Category Archives: Differential Logic

Alpha Now, Omega Later • 1

Posted on November 16, 2013 by Jon Awbrey

I am still in the middle of trying to catch up on some long put-off work but recent discussions of logical graphs and physics and the like on the Peirce List have bestirred me from my grindstone long enough to … Continue reading →

Posted in C.S. Peirce, Differential Logic, Dynamical Systems, Equational Inference, Laws of Form, Logic, Logical Graphs, Mathematics, Propositional Calculus, Semiotics, Sign Relations, Spencer Brown | Tagged , , , , , , , , , , , | 8 Comments

Differential Analytic Turing Automata • Discussion 1

Posted on October 14, 2013 by Jon Awbrey

Re: R.J. Lipton and K.W. Regan • Proving Cook’s Theorem Synchronicity Rules❢ I just started reworking an old exposition of mine on Cook’s Theorem, where I borrowed the Parity Function example from Wilf (1986), Algorithms and Complexity, and translated it … Continue reading →

Posted in Algorithms, Boolean Functions, C.S. Peirce, Cactus Graphs, Computational Complexity, Differential Analytic Turing Automata, Differential Logic, Logic, Logical Graphs, Peirce, Propositional Calculus, Turing Machines | Tagged , , , , , , , , , , , | 2 Comments

Special Classes of Propositions

Posted on May 31, 2013 by Jon Awbrey

Adapted from Differential Propositional Calculus • Special Classes of Propositions A basic proposition, coordinate proposition, or simple proposition in the universe of discourse is one of the propositions in the set Among the propositions in are several families of propositions … Continue reading →

Posted in Boolean Functions, Computational Complexity, Differential Logic, Equational Inference, Functional Logic, Indication, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Propositional Calculus, Visualization | Tagged , , , , , , , , , , , | 2 Comments

Strangers In Paradise

Posted on May 22, 2013 by Jon Awbrey

Re: Kilvington’s Sophismata Comment 1 On the one hand Aristotle gives us the logic of analogy (παραδειγμα).  On the other hand he cautions us that different paradigms may have no common measure.  It seems these Immortals are always getting ahead … Continue reading →

Posted in Albert Camus, Analogy, Aristotle, Differential Logic, Eleatic Stranger, Heraclitus, Incommensurability, Logic, Metabasis, Paradigmata, Paradox, Parmenides, Plato, Richard Kilvington, Sisyphus, Sophismata, Thomas Kuhn, Zeno | Tagged , , , , , , , , , , , , , , , , , | Leave a comment

Slip Slidin’ Away

Posted on April 11, 2013 by Jon Awbrey

And you give me the choice between a description that is sure but that teaches me nothing and hypotheses that claim to teach me but that are not sure. — Albert Camus • The Myth of Sisyphus Re: R.J. Lipton … Continue reading →

Posted in Albert Camus, C.S. Peirce, Change, Differential Logic, Infinity, Lewis Carroll, Logic, Mathematics, Meno, Modus Ponens, Motion, Paradox, Phenomenology, Sisyphus, Syllogism, Time, Zeno | Tagged , , , , , , , , , , , , , , , , | 3 Comments

The Present Is Big With The Future

Posted on April 1, 2013 by Jon Awbrey

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 … Continue reading →

Posted in Causality, Certainty, Chance, Contingency, Determination, Determinism, Differential Calculus, Differential Logic, Evil, Free Will, Freedom, Hologrammautomaton, Infinitesimals, Leibniz, Preëstablished Harmony, Theodicy | Tagged , , , , , , , , , , , , , , , | 17 Comments

Sign Relational Manifolds • 5

Posted on November 1, 2012 by Jon Awbrey

Let me try to say in intuitive terms what I think is really going on here. The problem we face is as old as the problem of other minds, or intersubjectivity, or even commensurability, and it naturally involves a whole … Continue reading →

Posted in C.S. Peirce, Cybernetics, Differential Geometry, Differential Logic, Geometry, Interoperability, Logic, Manifolds, Mathematics, Riemann, Semiotics, Sign Relational Manifolds, Sign Relations, Triadic Relations, Visualization | Tagged , , , , , , , , , , , , , , | Leave a comment

Sign Relational Manifolds • 4

Posted on October 30, 2012 by Jon Awbrey

Another set of notes I found on this theme strikes me as getting to the point more quickly and though they read a little rough in places I think it may be worth the effort to fill out their general … Continue reading →

Posted in C.S. Peirce, Cybernetics, Differential Geometry, Differential Logic, Geometry, Interoperability, Logic, Manifolds, Mathematics, Riemann, Semiotics, Sign Relational Manifolds, Sign Relations, Triadic Relations, Visualization | Tagged , , , , , , , , , , , , , , | 4 Comments

Sign Relational Manifolds • 3

Posted on October 23, 2012 by Jon Awbrey

I’m not sure when it was I first noticed the relationship between manifolds and semiotics but I distinctly recall the passage in Serge Lang’s Differential and Riemannian Manifolds which brought the triadic character of tangent vectors into high relief.  I … Continue reading →

Posted in C.S. Peirce, Cybernetics, Differential Geometry, Differential Logic, Geometry, Intentionality, Logic, Manifolds, Mathematics, Riemann, Semiotics, Sign Relational Manifolds, Sign Relations, Triadic Relations, Visualization | Tagged , , , , , , , , , , , , , , | Leave a comment

Sign Relational Manifolds • 2

Posted on October 22, 2012 by Jon Awbrey

A sense of how manifolds are applied in practice may be gleaned from the set of excerpts linked below, from Doolin and Martin (1990), Introduction to Differential Geometry for Engineers, which I used in discussing differentiable manifolds with other participants … Continue reading →

Posted in C.S. Peirce, Cybernetics, Differential Geometry, Differential Logic, Geometry, Interoperability, Logic, Manifolds, Mathematics, Riemann, Semiotics, Sign Relational Manifolds, Sign Relations, Triadic Relations, Visualization | Tagged , , , , , , , , , , , , , , | Leave a comment