All Liar, No Paradox • Comment 1

Posted on August 2, 2015 by Jon Awbrey

A statement S_0 asserts that a statement S_1 is a statement that S_1 is false.

The statement S_0 violates an axiom of logic, so it doesn’t really matter whether the ostensible statement S_1, the so-called liar, really is a statement or has a truth value.

When I endeavored some years ago to examine the so-called “liar paradox” from what I take to be a pragmatic, semiotic, sign relational standpoint, I arrived at a way of understanding it that dispelled, for me, every air of paradox about it.  I wrote out an outline of that analysis under the same title I’m using here and shared it in several discussion groups.  The couplet above is a bare bones rendering of that analysis.

The more rambling version can be found at the following locations.

Posted in C.S. Peirce, Epimenides, Foundations of Mathematics, Liar Paradox, Logic, Logical Graphs, Paradox, Pragmatics, Rhetoric, Semantics, Semiositis, Semiotics, Sign Relations, Syntax, Zeroth Law Of Semiotics, Zeroth Order Logic | Tagged , , , , , , , , , , , , , , , | 11 Comments

All Liar, No Paradox

Posted on August 1, 2015 by Jon Awbrey

A statement S_0 asserts that a statement S_1 is a statement that S_1 is false.

The statement S_0 violates an axiom of logic, so it doesn’t really matter whether the ostensible statement S_1, the so-called liar, really is a statement or has a truth value.

Posted in C.S. Peirce, Epimenides, Foundations of Mathematics, Liar Paradox, Logic, Logical Graphs, Paradox, Pragmatics, Rhetoric, Semantics, Semiositis, Semiotics, Sign Relations, Syntax, Zeroth Law Of Semiotics, Zeroth Order Logic | Tagged , , , , , , , , , , , , , , , | 14 Comments

Zeroth Law Of Semiotics • Comment 2

Posted on July 31, 2015 by Jon Awbrey

Re: Peirce List • Edwina Taborsky

My old avatar 0* (Zero-Aster) does incline to laconic verses but I hope to address a class of concrete applications which will serve to unpack their sense.

The main thing I wish to communicate is the possibility that many so-called insolubilia and paradoxes are merely cases of conceptual difficulty which can be resolved when viewed within the right sort of conceptual framework, namely, Peirce’s pragmatic semiotics or a natural extension of it.

cc: Cybernetics • Ontolog Forum • Structural Modeling • Systems Science
cc: FB | Semeiotics • Laws of Form (1) (2) • Peirce List (1) (2) (3)

Posted in C.S. Peirce, Denotation, Extension, Information = Comprehension × Extension, Liar Paradox, Logic, Nominalism, Peirce, Pragmatics, Rhetoric, Semantics, Semiositis, Semiotics, Sign Relations, Syntax, Zeroth Law Of Semiotics | Tagged , , , , , , , , , , , , , , , | 8 Comments

Zeroth Law Of Semiotics • Comment 1

Posted on July 31, 2015 by Jon Awbrey

New discussions of the so-called “Liar Paradox” have broken out at several places on the web in recent weeks, just to mention a couple of cases:

Bedevilments of that ilk always bring to mind — to my mind at least — the critical ways the Peircean paradigm of logic as semiotics differs from the fallback paradigm bedeviling the thinking of those who have yet to see by Peirce’s lights.

And that in turn brings to mind the following oldie but still goodie saying what I spy as the issue lying at the root of the “Liar” and many other pseudo-problems.

Zeroth Law Of Semiotics

Meaning is a privilege not a right.
Not all pictures depict.
Not all signs denote.

Never confuse a property of a sign,
just for instance, existence,
with a sign of a property,
for instance, existence.

Taking a property of a sign
for a sign of a property
is the zeroth sign of
nominal thinking
and the first
mistake.

Also Sprach 0*
2002 Oct 09

cc: Cybernetics • Ontolog Forum • Structural Modeling • Systems Science
cc: FB | Semeiotics • Laws of Form (1) (2) • Peirce List (1) (2) (3)

Posted in C.S. Peirce, Denotation, Extension, Information = Comprehension × Extension, Liar Paradox, Logic, Nominalism, Peirce, Pragmatics, Rhetoric, Semantics, Semiositis, Semiotics, Sign Relations, Syntax, Zeroth Law Of Semiotics | Tagged , , , , , , , , , , , , , , , | 7 Comments

Zeroth Law Of Semiotics

Posted on July 30, 2015 by Jon Awbrey

Meaning is a privilege not a right.
Not all pictures depict.
Not all signs denote.

