5 ideas
| 6408 | Russell needed three extra axioms to reduce maths to logic: infinity, choice and reducibility [Grayling] |
| Full Idea: In order to deduce the theorems of mathematics from purely logical axioms, Russell had to add three new axioms to those of standards logic, which were: the axiom of infinity, the axiom of choice, and the axiom of reducibility. | |
| From: A.C. Grayling (Russell [1996], Ch.2) | |
| A reaction: The third one was adopted to avoid his 'barber' paradox, but many thinkers do not accept it. The interesting question is why anyone would 'accept' or 'reject' an axiom. |
| 14082 | No sortal could ever exactly pin down which set of particles count as this 'cup' [Schaffer,J] |
| Full Idea: Many decent candidates could the referent of this 'cup', differing over whether outlying particles are parts. No further sortal I could invoke will be selective enough to rule out all but one referent for it. | |
| From: Jonathan Schaffer (Deflationary Metaontology of Thomasson [2009], 3.1 n8) | |
| A reaction: I never had much faith in sortals for establishing individual identity, so this point comes as no surprise. The implication is strongly realist - that the cup has an identity which is permanently beyond our capacity to specify it. |
| 14081 | Identities can be true despite indeterminate reference, if true under all interpretations [Schaffer,J] |
| Full Idea: There can be determinately true identity claims despite indeterminate reference of the terms flanking the identity sign; these will be identity claims true under all admissible interpretations of the flanking terms. | |
| From: Jonathan Schaffer (Deflationary Metaontology of Thomasson [2009], 3.1) | |
| A reaction: In informal contexts there might be problems with the notion of what is 'admissible'. Is 'my least favourite physical object' admissible? |
| 6414 | Two propositions might seem self-evident, but contradict one another [Grayling] |
| Full Idea: Two propositions might contradict each other despite appearing self-evident when considered separately. | |
| From: A.C. Grayling (Russell [1996], Ch.2) | |
| A reaction: Russell's proposal (Idea 5416) is important here, that self-evidence comes in degrees. If self-evidence was all-or-nothing, Grayling's point would be a major problem, but it isn't. Bonjour explores the idea more fully (e.g. Idea 3704) |
| 5492 | How can essences generate the right powers to vary with distance between objects? [Armstrong] |
| Full Idea: In Newtonian physics the distance between two objects determines the attractive forces between them, but then the objects will have to be sensitive to the distance, in order to 'know' what forces to generate; but distance isn't a causal power. | |
| From: David M. Armstrong (Two Problems for Essentialism [2001], p.170) | |
| A reaction: Ellis replies that he is not troubled, because he believes in essential properties which are separate from their causal roles. Indeed, how else could you explain their causal roles? Still, distance must be mentioned when explaining gravity. |