All Process, No Paradox

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Jon Awbrey

Mar 12, 2021, 12:00:21 PM3/12/21
to Cybernetic Communications, Laws of Form, Ontolog Forum, Peirce List, Structural Modeling, SysSciWG
Cf: All Process, No Paradox • 1

| This thing all things devours:
| Birds, beasts, trees, flowers;
| Gnaws iron, bites steel;
| Grinds hard stones to meal;
| Slays king, ruins town,
| And beats high mountain down.
| Tolkien • The Hobbit

Talking about time is a waste of time. Time is merely an abstraction from process
and what is needed are better languages and better pictures for describing process
in all its variety. In the sciences the big breakthrough in describing process came
with the differential and integral calculus, that made it possible to shuttle between
quantitative measures of state and quantitative measures of change. But every inquiry
into a new phenomenon begins with the slimmest grasp of its qualitative features and
labors long and hard to reach as far as a tentative logical description. What can avail
us in the mean time, still tuning up before the first measure, to reason about change in
qualitative terms?

Et sic deinceps ... (So it begins ...)


Jon Awbrey

Mar 13, 2021, 12:16:23 PM3/13/21
to Cybernetic Communications, Laws of Form, Ontolog Forum, Peirce List, Structural Modeling, SysSciWG
Cf: All Process, No Paradox • 7

| Unlike more superficial forms of expertise,
| mathematics is a way of saying less and less
| about more and more. A mathematical text is
| thus not an end in itself, but a key to a world
| beyond the compass of ordinary experience.
| G. Spencer Brown • Laws of Form

Re: Laws of Form
::: James Bowery

Dear James,

Sorry for the sluggish response … but I've been slogging through
a mass of mindless link repair due to the slew of url-extinctions
and url-mutations afflicting our web of maya over the last few years.
I've been working to recover-revise my better contributions to the
old LoF list along the lines of what Spencer Brown wrote about time
and imaginary logical values and the impact it had on my own work
with logical graphs from the early days on.

There was a time when I spent a lot of time thinking about the
“phenomenology of internal time consciousness” and such but that was
a long time passing. I think I first learned the word “phenomenology”
from readings in Bachelard and Sartre but my current take on it is more
heavily influenced by subsequent experiences in physics labs and libraries.

Physicists speak of the need to reflect on the circumstance that
even our most exalted theories get their first leg up from our
“naked eye” perception of “pointer readings”, that is, from the
superposition in our visual field of a needle on a graduated dial,
or the analogous incidentals in other sensory modes. As a rule,
a working physicist would never think of taking that “observation
of obvious” truths in too reductive a sense, since that would lead
to sheer sensationalism, and even the purest experimentalist has a
better appreciation for the role of theoretical conception than that.

Well, I didn't know I was gong to write this much when I opened the page,
but I started remembering experiences and thoughts from the earliest days.
At any rate, I think I'll blog this on my series about Process and Paradox
since that is occupying my mind at present and I wouldn't want to sidetrack
the time-phenomenology line.



inquiry into inquiry:
facebook page:

Jon Awbrey

Mar 16, 2021, 1:08:19 PM3/16/21
to Cybernetic Communications, Laws of Form, Ontolog Forum, Peirce List, Structural Modeling, SysSciWG
Cf: All Process, No Paradox • 8

| These are the forms of time, which imitates eternity
| and revolves according to a law of number.
| Plato • Timaeus 38 A
| Benjamin Jowett (trans.)

Re: Laws of Form ( )

Dear Seth, James, Lyle, All ...

Nothing about calling time an abstraction makes it a nullity.
I'm too much a realist about mathematical objects to ever mean
that. As a rule, on the other hand, I try to avoid letting
abstractions leave us so absent-minded as to forget the concrete
realities from which they are abstracted. Keeping time linked to
process, especially the orders of standard process we call “clocks”,
is just part and parcel of that practice.

Synchronicity being what it is, this very issue came up just last night in
a very amusing Facebook discussion about “windshield wipers slappin' time …”
( )

At any rate, this thread is already moving too fast for the pace
I keep these days but maybe I can resolve remaining confusions about
the game afoot by recycling a post I shared to the old Laws of Form list.
This was originally a comment on Lou Kauffman's blog back when he first
started it. Sadly, he wrote only a few more entries there in the time since.

