Jerry, Jon S, list,
Jerry, you wrote,
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.”
Yes, there's something pastlike about facts, even supposed facts. The
notion of fact seems to have a pastward perspective.
You continued,
Now, compare this logical view of a chemical principle with the
mathematical relation with the realism of matter in the synechism
(EP1, 312-333.):
I'm not sure what comparison you were making. Your sentence above needs
to be rewritten.
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?
[End quote]
As far as I can tell from Web searches, a Boscovichian point is a point
mass that can attract and repel. So, although it lacks shape, color,
etc., it is still richer than a generic mathematical point. I suspect
that Peirce would expect any point-particles that actually physically
exist to be richer than generic mathematical points that one simply
supposes in a physical continuum.
Peirce's general view is that a continuum _/has room for/_ points, or
instants, or whatever kind of singularities, but, as Jon S. emphasizes,
_/does not consist of/_ them, whether the given continuum is a
mathematical hypothetical object or is physical. In Peirce's sense, one
can say that a continuum "can contain" points, as long as one does not
thereby mean that a continuum consists of points. (Sometimes it seems
convenient to consider a line as a set of points, but I don't know
whether Peirce was willing to do so even if just for convenience.)
You wrote,
Would it be necessary for a legi-sign be something other than space
and time because they would not be points??
[End quote]
Legisigns aren't singular points but generals. Either way, they don't
need to be outside of space and time (or some mathematical
generalization of space and time), even in the case of a legisign that
helps represent a mathematical point. Even a sign that is, itself, a
singularity - some sort of extreme sinsign, I guess - does not need to
be outside of space and time, since space and time can harbor it without
being it (and other points). It's hard to think of sign, object,
interpretant, semiosis, as quite outside of space and time. All thought
is in signs because all thought takes time. Arguably mathematical
objects at their most abstract are not spatio-temporal, and insofar as
some serve as signs of others, those signs aren't spatio-temporal
either. But our minds need to experiment diagrammatically with them in
spacetime in order to learn anything about them. The idea that
mathematical objects are anything more than the diagrammatic legisigns
that represent them seems to require that those objects be more abstract
than we can fully achieve. I.e., we seek to make the mathematical
diagrammatic legisigns definite only in pertinent respects and vague in
all others, but keep falling short, so to speak. Peirce in his section
of "Truth and Falsity and Error," Baldwin's _Dictionary of Philosophy
and Psychology_ v. 2, 1911, pages 718-720, reprinted in CP 5.565-573,
see 567
http://www.gnusystems.ca/BaldwinPeirce.htm#Truth :
These characters equally apply to pure mathematics. Projective
geometry is not pure mathematics, unless it be recognized that
whatever is said of rays holds good of every family of curves of
which there is one and one only through any two points, and any two
of which have a point in common. But even then it is not pure
mathematics until for points we put any complete determinations of
any two-dimensional continuum. Nor will that be enough. A
proposition is not a statement of perfectly pure mathematics until
it is devoid of all definite meaning, and comes to this — that a
property of a certain icon is pointed out and is declared to belong
to anything like it, of which instances are given. The perfect truth
cannot be stated, except in the sense that it confesses its
imperfection. The pure mathematician deals exclusively with
hypotheses. Whether or not there is any corresponding real thing, he
does not care. His hypotheses are creatures of his own imagination;
but he discovers in them relations which surprise him sometimes. A
etaphysician may hold that this very forcing upon the
mathematician's acceptance of propositions for which he was not
prepared, proves, or even constitutes, a mode of being independent
of the mathematician's thought, and so a _/reality/ _. But whether
there is any reality or not, the truth of the pure mathematical
proposition is constituted by the impossibility of ever finding a
case in which it fails. This, however, is only possible if we
confess the impossibility of precisely defining it.
[End quote]
You wrote,
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?
I don't see why any Peircean regulatory principle would exclude
Boscovichian points. In the sense that the regulatory principle itself
is a continuum, it will not harbor or have room for Boscovichian points
(point masses that can physically attract and repel), since it is not a
physical continuum in the first place.
Best, Ben
On 3/2/2017 6:59 PM, Jerry LR Chandler 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
-----------------------------
PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON PEIRCE-L
to this message. PEIRCE-L posts should go to [email protected] . To
UNSUBSCRIBE, send a message not to PEIRCE-L but to [email protected] with the
line "UNSubscribe PEIRCE-L" in the BODY of the message. More at
http://www.cspeirce.com/peirce-l/peirce-l.htm .
