8 ideas
17809 | Gödel showed that the syntactic approach to the infinite is of limited value [Kreisel] |
Full Idea: Usually Gödel's incompleteness theorems are taken as showing a limitation on the syntactic approach to an understanding of the concept of infinity. | |
From: Georg Kreisel (Hilbert's Programme [1958], 05) |
17810 | The study of mathematical foundations needs new non-mathematical concepts [Kreisel] |
Full Idea: It is necessary to use non-mathematical concepts, i.e. concepts lacking the precision which permit mathematical manipulation, for a significant approach to foundations. We currently have no concepts of this kind which we can take seriously. | |
From: Georg Kreisel (Hilbert's Programme [1958], 06) | |
A reaction: Music to the ears of any philosopher of mathematics, because it means they are not yet out of a job. |
16062 | A necessary relation between fact-levels seems to be a further irreducible fact [Lynch/Glasgow] |
Full Idea: It seems unavoidable that the facts about logically necessary relations between levels of facts are themselves logically distinct further facts, irreducible to the microphysical facts. | |
From: Lynch,MP/Glasgow,JM (The Impossibility of Superdupervenience [2003], C) | |
A reaction: I'm beginning to think that rejecting every theory of reality that is proposed by carefully exposing some infinite regress hidden in it is a rather lazy way to do philosophy. Almost as bad as rejecting anything if it can't be defined. |
16061 | If some facts 'logically supervene' on some others, they just redescribe them, adding nothing [Lynch/Glasgow] |
Full Idea: Logical supervenience, restricted to individuals, seems to imply strong reduction. It is said that where the B-facts logically supervene on the A-facts, the B-facts simply re-describe what the A-facts describe, and the B-facts come along 'for free'. | |
From: Lynch,MP/Glasgow,JM (The Impossibility of Superdupervenience [2003], C) | |
A reaction: This seems to be taking 'logically' to mean 'analytically'. Presumably an entailment is logically supervenient on its premisses, and may therefore be very revealing, even if some people think such things are analytic. |
16060 | Nonreductive materialism says upper 'levels' depend on lower, but don't 'reduce' [Lynch/Glasgow] |
Full Idea: The root intuition behind nonreductive materialism is that reality is composed of ontologically distinct layers or levels. …The upper levels depend on the physical without reducing to it. | |
From: Lynch,MP/Glasgow,JM (The Impossibility of Superdupervenience [2003], B) | |
A reaction: A nice clear statement of a view which I take to be false. This relationship is the sort of thing that drives people fishing for an account of it to use the word 'supervenience', which just says two things seem to hang out together. Fluffy materialism. |
16064 | The hallmark of physicalism is that each causal power has a base causal power under it [Lynch/Glasgow] |
Full Idea: Jessica Wilson (1999) says what makes physicalist accounts different from emergentism etc. is that each individual causal power associated with a supervenient property is numerically identical with a causal power associated with its base property. | |
From: Lynch,MP/Glasgow,JM (The Impossibility of Superdupervenience [2003], n 11) | |
A reaction: Hence the key thought in so-called (serious, rather than self-evident) 'emergentism' is so-called 'downward causation', which I take to be an idle daydream. |
8511 | Stout first explicitly proposed that properties and relations are particulars [Stout,GF, by Campbell,K] |
Full Idea: In modern times, it was G.F. Stout who first explicitly made the proposal that properties and relations are as particular as the substances that they qualify. | |
From: report of G.F. Stout (The Nature of Universals and Propositions [1923]) by Keith Campbell - The Metaphysic of Abstract Particulars §1 | |
A reaction: Note that relations will have to be tropes, as well as properties. Williams wants tropes to be parts of objects, but that will be tricky with relations. If you place two objects on a table, how does the 'to the left of' trope come into existence? |
17811 | The natural conception of points ducks the problem of naming or constructing each point [Kreisel] |
Full Idea: In analysis, the most natural conception of a point ignores the matter of naming the point, i.e. how the real number is represented or by what constructions the point is reached from given points. | |
From: Georg Kreisel (Hilbert's Programme [1958], 13) | |
A reaction: This problem has bothered me. There are formal ways of constructing real numbers, but they don't seem to result in a name for each one. |