ABSTRACT
Even within the domain of discourse the principles of logic have been challenged, but, although construction of alternative systems has lead to the discovery that the principle of the Excluded Middle can be superseded, no one has yet built a logic which is based on insignificance or inconsistency. Let logic be taken for a moment as a mere game; even so it must preserve distinctions of significance, the distinctions of type between functions and individuals, the discreteness of individuals, the difference between theorems and contingent formulas. Indeed, metaphysicians and artists as well as “common-sense” people have often described reality as a continuum of blending sensations and emotions; yet it is equally true that the continuum of experience is a background against which manifestations are detached which are nearly discrete to perception and entirely so in conceptual analysis.
