Sign Relations, Triadic Relations, Relation Theory • Discussion 9

Once, there was nothing there, nothing moving on its own, just data and people shuffling it around.  Then something happened, and it … it knew itself.

William Gibson • Count Zero (1) (2)

Re: FB | Dan EverettOn the Origin of Symbols and the Descent of Signs

Continuing a discussion on the generative power of symbols (1) (2).

Here’s the skinny on the big three types of signs.  Despite its simplicity, or maybe because of it, the larger implications for the interpretive character of sign typing still go widely missed.

SemeioticTypes of Signs

There are three principal ways a sign may denote its objects.  The modes of representation are often referred to as kinds, species, or types of signs but it is important to recognize they are not ontological species, that is, they are not mutually exclusive features of description, since the same thing can be a sign in several different ways.

Beginning very roughly, the three main ways of being a sign can be described as follows.

  • An icon denotes its objects by virtue of a quality it shares with its objects.
  • An index denotes its objects by virtue of an existential connection it has to its objects.
  • A symbol denotes its objects solely by virtue of being interpreted to do so.

One of Peirce’s early delineations of the three types of signs affords a useful first approach to understanding their differences and their relationships to each other.

In the first place there are likenesses or copies — such as statues, pictures, emblems, hieroglyphics, and the like.  Such representations stand for their objects only so far as they have an actual resemblance to them — that is agree with them in some characters.  The peculiarity of such representations is that they do not determine their objects — they stand for anything more or less;  for they stand for whatever they resemble and they resemble everything more or less.

The second kind of representations are such as are set up by a convention of men or a decree of God.  Such are tallies, proper names, &c.  The peculiarity of these conventional signs is that they represent no character of their objects.  Likenesses denote nothing in particular;  conventional signs connote nothing in particular.

The third and last kind of representations are symbols or general representations.  They connote attributes and so connote them as to determine what they denote.  To this class belong all words and all conceptions.  Most combinations of words are also symbols.  A proposition, an argument, even a whole book may be, and should be, a single symbol.  (Peirce 1866, Lecture 7, 467–468).

Reference

  • Peirce, C.S. (1866), “The Logic of Science, or, Induction and Hypothesis”, in Writings of Charles S. Peirce : A Chronological Edition, Volume 1 (1857–1866), Peirce Edition Project, Indiana University Press, Bloomington and Indianapolis, IN, 1982.  Lowell Lectures of 1866, 357–504.

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Sign Relations, Triadic Relations, Relation Theory • Discussion 8

Re: FB | Dan EverettOn the Origin of Symbols and the Descent of Signs

Continuing a discussion on the primal character of symbols.

There are a few passages from Peirce going most quickly to the root of the matter and working to keep the main ideas in mind — before one gets too bogged down and bewildered by the full‑blown classification mania so common in the literature.

The following statement is key.

Thought is not necessarily connected with a brain.  It appears in the work of bees, of crystals, and throughout the purely physical world;  and one can no more deny that it is really there, than that the colors, the shapes, etc., of objects are really there.

C.S. Peirce, Collected Papers (CP 4.551)

I know that is a Golden Oldie, but as the years go by I find many people have taken away different messages from even the most familiar tunes, making it fruitful every now and again to accord old themes another turn.

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Sign Relations, Triadic Relations, Relation Theory • Discussion 7

Re: FB | Dan EverettOn the Origin of Symbols and the Descent of Signs

A conversation with Dan Everett on Facebook led me to explain the following point about symbols a little better, or at least in fewer words, than I think I’ve ever managed before.

Symbols are the genus, the equipotential stem cells of all signs.  Icons and indices are the degenerate species, the differentiated specializations.

This is a consequence of triadic relation irreducibility.  A further consequence is that symbols do not evolve from icons and indices but the latter devolve from symbols.

To say symbols are the genus of signs is to say every sign has the generic potential of a symbol.  This means when we see an apparent progression from degenerate species to genuine symbols it is not evolution or even development properly speaking but more akin to release of inhibition.

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Sign Relations, Triadic Relations, Relation Theory • Discussion 6

Re: FB | Charles S. Peirce SocietyAlain Létourneau

Alain Létourneau asks if I have any thoughts on Peirce’s Rhetoric.  I venture the following.

Classically speaking, rhetoric (as distinguished from dialectic) treats forms of argument which “consider the audience” — which take the condition of the addressee into account.  But that is just what Peirce’s semiotic does in extending our theories of signs from dyadic to triadic sign relations.  We often begin our approach to Peirce’s semiotics by saying he puts the interpreter back into the relation of signs to their objects.  But even Aristotle had already done that much.  Peirce’s innovation was to apply the pragmatic maxim, clarifying the characters of interpreters in terms of their effects — their interpretants — in the flow of semiosis.

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Differential Logic and Dynamic Systems • Discussion 7

Re: Differential Logic and Dynamic SystemsIntentional Propositions
Re: FB | Differential LogicMarius V. Constantin

Marius Constantin asks about the logical value of an intention which is not carried out.

