Jon, List:
> On Mar 2, 2017, at 7:36 PM, Jon Alan Schmidt <[email protected]> wrote:
>
> 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?
>
Jon: You are right in that this is CSP's view of continuity (which is nicely
framed in the book by Moore.)
At the same time, this is exactly the origin of problem.
Each chemical atom is an independent physical object such that the sum of the
microscopic property of mass gives rise to a mass that we can experience as a
unique form or type.
At the same time, each chemical element is a microscopic object that is
physically independent of all other chemical elements in that its physical
properties (attributes, signs, qualisign) are unique to its identity.
At the same time, the table of chemical elements is complete and each element
is independent of all other elements, YET the TABLE of ELEMENTS is ordered by
the integers, the atomic numbers.
My question
> Is it possible that a “regulatory principle of logic” is a continuity in the
> sense of excluding Boscovichian points?
is related directly to the notion of synechism which CSP defines:
EP 2:1 The word synechism is the English form of the Greek {synechismos}, from
{synechés}, continuous. For two centuries we have been affixing -ist and -ism
to words, in order to note sects which exalt the importance of those elements
which the stem-words signify. Thus, materialism is the doctrine that matter is
everything, idealism the doctrine that ideas are everything, dualism the
philosophy which splits everything in two. In like manner, I have proposed to
make synechism mean the tendency to regard everything as continuous.
(EP 2 2:3) There is a famous saying of Parmenides {esti gar einai, méden d’ ouk
einai}, “being is, and not-being is nothing.” This sounds plausible; yet
synechism flatly denies it, declaring that being is a matter of more or less,
so as to merge insensibly into nothing. [—]
Synechism, even in its less stalwart forms, can never abide dualism, properly
so called. [—]
At the same time, the realism of physics demonstrates the dualism and
equi-numeracity of positive and negative charges of all chemical atoms.
Is it conceivable that anyone can propose a resolution of these conundrums?
How does Ben’s notion of singularities fit into this picture?
How do Jeff’s questions fit into this picture?
>From the perspective of the philosophy of mathematics, how do these conundrums
>relate to the simplicity of set theory (and the nonsense?) of the “Laws of
>Form”?
Cheers
Jerry
> Regards,
>
> Jon Alan Schmidt - Olathe, Kansas, USA
> Professional Engineer, Amateur Philosopher, Lutheran Layman
> www.LinkedIn.com/in/JonAlanSchmidt
> <http://www.linkedin.com/in/JonAlanSchmidt> - twitter.com/JonAlanSchmidt
> <http://twitter.com/JonAlanSchmidt>
> On Thu, Mar 2, 2017 at 5:59 PM, Jerry LR Chandler
> <[email protected] <mailto:[email protected]>> 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 <[email protected]
>> <mailto:[email protected]>> 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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