[PEIRCE-L] Re: Differential Propositional Calculus

2020-03-07 Thread Jon Awbrey

Cf: Differential Propositional Calculus : 8
At: 
http://inquiryintoinquiry.com/2020/03/07/differential-propositional-calculus-%e2%80%a2-8/

Differential Extensions
===

An initial universe of discourse, A+, supplies the groundwork for any number of further extensions, beginning with the 
"first order differential extension", EA+.  The construction of EA+ can be described in the following stages:


Note. Breaking here because the rest of this
  post requires too much math formatting.
  Please see the blog post linked above or
  the wiki copy at the following location:

Differential Propositional Calculus : Part 2 : Differential_Extensions
https://oeis.org/wiki/Differential_Propositional_Calculus_%E2%80%A2_Part_2#Differential_Extensions

<...>

A proposition in a differential extension of a universe of discourse is called a "differential proposition" and forms 
the analogue of a system of differential equations in ordinary calculus.  With these constructions, the "first order 
extended universe" EA+ and the "first order differential proposition" f : EA->B, we have arrived, in concept at least, 
at the foothills of "differential logic".


Table 11 summarizes the notations needed to describe the first order differential extensions of propositional calculi in 
a systematic manner.


Table 11.  Differential Extension : Basic Notation
https://inquiryintoinquiry.files.wordpress.com/2020/03/differential-extension-basic-notation.png

Regards,

Jon

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Re: [PEIRCE-L] The Reality of Time

2020-03-07 Thread michaelcjm

All,
I often read that space is distinct from time,
Then we have in the slit experiment a hint that there are things we can 
see "sometimes".
This gave me the idea that time (where we always "are") is an extrusion, 
and dimensions other than time are an intrusion.

(Three of the latter, we are equipped to "know")
Michael Mitchell
amateur philosopher
Home-self-schooling catcher upper


On Thu, Mar 5, 2020 at 1:56 AM Jeffrey Brian Downard
 wrote:

Jon, List,

Consider what Peirce says about his cosmological conception of time
in a letter to Christine Ladd-Franklin. For the sake of clarity,
I'll separate and number the points he makes.

1.   I may mention that my chief avocation in the last ten years has
been to develop my cosmology. This theory is that the evolution of
the world is hyperbolic, that is, proceeds from one state of things
in the infinite past, to a different state of things in the infinite
future.

2.   The state of things in the infinite past is chaos, tohu bohu,
the nothingness of which consists in the total absence of
regularity. The state of things in the infinite future is death, the
nothingness of which consists in the complete triumph of law and
absence of all spontaneity.

3.   Between these, we have on our side a state of things in which
there is some absolute spontaneity counter to all law, and some
degree of conformity to law, which is constantly on the increase
owing to the growth of habit.

4.   As to the part of time on the further side of eternity which
leads back from the infinite future to the infinite past, it
evidently proceeds by contraries.  8.316

Focusing on the points made in 3 and 4, how might we understand the
contrast being made between our side of things, and the part of time
that is on the further side of eternity?

A helpful approach, I think, is to start with a mathematical
diagram. What kind of diagram might we use to clarify the hyperbolic
evolution from the infinite past to the infinite future? Using this
diagram, what is the contrast between our side of things and the
further side of eternity?

--Jeff

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

From: Jeffrey Brian Downard
Sent: Wednesday, March 4, 2020 11:37:06 PM
To: peirce-l@list.iupui.edu
Subject: Re: [PEIRCE-L] The Reality of Time

Hello Jon, List,

At the beginning of the post, you note that Peirce engaged in
"mathematical, phenomenological, semeiotic, and metaphysical"
inquiries concerning time. Do you have any suggestions about how we
might tease out the different threads? Each seems to involve
somewhat different methods.

--Jeff

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

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