7 ideas
18823 | To say there could have been people who don't exist, but deny those possible things, rejects Barcan [Stalnaker, by Rumfitt] |
Full Idea: Stalnaker holds that there could have been people who do not actually exist, but he denies that there are things that could have been those people. That is, he denies the unrestricted validity of the Barcan Formula. | |
From: report of Robert C. Stalnaker (Counterparts and Identity [1987]) by Ian Rumfitt - The Boundary Stones of Thought 6.2 | |
A reaction: And quite right too, I should have thought. As they say, Jack Kennedy and Marilyn Monroe might have had a child, but the idea that we should accept some entity which might have been that child but wasn't sounds like nonsense. Except as fiction….. |
10245 | One geometry cannot be more true than another [Poincaré] |
Full Idea: One geometry cannot be more true than another; it can only be more convenient. | |
From: Henri Poincaré (Science and Method [1908], p.65), quoted by Stewart Shapiro - Philosophy of Mathematics | |
A reaction: This is the culminating view after new geometries were developed by tinkering with Euclid's parallels postulate. |
8970 | Our notion of identical sets involves identical members, which needs absolute identity [Hawthorne] |
Full Idea: Our conceptual grip on the notion of a set is founded on the axiom of extensionality: a set x is the same as a set y iff x and y have the same members. But this axiom deploys the notion of absolute identity ('same members'). | |
From: John Hawthorne (Identity [2003], 3.1) | |
A reaction: Identity seems to be a primitive, useful and crucial concept, so don't ask what it is. I suspect that numbers can't get off the ground without it (especially, in view of the above, if you define numbers in terms of sets). |
16409 | Unlike Lewis, I defend an actualist version of counterpart theory [Stalnaker] |
Full Idea: I defend a version of counterpart theory that is quite different from Lewis's version, as it is tied to actualism (all that exists is part of the actual world) rather than possibilism (possible things may exist without actually existing). | |
From: Robert C. Stalnaker (Counterparts and Identity [1987], 1) | |
A reaction: This could be the theory I am after. I am sympathetic to both actualism and to counterpart theory. Off to the woodshed…. |
16411 | If possible worlds really differ, I can't be in more than one at a time [Stalnaker] |
Full Idea: Nothing can be in two places at once. If other possible worlds are really other universes, then clearly, you and I cannot be in them if we are here in this one. | |
From: Robert C. Stalnaker (Counterparts and Identity [1987], 2) | |
A reaction: This can be sensibly expressed without possible worlds. I can't embody my other possibilities while I am embodying this one (I'm too busy). Insofar as possible worlds are a good framework, they are just a precise map of common sense. |
16412 | If counterparts exist strictly in one world only, this seems to be extreme invariant essentialism [Stalnaker] |
Full Idea: Counterparts involve the thesis that domains of different possible worlds are disjoint: possible individuals exist in at most one possible world. This seems to suggest extreme essentialism, where nothing could differ from how it is. | |
From: Robert C. Stalnaker (Counterparts and Identity [1987], 2) | |
A reaction: He quotes Salmon (1981:236) as saying counterpart theory is particularly inflexible essentialism. This is a long way from my use of 'essentialism'. The problem is just the extent to which my counterpart is 'the same' as me. |
16410 | Extensional semantics has individuals and sets; modal semantics has intensions, functions of world to extension [Stalnaker] |
Full Idea: Semantic values in extensional semantics are extensions, like individuals for terms, and sets for predicates. In modal semantics we have intensions, functions from worlds to appropriate extensions. | |
From: Robert C. Stalnaker (Counterparts and Identity [1987], 2) | |
A reaction: It seems obvious that the meaning of a word like 'giraffe' must include possible giraffes, as well as actual and deceased giraffes. |