Peirce's Continuum

See this prior post and comments on Zalamea. For now just a brief excerpt from his book Peirce's Continuum:

"It should be obvious that a given model alone (actual, determinate) cannot, in principle, capture all the richness of a general concept (possible, indeterminate). [...] The existence of multiple ways of representing and modeling should avoid any identification of a mathematical concept with a mathematical object. [...]  It turns out that continuity is a protean concept, which [...]  can be modeled in several diverse ways. [...] The continuum (general)  can only be approached by its different signs (particular models) in representational contexts" (4 - 5).