Peirce’s Categories • 18

Re: Peirce’s Categories • 15

In These Uncertain Times, as people keep saying, it’s become even harder to concentrate than usual and I keep losing track of tricky points coming up in discussion which cry out for further discussion but then “human voices wake us, and we drown” or something … So let me go back to the list of loose ends I put together at the first of the month and try to address a few of them.

Here’s one juncture deserving of another look:

Every proposition is collective and copulative;  as I stated in a recent post, its dynamical object is “the entire universe” (CP 5.448n, EP 2:394, 1906), which is “the totality of all real objects” (CP 5.152, EP 2:209, 1903), while its immediate object is “the logical universe of discourse” (CP 2.323, EP 2:283, 1903).

This is a very important point, not the least because of the light it throws on a question John Corcoran raised on Facebook and elsewhere as to whether the logical universes of Peirce, or logicians in general, are conceived as referring to something like a holistic totality of existence or only a more limited universe of discourse relevant to a particular discussion.  I thought that significant enough to blog on it here:

Incidentally … lack of care in distinguishing different objects of the same signs, in particular, immediate and ultimate objects and their corresponding universes or object domains, has been the source of many misunderstandings in scattered discussions on Facebook of late.

But then I added:

Another issue arising here has to do with the difference between the “dimensionality of a relation” and the “number of correlates”.  Signs may have any number of correlates in the object domain without requiring the dimensionality of the relevant sign relation to be greater than three.  This is one of the consequences of “triadic relation irreducibility”.

And that raised a number of further replies from HR and objections from JAS … which I’ll say more about when I get a chance.


cc: CyberneticsOntolog • Peirce List (1) (2)Structural ModelingSystems Science

This entry was posted in Abstraction, Aristotle, C.S. Peirce, Category Theory, Logic, Logic of Relatives, Mathematics, Peirce, Peirce's Categories, Phenomenology, Pragmatic Maxim, Relation Theory, Semiotics, Triadic Relations, Triadicity, Type Theory and tagged , , , , , , , , , , , , , , , . Bookmark the permalink.

1 Response to Peirce’s Categories • 18

  1. Pingback: Survey of Precursors Of Category Theory • 2 | Inquiry Into Inquiry

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