In metaphysics a distinction is made between concrete objects and abstract objects. A paradigmatic example of a concrete object would be a table or a chair. Suppose that platonism with respect to mathematical objects is true. In that case numbers are the paradigmatic examples of abstract objects. Now, what makes a concrete object concrete? And what do we mean when we say that some object is an abstract object? I take it that, assuming God exists, any plausible definition of concrete and abstract objects must be compatible with these propositions:
- Concrete objects can be material (a table)
- Concrete objects can be immaterial (God or a human-mind)
- Concrete objects can be contingent (a table or a human-mind)
- Concrete objects can be necessary (God)
- Concrete objects can be located in time (a table)
- Concrete objects can be located at a single location (a table)
- Concrete objects can be located at multiple locations (tableware)
- Concrete objects can be outside time and space (God)
- Concrete objects can be caused (a table) or uncaused (God)
- Concrete objects can have causal powers (a rock, a mind)
- Abstract objects are always immaterial
- Abstract objects can be contingent (the property of being red)
- Abstract objects can be necessary (the number one, logical laws)
- Abstract objects can be located in time (the earth's equator)
- Abstract objects can be located at a single location (idem)
- Abstract objects can be located at multiple locations (red)
- Abstract objects can be outside time and space (the number two)
- Abstract objects can be caused (equator) or uncaused (two)
- Abstract objects can have causal powers (logical inference)
From this list it follows that we cannot simply define concrete objects as being objects that are located in time or space. The reason is that abstract objects can be located in time or space as well. Neither can we define concrete objects as objects having causal powers because some abstract objects also have causal powers. Further, we cannot define concrete objects as being material objects since there are also immaterial concrete objects. Because of this fact we cannot define abstract objects as being immaterial. It is also not possible to identify concrete objects with caused objects since abstract objects can be caused as well. Nor is it possible to identify concrete objects with contingent objects or abstract objects with necessary objects. After all, there are both necessary concrete and contingent abstract objects.
So, what features are left to define the notions of concrete and abstract objects? Should we say that concrete objects are accessible to empirical observation, whereas abstract objects are inaccessible to empirical observation? This is plainly false since a human-mind and God are not uncritically accessible to empirical observation. Similarly, the ultimate indivisible atomic building blocks of nature are arguably not empirically observable either. Moreover, the property of being red is in an important sense accessible to empirical observation. Should we hold that change is possible for concrete objects, whereas change is impossible for abstract objects? This is also obviously incorrect since for example the earth's equator can change.
It thus seems to me that there are in fact no ontological features left to provide an adequate definition of concrete and abstract objects. Therefore I propose to exclude the notions of concrete object and abstract object from metaphysics altogether.
The only genuine metaphysical distinction is the distinction between material objects and immaterial objects. If a certain type of platonism is true, we should divide the class of immaterial objects into the class of mental objects and the class of platonic objects. If platonism is false (which I believe is the case), all immaterial objects are mental objects. In that case objects such as the earth's equator, properties such as being red, logical laws or the number two exist only in our minds.