Fw: [PEIRCE-L] The Reality of Time

[Jeffrey Brian Downard]

Hi Jon S, List


It looks like we are barking up the same trees.


As Peirce points out in the 8th Cambridge Conferences Lecture in RLT, the 
self-returning character of a space or time manifold is a topological character 
of unbounded manifolds generally. We don't need to add in postulates concerning 
straightness and a line called the absolute needed for a projective geometry 
for the point about the self-returning character of hyperbolic manifolds to 
hold.


Hyperbolic manifolds come in different shapes. Some have an odd number of 
twists (i.e., cross-caps) in them. Others have an even number or no twists at 
all. Some manifolds, for instance, have the intrinsic character of a torus with 
no twists. If a torus has two or more holes, then it is hyperbolic in 
character. If it has one hole it is parabolic. If it has no holes, then it is 
elliptical. Roughly, a similar point holds for the number of cross caps found 
in a manifold.


Peirce makes this point when he suggests that the first question we should ask 
about our experience of time is its Euler characteristic or Listing number. On 
my reading of Peirce, it is important that we start by asking these kinds of 
questions about the topological character of our experience of time before 
turning to questions of how time is ordered--projectively or metrically.


That is, we need to ask these phenomenological questions about our experience 
of time before turning to metaphysical questions about its real nature. By 
asking these phenomenological questions about the character of our experience, 
we put ourselves in a better position to analyze the surprising observations 
that are calling out for metaphysical hypotheses. For example, we ask:  why 
does our experience of space seem have three dimension while time has only one, 
and why is time ordered in a manner that space is not? In turn, we hope to put 
ourselves in a better position to measure the data that are being used to test 
those explanations.


--Jeff




Jeffrey Downard
Associate Professor
Department of Philosophy
Northern Arizona University
(o) 928 523-8354

From: Jon Alan Schmidt 
Sent: Monday, March 9, 2020 9:23:49 AM
To: peirce-l@list.iupui.edu
Subject: Re: [PEIRCE-L] The Reality of Time

Jeff, List:

How can time be hyperbolic, yet return into itself?  The answer is found in 
projective geometry, which introduces a "line at infinity" such that the 
different conic sections are distinguished only by how many times they 
intersect it--zero for an ellipse, which is finite; one for a parabola, which 
extends to infinity in only one direction, either positive or negative; and two 
for a hyperbola, which extends to infinity in two directions, both positive and 
negative.  All three can then be conceptualized as closed curves such that the 
line at infinity never intersects an ellipse, is tangent to a parabola at one 
point, and crosses a hyperbola at two points (see attached "Projective 
Conics.jpg"; read its 
source to learn 
more).

These two points are the limits that divide a hyperbolic continuum into two 
portions, which have both of those limits in common.  As Peirce explains, we 
can then proceed to measure each portion using numbers such that one limit 
corresponds to positive infinity and the other to negative infinity.

CSP:  A hyperbolic quantity is one which varies from zero through all positive 
values to positive infinity (a "logarithmic" infinity, which is not equal to 
negative infinity), through that to a wholly new line of quantity where it 
descends through positive values to a sort of zero upon another line and thence 
through negative values through negative infinity to ordinary negative 
quantities, and so back to zero. (NEM 2:266; 1895)

CSP:  A circuit of states is a line of variation of states which returns into 
itself and has no extreme states ...
The order of states in a line of variation may be shown by attaching to 
sensibly different states different numbers. For if the line of variation forms 
a circuit, its states are related to one another like the real numbers, 
rational and irrational, positive and negative, including ∞ [infinity] ...
The numbers may occur in every assignable part of the circuit [parabolic], or 
may be contained between two limits [hyperbolic], or a part of the series of 
numbers may cover the whole circuit [elliptical]. In the last case 
[elliptical], we suppose the remaining numbers to be assigned to the circuit 
taken over and over again in regular arithmetical progression. In the second 
case [hyperbolic], we are at liberty to fill up the vacant part of the circuit 
with a second series of numbers which will be distinguished by having a 
quantity not a number added to it ...
[Measurement is] Hyperbolic, when the entire line of [real]* numbers occupies 
but a portion of the circuit of variation, and leaves a portion vacant …
In hyperbolic motion th

Re: [PEIRCE-L] The Reality of Time

[Jon Alan Schmidt]

Jeff, List:

JD:  As Peirce points out in the 8th Cambridge Conferences Lecture in
RLT, the self-returning character of a space or time manifold is a
topological character of unbounded manifolds generally. We don't need to
add in postulates concerning straightness and a line called the absolute
needed for a projective geometry for the point about the self-returning
character of hyperbolic manifolds to hold.


I have not dug into RLT on this topic yet, since I only have a hard copy
rather than a searchable PDF.  Which specific pages do you have in mind?

JD:  Hyperbolic manifolds come in different shapes. Some have an odd number
of twists (i.e., cross-caps) in them. Others have an even number or no
twists at all. Some manifolds, for instance, have the intrinsic character
of a torus with no twists. If a torus has two or more holes, then it is
hyperbolic in character. If it has one hole it is parabolic. If it has no
holes, then it is elliptical. Roughly, a similar point holds for the number
of cross caps found in a manifold.


I have already admitted that projective geometry is a conceptual stretch
for me, and topology is even more so.  Is there a relatively simple primer
anywhere online for hyperbolic/parabolic/elliptical toruses in topology,
like the one that I found and linked for hyperbolic/parabolic/elliptical
circles in projective geometry?

