The Difference That Makes A Difference That Peirce Makes • 13

Posted on June 22, 2017 by Jon Awbrey

I would like to return to a point where the paths of discussion began to diverge and then bifurcated so chaotically that I could not track them further, namely, here:

Re: Peirce List • JA • GF • JA

I imagine different readers derive different morals from the passage Gary Fuhrman quoted.  It resonates for me with a host of themes going back to my Vita Nuova in many dimensions of life during my first years of college.  But memories from fifty years ago are hard to put in order and so what comes more freshly to mind are later harvests of those seeds.

One of those outgrowths was the work I did applying Peirce’s paradigm to fundamental problems in AI, or Intelligent Systems Engineering as my advisor in Systems Engineering preferred to call it.  I posted a link to a section from one of my project reports:

Many distractions kept me from following up at the time, so I’ll copy here the introduction of that section with the aim of moving forward from there.

Functional Logic • Inquiry and Analogy

Functional Conception of Quantification Theory

Up till now quantification theory has been based on the assumption of individual variables ranging over universal collections of perfectly determinate elements.  Merely to write down quantified formulas like \forall_{x \in X} f(x) and \exists_{x \in X} f(x) involves a subscription to such notions, as shown by the membership relations invoked in their indices.  Reflected on pragmatic and constructive principles, however, these ideas begin to appear as problematic hypotheses whose warrants are not beyond question, projects of exhaustive determination that overreach the powers of finite information and control to manage.  Therefore, it is worth considering how we might shift the scene of quantification theory closer to familiar ground, toward the predicates themselves that represent our continuing acquaintance with phenomena.

Posted in Automata, C.S. Peirce, Category Theory, Chomsky, Complementarity, Dewey, Formal Languages, Inquiry, Laws of Form, Logic, Logic of Relatives, Logic of Science, Logical Graphs, Mathematics, Peirce, Philosophy, Physics, Pragmatism, Quantum Mechanics, Relation Theory, Relativity, Science, Scientific Method, Semiotics, Spencer Brown | Tagged , , , , , , , , , , , , , , , , , , , , , , , , | Leave a comment

The Difference That Makes A Difference That Peirce Makes • 12

Posted on June 20, 2017 by Jon Awbrey

Re: Peirce List • Kirsti Määttänen

I have a sense of what Peirce meant by the “Logic of Science” and what Dewey meant by calling Logic the “Theory of Inquiry”.  If that’s logic in the narrow sense and not Logic in the Grandest Metaphysical Sense then it’s been enough for me, ever since I said farewell to the foundational crises of my youth and set to work on tools to help us reason.

That is what logic means to me.

Posted in Automata, C.S. Peirce, Category Theory, Complementarity, Dewey, Formal Languages, Inquiry, Laws of Form, Logic, Logic of Relatives, Logic of Science, Logical Graphs, Mathematics, Peirce, Philosophy, Physics, Pragmatism, Quantum Mechanics, Relation Theory, Relativity, Science, Scientific Method, Semiotics, Spencer Brown | Tagged , , , , , , , , , , , , , , , , , , , , , , , | Leave a comment

The Difference That Makes A Difference That Peirce Makes • 11

Posted on June 17, 2017 by Jon Awbrey

Re: Peirce List • Kirsti Määttänen • Jon Awbrey • John Sowa

The most important difference between linguistics and logic is that linguistics is descriptive while logic is normative.

Yes, some grammarians try to treat grammar as prescriptive, but most in modern times have given up on that and realize that usage will have its day and win out in the long run.  And even when grammar appears to dictate form it does so only on the plane of signs, sans objects, and so remains a flat affair.

It is only logic that inhabits all three dimensions O \times S \times I of sign relations, inquiring into how we ought to conduct our transactions with signs in order to realize their objectives.  A normative science has different aims even when it looks on the same materials as a descriptive science.  So logic may have abstractions from language among its materials but it is more than abstract linguistics — it is an augmentation of language.

