In Philosophy
The type-token distinction identifies that physical objects are tokens of a particular type of thing. The "type" that it is a part of itself is an abstract object. The abstract-concrete distinction is often introduced and initially understood in terms of paradigmatic examples of objects of each kind:
| Abstractum | Concreta |
| Tennis | A tennis game |
| Redness | The red coloring of an apple |
| Five | Five cats |
| Justice | A just action |
| Human | Socrates |
Abstract objects have often garnered the interest of philosophers because they are taken to raise problems for popular theories. In ontology, abstract objects are considered problematic for physicalism and some forms of naturalism. Historically, the most important ontological dispute about abstract objects has been the problem of universals. In epistemology, abstract objects are considered problematic for empiricism. If abstracta lack causal powers or spatial location, how do we know about them? It is hard to say how they can affect our sensory experiences, and yet we seem to agree on a wide range of claims about them. Some, such as Edward Zalta and arguably Plato (in his Theory of Forms), have held that abstract objects constitute the defining subject matter of metaphysics or philosophical inquiry more broadly. To the extent that philosophy is independent of empirical research, and to the extent that empirical questions do not inform questions about abstracta, philosophy would seem specially suited to answering these latter questions.
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