“Logic too depends on presuppositions with which nothing in the real world corresponds, for example on the presupposition that there are identical things, that the same thing is identical at different points of time: but this science came into existence through the opposite belief (that such conditions do obtain in the real world). It is the same with mathematics, which would certainly not have come into existence if one had known from the beginning that there was in nature no exactly straight line, no real circle, no absolute magnitude.” —Menschliches, Allzumenschliches – Ein Buch Für Freie Geister, Friedrich Nietzsche, 1878, §11
“Number. —The invention of the laws of numbers was made on the basis of the error, dominant even from the earliest times, that there are identical things (but in fact nothing is identical with anything else); at least that there are things (but there is no ‘thing’). The assumption of plurality always presupposes the existence of something that occurs more than once: but precisely here error already holds sway, here already we are fabricating beings, unities which do not exist.” —Menschliches, Allzumenschliches – Ein Buch Für Freie Geister, Friedrich Nietzsche, 1878, §19
Hume also acknowledges that all reasoning depends upon construing classes of objects as the same, though they may not be the same, in An Enquiry Concerning Human Understanding, 1748, in Sect. IX. Of the Reason of Animals, §82:
“All our reasonings concerning matter of fact are founded on a species of Analogy, which leads us to expect from any cause the same events, which we have observed to result from similar causes. Where the causes are entirely similar, the analogy is perfect, and the inference, drawn from it, is regarded as certain and conclusive: nor does any man ever entertain a doubt where he sees a piece of iron, that it will have weight and cohesion of parts; as in all other instances, which have ever fallen under his observation. But where the objects have not so exact a similarity, the analogy is less perfect, and the inference is less conclusive; though still it has some force, in proportion to the degree of similarity and resemblance.”
But unlike Nietzsche, who sees it as a necessary deception and illusion, he merely takes it as a matter of course. This also gets into Set Theory and Genre Theory/Functional Grammar, because as Georg Cantor noted, “A set is a Many that allows itself to be thought of as a One.” So, the same configurations of field, tenor and mode are classified as belonging to the same register in Functional Grammar, which give rise to the same text types, but ultimately no text is, strictly speaking, “identical” to any other. They are merely assumed to be a One or our thinking would be impotent and chaotic.
[responsivevoice_button voice="US English Male"]