Posted in Automata, C.S. Peirce, Category Theory, Chomsky, Complementarity, Formal Languages, Inquiry, Laws of Form, Logic, Logic of Relatives, Logical Graphs, Mathematics, Peirce, Philosophy, Physics, Pragmatism, Quantum Mechanics, Relation Theory, Relativity, Science, Scientific Method, Semiotics, Spencer Brown | Tagged , , , , , , , , , , , , , , , , , , , , , , | Leave a comment

The Difference That Makes A Difference That Peirce Makes • 10

Posted on June 16, 2017 by Jon Awbrey

Re: Peirce List • Jon Alan Schmidt

JA:
As I am realizing more and more in recent years, analyzing and classifying signs as a substitute for analyzing and classifying objects is the first slip of a slide into nominalism, namely, the idea that the essence or reality of objects is contained in the signs we use to describe them.

The operative phrase in what I wrote is “as a substitute for”.  We always have the task of classifying signs and classifying objects but the problems arise when your favorite ism thinks that half the work will do double duty.  It hardly ever does.

Dyadic forms of correspondence between syntactic structures and objective functions are always nice when you can get them and it’s always worth taking advantage of them when they occur.  It would make things a whole lot simpler if the forms of signs always mirrored the forms of their objects.  That is one of the attractions of Fregean compositionality and Russell’s isomorphism theory and it’s one of the reasons programming language designers keep to the realm of context-free languages for as long as they can.  Taking the Chomsky–Schützenberger Hierarchy as our first rough guide to the complexity of formal languages and the competencies demanded of their processors, we run into a critical point at the threshold between context-free and context-sensitive languages where the mirror of language breaks and the triadic nature of genuine symbols can no longer be avoided.

Posted in Automata, C.S. Peirce, Category Theory, Chomsky, Complementarity, Formal Languages, Inquiry, Laws of Form, Logic, Logic of Relatives, Logical Graphs, Mathematics, Peirce, Philosophy, Physics, Pragmatism, Quantum Mechanics, Relation Theory, Relativity, Science, Scientific Method, Semiotics, Spencer Brown | Tagged , , , , , , , , , , , , , , , , , , , , , , | Leave a comment

The Difference That Makes A Difference That Peirce Makes • 9

Posted on June 13, 2017 by Jon Awbrey

Re: Peirce List | Jay Zeman • JFS • GF • GF • GF • GR • JA • JA • JA • GF • JA • GR • JFS
Re: Peirce List | Rheme and Reason • JA • GF • JFS

The just-so-story that relative terms got their meanings by blanking out pieces of clauses and phrases, plus the analogies to poly-unsaturated chemical bonds, supply a stock of engaging ways to introduce the logic of relative terms and the mathematics of relations but they both run into cul-de-sacs when taken too literally, and for the same reason.  They tempt one to confuse the syntactic accidents used to suggest formal objects with the essential forms of the objects themselves.  That is the sort of confusion that leads to syntacticism and on to its kindred nominalism.

Here’s a short note I wrote the last time questions about rhemes or rhemata came up.

I wanted to check out some impressions I formed many years ago — this would have been the late 1960s and mainly from CP 3 and 4 — about Peirce’s use of the words rhema, rheme, rhemata, etc.

Rhema, Rheme

  • CP 2.95, 250-265, 272, 317, 322, 379, 409n
  • CP 3.420-422, 465, 636
  • CP 4.327, 354, 395n, 403, 404, 411, 438, 439, 441, 446, 453, 461, 465, 470, 474, 504, 538n, 560, 621

Reviewing the variations and vacillations in Peirce’s usage over the years, I’ve decided to avoid the whole complex of rhematic terms for now.  As I’ve come to realize more and more in recent years, analyzing and classifying signs as a substitute for analyzing and classifying objects is the first slip of a slide into nominalism, in effect, thinking the essence or reality of objects is contained in the signs we use to describe them.

Resources

Posted in C.S. Peirce, Complementarity, Inquiry, Laws of Form, Logic, Logic of Relatives, Logical Graphs, Mathematics, Pragmatism, Relation Theory, Scientific Method, Semiosis, Semiotics, Sign Relations, Spencer Brown, Visualization | Tagged , , , , , , , , , , , , , , , | 1 Comment

The Present Is Big With The Future • Comment 2

Posted on June 9, 2017 by Jon Awbrey

My interest in this theme of Leibniz goes back to a time when I began exploring generalized measures of determination and qualitative analogues of differential calculus — doctrines of absolute determinism or predestination had long ago loosened their hold on my mind — but a comment on my recent posting prompts me to add the following clarification.

