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8. Modes of Existence / E. Nominalism / 6. Mereological Nominalism

[universals are wholes, though found in parts]

5 ideas
'Red' is a single concrete object in space-time; 'red' and 'drop' are parts of a red drop [Quine]
     Full Idea: Why not view 'red' as naming a single concrete object extended in space and time? ..To say a drop is red is to say that the one object, the drop, is a spatio-temporal part of the other, red, as a waterfall is part of a river.
     From: Willard Quine (Identity, Ostension, and Hypostasis [1950], 2)
Red is the largest red thing in the universe [Quine]
     Full Idea: Red is the largest red thing in the universe - the scattered total thing whose parts are all the red things.
     From: Willard Quine (Identity, Ostension, and Hypostasis [1950], 3)
'Mereological Nominalism' sees whiteness as a huge white object consisting of all the white things [Armstrong]
     Full Idea: Mereological Nominalism views a property as the omnitemporal whole or aggregate of all the things said to have the property, so whiteness is a huge white object whose parts are all the white things.
     From: David M. Armstrong (Universals [1995], p.503)
     A reaction: A charming proposal, in which bizarre and beautiful unities thread themselves across the universe, but white objects may also be soft and warm.
'Mereological Nominalism' may work for whiteness, but it doesn't seem to work for squareness [Armstrong]
     Full Idea: Mereological Nominalism has some plausibility for a case like whiteness, but breaks down completely for other universals, such as squareness.
     From: David M. Armstrong (Universals [1995], p.503)
     A reaction: A delightful request that you attempt a hopeless feat of imagination, by seeing all squares as parts of one supreme square. A nice objection.
A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price]
     Full Idea: One way for a nominalist to reject appeal to all abstract objects, including sets, is to only appeal to nominalistically acceptable objects, including mereological sums.
     From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §4)
     A reaction: I'm suddenly thinking that this looks very interesting and might be the way to go. The issue seems to be whether mereological sums should be seen as constrained by nature, or whether they are unrestricted. See Mereology in Ontology...|Intrinsic Identity.