Category Archives: Logic of Science

Objects, Models, Theories : 2

Posted on November 20, 2013 by Jon Awbrey

Re: K.W. Regan • The Graph Of Math Re: Artem Kaznatcheev • Three Types Of Mathematical Models What — if anything — is the common sense that connects the different senses of the word model, as it has been used … Continue reading →

Posted in Adaptive Systems, Analogy, Aristotle, Artificial Intelligence, Biological Systems, C.S. Peirce, Computational Complexity, Evolution, Gödel, Information, Inquiry, Inquiry Driven Systems, Learning Theory, Logic, Logic of Science, Mathematical Models, Mental Models, Model Theory, Natural Intelligence, Peirce, Pragmata, Semiotics | Tagged , , , , , , , , , , , , , , , , , , , , , | 8 Comments

Definition and Determination • 10

Posted on October 7, 2013 by Jon Awbrey

The moment, then, that we pass from nothing and the vacuity of being to any content or sphere, we come at once to a composite content and sphere.  In fact, extension and comprehension — like space and time — are … Continue reading →

Posted in C.S. Peirce, Comprehension, Constraint, Definition, Determination, Extension, Form, Indication, Information = Comprehension × Extension, Inquiry, Intension, Logic, Logic of Science, Mathematics, Peirce, Semiotics, Sources | Tagged , , , , , , , , , , , , , , , , | 11 Comments

Objects, Models, Theories • 1

Posted on September 10, 2013 by Jon Awbrey

Happy Birthday, Charles Sanders Peirce❢ — September 10, 1839 Re: Artem Kaznatcheev • Three Types of Mathematical Models Comment 1 In speaking of models one tends to find denizens of different disciplines talking at cross purposes to one another.  Logicians … Continue reading →

Posted in Adaptive Systems, Analogy, Biological Systems, C.S. Peirce, Information, Inquiry, Inquiry Driven Systems, Learning Theory, Logic, Logic of Science, Mathematical Models, Mathematics, Mental Models, Model Theory, Pragmata, Semiotics, Sign Relations, Triadic Relations, Visualization | Tagged , , , , , , , , , , , , , , , , , , | 8 Comments

What Is A Theorem That A Human May Prove It?

Posted on June 19, 2013 by Jon Awbrey

Re: Gil Kalai • Why Is Mathematics Possible? • Tim Gowers’ Take On The Matter Comment 1 To the extent that mathematics has to do with reasoning about possible existence, or inference from pure hypothesis, a line of thinking going … Continue reading →

Posted in Abduction, Analogy, Aristotle, C.S. Peirce, Conjecture, Deduction, Epistemology, Hypothesis, Induction, Inquiry, Logic, Logic of Science, Mathematics, Peirce, Proof Theory, Retroduction, Theorem Proving, Warren S. McCulloch | Tagged , , , , , , , , , , , , , , , , , | 2 Comments

C.S. Peirce • The Proper Treatment of Hypotheses

Posted on June 19, 2013 by Jon Awbrey

Selection from C.S. Peirce, “Hume On Miracles” (1901), CP 6.522–547 530.   Now the testing of a hypothesis is usually more or less costly. Not infrequently the whole life’s labor of a number of able men is required to disprove a … Continue reading →

Posted in Abduction, Hypothesis, Inquiry, Logic of Science, Peirce, References, Retroduction, Sources | Tagged , , , , , , , | 1 Comment

What part do arguments from authority play in mathematical reasoning?

Posted on May 14, 2013 by Jon Awbrey

In forming your answer you may choose to address any or all of the following aspects of the question: Descriptive What part do arguments from authority actually play in mathematical reasoning? Normative What part do arguments from authority ideally play … Continue reading →

Posted in Artificial Intelligence, Authority, Control, Control Theory, Cybernetics, Fixation of Belief, History of Mathematics, History of Science, Information, Information Theory, Inquiry, Inquiry Driven Systems, Intelligent Systems, Intuition, Logic, Logic of Science, Mathematical Intuition, Mathematical Reasoning, Operations Research, Optimal Control, Optimization, Philosophy of Science, Scientific Method | Tagged , , , , , , , , , , , , , , , , , , , , , , | 2 Comments

C.S. Peirce : Information = Comprehension × Extension

Posted on May 8, 2013 by Jon Awbrey

Re: R.J. Lipton and K.W. Regan • A Most Perplexing Mystery The inverse relationship between symmetry and diversity — that we see for example in the lattice-inverting map of a Galois correspondence — is a variation on an old theme … Continue reading →

Posted in C.S. Peirce, Comprehension, Diversity, Extension, Information, Information = Comprehension × Extension, Inquiry, Intension, Logic, Logic of Science, Peirce, Reciprocity, Semiotics, Sign Relations, Symmetry, Variety | Tagged , , , , , , , , , , , , , , , | 13 Comments

Poems and Programs

Posted on February 27, 2013 by Jon Awbrey

Words that do … A trendy misunderstanding has reared its head as to what the discipline of computing, indeed the logic of science, are all about.  I blame Penrose, of course, but he is only the most recent promulgator of … Continue reading →

Posted in Aesthetics, Artistic Differences, Computability, Effective Description, Ethics, Existential Choice, Finitude, Form, Imagination, Information, Inquiry, Limitation, Logic of Science, Matter, Mortality, Poetry, Programming, Volition | Tagged , , , , , , , , , , , , , , , , , | 1 Comment

Semeiotic

Posted on July 30, 2008 by Jon Awbrey

Theory of Signs Semeiotic is one of the terms C.S. Peirce used for his theory of triadic sign relations and it serves to distinguish his theory of signs from other approaches to the same subject matter, more generally referred to … Continue reading →

Posted in C.S. Peirce, Icon Index Symbol, Logic, Logic of Relatives, Logic of Science, Mathematics, Peirce, Pragmatics, Relation Theory, Semantics, Semeiosis, Semeiotic, Semiosis, Semiotics, Sign Relations, Syntax, Triadic Relations | Tagged , , , , , , , , , , , , , , , , | 9 Comments