I tend to read theological visions metaphorically, more in axiological and teleological veins.  So I take Leibniz as presenting an ideal limit of a perfect information cybernetic system — how the universe would look to an ideal observer, from a God’s Eye View.  I do not know if it is possible to imagine such a point of view within the bounds of logic alone, but Leibniz appears to believe God at least can have his cake and eat it, too, as indicated by the follow passage.

There must therefore be no doubt that effects follow their causes determinately, in spite of contingency and even of freedom, which nevertheless exist together with certainty or determination.

References

Resources

Posted in C.S. Peirce, Determination, Differential Calculus, Differential Logic, Hologrammautomaton, Infinitesimals, Leibniz, Logic, Logical Graphs, Mathematics, Peirce, Preëstablished Harmony, Propositional Calculus, Visualization | Tagged , , , , , , , , , , , , , | 8 Comments

The Present Is Big With The Future • Comment 1

Posted on June 2, 2017 by Jon Awbrey

Re: Peirce List • John Sowa
Re: Peirce List • Jon Awbrey

Here is a passage from Leibniz where he half decrypts half encrypts the big idea sparking his discovery of the differential calculus.

The Present Is Big With The Future

Now that I have proved sufficiently that everything comes to pass according to determinate reasons, there cannot be any more difficulty over these principles of God’s foreknowledge.  Although these determinations do not compel, they cannot but be certain, and they foreshadow what shall happen.

It is true that God sees all at once the whole sequence of this universe, when he chooses it, and that thus he has no need of the connexion of effects and causes in order to foresee these effects.  But since his wisdom causes him to choose a sequence in perfect connexion, he cannot but see one part of the sequence in the other.

It is one of the rules of my system of general harmony, that the present is big with the future, and that he who sees all sees in that which is that which shall be.

What is more, I have proved conclusively that God sees in each portion of the universe the whole universe, owing to the perfect connexion of things.  He is infinitely more discerning than Pythagoras, who judged the height of Hercules by the size of his footprint.  There must therefore be no doubt that effects follow their causes determinately, in spite of contingency and even of freedom, which nevertheless exist together with certainty or determination.

I have a vague memory of having once looked on the Latin text, where the word big was gravis, meaning pregnant, in the original.  But it was a long time ago, and I’ll need to check that out again sometime.

Incidentally, working out the logical analogue of differential calculus is the object of my efforts on differential logic.  This work led me to develop an extension of Peirce’s alpha graphs that is efficient enough in both conceptual and computational terms to carry the load.  For an introduction, see the following articles.

Reference

  • Gottfried Wilhelm (Freiherr von) Leibniz, Theodicy : Essays on the Goodness of God, the Freedom of Man, and the Origin of Evil, edited with an introduction by Austin Farrer, translated by E.M. Huggard from C.J. Gerhardt’s edition of the Collected Philosophical Works, 1875–1890.  Routledge 1951.  Open Court 1985.  Paragraph 360, page 341.

cc: Peirce List

Posted in C.S. Peirce, Determination, Differential Calculus, Differential Logic, Hologrammautomaton, Infinitesimals, Leibniz, Logic, Logical Graphs, Mathematics, Peirce, Preëstablished Harmony, Propositional Calculus, Visualization | Tagged , , , , , , , , , , , , , | 10 Comments

The Difference That Makes A Difference That Peirce Makes • 8

Posted on May 31, 2017 by Jon Awbrey

Re: Peirce List • James Albrecht

Among the subtle shifts in scientific thinking that occurred in the mid 1800s, George Boole gave us a functional interpretation of logic, associating every propositional expression — at the most basic level of logic we now describe in terms of boolean algebras, boolean functions, propositional calculi, or Peirce’s alpha graphs — with a function from a universe of discourse X to a domain of two values, say \mathbb{B} = \{ 0, 1 \}, normally interpreted as logical values, false and true, respectively.  This may seem like a small change so far as conceptual revolutions go but it made a big difference in the future development, growth, and power of our logical systems.

