11 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….. |
| 17818 | How many? must first partition an aggregate into sets, and then logic fixes its number [Yourgrau] |
| Full Idea: We want to know How many what? You must first partition an aggregate into parts relevant to the question, where no partition is privileged. How the partitioned set is to be numbered is bound up with its unique members, and follows from logic alone. | |
| From: Palle Yourgrau (Sets, Aggregates and Numbers [1985], 'New Problem') | |
| A reaction: [Compressed wording of Yourgrau's summary of Frege's 'relativity argument'] Concepts do the partitioning. Yourgau says this fails, because the same argument applies to the sets themselves, as well as to the original aggregates. |
| 17822 | Nothing is 'intrinsically' numbered [Yourgrau] |
| Full Idea: Nothing at all is 'intrinsically' numbered. | |
| From: Palle Yourgrau (Sets, Aggregates and Numbers [1985], 'What the') | |
| A reaction: Once you are faced with distinct 'objects' of some sort, they can play the role of 'unit' in counting, so his challenge is that nothing is 'intrinsically' an object, which is the nihilism explored by Unger, Van Inwagen and Merricks. Aristotle disagrees... |
| 17817 | Defining 'three' as the principle of collection or property of threes explains set theory definitions [Yourgrau] |
| Full Idea: The Frege-Maddy definition of number (as the 'property' of being-three) explains why the definitions of Von Neumann, Zermelo and others work, by giving the 'principle of collection' that ties together all threes. | |
| From: Palle Yourgrau (Sets, Aggregates and Numbers [1985], 'A Fregean') | |
| A reaction: [compressed two or three sentences] I am strongly in favour of the best definition being the one which explains the target, rather than just pinning it down. I take this to be Aristotle's view. |
| 17815 | We can't use sets as foundations for mathematics if we must await results from the upper reaches [Yourgrau] |
| Full Idea: Sets could hardly serve as a foundation for number theory if we had to await detailed results in the upper reaches of the edifice before we could make our first move. | |
| From: Palle Yourgrau (Sets, Aggregates and Numbers [1985], 'Two') |
| 17821 | You can ask all sorts of numerical questions about any one given set [Yourgrau] |
| Full Idea: We can address a set with any question at all that admits of a numerical reply. Thus we can ask of {Carter, Reagan} 'How many feet do the members have?'. | |
| From: Palle Yourgrau (Sets, Aggregates and Numbers [1985], 'On Numbering') | |
| A reaction: This is his objection to the Fregean idea that once you have fixed the members of a set, you have thereby fixed the unique number that belongs with the set. |
| 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. |
| 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. |
| 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. |
| 468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
| Full Idea: In singing and playing the lyre, a boy will be likely to reveal not only courage and moderation, but also justice. | |
| From: Damon (fragments/reports [c.460 BCE], B4), quoted by (who?) - where? |