{ Information = Comprehension × Extension } Revisited • Selection 2

Posted on January 28, 2019 by

Over the course of Selection 1 Peirce introduces the ideas he needs to answer stubborn questions about the validity of scientific inference.  Briefly put, the validity of scientific inference depends on the ability of symbols to express superfluous comprehension, the measure of which Peirce calls information.

Selection 2 sharpens our picture of symbols as general representations, contrasting them with two species of representation whose characters fall short of genuine symbols.

For this purpose, I must call your attention to the differences there are in the manner in which different representations stand for their objects.

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, pp. 467–468)

Reference

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

Resources

cc: Systems Science • Structural Modeling • Ontolog Forum

Posted in Abduction, C.S. Peirce, Comprehension, Deduction, Extension, Hypothesis, Icon Index Symbol, Induction, Inference, Information = Comprehension × Extension, Information Theory, Inquiry, Intension, Logic, Logic of Science, Peirce, Peirce's Categories, Pragmatic Semiotic Information, Pragmatism, Scientific Method, Semiotics, Sign Relations | Tagged , , , , , , , , , , , , , , , , , , , , , | 1 Comment

{ Information = Comprehension × Extension } Revisited • Selection 1

Posted on January 26, 2019 by

Our first text comes from Peirce’s Lowell Lectures of 1866, titled “The Logic of Science, or, Induction and Hypothesis”.  I still remember the first time I read these words and the light that lit up the page and my mind.

Let us now return to the information.  The information of a term is the measure of its superfluous comprehension.  That is to say that the proper office of the comprehension is to determine the extension of the term.  For instance, you and I are men because we possess those attributes — having two legs, being rational, &c. — which make up the comprehension of man.  Every addition to the comprehension of a term lessens its extension up to a certain point, after that further additions increase the information instead.

Thus, let us commence with the term colour;  add to the comprehension of this term, that of red.  Red colour has considerably less extension than colour;  add to this the comprehension of dark;  dark red colour has still less [extension].  Add to this the comprehension of non-blue — non-blue dark red colour has the same extension as dark red colour, so that the non-blue here performs a work of supererogation;  it tells us that no dark red colour is blue, but does none of the proper business of connotation, that of diminishing the extension at all.  Thus information measures the superfluous comprehension.  And, hence, whenever we make a symbol to express any thing or any attribute we cannot make it so empty that it shall have no superfluous comprehension.

I am going, next, to show that inference is symbolization and that the puzzle of the validity of scientific inference lies merely in this superfluous comprehension and is therefore entirely removed by a consideration of the laws of information.

(Peirce 1866, p. 467)

Reference

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

Resources

cc: Systems Science • Structural Modeling • Ontolog Forum

Posted in Abduction, C.S. Peirce, Comprehension, Deduction, Extension, Hypothesis, Icon Index Symbol, Induction, Inference, Information = Comprehension × Extension, Information Theory, Inquiry, Intension, Logic, Logic of Science, Peirce, Peirce's Categories, Pragmatic Semiotic Information, Pragmatism, Scientific Method, Semiotics, Sign Relations | Tagged , , , , , , , , , , , , , , , , , , , , , | 2 Comments

{ Information = Comprehension × Extension } • Discussion 9

Posted on January 25, 2019 by

Re: Ontolog Forum • Mihai Nadin

Here’s an article of mine bearing on the present topic, namely, the relationship between Peirce’s theory of triadic sign relations and his theory of inquiry.  It also gives a smattering of historical context, bracketing Peirce between Aristotle and Dewey.

  • Awbrey, J.L., and Awbrey, S.M. (1995), “Interpretation as Action : The Risk of Inquiry”, Inquiry : Critical Thinking Across the Disciplines 15(1), pp. 40–52.  Archive.  Journal.  Online.

Resources

cc: Systems Science • Structural Modeling

Posted in Abduction, C.S. Peirce, Comprehension, Deduction, Extension, Hypothesis, Icon Index Symbol, Induction, Inference, Information = Comprehension × Extension, Information Theory, Inquiry, Intension, Logic, Logic of Science, Peirce, Peirce's Categories, Pragmatic Semiotic Information, Pragmatism, Scientific Method, Semiotics, Sign Relations | Tagged , , , , , , , , , , , , , , , , , , , , , | 1 Comment

{ Information = Comprehension × Extension } • Discussion 8

Posted on January 24, 2019 by

Re: Structural Modeling • Joseph Simpson

Links to previous Selections, Comments, and Discussions on this topic can be found here.  See especially the section on I = C × E.

My plan going forward is to review this material in a systematic manner, redeeming the benefit of what second and third thoughts have surfaced in the meantime.  I’ve studied Peirce for just over 50 years now and I’m still seeing new facets of his work each time I return to what I thought was familiar business.

