11 ideas
| 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. |
| 10467 | Individuals consist of 'compresent' tropes [Bacon,John] |
| Full Idea: 'Qualitons' or 'relatons' (quality and relation tropes) are held to belong to the same individual if they are all 'compresent' with one another. | |
| From: John Bacon (Tropes [2008], §4) | |
| A reaction: There is a perennial problem with bundles - how to distinguish accidental compresence (like people in a lift) from united compresence (like people who make a family). |
| 10464 | A trope is a bit of a property or relation (not an exemplification or a quality) [Bacon,John] |
| Full Idea: A trope is an instance or bit (not an exemplification) of a property or a relation. Bill Clinton's eloquence is not his participating in the universal eloquence, or the peculiar quality of his eloquence, but his bit, and his alone, of eloquence. | |
| From: John Bacon (Tropes [2008], Intro) | |
| A reaction: If we have identified something as a 'bit' of something, we can ask whether that bit is atomic, or divisible into something else, and we can ask what are the qualities and properties and powers of this bit, we seems to defeat the object. |
| 10465 | Trope theory is ontologically parsimonious, with possibly only one-category [Bacon,John] |
| Full Idea: A major attraction of tropism has been its promise of parsimony; some adherents (such as Campbell) go so far as to proclaim a one-category ontology. | |
| From: John Bacon (Tropes [2008], §2) | |
| A reaction: This seems to go against the folk idiom which suggests that it is things which have properties, rather than properties ruling to roost. Maybe if one identified tropes with processes, the theory could be brought more into line with modern physics? |
| 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? |
| 10466 | Maybe possible worlds are just sets of possible tropes [Bacon,John] |
| Full Idea: Meinongian tropism has the advantage that possible worlds might be thought of as sets of 'qualitons' and 'relatons' (quality and relational tropes). | |
| From: John Bacon (Tropes [2008], §3) | |
| A reaction: You are still left with 'possible' to explain, and I'm not sure that anything is explain here. If the actual world is sets of tropes, then possible worlds would also have to be, I suppose. |