Inquiry Into Inquiry

Re: Peirce List • JA • JFS • JA

What interests me about Peirce’s first articulation of the “laws of information” in his early lectures on the “Logic of Science” is how the primal twins of Inquiry and Semiotics nestle so closely in their first nest that we can see their kinship far better and more easily than we ever will again.  (I am cautiously optimistic their further development won’t go the way it did for Rome.)

More than that, whatever disclaimers Peirce may have made about his own originality, I don’t think anyone can fairly encounter his definition of a term’s information as “the measure of its superfluous comprehension” without being downright shocked at its novelty.

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Re: Peirce List • John Sowa

What you say goes to the heart of a problem I saw in Natural Propositions, whether it was Peirce’s account or Stjernfelt’s analysis I did not have time to decide as the schedule of the slow reading went too fast for me to take it up on the List.  I marked the critical passages and my copy of the book is around here someplace but I am trying to stay focused on the subject matter and the set of problems I introduced under the above subject line.

There are many issues about cross-disciplinary communication, the varieties of quasi-religious belief about the uses of words in the whole proposition-sentence-statement complex, the various uses Peirce and others use across contexts, disciplines, historical time, and even within the same discussion.  But I think it’s best to hold the forte on that for now.

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Re: Peirce List • Jeffrey Brian Downard

JBD quoting CSP:

I restricted myself to terms, because at the time this chapter was first written (1867), I had not remarked that the whole doctrine of breadth and depth was equally applicable to propositions and to arguments.  The breadth of a proposition is the aggregate of possible states of things in which it is true;  the breadth of an argument is the aggregate of possible cases to which it applies.  The depth of a proposition is the total of fact which it asserts of the state of things to which it is applied;  the depth of an argument is the importance of the conclusions which it draws.  In fact, every proposition and every argument can be regarded as a term. —1893.  (C.S. Peirce, Collected Papers, CP 2.407 n. 1)

A very apt quote.  It reinforces an impression I had formed and tried to express on several occasions under the heading of contemporary category theory and computer science jargon about “polymorphism”.

There is never anything simple about the development of Peirce’s thought over time so I think the whole question of information “deserves further research”, as they say.

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Re: Peirce List • John Sowa

I gave Frederik Stjernfelt’s Natural Propositions a careful reading back when the Peirce List took it up.  The following archive links will take you to the topic thread and initial post.

• Peirce List • Frederik Stjernfelt

There are remnants of my own comments and reflections at the following locations.

• C.S. Peirce • Syllabus • Selection 1 • Selection 2
• Semiotic Theory Of Information • (1) • (2) • (3) • (4) • (5) • (6)

I have in mind getting back to the issues raised by that reading someday but it would take me too far afield from my current focus to do that now.

The short shrift for now is that Peirce is not talking about propositions in the sense of “double signs, informational signs, quasi-propositions, or Dicisigns” at this juncture but rather the simpler sorts of propositions falling under the head of propositional calculus as currently understood, most felicitously dealt with of course by means of Peirce’s own Alpha Graphs.

The concept of information arising this context is rather distinct.  Peirce’s early notion of information, however roughly cut, is clearer and stronger in its underlying realism than the residual nominalism of his later formulations, at least, as interpreted by others.

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Re: Peirce List • John Sowa

JFS:

A more fundamental term is proposition, which is informally defined as the “meaning” of a sentence.  That meaning is usually analyzed as comprehension (also known as intension) and extension.

The easier-on-the-eyes blog copy of my first Discussion post, from which point it is easier to follow the links to the first six Selections from Peirce, is here:

• { Information = Comprehension × Extension } • Discussion 1

The word proposition occurs only twice in the first six Selections, once in Selection 2 and once in Selection 4, so maybe it’s worth our pausing to see how Peirce uses the word in this place and time:

• { Information = Comprehension × Extension } • Selection 2

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, p. 468)

• { Information = Comprehension × Extension } • Selection 4

Accordingly, if we are engaged in symbolizing and we come to such a proposition as “Neat, swine, sheep, and deer are herbivorous”, we know firstly that the disjunctive term may be replaced by a true symbol.  (Peirce 1866, p. 469)

For now I’ll just add those two observations to the hopper and we can take up the issue of propositions in more detail as it arises in the relevant context.

It is good John Sowa read us the “Freedom Of Interpretation Act” right at the start, as it will serve us in good stead on down the road, but again I’ll have to leave its consequences until a few folks have had a chance to delve further into Peirce’s text, at which point I think its significance will become clear.

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A puzzle in Peirce I have puzzled over for as long as I can remember involves the relationship between his theory of signs, marking the characters of icons, indices, and symbols, and his theory of inquiry, bearing the three inferences of abduction, induction, and deduction.  I have long felt the resolution would lie in his theory of information, epitomized by the formula “Information = Comprehension × Extension”.

Last summer looked ripe for another run at the problem, which I had begun tackling once before in a series of blog posts on Peirce’s “Logic of Science” lectures at Harvard University (1865) and the Lowell Institute (1866).

There’s a working draft of those selections and comments here:

• Information = Comprehension × Extension

I serialized the selections and comments on my blog as I worked through them.

• Introductory Comment

• Six Selections from Peirce’s Lectures • (1) • (2) • (3) • (4) • (5) • (6)

By September I had come to what I imagined was a new understanding of the relationship between the types of signs and the types of inference, at which time I put the whole matter away to cool, it being far harder to judge a new idea when it’s hot.  At any rate, I think a year is long enough to gain a cool eye or two, so I will try sharing the new improved analysis to the wider world.

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