The Present Is Big With The Future • Comment 1

Re: Peirce List Discussion • John Sowa

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

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.

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.

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:

Posted in C.S. Peirce, Determination, Determinism, Differential Calculus, Differential Logic, Hologrammautomaton, Infinitesimals, Leibniz, Logic, Logical Graphs, Mathematics, Peirce, Propositional Calculus, Universal Harmony | Tagged , , , , , , , , , , , , , | 1 Comment

The Difference That Makes A Difference That Peirce Makes : 8

Re: Peirce List Discussion • 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.

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The Difference That Makes A Difference That Peirce Makes : 7

Re: Peirce List Discussion • GFGFGR

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.
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The Difference That Makes A Difference That Peirce Makes : 6

Re: Peirce List Discussion • 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.

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The Difference That Makes A Difference That Peirce Makes : 5

Re: Peirce List Discussion • Gary Richmond

When I think back to the conceptual changes my first university physics courses put me through, a single unifying theme emerges.  Relativity Theory and Quantum Mechanics had a way of making the observer an active participant in the action observed, having a local habitation, a frame of reference, and a bounded sphere of influence within the universe, no longer an outsider looking in.  As I soon discovered in my wanderings through the libraries and bookstores of my local habitation, this very theme was long ago prefigured in the corpus of C.S. Peirce’s work, most strikingly in his Logic of Relatives and Pragmatic Maxim, taken as a basis for his relational theories of information, inquiry, and signs.

It is more this level of underground conceptual revolution that comes to mind when I think of Peirce’s impact on the development of physical theory, needless to say science in general, more than any particular doctrines about continua, especially since continua posed no novelty to classical mechanics, indeed, if anything, were more catholic within its realm, while quantum mechanics introduced an irreducible aspect of discreteness to physics.

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The Difference That Makes A Difference That Peirce Makes : 4

Re: Peirce List Discussion • Mike Bergman

The mathematical perspectives and theories that made modern physics possible, perhaps even inevitable, were developed by many mathematicians, both abstract and applied, all throughout the 19th Century.  There was a definite sea change in the way scientists began to view the relationship between mathematical models and the physical world, passing from a monolithic concept to variational choices among multiple approaches, models, perspectives, and theories.

Charles Sanders Peirce was an astute observer and active participant in this transformation but it has always been difficult to trace his true impact on its course — so much of what he contributed operated underground, rhizome like, and without recognition.  But I think it’s fair to say that Peirce articulated the springs and catches of the workings of science better than any other reflective practitioner in his or subsequent times.  And I think the full import of his information-theoretic and pragmatic-semiotic approaches to scientific inquiry is a task for the future to work out.

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Icon Index Symbol • 17

Questions Concerning Certain Faculties Claimed For Signs

Re: Peirce List Discussion • Helmut Raulien

Our object being to clarify the relationships among icons, indices, and symbols, I believe the maximum benefit possible at this point is to be gained from studying the simple examples of triadic relations and sign relations discussed in the following places:

Once we get used to dealing with small examples like that we can move on to tackling more complex examples on the order of those we might encounter in realistic applications.

The sort of sign relation we normally encounter in practice will be a subset L of a cartesian product O \times S \times I, where the object, sign, and interpretant-sign domains all have infinitely many members in principle, though of course we tend to get by with finite samples at any given moment and it may even be possible to start small and build capacity over time.

All the objects we need to reference in a given application will go into the object domain O and all the signs and interpretant-signs we need to denote these objects will go into the sign domain S and the interpretant-sign domain I.

It may be useful to note at this point that there are such things as monadic projections:

\begin{array}{lll}  \mathrm{proj}_O & : & O \times S \times I \to O  \\[4pt]  \mathrm{proj}_S & : & O \times S \times I \to S  \\[4pt]  \mathrm{proj}_I & : & O \times S \times I \to I  \end{array}

For example, \mathrm{proj}_O (L) gives the set of all elements in O that actually occur as first correlates in L, sometimes called the O-range.

There are interesting classes of relations that take place internal to the various domains.  For example, there are the syntactic relations or parsing relations that operate within the sign domain, relating complex signs to their component signs.

But that’s a topic a little ways down the road …

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