Among other things, the functional interpretation of logic enables the construction of a bridge from propositional logic, whose subject matter now consists of functions of the form f : X \to \mathbb{B}, to probability theory, that deals with probability distributions or probability densities of the form p : X \to [0, 1], with values in the unit interval [0, 1] of the real number line \mathbb{R}.  This allows us to view propositional logic as a special case within the frame of a more general statistical theory.  This turns out to be a very useful perspective in real-world research when it comes to moving back and forth between qualitative observations and the data given by quantitative measurement.  And it gives us a bridge still further, connecting deductive and inductive reasoning, as Boole well envisioned.

Posted in C.S. Peirce, Complementarity, Inquiry, Laws of Form, Logic, Mathematics, Peirce, Philosophy, Physics, Pragmatism, Quantum Mechanics, Relativity, Science, Scientific Method, Semiotics, Spencer Brown | Tagged , , , , , , , , , , , , , , , | Leave a comment

The Difference That Makes A Difference That Peirce Makes • 7

Posted on May 31, 2017 by Jon Awbrey

Re: Peirce List • GF • GF • GR

In our “Inquiry as Action : Risk of Inquiry” paper, originally presented at a conference on “Hermeneutics and the Human Sciences”, Susan and I sought to trace the interminglings of signs and inquiry and the theories thereof.  We pursued their trajectory through three points of reference:  Aristotle, Peirce, and Dewey.  We noted both convergences and divergences in the views of the assembled authors, and the course of true signs never did run smooth, as everyone knows, or eventually finds out

We characterized Aristotle’s treatment “On Interpretation” (where the implied relationship between a sign and its object is a two-step linkage that pivots on what Peirce would call an interpretant sign) as “in part a reasonable approximation and in part a suggestive metaphor, suitable as a first approach to a complex subject”.  It makes for a good start, but ultimately falls short of grasping the full triadicity of sign relations.

References

  • Awbrey, J.L., and Awbrey, S.M. (1992), “Interpretation as Action : The Risk of Inquiry”, The Eleventh International Human Science Research Conference, Oakland University, Rochester, Michigan.
  • 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.
Posted in C.S. Peirce, Complementarity, Inquiry, Laws of Form, Logic, Mathematics, Peirce, Philosophy, Physics, Pragmatism, Quantum Mechanics, Relativity, Science, Scientific Method, Semiotics, Spencer Brown | Tagged , , , , , , , , , , , , , , , | Leave a comment

The Difference That Makes A Difference That Peirce Makes • 6

Posted on May 30, 2017 by Jon Awbrey

Re: Peirce List • Gary Fuhrman

The uses to which Susan Awbrey and I turned Aristotle’s passage from De Interp can be found in our paper from 1992/1995.

  • Awbrey, J.L., and Awbrey, S.M. (1992), “Interpretation as Action : The Risk of Inquiry”, The Eleventh International Human Science Research Conference, Oakland University, Rochester, Michigan.
  • 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.

To get the ball rolling, or ping-ponging as the case may be, let me refer to a few points from our Inquiry paper that came to mind as I skimmed Gary Fuhrman’s post on “Rhematics” and Gary Richmond’s comment on it.

The main thing that strikes me is a thing that never ceases to surprise me — I see there remains a persistent desire to parse symbols into simpler signs like icons and indices, or to say that genuine triadicity has its genesis in some kind of coitus between degenerate species.  I suppose bi-o-logical metaphors are bound to lead innocents down that path, and I guess we all fall into the sinns of simile from time to time, but due care of our semiotic souls should keep us from turning that error into doctrine, if we wit what’s good for us.

Posted in C.S. Peirce, Complementarity, Inquiry, Laws of Form, Logic, Mathematics, Peirce, Philosophy, Physics, Pragmatism, Quantum Mechanics, Relativity, Science, Scientific Method, Semiotics, Spencer Brown | Tagged , , , , , , , , , , , , , , , | Leave a comment