divergences between operationalism and metalogical dualism

by metalogike

AB: There is no one, only the count-as-one.

Reply: There is no one, only ones.

AB: This [operational interpretation of the count-as-one] is the most general definition of a structure.

Reply: Indeed, but because it is the most general, it is not the best. To give the most general definition of unity is, since the one is not, to vitiate structures, of which the unity of each is heterogeneous to the others, to the zero-point of simple consistency.  It is from the point of view of the All, that is, or of a total language that unity is operational (which is to say, nominal).

AB: The Idea of the Good is the most majestic form of the Great Temptation to deny that ontology is a situation, specifically one which reverses the vector of every other situation, by giving an axiomatic (implicit) definition of the pure multiple.

Reply: The Idea of the Good, or diagonalization, is the witness not of the incoherence (inconsistency) of ontology, but of its incompleteness, which however is also to say, of its inconsistency if imagined as completeso that any strictly axiomatic presentation is not merely implicit but necessarily falls infinitely short in its deductive consequences of ontology – or even, for that matter, of arithmetic – and this condition (the infinite excess even of ordinary arithmetic over its axiomatic presentation) must be dealt with at the outset.