List: I adapted some of my posts from last summer in threads like "Is Synechism Necessary?" (here <https://list.iupui.edu/sympa/arc/peirce-l/2019-08/msg00029.html>), "Vargas on Continuity" (here <https://list.iupui.edu/sympa/arc/peirce-l/2019-09/msg00025.html>), and "Defining Continuity" (here <https://list.iupui.edu/sympa/arc/peirce-l/2019-09/msg00041.html>) to write a paper, "Peirce's Topical Continuum: A 'Thicker' Theory." I submitted it to *Transactions of the Charles S. Peirce Society*, and it is included in the current issue of that journal ( https://www.jstor.org/stable/10.2979/trancharpeirsoc.56.1.04). The following is the abstract.
Although Peirce frequently insisted that continuity was a core component of his philosophical thought, his conception of it evolved considerably during his lifetime, culminating in a theory grounded primarily in topical geometry. Two manuscripts, one of which has never before been published, reveal that his formulation of this approach was both earlier and more thorough than most scholars seem to have realized. Combining these and other relevant texts with the better-known passages highlights a key ontological distinction: a collection is bottom-up, such that the parts are real and the whole is an *ens rationis*, while a continuum is top-down, such that the whole is real and the parts are *entia rationis*. Accordingly, five properties are jointly necessary and sufficient for Peirce's topical continuum: rationality, divisibility, homogeneity, contiguity, and inexhaustibility. The article thus attempts to meet Matthew E. Moore's challenge <https://link.springer.com/article/10.1007/s11229-013-0337-6> to provide "a well-defined conception [of continuity], fully equipped to do all the philosophical work Peirce thought that it could do." Here are my one-sentence summaries of the five properties, employing Peirce's terminology of "portion" for a part and "limit" for a connection between parts (R 144, c. 1900). - Rationality - every portion conforms to one general law or Idea, which is the final cause by which the ontologically prior whole calls out its parts. - Divisibility - every portion is an indefinite *material* part, unless and until it is deliberately marked off with a limit to become a distinct *actual *part. - Homogeneity - every portion has the same dimensionality as the whole, while every limit between portions is a topical singularity of lower dimensionality. - Contiguity - every portion has a limit in common with each adjacent portion, and thus the same mode of immediate connection with others as every other has. - Inexhaustibility - limits of any multitude, or even exceeding all multitude, may always be marked off to create additional actual parts within any previously uninterrupted portion. I welcome feedback on this hypothetical/mathematical analysis of continuity, as well as suggestions of its potential implications for other fields of study. For example, over the last several months I have been exploring its applications in phenomenology/phaneroscopy, logic/semeiotic, and metaphysics, especially as they contribute to a comprehensive Peircean philosophy of time. Contrary to Moore's negative answer to his own question <http://revistas.pucsp.br/cognitiofilosofia/article/download/16603/12457>, my hope is that this formulation (or something like it) might facilitate demonstrating that synechism is as central to Peirce's entire system of thought as he consistently maintained. Thanks, Jon Alan Schmidt - Olathe, Kansas, USA Structural Engineer, Synechist Philosopher, Lutheran Christian www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt
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