Thursday, March 13, 2014

Peirce's Continuum continued

Continuing from this post:

"Veronese's continuum -- intuitive, prelogical, pretopological -- starts from a non-set theoretic notion of emptiness, a weaving and amalgamating synthetic notion which can be viewed as a smooth fluid, both finite and unlimited, in which parts melt naturally with the whole" (31).

On 32 he discusses Brouer's continuum, where human minds can both mark the continuum and observe it, sounding a lot like Bryant's use of Spencer-Brown. Brouer calls this 'two-oneness' (32) (akin to our notions of Buddhist emptiness as 'not one, not two'), and how the general possibilia of continuum moves into the actual particular (33). This leads to a theory of 'boundaries unfolding' (34).

Starting on 36 he talks of Vopenka's alternative set theory, which "breaks the usual set theoretic equivalence between intensionality and extensionality." I'm again reminded of Bryant's notions of the difference between the two, where the virtual withdrawn of a suobject's endo-structure is intensional, and the actual exo-relations in its parts are extensional. Zalamea also notes that "very little of the indefinite and infinite range of intensional possibilia can be effectively actualized" (36). For Peirce, "the realm of possibilia and the intensionality of real potentials reign over the actual extensionality of existence" (37).

Note: All of which are discussed from other vantages in this thread (shameless plug).

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