JD:  Peirce makes this point when he suggests that the first question we
should ask about our experience of time is its Euler characteristic or
Listing number. On my reading of Peirce, it is important that we start by
asking these kinds of questions about the topological character of our
experience of time before turning to questions of how time is
ordered--projectively or metrically.


"Topological character" is mathematical, while "our experience of time" is
phenomenological.  How would you suggest that we translate back and forth
between the two sciences?

JD:  That is, we need to ask these phenomenological questions about our
experience of time before turning to metaphysical questions about its real
nature. By asking these phenomenological questions about the character of
our experience, we put ourselves in a better position to analyze the
surprising observations that are calling out for metaphysical hypotheses.


I agree, and so does Peirce.

CSP:  The only important thing here is our metaphysical phenomenon, or
familiar notion, that the past is a matter for knowledge but not for
endeavor, that the future is an object that we may hope to influence, but
which cannot affect us except through our anticipations, and that the
present is a moment immeasurably small through which, as their limit, past
and future can alone act upon one another. Whether this be an illusion or
not, it is the phenomenon of which the metaphysician has to give an
account. (CP 8.113; c. 1900)


Our *phenomenological *experience of time prompts our *mathematical *hypotheses
about time.  We then employ *logical/semeiotic* principles in order to
ascertain the *metaphysical *reality of time.

JD:  For example, we ask: why does our experience of space seem have three
dimension while time has only one, and why is time ordered in a manner that
space is not? In turn, we hope to put ourselves in a better position to
measure the data that are being used to test those explanations.


The Peirce quote above explains how our phenomenological experience
requires something like the "arrow of time" to account for the undeniable
difference between our memory of the past and our anticipation of the
future.  Elsewhere he suggests that this is precisely what *requires *time
to be one-dimensional, which is obviously not the case with space.

CSP:  For example, every-day experience is that events occur in time, and
that time has but one dimension. So much appears necessary. For we should
be utterly bewildered by the suggestion that two events were each anterior
to the other or that, happening at different times, one was not anterior to
the other. But a two-dimensional anteriority is easily shown to involve a
self-contradiction. So, then, that time is one-dimensional is, for the
present, necessary; and we know not how to appeal to special experience to
disprove it. But that space is three dimensional involves no such
necessity. We can perfectly well suppose that atoms or their corpuscles
move freely in four or more dimensions. (CP 1.273; 1902)


Along similar lines, a manuscript that was presumably an early draft of
some ideas for RLT, "Abstracts of 8 Lectures" (R 942), begins with this
interesting passage.

CSP:  We thus see that the bare Nothing of Possibility logically leads to
continuity.
For the first step a unidimensional continuum is formed.
Logically, this step is of the nature of induction. Now induction arranges
possible experience after the type of logical law. But the logical law *par
excellence* is that of logical sequence. Hence, the first dimension of the
continuum of quality is a sequence. A sequen

[PEIRCE-L] Peirce and Coimbra + Reading Peirce

[Robert Junqueira]

List,
I am very happy to share the following:

1.
http://www.conimbricenses.org/encyclopedia/charles-sanders-peirce-coimbra/

2. https://www.youtube.com/watch?v=FL1uR-FLgY8&t=6s

The 1st is an encyclopedia entry, and the 2nd is an audio-recording.

1. As I am now preparing a PhD project on Peirce's semiotics to submit to
the Faculty of Arts and Humanities of the University of Coimbra, concerning
his reception of medieval *doctrina signorum*, any comments are welcome.

2. I will keep on "reading Peirce out loud"; suggestions on texts to
include in the series are also welcome.


Best regards,
Robert

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[PEIRCE-L] Re: Pragmatic Theory Of Truth

[Jon Awbrey]

Cf: Pragmatic Theory Of Truth : 22
At: 
http://inquiryintoinquiry.com/2020/03/09/pragmatic-theory-of-truth-%e2%80%a2-22/

Re: Systems Science ( 
https://groups.google.com/d/topic/syssciwg/H673ep6U_Ug/overview )
::: Scott Jackson ( 
https://groups.google.com/d/msg/syssciwg/H673ep6U_Ug/lQJ7Yr5DHQAJ )

All,

Discussions of "thinking and flawed decisions" arising in the Systems Science Working Group naturally brought the topic 
of Pragmatic Truth and all its bedeviled vicissitudes back to this Peircean's mind.


I have often observed how belief systems act in a way like immune systems, generating "antibodies" to combat the 
"antigens" of any ideas beyond their comfort zones.


Elsewhere, I described these phenomena under the heading of Information 
Resistance
( 
https://inquiryintoinquiry.com/2015/06/10/information-resistance-%e2%80%a2-%cf%89/
 )

* "The hardest thing to understand about information is people's resistance to 
it."

The locus pragmaticus for the study of belief systems
and the impact of information and inquiry on them is
C.S. Peirce's "The Fixation of Belief".  See the
preceding post in this series for comment and links:
( 
https://inquiryintoinquiry.com/2020/01/06/pragmatic-theory-of-truth-%e2%80%a2-21/
 )

Reference
=

* Peirce, C.S. (1877), "The Fixation of Belief", Popular Science Monthly 12, 
1–15.
( https://arisbe.sitehost.iu.edu/menu/library/bycsp/fixation/fx-frame.htm ),


Resource


* Pragmatic Theory Of Truth
( https://oeis.org/wiki/Pragmatic_Theory_Of_Truth )

Regards,

Jon

inquiry into inquiry: https://inquiryintoinquiry.com/
academia: https://independent.academia.edu/JonAwbrey
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