Resources

cc: Systems Science • Ontolog Forum

Posted in Abduction, C.S. Peirce, Comprehension, Deduction, Extension, Hypothesis, Icon Index Symbol, Induction, Inference, Information = Comprehension × Extension, Information Theory, Inquiry, Intension, Logic, Logic of Science, Peirce, Peirce's Categories, Pragmatic Semiotic Information, Pragmatism, Scientific Method, Semiotics, Sign Relations | Tagged , , , , , , , , , , , , , , , , , , , , , | 1 Comment

{ Information = Comprehension × Extension } • Revisited

Posted on January 23, 2019 by

Three summers ago I hit on what struck me as a new insight into one of the most recalcitrant problems in Peirce’s semiotics and logic of science, namely, the relation between “the manner in which different representations stand for their objects” and the way in which different inferences transform states of information.  I roughed out a sketch of my epiphany in a series of blog posts then set it aside for the cool of later reflection.  Now looks to be that later and looking out my window it is certainly cooler.

A first pass through the variations of representation and reasoning distinguishes the axes of iconic, indexical, and symbolic manners of representation on the one hand and the axes of abductive, inductive, and deductive modes of inference on the other.  Early and often Peirce will argue for a natural correspondence between the main modes of inference and the main manners of representation but his early arguments differ from his later accounts in ways deserving a second look.  This is partly for the extra points in his line of reasoning and partly for his explanation of indices as signs constituted by convening the variant conceptions of sundry interpreters.

Resources

cc: Systems Science • Structural Modeling • Ontolog Forum

Posted in Abduction, C.S. Peirce, Comprehension, Deduction, Extension, Hypothesis, Icon Index Symbol, Induction, Inference, Information = Comprehension × Extension, Information Theory, Inquiry, Intension, Logic, Logic of Science, Peirce, Peirce's Categories, Pragmatic Semiotic Information, Pragmatism, Scientific Method, Semiotics, Sign Relations | Tagged , , , , , , , , , , , , , , , , , , , , , | 1 Comment

Pragmatic Semiotic Information • Discussion 17

Posted on January 17, 2019 by

Re: Systems Science • Kent Palmer

The best way to get a handle on what Peirce meant by his formula,

\mathrm{Information} = \mathrm{Comprehension} \times \mathrm{Extension},

is to study a suitable sample of critical passages from his Lectures of 1865–1866 on the Logic of Science.  The most instructive texts are those where he illustrates the abstract forms with concrete materials and minimal examples, simple but just complex enough to flesh out the most significant dimensions of the case.

I’ll be getting to that directly …

But I wanted to flag the following comment by Kent Palmer for future discussion, as doubt and uncertainty play a motivating role in both Peirce’s theory of inquiry and the revolution in our handling of information brought on by Shannon’s groundbreaking work.

Kent Palmer:
But then I noticed I had transformed Peirce’s formulation in order to make that connection and I was struck by doubt.  Notice doubt is at the level of hyper-intension defined by Tichy.  In fact, it is interesting that doubt is Cartesian and Husserl attempts to clarify doubt and refine it with his Epoche and Bracketing strategy.  But doubt is noetic not a noema.  Doubt is in the Husserlian hierarchy.  It turns out that doubt is fairly low in Husserl’s noetic Hierarchy because he starts with Meaning as Intentional Morphe forming hyle and comes down from there, exactly the opposite of Analytic Philosophy that starts with Extension and begrudgingly adds each level of intension.  Intentional morphe with hyle splits into noesis and noema.  Notice that the schema here is Form.

cc: Ontolog Forum • Structural Modeling

Posted in Abduction, Aristotle, C.S. Peirce, Comprehension, Deduction, Definition, Determination, Extension, Hypothesis, Induction, Inference, Information, Information = Comprehension × Extension, Inquiry, Intension, Intention, Logic, Logic of Science, Mathematics, Measurement, Observation, Peirce, Perception, Phenomenology, Physics, Pragmatic Semiotic Information, Pragmatism, Probability, Quantum Mechanics, Scientific Method, Semiotics, Sign Relations | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 1 Comment

Pragmatic Semiotic Information • Discussion 16

Posted on January 16, 2019 by

Re: Systems Science • Kent Palmer

As a general rule Peirce avoided in advance many of the problems bedeviling later philosophies of science in the 20th Century.  Doing so came rather naturally to him as he rarely succumbed to the cycloptic species of reductionism afflicting so many modern isms.

In particular, it’s not so much that Peirce sought a way to jam together the extensions and intensions of concepts and other symbols, the stuffs empiricism and rationalism are made on, as that he grasped the whole body of information, the “synthetic unity of apperception” of which extensions and intensions are but the facets or lower dimensional projections.

That integral core of information borne by signs is the prize we’ll keep in view, stereoscopically, as we make our way into the texts of the 1860s.

cc: Ontolog Forum • Structural Modeling

Posted in Abduction, Aristotle, C.S. Peirce, Comprehension, Deduction, Definition, Determination, Extension, Hypothesis, Induction, Inference, Information, Information = Comprehension × Extension, Inquiry, Intension, Intention, Logic, Logic of Science, Mathematics, Measurement, Observation, Peirce, Perception, Phenomenology, Physics, Pragmatic Semiotic Information, Pragmatism, Probability, Quantum Mechanics, Scientific Method, Semiotics, Sign Relations | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 1 Comment