The classification even/odd is radical: it provides what modern mathematicians call a partition of the whole set. Numbers themselves very early on got classified into even and odd, the most fundamental numerical distinction after the classification one and many which is even more basic. Psychologically human beings have a very strong inclination to proceed by straight two-valued distinctions, light/dark, this/that, on/off, sacred/profane, Greek/Barbarian, Jew/Gentile, good/evil and so on - more complex gradations are only introduced later and usually with great reluctance Science has eventually recognized the complexity of nature and apart from gender there are not many true scientific dichotomies left though we still have the classification of animals into vertebrates and invertebrates. Plato thought that this principle, dichotomy, was so fundamental that all knowledge was based on it - the reason for this being because the brain works in this way, the nerve synapsis is either ‘on’ or ‘off’. What people do ‘naturally’ is to make distinctions of type not number and the favourite principle of division by type is the two-valued either/or principle.

Animals and so-called primitive peoples do not bother to make nice distinctions between entities on the basis of number and even today, when deprived of technological aids, we are not at all good at it ( Note 1).

Odd vs even numbers