Re: Lou Kauffman
::: Iterants, Imaginaries, Matrices

As serendipity would have it, Lou Kauffman, who knows a lot about
the lines of inquiry Charles Sanders Peirce and George Spencer Brown
pursued into graphical syntaxes for logic, just last month opened a blog
and his very first post touched on perennial questions of logic and time —
Logos and Chronos — puzzling the wits of everyone who has thought about
them for as long as anyone can remember. Just locally and recently
these questions have arisen in the following contexts:

[Links omitted here. Please see the blog post linked above for the list.]

Kauffman's treatment of logic, paradox, time, and imaginary truth values
led me to make the following comments I think are very close to what I'd
been struggling to say before.

Let me get some notational matters out of the way before continuing.

I use B for a generic 2-point set, usually {0, 1} and typically but
not always interpreted for logic so that 0 = false and 1 = true.
I use “teletype” parentheses (...) for negation, so that (x) = ¬x
for x in B. Later on I’ll be using teletype format lists
(x_1, ..., x_k) for minimal negation operators.

[ See ]

As long as we’re reading x as a boolean variable x in B
the equation x = (x) is not paradoxical but simply false.
As an algebraic structure B can be extended in many ways
but it remains a separate question what sort of application,
if any, such extensions might have to the normative science
of logic.

On the other hand, the assignment statement x := (x) makes perfect sense
in computational contexts. The effect of the assignment operation on the
value of the variable x is commonly expressed in time series notation as
x' = (x) and the same change is expressed even more succinctly by defining
dx = x' − x and writing dx = 1.

Now suppose we are observing the time evolution of a system X
with a boolean state variable x : X → B and what we observe is
the following time series.

Table. Time Series 1 (also attached)

Computing the first differences we get:

Table. Time Series 2 (also attached)

Computing the second differences we get:

Table. Time Series 3 (also attached)

This leads to thinking of the system X as having an extended state
(x, dx, d²x, ...), and this additional language gives us the facility
of describing state transitions in terms of the various orders of
differences. For example, the rule x' = (x) can now be expressed
by the rule dx = 1.

The following article has a few more examples along these lines.

Differential Analytic Turing Automata (DATA)


Differential Logic and Dynamic Systems



All Process, No Paradox • 2 • Time Series 1.png
All Process, No Paradox • 2 • Time Series 2.png
All Process, No Paradox • 2 • Time Series 3.png

Jason the Goodman

Mar 16, 2021, 2:18:09 PM3/16/21
to, Laws of Form, Ontolog Forum, Peirce List, Structural Modeling, SysSciWG

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Jon Awbrey

Mar 17, 2021, 9:24:23 AM3/17/21
to Cybernetic Communications, Laws of Form, Ontolog Forum, Peirce List, Structural Modeling, SysSciWG
Cf: All Process, No Paradox • 3

| Consider what effects that might conceivably
| have practical bearings you conceive the
| objects of your conception to have. Then,
| your conception of those effects is the
| whole of your conception of the object.
| Charles S. Peirce • “Issues of Pragmaticism”

Re: Peirce List
::: Paul Eduardo

A riddle is a description of something, typically in metaphorical, oblique,
and very partial terms, from which the respondent must abduce the identity
of the thing described. One of the interesting things about Gollum’s riddle
is the pragmatic way he describes the object of his conception in terms of
its effects on the contents of a whole universe of discourse. If we weren’t
at hazard for being devoured ourselves, we’d be at leisure to sit down and
work out a logical analysis of those effects. There are a few fine points
we’d have to settle, like when he says this thing devours all things —
Does it devour itself or other things only?

I meant to write more, but it’s later than I thought it would be by now …



Jon Awbrey

Mar 17, 2021, 1:20:35 PM3/17/21
to Cybernetic Communications, Laws of Form, Ontolog Forum, Peirce List, Structural Modeling, SysSciWG
All Process, No Paradox • 4


While looking for something else on the web, I ran across an old note
I had written in reply to an inquiry on the Conceptual Graphs List,
and it seemed to express one of the points of the present thesis in
a fairly clear fashion, so here’s the part I found fit to revive.

Time Representation

The point of view that develops from fundamental physical considerations
is that the concept of Process is more fundamental than the concept of Time,
since references to a time parameter are simply references to a process taken
as standard, in other words, a clock.

