Mathematics, Ordinality, Time

The influential Pythagorean concept of Number is not only Cardinal, as has been previously discussed, but Ontological, i. e. a fundamental constituent of objective Reality.  Protagoras is an early critic of the latter, denying the objectivity of Numbers.  He thus anticipates Berkeley's thesis that Number is a Secondary Quality.  Kant further systematizes the counter to Pythagoreanism, by associating Mathematics with the Forms of Intuition.  However, the association is only vaguely posited, grounded only by the brief suggestion that it is to specifically Space, perhaps because a Line helps him explain how Addition is a Synthetic operation.  He thus misses a more rigorous derivation, but from Time, and in terms of Ordinal Numerology.  For, his concept of Time as Succession is Ordinal, i. e. constituted by moments following one after another, and, hence, always the possible ground of a sequence of First, Second, etc.  He further misses that the fundamental Mathematical operation--Addition--is nothing but a representation of Counting, which is an Ordinal process, even if the terms of the process are Cardinal Numbers.  In other words, what is commonly expressed as a sequence of Cardinal Numbers--One, Two, Three, etc.--is, more precisely, Ordinal--First, One; Second, Two; Third, Three, etc.--in which the Temporal Form of Intuition is made explicit.  But Counting is also the basis of Measurement.  Thus, the Kantian concept of the fundamental structure of Intuition as Ordinal completes the Protagorean critique of Pythagoreanism expressed by 'Man is the measure of all things'.