Never confuse a property of a sign,
just for instance, existence,
with a sign of a property,
for instance, existence.

Taking a property of a sign
for a sign of a property
is the zeroth sign of
nominal thinking
and the first
mistake.

Also Sprach 0*
9 October 2002

cc: Cybernetics • Ontolog Forum • Structural Modeling • Systems Science
cc: FB | Semeiotics • Laws of Form (1) (2) • Peirce List (1) (2) (3)

Posted in C.S. Peirce, Denotation, Extension, Information = Comprehension × Extension, Liar Paradox, Logic, Nominalism, Peirce, Pragmatics, Rhetoric, Semantics, Semiositis, Semiotics, Sign Relations, Syntax, Zeroth Law Of Semiotics | Tagged , , , , , , , , , , , , , , , | 15 Comments

Semiositis • 1

Posted on July 10, 2015 by Jon Awbrey

Re: Cathy O’Neil • Profit as Proxy for Value
Re: Michael Harris • Xenomoney

There is a deep and pervasive analogy between systems of commerce and systems of communication, turning on their near‑universal use of symbola (images, media, proxies, signs, symbols, tokens, etc.) to stand for pragmata (objects, objective values, the things we really care about, or would really care about if we examined our values in practice thoroughly enough).

Both types of sign‑using systems are prey to the same sort of dysfunction or functional disease — it sets in when users confound signs and objects so severely as to take signs for ends instead of means.

There is a vast literature on this topic, once you think to go looking for it.  And it’s a perennial theme in fable and fiction.

Resource

cc: FB | Semeiotics • Mathstodon

Posted in Analogy, C.S. Peirce, Commerce, Communication, Mathematics, Pragmatics, Semantics, Semiosis, Semiositis, Semiotics, Sign Relations, Syntax, Systems Theory, Triadic Relations | Tagged , , , , , , , , , , , , , | 5 Comments

Relations & Their Relatives • Discussion 12

Posted on July 7, 2015 by Jon Awbrey

Re: Peirce List • Helmut Raulien

Definitions and examples for relation composition and the two most commonly arising types of relation reduction can be found in the following articles.

A previous post on this thread gives a thumbnail sketch of the main themes:

Peirce’s idea of reducibility and irreducibility is the more fundamental concept, having to do with the question of whether relations can be derived from others by relational composition, and this type of operation is invoked in every variety of formal construction.  Consequently, projective reducibility does nothing to defeat Peirce’s thesis about the primal nature of triadic relations.

But people sometimes confuse the two ideas of reducibility, compositional and projective, so it’s good to clarify the differences between them.  Projective reducibility, when you can get it, is more of a “consolation prize” for dyadic reductionists, who tend to ignore the fact that you can’t do anything constructive without triadic relations being involved the mix.  Still, it’s a useful property and good to recognize it when it occurs.

Posted in C.S. Peirce, Category Theory, Control, Cybernetics, Dyadic Relations, Information, Inquiry, Logic, Logic of Relatives, Mathematics, Peirce, Relation Theory, Semiosis, Semiotics, Sign Relations, Systems Theory, Triadic Relations | Tagged , , , , , , , , , , , , , , , , | 12 Comments

Relations & Their Relatives • Discussion 11

Posted on July 6, 2015 by Jon Awbrey

Re: Peirce List • Helmut Raulien
Cf: Relation Reduction • Examples of Projectively Reducible Relations

I constructed the “Ann and Bob” examples of sign relations back at the beginning of my Systems Engineering program when I had to explain how triadic sign relations would naturally come up in building intelligent systems possessed of a capacity for inquiry.

My advisor asked me for a simple, concrete, but not too trivial example of a sign relation and after cudgeling my wits for a while this is what fell out.  Up till then I had never much considered finite examples of sign relation as the cases arising in logic almost always have formal languages with infinite numbers of elements as their syntactic domains if not also infinite numbers of elements in their object domains.

