x is an abstract object if and only if x has no spatiotemporal location, cannot bring about effects, is imperceptible by the senses yet is in principle thinkable. NUMBER and UNIVERSALS might be abstract objects. It is controversial whether abstract objects exist and, if they do, whether they necessarily exist.Flew and Priest (1983)
The first statement lists four conditions of something being an abstract object: 1) no spatiotemporal location; 2) cannot bring about effects; 3) imperceptible by the senses, and; 4) in principle thinkable.
Something not being in space and time is fairly uncontroversial. The second and third may raise some eyebrows as to whether abstract objects have an effect in the space and time, and whether their effects are found in reality and sensed. Again, some will argue that if something is thinkable, it exists, whether it is a concrete object or an abstract one.
I will argue that since something called an abstract object has no spatial and temporal location, does not affect matter in space and time, and is imperceptible, it is only “existent” as a thought of an object, and not a thing in itself. The application of the term object therefore seems to be is a misnomer.