Abstract entities are things like numbers, classes, relations, and colors which are real existents having no spatiotemporal presence. It might better comport with the contemporary philosophical zeitgeist to identify abstract entities with mental states (if not mere brain states!), but this approach is less than satisfactory. My idea of Boltzmann’s constant is irreparably a first-person phenomenon, as is my hypothetical interlocutor’s idea of the same, but the number itself is clearly not captive to first-person status. The account of how ideas can be mediated between minds falls victim to an infinite regress if ideas do not at some point refer to a third-person object. Moreover, ideas qua ideas have the property of belonging to the mind holding them, but physical constants lack this property; therefore, they cannot be identical to their mental conception. The same applies to other abstract entities.

Thus abstract entities can be considered to be real objects to which the identity relation applies but which are not individuated in space-time and are not themselves minds. (Minds may be a kind of individual thing which is not abstract and not spatiotemporal, but space forbids a treatment of this case here.) Each abstract object is the locus of a given set of properties, and so can be said to possess essence or whatness. Each can be identified by some description or definition (e.g., that proposition which is expressed by the English sentence “Blancmange is white”), and so can be said to possess individuation or thatness. Their thatness is of a qualitatively different kind than that of concrete minds and spatiotemporal objects, which cases may call for differing accounts of individuation.

A fictitious object, or fiction, is a kind of abstract entity that originates in the mind of an author. Its essential properties, or its whatness, are determined by the author and can be mediated to readers’ minds linguistically. Its thatness obtains only in the minds of the author and the reader, and not in the real state of affairs.

Yet fictions are not to be identified with ideas or conceptions. It is true that I must have a conception of Trogdor the Burninator in order to think about him, but this approach may again create an infinite regress, since if I need an idea of Trogdor to think about him, I also need an idea of my idea of Trogdor to have my idea of Trogdor. Furthermore, this requirement is no less true of non-fictional, concrete, spatiotemporal objects like the Graber Administration Building.

Also, fictions are counterfactual, but must be conceivable; inconceivable objects may not participate in existence in any sense. The legendary Square Circle of Bow Mar may be claimed to be gilded and thirteen stone in weight, but the mythic device cannot be said to exist even abstractly, since it cannot be meaningfully conceived. A non-contradictory fiction, like a pro-life Democrat elected to national office, is not similarly disadvantaged, but to qualify as fictional it necessarily does not obtain in the real state of affairs.

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• Posted by Tim on Friday, January 6, 2006 at 1:26:27 pm PST
• Category: School, Philosophy
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