Properties of primes and natural mathematics: a minimalist algorithm for prime numbers

Abstract

This paper discusses precise quantification by means of number systems on the analogy of Jaspers’ (2005) earlier analysis of the comparatively vague type of quantification expressed by predicate calculus operators {all/every/each, some, no}. It is argued that numbers provide an interesting testing ground for the validity of the Boolean approach to quantifiers in Jaspers (2005). More specifically, this excursion into maths is undertaken to show that a very basic cognitive- logical system of oppositions which underlies natural language logic governs natural mathematics as well. The concrete starting point of the article is Popper’s twin prime problem, which is followed by a discussion of number systems, more specifically the distinction between the natural number system {(0,) 1, 2,...} and the prime number system. The former type of system will be argued to be orders characterized by the operation of addition/subtraction. The prime number sequence is different in that it is multiplicative/ divisional rather than additive. It is generally recognized in mathematical circles that the latter type of sequence is more complex than the former. This fact tallies well with (and hence provides indirect support for) the linguistic findings in Jaspers (2005), whose core was the claim that natural language disjunction – known to be isomorphic with addition in algebra – is cognitively and lexically less complex than conjunction, which is isomorphic with multiplication.