But it is not the abstractness of abstract objects that makes them lack clear identity conditions, since some abstract objects, like sets, have clear and intelligible conditions of identity.
Abstractness says that every mathematical object is abstract, where an object is said to be abstract just in case it is non-spatiotemporal and (therefore) causally inefficacious.
Assuming, contra Linksy and Zalta (1996), that abstractness is, necessarily, an essential feature of abstract entities, then it follows that <2+2=4> is in fact abstract.
(Even if they are shadows of our sentences in some sense, they are not shadows in another sense, at least if the Easy Arguments for mind-independence and abstractness are successful: what is mind-independent and abstract is, in a clear sense, not merely a shadow of sentences).
Just to mention a few, the type-theoretical hierarchy imposed on properties appears to be highly artificial and multiplies properties ad infinitum (e.g., since presumably properties are abstract, for any property P of type n, there is an abstractness of type n+1 that P exemplifies).
They serve this purpose because the relative abstractness, comprehensiveness, and concentration of the verbal expressions of beliefs enable them to serve better than most other forms of religious symbolism as stable identifying marks in pluralistic, changing, proselytizing, and missionary situations.
Partly in response to the manifestos of the Russian Futurists (1912 13), the young poets founded Acmeism, a school that affirmed "beautiful clarity" (Kuzmin's term) in place of the vagueness and abstractness of Russian Symbolism.
In practice, people seem to think in ways that combine abstractness and concreteness.
The media's obsession with quantitative deduction overlooks the abstractness, the magic, of two superstars whose very interpretation of the art – Ronaldo, the razor-edge machine of rationale, and Messi, the aesthetic magician of chaos – is framed in classically diametric opposites.
In a sense, it is impossible to speak of purely abstract music; any work of art must have some "content," some series of images, states of mind, or moods that the artist is trying to project or communicate if only the sense of pure abstractness.
The aspect of his style already perfected here is the beautiful abstractness of his descriptions: "Autumn was arriving, everything appeared to be sitting down, somewhere something was coming to a standstill, nature seemed at times to be rubbing its eyes".
