A number is a nominalization and as such a distortion of our communication.
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. – Our sensations of space and time are false, for tested consistently they lead to logical contradictions. The establishment of conclusions in science always unavoidably involves us in calculating with certain false magnitudes: but because these magnitudes are at least constant, as for example are our sensations of time and space, the conclusions of science acquire a complete rigorousness and certainty in their coherence with one another; one can build on them – up to that final stage at which our erroneous basic assumptions, those constant errors, come to be incompatible with our conclusions, for example in the theory of atoms. Here we continue to feel ourselves compelled to assume the existence of a ‘thing’ or material ‘substratum’ which is moved, while the whole procedure of science has pursued the task of resolving everything thing-like (material) in motions: here too our sensations divide that which moves from that which is moved, and we cannot get out of this circle because our belief in the existence of things has been tied up with our being from time immemorial. – When Kant says ‘the understanding does not draw its laws from nature, it prescribes them to nature’, this is wholly true with regard to the concept of nature which we are obliged to attach to nature (nature = world as idea, that is as error), but which is the summation of a host of errors of the understanding. – To a world which is not our idea the laws of numbers are wholly inapplicable: these are valid only in the human world.
Human, All Too Human, book 1, paragraph 19