The illustration at hand involves two sign relations:

  • L_\text{A} is the sign relation that captures how Ann interprets the signs in the set S = I = \{ {}^{\backprime\backprime}\text{Ann}{}^{\prime\prime}, {}^{\backprime\backprime}\text{Bob}{}^{\prime\prime}, {}^{\backprime\backprime}\text{I}{}^{\prime\prime}, {}^{\backprime\backprime}\text{you}{}^{\prime\prime} \} to denote the objects in O = \{ \text{Ann}, \text{Bob} \}.
  • L_\text{B} is the sign relation that captures how Bob interprets the signs in the set S = I = \{ {}^{\backprime\backprime}\text{Ann}{}^{\prime\prime}, {}^{\backprime\backprime}\text{Bob}{}^{\prime\prime}, {}^{\backprime\backprime}\text{I}{}^{\prime\prime}, {}^{\backprime\backprime}\text{you}{}^{\prime\prime} \} to denote the objects in O = \{ \text{Ann}, \text{Bob} \}.

Each of the sign relations, L_\text{A} and L_\text{B}, contains eight triples of the form (o, s, i) where o is an object in the object domain O, s is a sign in the sign domain S, and i is an interpretant sign in the interpretant domain I.  These triples are called elementary or individual sign relations, as distinguished from the general sign relations that generally contain many sign relational triples.

If this much is clear we can move on next time to discuss the two types of reducibility and irreducibility that arise in semiotics.

To be continued …

Posted in C.S. Peirce, Category Theory, Control, Cybernetics, Dyadic Relations, Information, Inquiry, Logic, Logic of Relatives, Mathematics, Peirce, Relation Theory, Semiosis, Semiotics, Sign Relations, Systems Theory, Triadic Relations | Tagged , , , , , , , , , , , , , , , , | 12 Comments

Inquiry, Signs, Relations • 1

Posted on July 5, 2015 by Jon Awbrey

Re: Michael Harris • A Non-Logical Cognitive Phenomenon

Human spontaneous non-demonstrative inference is not, overall, a logical process.  Hypothesis formation involves the use of deductive rules, but is not totally governed by them;  hypothesis confirmation is a non-logical cognitive phenomenon:  it is a by-product of the way assumptions are processed, deductively or otherwise.  (Sperber and Wilson, p. 69).

From a Peircean standpoint this raises the question of abductive reasoning and its role in the cycle of inquiry.

As I read him, Peirce began with a quest to understand how science works, which required him to examine how symbolic mediations inform inquiry, which in turn required him to develop the logic of relatives beyond its bare beginnings in De Morgan.  There are therefore intimate links, which I am still trying to understand, among his respective theories of inquiry, signs, and relations.

There’s a bit on the relation between interpretation and inquiry and a bit more on the three types of inference — abduction, deduction, induction — in the following paper and project report.

Reference

  • Sperber, D. and Wilson, D. (1995), Relevance : Communication and Cognition, Second Edition, Blackwell, Oxford, UK.
Posted in Abduction, Action, Analogy, C.S. Peirce, Cognition, Cognitive Science, Communication, Deduction, Foundations of Mathematics, Induction, Information, Information Theory, Inquiry, Inquiry Into Inquiry, Interpretation, Logic, Logic of Relatives, Logic of Science, Mathematics, Michael Harris, Peirce, Philosophy, Philosophy of Mathematics, Philosophy of Science, Pragmatism, Relation Theory, Relevance, Semiotics, Sign Relations, Triadic Relations | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | Leave a comment

Relations & Their Relatives • Discussion 10

Posted on July 2, 2015 by Jon Awbrey

Re: Peirce List Discussion • Helmut Raulien

The facts about relational reducibility are relatively easy to understand and I included links to relevant discussions in my earlier survey of relation theory.

The following article discusses relational reducibility and irreducibility in general terms and gives concrete examples of reducible and irreducible triadic relations of the sort we find in mathematics and semiotics, illustrating the two types of reducibility that usually come up in these settings.

These examples were introduced in the following articles on triadic relations and sign relations and I believe one could learn a lot from their careful consideration.

Posted in C.S. Peirce, Combinatorics, Dyadic Relations, Graph Theory, Group Theory, Logic, Logic of Relatives, Mathematics, Peirce, Peirce List, Relation Theory, Semiotics, Sign Relations, Tertium Quid, Thirdness, Triadic Relations, Triadicity | Tagged , , , , , , , , , , , , , , , , | 12 Comments