals [1978]) by David Lewis - Armstrong on combinatorial possibility 'The demand' | |
| A reaction: So p would imply possibly-not-possibly-p. |
| 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) |
| 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) |
| 7024 | Properties are universals, which are always instantiated [Armstrong, by Heil] |
| Full Idea: Armstrong takes properties to be universals, and believes there are no 'uninstantiated' universals. | |
| From: report of David M. Armstrong (A Theory of Universals [1978]) by John Heil - From an Ontological Point of View §9.3 | |
| A reaction: At first glance this, like many theories of universals, seems to invite Ockham's Razor. If they are always instantiated, perhaps we should perhaps just try to talk about the instantiations (i.e. tropes), and skip the universal? |
| 9478 | Even if all properties are categorical, they may be denoted by dispositional predicates [Armstrong, by Bird] |
| Full Idea: Armstrong says all properties are categorical, but a dispositional predicate may denote such a property; the dispositional predicate denotes the categorical property in virtue of the dispositional role it happens, contingently, to play in this world. | |
| From: report of David M. Armstrong (A Theory of Universals [1978]) by Alexander Bird - Nature's Metaphysics 3.1 | |
| A reaction: I favour the fundamentality of the dispositional rather than the categorical. The world consists of powers, and we find ourselves amidst their categorical expressions. I could be persuaded otherwise, though! |
| 10729 | Universals explain resemblance and causal power [Armstrong, by Oliver] |
| Full Idea: Armstrong thinks universals play two roles, namely grounding objective resemblances and grounding causal powers. | |
| From: report of David M. Armstrong (A Theory of Universals [1978]) by Alex Oliver - The Metaphysics of Properties 11 | |
| A reaction: Personally I don't think universals explain anything at all. They just add another layer of confusion to a difficult problem. Oliver objects that this seems a priori, contrary to Armstrong's principle in Idea 10728. |
| 4031 | It doesn't follow that because there is a predicate there must therefore exist a property [Armstrong] |
| Full Idea: I suggest that we reject the notion that just because the predicate 'red' applies to an open class of particulars, therefore there must be a property, redness. | |
| From: David M. Armstrong (A Theory of Universals [1978], p.8), quoted by DH Mellor / A Oliver - Introduction to 'Properties' §6 | |
| A reaction: At last someone sensible (an Australian) rebuts that absurd idea that our ontology is entirely a feature of our language |
| 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. |
| 10024 | The type-token distinction is the universal-particular distinction [Armstrong, by Hodes] |
| Full Idea: Armstrong conflates the type-token distinction with that between universals and particulars. | |
| From: report of David M. Armstrong (A Theory of Universals [1978], xiii,16/17) by Harold Hodes - Logicism and Ontological Commits. of Arithmetic 147 n23 | |
| A reaction: This seems quite reasonable, even if you don’t believe in the reality of universals. I'm beginning to think we should just use the term 'general' instead of 'universal'. 'Type' also seems to correspond to 'set', with the 'token' as the 'member'. |
| 10728 | A thing's self-identity can't be a universal, since we can know it a priori [Armstrong, by Oliver] |
| Full Idea: Armstrong says that if it can be proved a priori that a thing falls under a certain universal, then there is no such universal - and hence there is no universal of a thing being identical with itself. | |
| From: report of David M. Armstrong (A Theory of Universals [1978], II p.11) by Alex Oliver - The Metaphysics of Properties 11 | |
| A reaction: This is a distinctively Armstrongian view, based on his belief that universals must be instantiated, and must be discoverable a posteriori, as part of science. I'm baffled by self-identity, but I don't think this argument does the job. |
| 19434 | There may be a world where dogs smell their game at a thousand leagues [Leibniz] |
| Full Idea: There will perhaps be a world in which dogs will have sufficiently good noses to scent their game at a thousand leagues. | |
| From: Gottfried Leibniz (Letters to Coste [1707], 1707) | |
| A reaction: Wonderful. This should immediately replace Lewis's much repeated example of a world containing a talking donkey. We should always honour the first person to suggest an idea. That is one of the motivations for this collection of ideas. |