What is abstract?


een ontic and epistemic uses of the word. 

Ontic Senses of ‘Abstract’

a. Non-spatio-temporal.  The prevalent sense of ‘abstract’ in the Anglosphere is:  not located in space or in time.  Candidates for abstract status in this sense: sets, numbers, propositions, unexemplified universals.  The set of prime numbers less than 10 is nowhere to be found in space for the simple reason that it is not in space.    If you say it is, then tell me where it is. The same holds for all sets as sets are understood in set theory.   (My chess set is not a set in this sense.)  Nor are sets in time, although this is less clear: one could argue that they, or rather some of them, are omnitemporal, that they exist at every time. That {1, 3, 5, 7, 9} should exist at some times but not others smacks of absurdity, but it doesn’t sound absurd to say that this set  exists at all times. 

This wrinkle notwithstanding, sets are among the candidates for abstract status in the (a) sense.

The same goes for numbers.  They are non-spatio-temporal.

If you understand a proposition to be the Fregean sense of a declarative sentence from which all indexical elements, including tenses of verbs, have been extruded, then propositions so understood are candidates for abstract status in sense (a).

Suppose perfect justice is a universal and suppose there is no God. Then perfect justice is an unexemplified universal.  If there are unexemplified universals, then they are abstract in the (a) sense.

This (a) criterion implies that God is an abstract object.  For God, as classically conceived, is not in space or in time, and this despite the divine omnipresence.  But surely there is a huge different between God who acts, even if, as impassible, he cannot be acted upon, and sets, numbers, propositions and the like that are incapable of either acting or being acted upon.  And so we are led to a second understanding of ‘abstract’ as that which is:

b. Causally inert.  Much of what is abstract in the (a) sense will be causally inert and thus abstract in the (b) sense.  And vice versa.  My cat can bite me, but the set having him as its sole member cannot bite me.  Nor can I bite this singleton or toss it across the room, as I can the cat.  Sets are abstract  in that they cannot act or be acted upon.  A less robust way of putting it:  Sets cannot be the terms of causal relations.  This formulation is neutral on the question whether causation involves agency in any sense. 

I welcome comments and criticism

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