 Nominalism (also called anti-realism): This is the view that there are no such things as numbers, or universals, or whatever sort of alleged abstract objects are under discussion. Thus, for instance, a nominalist about properties would say that while there are such things as red balls and red houses, there is no such thing as the property of redness, over and above the red balls and red houses. And a nominalist about numbers would say that while there are such things as piles of three stones, and perhaps “3-ideas” existing in people's heads, there is no such thing as the number 3. As we will see below, there are many different versions of each of these kinds of nominalism, but for now, we don't need anything more than this general formulation of the view. (Sometimes ‘nominalism’ is used to denote the view that there are no such things as abstract objects; on this usage, ‘nominalism’ is synonymous with ‘anti-platonism’, and views like immanent realism count as versions of nominalism. In contrast, on the usage employed in this essay, ‘nominalism’ is essentially synonymous with ‘anti-realism’, and so views like immanent realism will not count as versions of nominalism here.)