Nietzsche proposes an eternal recurrence. The idea has a fatal flaw:
Nietzsche’s labyrinthine walk repeats itself, either 1) by its circularity or because 2) the labyrinth itself repeats. Neither of these alternatives work.
There can be no multiplicity of objects that are identical unless by being in the company of others “they” are made a plurality of distinguishable instances. The labyrinth, by Nietzschean definition, is fixed and the objects within it are distinguishable. However, there is no spatial, distinguishing marks between the parts of one labyrinth and the parts of another, identical, labyrinth; nor, similiarly, are there temporally evidenced distinguishing marks between recurrences of objects within the labyrinth. There is no possibility of their “recurrence”.
DISCUSSION
This refutation depends on an idea that objects are in actuality neither multiple nor singular. This certainly does not make them relative, except in the manner of their arising. but the manner of their arising is utterly empty or as Kant would have it “mere appearances” regarding the object itself of which we can say nothing at all.
Multiplicities and their single objects arise as relationships, i.e. differences between objects. Nietzsche’s idea presents the limit case of this standard ontology where differences are not in evidence. Such Platonicaly real, Nietzschean objects carry their distinguishing marks with them. Such entities, as also populate standard mathematics for example, are deemd to be, as Strawson might put it, reidentifiable. They are countable, as “one” if need be.
But it is difficult to consider the reidentifiability and the naturalistically real nature, of “one object” if that object is alone. “One object”, I argue, is not an “object”, and if we so construe it then it is because the single object is mistakenly taken to be “one” when we cast it in the default case of it being among others that can identify it. Now we must walk a tightrope, between those two, destructive, competing interpretations that have plagued non-Platonic Kantian and Wittgensteinian philosophies; philosophies which seemed to show a struggle, an awareness of the limitations of parts in expressing the whole. Strawson and other “ontological” interpreters of Kant argue that if an object is not reidentifiable then it is simply an incoherence. Granted, but only in consideration of the case of single objects that are countable by being among others. In the limit case, where an object is alone then, against Strawson, it would seem more rationale, more intuitive, more naturalistic, to regard such an object as uncountable and not reidentifiable.
Strawson’s other, mistaken, interpretation is that Kant was an idealist. That, even if we cannot reidentify an object then if it is a bona fide object it, nevertheless, can be so reidentified. Our psychological difficulties regarding identification of single objects, of monads, should not, so the Strawsonian argument must go (an argument echoed in Fregean arithmetical realism) prevent us from seeing all bona fide objects as being “in themselves” reidentifiable and real.
But the ontology I argue for - the ontology of the indistinguishability of the monad, or the realism of the uncountable object “alone”, is not a relativism nor is it a Strawsonian-warped interpretation of Kantian ontology corrupted by a Stawsonian-engineered, physical, thing-in-itself; nor yet is it an idealism crippled by skeptical doubt and the limits of sensory, psychological interpretation. The new “ontology” I describe can only be suggested, by Wittgensteinian elucidation if need be, but that is the nature of the transcendentally ideal, object-manifesting framework. There really is something new out there.