Relations & Their Relatives : 10

Re: Peirce List DiscussionJim Willgoose

Here is the series of blog posts on Chapter 3 (The Logic of Relatives) from Peirce’s 1880 “Algebra of Logic” up to the point where I left off on May Day.

Up to this point we are still dealing mainly with dyadic relations and as interesting as those may be, especially to a graph theorist, the level of complexity it takes for the first signs of semiosis to get up and running does not come into play until we reach the playing field of triadic relations.

Posted in Logic, Logic of Relatives, Mathematics, Peirce, Peirce List, Relation Theory, Semiotics, Sign Relations, Tertium Quid, Thirdness, Triadic Relations, Triadicity | Tagged , , , , , , , , , , , | 1 Comment

My Thematics • 2

Communication is so much harder
Than mere invention or discovery.

Will they have in mind what I have in mind?
Will I find the signs?   Will I have the time?

There is so much shadow there must be light!

Posted in Anthem, Anthematics, Communication, Discovery, Inquiry, Invention, Mantra, Mathematics, Meditation, Morpheus, Morphism, Mythematics, Nostalgebra, Nostalgia, Reflection, Semeiosis, Semiosis, Semiotics | Tagged , , , , , , , , , , , , , , , , , | 1 Comment

My Thematics • 1

I miss the days I’d spend my days
And nights dreaming mathematics

Posted in Anthem, Anthematics, Mathematics, Morpheus, Morphism, Mythematics, Nostalgebra, Nostalgia | Tagged , , , , , , , | 1 Comment

Relations & Their Relatives : 9

Re: Peirce List DiscussionHelmut Raulien

In discussing Peirce’s concept of a triadic sign relation as existing among objects, signs, and interpretant signs the question arises whether any of the classes so related are classes by themselves, that is, whether there is necessarily anything distinctive about the being of an object, the being of a sign, or the being of an interpretant sign.

Maybe I can clear up a few points about the relational standpoint by resorting to a familiar case of a triadic relation, one I’m guessing we all mastered early in our schooling, namely, the one involved in the operation of subtraction, x - y = z.  When I was in school we learned a set of quaint terms for the numbers x, y, z in the relation and I wasn’t sure they still taught such things so I checked the web and found a page that described the terms just as I remembered them:

Maths Is Fun • Subtraction

  • The number x is called the minuend.
  • The number y is called the subtrahend.
  • The number z is called the difference.

So we come to the questions:

  • Are minuends a class by themselves?
  • Are subtrahends a class by themselves?
  • Are differences a class by themselves?

To answer these questions we need to observe the distinction between relational roles and absolute essences (inherent qualities, ontological substances, or permanent properties).

If our notion of number is generous enough to include negative numbers then any number can appear in any one of the three places, so minuend, subtrahend, and difference are relational roles and not absolute essences.  We can tell this because it follows from the definition of the subtraction operation.

When it comes time to ask the same questions of objects, signs, and interpretant signs then any hope of a definitive answer must come from the definition of a sign relation we’ve chosen to fit our subject matter.

Posted in Logic, Logic of Relatives, Mathematics, Peirce, Peirce List, Relation Theory, Semiotics, Sign Relations, Tertium Quid, Thirdness, Triadic Relations, Triadicity | Tagged , , , , , , , , , , , | 1 Comment

Information Resistance • Ω

The hardest thing to understand about information is people’s resistance to it.

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Signs Of Signs • 4

Re: Michael HarrisLanguage About Language

But then inevitably I find myself wondering whether a proof assistant, or even a formal system, can make the distinction between “technical” and “fundamental” questions. There seems to be no logical distinction. The formalist answer might involve algorithmic complexity, but I don’t think that sheds any useful light on the question. The materialist answer (often? usually?) amounts to just-so stories involving Darwin, and lions on the savannah, and maybe an elephant, or at least a mammoth. I don’t find these very satisfying either and would prefer to find something in between, and I would feel vindicated if it could be proved (in I don’t know what formal system) that the capacity to make such a distinction entails appreciation of music.

Peirce proposed a distinction between corollarial and theorematic reasoning in mathematics that strikes me as similar to the distinction that Michael Harris seeks between technical and fundamental questions.

I can’t say I have a lot of insight into how the line might be drawn, but I recall a number of traditions pointing to the etymology of theorem as having to do with the observation of objects and practices whose depth of detail always escapes full accounting by any number of partial views.

On the subject of music, all I have is this incidental —

Riffs & Rotes

Perhaps it takes a number theorist to appreciate it …

Posted in Aesthetics, Category Theory, Coherentism, Communication, Connotation, Form, Formal Languages, Foundations of Mathematics, Higher Order Propositions, Illusion, Information, Information Theory, Inquiry, Inquiry Into Inquiry, Interpretation, Interpretive Frameworks, Intuition, Language, Logic, Mathematics, Music, Objective Frameworks, Objectivism, Peirce, Philosophy, Philosophy of Mathematics, Pragmata, Pragmatics, Pragmatism, Recursion, Reflection, Riffs and Rotes, Semantics, Semiotics, Set Theory, Sign Relations, Syntax, Translation, Triadic Relations, Type Theory | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 2 Comments

Signs Of Signs • 3

Re: Michael HarrisLanguage About Language

And if we don’t, who puts us away?

One’s answer, or at least one’s initial response to that question will turn on how one feels about formal realities.  As I understand it, reality is that which persists in thumping us on the head until we get what it’s trying to tell us.  Are there formal realities, forms that drive us in that way?

Discussions like these tend to begin by supposing we can form a distinction between external and internal.  That is a formal hypothesis, not yet born out as a formal reality.  Are there formal realities that drive us to recognize them, to pick them out of a crowd of formal possibilities?

Posted in Aesthetics, Category Theory, Coherentism, Communication, Connotation, Form, Formal Languages, Foundations of Mathematics, Higher Order Propositions, Illusion, Information, Information Theory, Inquiry, Inquiry Into Inquiry, Interpretation, Interpretive Frameworks, Intuition, Language, Logic, Mathematics, Objective Frameworks, Objectivism, Peirce, Philosophy, Philosophy of Mathematics, Pragmata, Pragmatics, Pragmatism, Recursion, Reflection, Semantics, Semiotics, Set Theory, Sign Relations, Syntax, Translation, Triadic Relations, Type Theory | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | Leave a comment