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Ideas of Achille Varzi, by Text

[American, fl. 2003, Professor at Columbia University.]

2003 Mereology
1 p.2 Parts may or may not be attached, demarcated, arbitrary, material, extended, spatial or temporal
     Full Idea: The word 'part' can used whether it is attached, or arbitrarily demarcated, or gerrymandered, or immaterial, or unextended, or spatial, or temporal.
     From: Achille Varzi (Mereology [2003], 1)
1 p.3 Mereology need not be nominalist, though it is often taken to be so
     Full Idea: While mereology was originally offered with a nominalist viewpoint, resulting in a conception of mereology as an ontologically parsimonious alternative to set theory, there is no necessary link between analysis of parthood and nominalism.
     From: Achille Varzi (Mereology [2003], 1)
     A reaction: He cites Lesniewski and Leonard-and-Goodman. Do you allow something called a 'whole' into your ontology, as well as the parts? He observes that while 'wholes' can be concrete, they can also be abstract, if the parts are abstract.
2.1 p.4 'Part' stands for a reflexive, antisymmetric and transitive relation
     Full Idea: It seems obvious that 'part' stands for a partial ordering, a reflexive ('everything is part of itself'), antisymmetic ('two things cannot be part of each other'), and transitive (a part of a part of a thing is part of that thing) relation.
     From: Achille Varzi (Mereology [2003], 2.1)
     A reaction: I'm never clear why the reflexive bit of the relation should be taken as 'obvious', since it seems to defy normal usage and common sense. It would be absurd to say 'I'll give you part of the cake' and hand you the whole of it. See Idea 10651.
2.1 p.5 If 'part' is reflexive, then identity is a limit case of parthood
     Full Idea: Taking reflexivity as constitutive of the meaning of 'part' amounts to regarding identity as a limit case of parthood.
     From: Achille Varzi (Mereology [2003], 2.1)
     A reaction: A nice thought, but it is horribly 'philosophical', and a long way from ordinary usage and common sense (which is, I'm sorry to say, a BAD thing).
2.1 p.5 Maybe set theory need not be well-founded
     Full Idea: There are some proposals for non-well-founded set theory (tolerating cases of self-membership and membership circularities).
     From: Achille Varzi (Mereology [2003], 2.1)
     A reaction: [He cites Aczel 1988, and Barwise and Moss 1996]
2.1 p.5 Conceivability may indicate possibility, but literary fantasy does not
     Full Idea: Conceivability may well be a guide to possibility, but literary fantasy is by itself no evidence of conceivability.
     From: Achille Varzi (Mereology [2003], 2.1)
     A reaction: Very nice. People who cite 'conceivability' in this context often have a disgracefully loose usage for the word. Really, really conceivable is probably our only guide to possibility.
2.2 p.6 The parthood relation will help to define at least seven basic predicates
     Full Idea: With a basic parthood relation, we can formally define various mereological predicates, such as overlap, underlap, proper part, over-crossing, under-crossing, proper overlap, and proper underlap.
     From: Achille Varzi (Mereology [2003], 2.2)
     A reaction: [Varzi offers some diagrams, but they need interpretation]
3 p.8 Are there mereological atoms, and are all objects made of them?
     Full Idea: It is an open question whether there are any mereological atoms (with no proper parts), and also whether every object is ultimately made up of atoms.
     From: Achille Varzi (Mereology [2003], 3)
     A reaction: Such a view would have to presuppose (metaphysically) that the divisibility of matter has limits. If one follows this route, then are there only 'natural' wholes, or are we 'unrestricted' in our view of how the atoms combine? I favour the natural route.
3.2 p.9 Sameness of parts won't guarantee identity if their arrangement matters
     Full Idea: We might say that sameness of parts is not sufficient for identity, as some entities may differ exclusively with respect to the arrangement of the parts, as when we compare 'John loves Mary' with 'Mary loves John'.
     From: Achille Varzi (Mereology [2003], 3.2)
     A reaction: Presumably wide dispersal should also prevent parts from fixing wholes, but there is so much vagueness here that it is tempting to go for unrestricted composition, and then work back to the common sense position.
4.1 p.14 There is something of which everything is part, but no null-thing which is part of everything
     Full Idea: It is common in mereology to hold that there is something of which everything is part, but few hold that there is a 'null entity' that is part of everything.
     From: Achille Varzi (Mereology [2003], 4.1)
     A reaction: This comes out as roughly the opposite of set theory, which cannot do without the null set, but is not keen on the set of everything.
4.3 p.18 'Composition is identity' says multitudes are the reality, loosely composing single things
     Full Idea: The thesis known as 'composition is identity' is that identity is mereological composition; a fusion is just the parts counted loosely, but it is strictly a multitude and loosely a single thing.
     From: Achille Varzi (Mereology [2003], 4.3)
     A reaction: [He cites D.Baxter 1988, in Mind] It is not clear, from this simple statement, what the difference is between multitudes that are parts of a thing, and multitudes that are not. A heavy weight seems to hang on the notion of 'composed of'.