There are no abstract objects

1 The thesis Suppose you start out inclined towards 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, 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. 1 But 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. 1 The latter example is due to van Inwagen (2004).