20 ideas
| 8349 | The best way to do ontology is to make sense of our normal talk [Davidson] |
| Full Idea: I do not know any better way of showing what there is than looking at the assumptions needed to make sense of our normal talk. | |
| From: Donald Davidson (Causal Relations [1967], §4) | |
| A reaction: Davidson was a pupil of Quine. This I take to be the last flowering of twentieth century linguistic philosophy. The ontology we deduce from talk in a children's playground might be very bizarre, but we are unlikely to endorse it. 'Honest, it's true!' |
| 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) |
| 8348 | If we don't assume that events exist, we cannot make sense of our common talk [Davidson] |
| Full Idea: The assumption, ontological and metaphysical, that there are events, is one without which we cannot make sense of much of our most common talk. | |
| From: Donald Davidson (Causal Relations [1967], §4) | |
| A reaction: He considers events to be unanalysable basics. Explanation of normal talk also needs ghosts, premonitions, telepathy and Father Christmas. It is extremely hard to individuate events, unless they are subatomic, and rather numerous. |
| 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. |
| 8347 | Explanations typically relate statements, not events [Davidson] |
| Full Idea: Explanations typically relate statements, not events. | |
| From: Donald Davidson (Causal Relations [1967], §4) | |
| A reaction: An oddly linguistic way of putting our attempts to understand the world. Presumably the statements are supposed to be about the events (or whatever), and they are supposed to be true, so we are trying to relate features of the world. |
| 13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
| Full Idea: In a single day there lies open to men of learning more than there ever does to the unenlightened in the longest of lifetimes. | |
| From: Posidonius (fragments/reports [c.95 BCE]), quoted by Seneca the Younger - Letters from a Stoic 078 | |
| A reaction: These remarks endorsing the infinite superiority of the educated to the uneducated seem to have been popular in late antiquity. It tends to be the religions which discourage great learning, especially in their emphasis on a single book. |
| 10371 | Distinguish causation, which is in the world, from explanations, which depend on descriptions [Davidson, by Schaffer,J] |
| Full Idea: Davidson distinguishes between causation, an extensional relation that holds between coarse events, and explanation, which is an intensional relation that holds between the coarse events under a description. | |
| From: report of Donald Davidson (Causal Relations [1967]) by Jonathan Schaffer - The Metaphysics of Causation 1.2 | |
| A reaction: I'm unclear why everything has to be so coarse, when reality and causal events seem to fine-grained, but the distinction strikes me as good. Explanations relate to human understanding and human interests. Cf. Anscombe's view. |
| 8403 | Either facts, or highly unspecific events, serve better as causes than concrete events [Field,H on Davidson] |
| Full Idea: It is best to avoid Davidson's view that only quite concrete events can serve as causes; we should either say that facts as well as events can serve as causes; or that the events can be highly unspecific, including 'omissions'. | |
| From: comment on Donald Davidson (Causal Relations [1967]) by Hartry Field - Causation in a Physical World 1 | |
| A reaction: Something NOT happening might be the main cause of an effect (drought), or an effect may mainly result from a situation rather than an event (famine). |
| 8346 | Full descriptions can demonstrate sufficiency of cause, but not necessity [Davidson] |
| Full Idea: The fuller we make the description of a cause, the better our chances of demonstrating that it was sufficient (as described) to produce the effect, and the worse our chances of demonstrating that it was necessary. (For the effect, it is the opposite). | |
| From: Donald Davidson (Causal Relations [1967], §3) | |
| A reaction: If the fullness of description is relevant, this suggests that Davidson is focusing on human explanations, rather than on the ontology of causation. If the cause IS necessary, why wouldn't a better description make that clearer? |
| 4778 | A singular causal statement is true if it is held to fall under a law [Davidson, by Psillos] |
| Full Idea: For Davidson, what makes singular causal statements true is the existence of some regularities or laws. All causal is nomological: c causes e iff there is a law that connects events like c with events like e. | |
| From: report of Donald Davidson (Causal Relations [1967]) by Stathis Psillos - Causation and Explanation §2.6 | |
| A reaction: I wonder if the cart is before the horse here. Scriven says this is just a claim that there are "phantom laws". It is the Humean view of causation, but surely the laws come after the causation, so can't be used to explain it? |
| 20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |
| Full Idea: Posidonius defined time thus: it is an interval of motion, or the measure of speed and slowness. | |
| From: report of Posidonius (fragments/reports [c.95 BCE]) by John Stobaeus - Anthology 1.08.42 | |
| A reaction: Hm. Can we define motion or speed without alluding to time? Looks like we have to define them as a conjoined pair, which means we cannot fully understand either of them. |