Abstract Objects

An abstract object is a non-physical, non-mental object that exists outside of space and time and is wholly unextended. For example, one might think that numbers are abstract objects; e.g., it is plausible to think that if the number 3 exists, then it is not a physical or mental object, and it does not exist in space and time. Likewise, one might think that properties and relations are abstract objects; e.g., it is plausible to think that if redness exists, over and above the various red balls and red houses and so on, then it is an abstract object—i.e., it is non-physical, non-mental, non-spatiotemporal, and so on. Other kinds of objects that are often taken by philosophers to be abstract objects are propositions, sentence types, possible worlds, logical objects, and fictional objects. The view the that there are abstract objects—known as platonism—is of course extremely controversial. Many philosophers think there are just no such things as abstract objects. Philosophers who endorse this antiplatonist view have to endorse some other view of objects of the above kinds—i.e., numbers, properties, propositions, etc.; in particular, in connection with each of these kinds of objects, they have to say either that these objects are physical or mental objects or that there are just no such things. There is a vast literature on the existence and nature of abstract objects. This article focuses mostly (but not entirely) on the existence question—that is, the question of whether there are any such things as abstract objects. In addition, it focuses to some extent (though, again, not entirely) on the specific version of this question that is concerned with the existence of abstract mathematical objects.