Jerry C., LIst: Peirce makes it very clear elsewhere (and repeatedly) that a *true *continuum does not contain *any *points or other definite, indivisible parts. He defines it as that which has *indefinite *parts, all of which have parts of the same kind, such that it is *undivided* yet infinitely *divisible--*e.g., into infinitesimal lines rather than points. Does that help at all?
Regards, Jon Alan Schmidt - Olathe, Kansas, USA Professional Engineer, Amateur Philosopher, Lutheran Layman www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt On Thu, Mar 2, 2017 at 5:59 PM, Jerry LR Chandler < jerry_lr_chand...@icloud.com> wrote: > List, Ben: > > Your recent posts contribute to a rather curious insight into CSP’s > beliefs about the relationships between mathematics, chemistry and logic of > scientific hypotheses. > > On Mar 2, 2017, at 10:58 AM, Benjamin Udell <baud...@gmail.com> wrote: > > from MS 647 (1910) which appeared in Sandra B. Rosenthal's 1994 book _Charles > Peirce's Pragmatic Pluralism_: > > An Occurrence, which Thought analyzes into Things and Happenings, is > necessarily Real; but it can never be known or even imagined in all its > infinite detail. A Fact, on the other hand[,] is so much of the real > Universe as can be represented in a Proposition, and instead of being, like > an Occurrence, a slice of the Universe, it is rather to be compared to a > chemical principle extracted therefrom by the power of Thought; and though > it is, or may be Real, yet, in its Real existence it is inseparably > combined with an infinite swarm of circumstances, which make no part of the > Fact itself. It is impossible to thread our way through the Logical > intricacies of being unless we keep these two things, the Occurrence and > the Real Fact, sharply separate in our Thoughts. [Peirce, MS 647 (1910)] > > In that quote Peirce very clearly holds that not all will be known or can > even be imagined. > > In MS 647, he compares a fact with "a chemical principle extracted > therefrom by the power of Thought;” That is, the notion of a fact is in > the past tense. It is completed and has an identity. It is no longer is > question about the nature of what happened during the occurrence. Thus the > separation from: "in its Real existence it is inseparably combined with > an infinite swarm of circumstances, which make no part of the Fact itself. > ” > > Now, compare this logical view of a chemical principle with the > mathematical relation with the realism of matter in the synechism (EP1, > 312-333.): > > The things of this world, that seem so transitory to philosophers, are not > continuous. They are composed of discrete atoms, no doubt *Boscovichian* > <https://en.wikipedia.org/wiki/Roger_Joseph_Boscovich>* points (my > emphasis)*. The really continuous things, Space, and Time, and Law, are > eternal.” > > Do you believe that CSP is asseerting that there exist two clear and > distinctly different notions of mathematical points? > That is, the Boscovichian points of discrete atoms as contrasted with the > points of ”really continuous things, space, time and Law"? > > What would be an alternative hypothesis? That true continuity does not > contain points? > Would it be necessary for a legi-sign be something other than space and > time because they would not be points?? > > Any ideas on the ontological status of Boscovichian points from your > perspective of singularities? > > More precisely, what is the meaning of > > Synechism … it is a regulative principle of logic, prescribing what sort > of hypothesis is fit to be entertained and examined.?? > > Is it possible that a “regulatory principle of logic” is a continuity in > the sense of excluding Boscovichian points? > > Very confusing, to say the least. > > Cheers > > Jerry >
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