MVC:
I have in my intention to give like, but I didn’t.
What is the value (logic) of this proposition?

Dear Marius,

A difference between an expected state and an observed state is called a Surprise.  A surprise calls for an explanation.

A difference between an intended state and an observed state is called a Problem.  A problem calls for a plan of action.

There’s more discussion in the following essay and section.

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Peirce’s 1870 “Logic of Relatives” • Comment 3

Anything that is a Giver of Anything to a Lover of Anything
\text{Figure 21. Anything that is a Giver of Anything to a Lover of Anything}

In passing to more complex combinations of relative terms and the extensional relations they denote, as we began to do in Comments 10.6 and 10.7, I used words like composite and composition along with the usual composition sign ``\circ" to describe their structures.  That amounts to loose speech on my part and I may have to reform my Sprach at a later stage of the Spiel.

At any rate, we need to distinguish the more complex forms of combination encountered here from the ordinary composition of dyadic relations symbolized by ``\circ", whose result must stay within the class of dyadic relations.  We can draw that distinction by means of an adjective or a substantive term — so long as we see it we can parse the words later.

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Charles Sanders Peirce, George Spencer Brown, and Me • 16

Re: Conceptual GraphsGary Zhu

GZ:
I’m quite confused on why people are interested in Laws of Form.
What is LOF trying to do? Is it just rewriting logic or is there
something more fundamental. e.g. a universal algebraic system?
What does GSB has to do with DNA, or DNA computing?
What does Lou’s work in topology has to do with GSB?
What does GSB’s theory has to do with knot theory?
What does GSB’s theory has to do with quaternions?
How can GSB’s theory be used for designing circuits?
What’s wrong with Frege?

Dear Gary,

I am deep in the middle of other work right now, but here’s a smattering of resources relevant to the relation between Peirce’s logical graphs and Spencer Brown’s calculus of indications, at least so far as the core subjects of boolean functions and propositional calculus are concerned.

As far as the extension to relations and quantification, I start from where Peirce started in 1870 and follow up several of his more radical ideas, ones he himself did not fully develop.  That is what I’m doing on the 1870 Logic of Relatives thread.

Regards,

Jon

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Peirce’s 1870 “Logic of Relatives” • Discussion 5

Re: Conceptual GraphsPeiyuan Zhu

PZ:
I’m studying imprecise probabilities which initially works as an extension in Boole’s Laws of Thoughts.  It seems like Boole was solving a set of algebraic equations for probabilities where some of the probabilities do not have precise values therefore need to be bounded.  Has anyone studied Boole’s algebraic system of probabilities?  Is Peirce extending Boole’s algebraic system in his Logic of Relatives?

Dear Peiyuan,

Issues related to the ones you mention will come up in the Selections and Commentary I’m posting on Peirce’s 1870 Logic of Relatives, the full title of which, “Description of a Notation for the Logic of Relatives, Resulting from an Amplification of the Conceptions of Boole’s Calculus of Logic”, is sufficient hint of the author’s intent, namely, to extend the correspondence Boole discovered between the calculus of propositions and the statistics of simple events to a correspondence between the calculus of relations and the statistics of complex events, contingency matrices, higher order correlations, and ultimately the full range of information theory.

But it will take a while to develop all that …

Regards,
Jon

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Peirce’s 1870 “Logic of Relatives” • Discussion 4

Re: Peirce’s 1870 “Logic of Relatives” • Proto-Graphical Syntax
Re: FB | Ancient LogicHenning Engebretsen

HE:
What’s your point, it’s obviously too graphical, but perhaps you are driving at something else.  Explain?

Dear Henning,

My aim here is to survey the source from which radiates all our most enlightening graphical systems of logic — from Peirce’s own entitative and existential graphs, to Spencer Brown’s calculus of indications, to John Sowa’s conceptual graphs.  The first glimmerings of that evolution go further back than widely appreciated, being especially well marked in Peirce’s 1870 “Logic of Relatives”, as I hope to make clear in time.

Regards,
Jon

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Peirce’s 1870 “Logic of Relatives” • Discussion 3

All other sciences without exception depend upon the principles of mathematics;  and mathematics borrows nothing from them but hints.

C.S. Peirce • “Logic of Number”

A principal intention of this essay is to separate what are known as algebras of logic from the subject of logic, and to re‑align them with mathematics.

G. Spencer Brown • Laws of Form

Re: Peirce’s 1870 “Logic of Relatives” • Overview
Re: Laws of Form • James Bowery (1) (2)

Dear James,

I am pleased to see you engaging the material on Peirce’s Logic of Relatives.  For my part I’ll need to lay out several more Selections before the major themes of Peirce’s essay begin to emerge from the supporting but sometimes distracting details.

In the meantime two clues to the Big Picture can be gleaned from the paired epigraphs I put up in lights at the top of the post.  For what we have here is a return to the thrilling days of yesteryear when the mathematics of logic was still mathematics, shortly before Frege (maybe unwittingly) and Russell (in a way less wittingly) detoured it down the linguistic U‑turn to nominalism.

Regards,
Jon

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