Hi Jon A, John S, List, Thanks for the reference, Jon. I've found a number of texts to be helpful, including Allen Hatcher's Algebraic Topology, which is online and free. It was recommended by a professor named Wildberger who has a course on Youtube on the subject.
Having said that, there is precious little in Hatcher's text on the generation of topological spaces. In particular, there is little that explains how the greatest continuum of possible generators of dimensions such a space might be related--so that the dimensions would be vague. Do you know of works on topology where such a conception has been explored--because I've not found much that is helpful in sorting out the conception that Peirce seems to be holding up as a kind of limiting case of vagueness and continuity with respect to how the dimensions might be understood in their generation and relations. What is more, I don't see much of anything in the literature on the EG that uses the conception of a book of sheets to explore Peirce's suggestion. I think a model can be constructed that would illustrate the limiting case of a continuum of vague dimensions (i.e., sheets) and also help us to see how more definite dimension might be understood to evolve from it--as well as what is involved in such a model of the growth of more determinate dimensions from a vague continuum of sheets. For example, one of the ideas that might be explored is how sheets of interrogation might be pictured to evolve first--with relatively vague questions being scribed on such sheets in relations of different colors representing possibilities, and then later sheets of assertion and destination giving rise to hypotheses, etc. If you know of such sources, please share them. Or, if you have ideas about how to construct such models in topology or in the EG, I would be interested to hear the suggestions. --Jeff Jeffrey Downard Associate Professor Department of Philosophy Northern Arizona University (o) 928 523-8354 ________________________________________ From: Jon Awbrey [jawb...@att.net] Sent: Wednesday, November 9, 2016 6:46 PM To: Jeffrey Brian Downard Cc: John F Sowa; Edwina Taborsky; peirce-l@list.iupui.edu Subject: Re: Metaphysics and Nothing (was Peirce's Cosmology) Jeff, Topology is the most general study of geometric space. It is critical here to get beyond the “popular” accounts and learn the basics from a real math book. A classic introduction is General Topology by J.L. Kelley but there are lots of equally good choices out there. Jon http://inquiryintoinquiry.com > On Nov 9, 2016, at 6:34 PM, Jeffrey Brian Downard <jeffrey.down...@nau.edu> > wrote: > > John Sowa, Jon Awbrey, Edwina, List, > > I wanted to see if anyone have might suggestions for thinking about the > analogy between (1) mathematical models of the differentiation of spaces > starting with a vague continuum of undifferentiated dimensions and trending > towards spaces having determinate dimensions to (2) models for logic > involving similar sorts of dimensions? How might we understand processes of > differentiation of dimensions in the case of logic?
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