Peircean Continuum

Traits of Peircean continuum#

1. Generacity and Supermultitudeness. 
   1. The general - can live in the realm of possibilia, not determinate nor actual, and which opposes the particular mode of the existential; continuity is genericity via relative logic. (fundamental theorems of the logic of relatives are no more than corresponding continuity theoreoms in the uniform topological space of first-order logic elementary classes.) 
   2. Supermultitudinous. The size muyst be fully generic and cannot be bounded by any other actually determined size.
2. reflexivity and Inextensibility.
   1. Reflexivity. The continuum is defined as something any part of which however small itself has parts of the same kind. (thus gesturing towards self-similarity and fractal). Thus thera re no points, no exact boundary between any parts. It is intrinsically doubtful percisely where each number is placed (i.e. first and foremost topological without being equipped with a distance; also recall structuralism where numbers only matter in their mutual relation; no absolute position for numbers).
   2. Inextensibility. Implied by reflexivity: cannot be composed of points. Number cannot possibly express continuity. Lengths are not measurable by numbers, nor by limits of series of them.
3. Modality and Plasticity.
   1. Modal: it is a complex modal logis, a collection of all that is possible, in whatever dimension it be continuous.
   2. Plasticity. Felxible, plastic, homogeneous, without irregularities (since these are individuations/actualizations).

Actualization/individuation is symmetry breaking.