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Aihe: Re: [PEIRCE-L] Re: Did Peirce Anticipate the Space-Time Continuum?
Päiväys: 29.5.2017 18:13
Lähettäjä: kirst...@saunalahti.fi
Vastaanottaja: Jerry LR Chandler <jerry_lr_chand...@me.com>
Jerry,
Well, stricly speaking you are not taking up a triad, but three
interconnected propositions.
Anyway, you asked about MY views .
- Euclidean geometric line does not even exist outside Euclidean
geometry. It is an abstraction, a part of results of systematic human
imagination. Thus there is no sense in assumiming it has any properties
outside the geometry in question. Continuity was assumed, that is true.
But as it turned out, Euclidean geometry could only deal with issues of
limited scale. - Continuity demands unlimited scale.
- Any Euclidean geometric line is treated as(and assumed to be)
continuous. But so is the case with non-Euclidean geometry just as well.
- It was only the (pre)supposition that a geometric line is and will be
forever straight, not bend, that was put into question. With the very
good results. - Thus became modern topology into being!
- It makes no sense to ask whether a continuum is continuous or not. Of
course any continuum is continuous, It is presupposed. But within its
own limits. So no answer to this question can provide any answet to the
question of continuity per se.
Here comes functional geometry and differential and integral calculus to
the fore. SCP handled them like water in his tab. - Euclid did not have
any inkling of these issues.
Infinity became something mathematicians could and did handle. - Or
could they, really?
Just provisional answers,
Kirsti
Jerry LR Chandler kirjoitti 29.5.2017 17:42:
Kirsti, List:
Could you expand your intervention to give some examples of how YOU
assign tangible meaning to CP 1.501?
Other comments will have to wait, but for one.
A Euclidian geometric line has continuity.
A Euclidian geometric line is continuous.
A Continuum is continuous.
Do you agree with this triad? :-)
Cheers
jerry
On May 29, 2017, at 9:05 AM, kirst...@saunalahti.fi wrote:
Dear listers,
I do not think the title of this thread is well-thought. There is
nothing such as a "Space-Time Continuum" which could be reasonably
discussed about. Even though it is often repeated chain of words.
For the first: Continuity does not mean the same as does 'continuum'.
- and this is not a trifle issue. Within philosopy one should mind
one's wordings.
For the second: Take into true consideration the quote provided:
MB
One of my favorite Peirce quotes... "space does for different
subjects
of one predicate precisely what time does for different predicates
of
the same subject." (CP 1.501)
Here CSP is clearly talking about conceptual issues & philosophizing.
The key point being the relation between 'subject' and 'predicate'.
CSP differentiates between considerations of space and time. At least
he does so in separating the issues for a specific approach
&consideration each approach needs.
What CSP is saying, is to my mind, that continuity in time and
continuity in space need to be fully grasped BEFORE taking them both
as an issue to be tackled. Especially by such a concept as a
continuum.
A continuum has a beginning and an end. It is presupposed in the very
concept. The very idea of a big (or little) bang as a start or an end
just illustrates current minds, current common sense. The still
dominating nominalistic world-view.
What is non-Eucleidean geometry about? It is about radically changing
the scale. Any line which appeared to previous imagination as a
straight one, and necessarily so, does not appear so after the fact
that the earth is round had been fully digested.
This is not assumed to play any part in the invention of non-Euclidean
geometry. And it does not in the stories and histories told about it.
The earth does appear flat, in the experiential world of all human
beings. And goes on to appear so untill interplanetary tourism becomes
commonplace. Flat, although somewhat bumby.
I am curious about possible responses. Do wish I'll get some.
Kirsti
John F Sowa kirjoitti 20.5.2017 00:28:
Jeff and Mike,
Those are important points.
JBD
In a broad sense, Sir William Rowan Hamilton anticipated Einstein's
idea that space and time can be conceived as parts of a four
dimensional
continuum. In fact, he used the algebra of quaternions to articulate
a
formal framework for conceiving of such physical relations as part
of a
four dimensional field.
Peirce was familiar with Hamilton's work. And when he was editing
the second edition of his father's book _Linear Algebra_, he added
some important theorems to it. In particular, he proved that the
only N-dimensional algebras that had division were the real line
(1D), the complex field (2D), quaternions (4D), and octonions (8D).
MB
One of my favorite Peirce quotes... "space does for different
subjects
of one predicate precisely what time does for different predicates
of
the same subject." (CP 1.501)
He also discussed non-Euclidean geometry. While he was still at the
US C&GS, he proposed a project to determine whether the sum of the
angles of triangles at astronomical distances was exactly 180
degrees.
Simon Newcomb rejected that project.
John
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