Counting, Cardinal Numbers, Ordinal Numbers

A common confusion between Cardinal Numbers and Ordinal Numbers is evident in the phrase 'learning how to count'.  Since one has likely already learned how to count in one's native language, 'learning how to count' in a foreign language cannot consist in the development of a new skill.  Rather, it means, more precisely, learning what the names of Numbers are in a foreign language.  But the process is no different in one's native language--what a child who knows 'how to count up to Seven' needs to learn next is not a repetition of the process, but that the name of the next number is 'Eight'.  And likewise with all the Numbers, starting with 'One'.  Thus, 'how to count' is distinct from 'naming the Numbers in order'.  Now, regardless of whether or not the structure is to be classified as 'a priori', the process of Counting has a subjective Ordinal structure--a starting point, a next, etc., which Kant calls 'succession'--that governs any act of naming an sequence of terms, such as Cardinal Numbers.  So, even if a child has not learned the names 'First', 'Second', etc., implicit knowledge of Ordinality is presupposed in any 'learning to count'.  In other words, 'learning how to count' in English means learning that first is 'One', second is 'Two', etc., which not only distinguishes Cardinal Numbers from Ordinal Numbers, but illustrates that the latter are prior to former, even functioning as such only implicitly.  Indeed, the concept of Priority is itself Ordinal, and, hence, the assertion 'Cardinality is prior to Ordinality' is contradictory.  Kant's exposition of his concept of Mathematics as a priori might have been clearer with an emphatic characterization of its basis as Ordinal Numerology.