Tag Archives: Foundations of Mathematics

Survey of Relation Theory • 2

In this Survey of blog and wiki posts on Relation Theory, relations are viewed from the perspective of combinatorics, in other words, as a topic in discrete mathematics, with special attention to finite structures and concrete set-theoretic constructions, many of … Continue reading

Posted in Algebra, Algebra of Logic, C.S. Peirce, Category Theory, Combinatorics, Discrete Mathematics, Duality, Dyadic Relations, Foundations of Mathematics, Graph Theory, Logic, Logic of Relatives, Mathematics, Peirce, Relation Theory, Semiotics, Set Theory, Sign Relational Manifolds, Sign Relations, Surveys, Triadic Relations, Triadicity, Type Theory | Tagged , , , , , , , , , , , , , , , , , , , , , , | 3 Comments

All Liar, No Paradox • Comment 1

A statement asserts that a statement is a statement that is false. The statement violates an axiom of logic, so it doesn’t really matter whether the ostensible statement the so-called liar, really is a statement or has a truth value. … Continue reading

Posted in C.S. Peirce, Epimenides, Foundations of Mathematics, Liar Paradox, Logic, Logical Graphs, Paradox, Pragmatics, Rhetoric, Semantics, Semiositis, Semiotics, Sign Relations, Syntax, Zeroth Law Of Semiotics, Zeroth Order Logic | Tagged , , , , , , , , , , , , , , , | 5 Comments

All Liar, No Paradox

A statement asserts that a statement is a statement that is false. The statement violates an axiom of logic, so it doesn’t really matter whether the ostensible statement the so-called liar, really is a statement or has a truth value.

Posted in C.S. Peirce, Epimenides, Foundations of Mathematics, Liar Paradox, Logic, Logical Graphs, Paradox, Pragmatics, Rhetoric, Semantics, Semiositis, Semiotics, Sign Relations, Syntax, Zeroth Law Of Semiotics, Zeroth Order Logic | Tagged , , , , , , , , , , , , , , , | 4 Comments

Inquiry, Signs, Relations • 1

Re: Michael Harris • A Non-Logical Cognitive Phenomenon Human spontaneous non-demonstrative inference is not, overall, a logical process.  Hypothesis formation involves the use of deductive rules, but is not totally governed by them;  hypothesis confirmation is a non-logical cognitive phenomenon:  … Continue reading

Posted in Abduction, Action, Analogy, C.S. Peirce, Cognition, Cognitive Science, Communication, Deduction, Foundations of Mathematics, Induction, Information, Information Theory, Inquiry, Inquiry Into Inquiry, Interpretation, Logic, Logic of Relatives, Logic of Science, Mathematics, Michael Harris, Peirce, Philosophy, Philosophy of Mathematics, Philosophy of Science, Pragmatism, Relation Theory, Relevance, Semiotics, Sign Relations, Triadic Relations | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | Leave a comment

Signs Of Signs • 4

Re: Michael Harris • Language 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 … Continue reading

Posted in Aesthetics, C.S. Peirce, 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 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 Harris • Language 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 … Continue reading

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

Signs Of Signs • 2

Re: Michael Harris • Language About Language I compared mathematics to a “consensual hallucination,” like virtual reality, and I continue to believe that the aim is to get (consensually) to the point where that hallucination is a second nature. I … Continue reading

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

Signs Of Signs • 1

Re: Michael Harris • Language About Language There is a language and a corresponding literature that approaches logic and mathematics as related species of communication and information gathering, namely, the pragmatic-semiotic tradition passed on to us through the lifelong efforts … Continue reading

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

Survey of Relation Theory • 1

In this Survey of blog and wiki posts on Relation Theory, relations are viewed from the perspective of combinatorics, in other words, as a topic in discrete mathematics, with special attention to finite structures and concrete set-theoretic constructions, many of … Continue reading

Posted in Algebra, Algebra of Logic, C.S. Peirce, Category Theory, Combinatorics, Discrete Mathematics, Duality, Dyadic Relations, Foundations of Mathematics, Graph Theory, Logic, Logic of Relatives, Mathematics, Peirce, Relation Theory, Semiotics, Set Theory, Sign Relational Manifolds, Sign Relations, Surveys, Triadic Relations, Triadicity, Type Theory | Tagged , , , , , , , , , , , , , , , , , , , , , , | 1 Comment

Survey of Precursors Of Category Theory • 1

A few years ago I began a sketch on the “Precursors of Category Theory”, aiming to trace the continuities of the category concept from Aristotle, to Kant and Peirce, through Hilbert and Ackermann, to contemporary mathematical practice.  A Survey of … Continue reading

Posted in Abstraction, Ackermann, Analogy, Aristotle, C.S. Peirce, Carnap, Category Theory, Diagrams, Dyadic Relations, Equational Inference, Form, Foundations of Mathematics, Functional Logic, Hilbert, History of Mathematics, Hypostatic Abstraction, Kant, Logic, Logic of Relatives, Mathematics, Peirce, Propositions As Types Analogy, Relation Theory, Saunders Mac Lane, Semiotics, Sign Relations, Surveys, Triadic Relations, Type Theory, Universals | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 18 Comments