Helmut, List: According to Peirce, "Continuity represents 3ns almost to perfection" (CP 1.337, c. 1882). When we prescind discreteness from continuity, we are prescinding 2ns from 3ns, and we cannot prescind continuity from discreteness because we cannot prescind 3ns from 2ns. Since prescission "consists in supposing a state of things in which one element is present without the other, the one being logically possible without the other" (EP 2:270, 1903), the upshot is that 2ns is logically possible without 3ns, but 3ns is not logically possible without 2ns. Put another way, 3ns always *involves *2ns as well as 1ns, and 2ns always *involves *1ns. Nevertheless, 2ns cannot be *built up* from 1ns, and 3ns cannot be *built up* from 1ns and/or 2ns.
For example, a continuous line involves any discrete points within it, but it cannot be built up from any multitude of such points. The continuous whole (line) is ontologically prior to any discrete parts (points), which are indefinite (infinitesimal "linelets") unless and until they are deliberately marked off within it. Likewise, as I said before, the entire universe is an inexhaustible continuum (3ns) of indefinite possibilities (1ns), some of which are actualized (2ns). In Peirce's words, "The whole universe of true and real possibilities forms a continuum, upon which this Universe of Actual Existence is, by virtue of the essential 2ns of Existence, a discontinuous mark--like a line figure drawn on the area of the blackboard" (NEM 4:345, 1898; see also CP 6.203-209, 1898). Regards, Jon Alan Schmidt - Olathe, Kansas, USA Structural Engineer, Synechist Philosopher, Lutheran Christian www.LinkedIn.com/in/JonAlanSchmidt / twitter.com/JonAlanSchmidt On Mon, Feb 12, 2024 at 11:01 AM Helmut Raulien <h.raul...@gmx.de> wrote: > > List, I think, we can prescind discreteness from continuity, e.g. by > supposing the formation of attractors, or coagulation, or reentry (logical > or actual loops), but we cannot prescind continuity from discreteness. So > everything including thirdness is at first based on continuity, even if it > requires discreteness. I think, that thirdness requires discreteness, > because a relation as part of structure, and a habit too, can and has to be > prescinded (or discriminated, or dissociated) as something discrete from > continuity, to logically handle it. > > Best, Helmut >
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