There are No Abstract Objects
Dorr (Cian)
Source: Sider (Ted), Hawthorne (John) & Zimmerman (Dean), Eds. - Contemporary Debates in Metaphysics
Paper - Abstract

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Author’s Introduction1

  1. Suppose you start out inclined toward the hard-headed view that the world of material objects is the whole of reality. You elaborate: 'Everything there is is a material object; the sort of thing you could bump into; the sort of thing for which it would be sensible to ask how much it weighs, what shape it is, how fast it is moving, and how far it is from other material objects. There is nothing else.' You develop some practice defending your thesis from the expected objections, from believers in ghosts, God, immaterial souls, Absolute Space, and so on. None of this practice will do you much good the first time you are confronted with the following objection:
      What about numbers and properties? These are obviously not material objects. It would be crazy to think that you might bump into the number two, or the property of having many legs. One would have to be confused to wonder how much these items weigh, or how far away they are. But obviously there are numbers and properties. Surely even you don't deny that there are four prime numbers between one and ten, or that spiders and insects share many important anatomical properties. These well-known truths evidently imply that there are numbers, and that there are properties. So your thesis is false. Not everything is a material object.
  2. This disconcertingly simple objection is probably quite unlike anything you expected to have to deal with when you first announced your thesis. It is confusing precisely because it is so very simple: if the argument did lead you to give up your initial materialist beliefs, the fact that you ever held those beliefs in the first place should seem profoundly puzzling. How on earth could you have failed to notice the inconsistency between your belief that spiders and insects share many important anatomical properties and your belief that everything is a material object? Seeing this, you will quite naturally wonder whether your disagreement with the objector might not be merely verbal. You may want to begin your reply by making distinctions: “Of course there is in a sense such a thing as the number two; but in another important sense it is true that material objects are all there are.”
  3. While I have no particular interest in defending the view that the world of material objects is the whole of reality, I think that this reply is right on target.

In-Page Footnotes

Footnote 1: Truncated rather arbitrarily!

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