We can always develop another “naive physics”, natural language “tense logic”,
or implicit psychological theory of time, and maybe that’s all we need in
particular settings, but if we push for a deeper logical analysis of timed
processes themselves then we need a logical framework able to deal with
relations between systems which undergo changes in their properties,
as described by logical statements.

That is the impulse motivating Differential Logic. As it turns out,
Peirce’s way of doing logic, especially in graphical form, is naturally
adapted to dealing with change and difference in logical form.


Logical Graphs • Introduction

Logical Graphs • Formal Development

Differential Propositional Calculus • Part 1

Differential Propositional Calculus • Part 2



Jon Awbrey

Mar 18, 2021, 1:30:56 PM3/18/21
to Cybernetic Communications, Laws of Form, Ontolog Forum, Peirce List, Structural Modeling, SysSciWG
Cf: All Process, No Paradox • 9

Re: Peirce List
::: Helmut Raulien


Continuing my review of previous discussions concerned with various proposals
to extend bivalent logic to encompass sundry dimensions of alterity, diversity,
dynamics, imagination, indeterminacy, information, interpretation, intuitionism,
likelihood, mutability, probability, relativity, time, uncertainty, and so on.

For continuity's sake I'm recycling my replies to a comment
by Helmut Raulien on the Peirce List which raised a host of
questions about Peirce's categories, logic, and semiotics
in the light of Spencer Brown's Laws of Form.

Comment 1

George Spencer Brown's Laws of Form tends to be loved
XOR ( ) hated
by most folks, with few coming down in between. I ran across
the book early in my undergrad years, shortly after encountering
C.S. Peirce, so I could recognize how it roughly revived Peirce's
logical graphs, emphasizing the entitative interpretation of the
abstract formal calculus immanent in Peirce's “Alpha” graphs.
It took me a solid decade to gain a modicum of clarity about
all that “imaginary truth value” and “re-entry” folderol.
I will say some things about that later on.

Comment 2

I mulled the matter over for a fair spell of days and nights and
decided it wouldn't be good to jump into the middle of the muddle
about re-entry and imaginary truth values right off the bat, that
it would be better in the long run to get a solid grip on what is
going on with the propositional level of Peirce's logical graphs
and how Spencer Brown's elaborations can be seen to manifest the
same spirit of reasoning, if read the right way. Toward that end
I'll append a list of resources breaking the ice on this approach.


Logic Syllabus
( )

Semeiotic, Semiotics
( )

Precursors Of Category Theory
( )

Logical Graphs
( )

( )

Formal Development
( )



Jon Awbrey

Mar 19, 2021, 9:54:17 AM3/19/21
to Cybernetic Communications, Laws of Form, Ontolog Forum, Peirce List, Structural Modeling, SysSciWG
Cf: All Process, No Paradox • 6

Re: R.J. Lipton • Anti-Social Networks

Re: Lou Kauffman • Iterants, Imaginaries, Matrices


Comments I made elsewhere about computer science and
(anti-)social networks have a connection with the work
in progress on this thread, so it may steal a march to
append them here.

Comment 1

I have been interested for a long time now in using graphs to do logic.
For that you need more than positive links — negative relations are more
generative than positive relations. The logical situation is analogous to
social networks where people can “unlike” or “¬like” other people or website
networks where the information at one node may contradict the information at
another node. In my pursuits it turns out that particular species of graph-
theoretic “cacti” are much more useful than the garden variety trees and
unsigned graphs.

Comment 2

For what it’s worth, here is my exposition of “painted cacti”
and their application to propositional calculus.

Cactus Language • Overview

Part 1 • Syntax

Part 2 • Generalities About Formal Grammars

Part 3 • Stylistics, Mechanics, Semantics

A “painted cactus” is a rooted cactus with any number
of symbols from a finite alphabet attached to each node.
In their ordinary logical interpretations these symbols
(“paints”) stand for boolean variables.

Triangles are interesting in computational contexts because
they arise in case-breakdown expressions. In one of the common
interpretations of cactus graphs, a rooted triangular lobe says
the values of the two non-root nodes are logically inequivalent.


Futures Of Logical Graphs

Propositional Equation Reasoning Systems


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