Category Archives: Foundations of Mathematics

Survey of Precursors Of Category Theory • 2

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, Foundations of Mathematics, Functional Logic, Hilbert, History of Mathematics, Hypostatic Abstraction, Kant, Logic, Mathematics, Peirce, Propositions As Types Analogy, Relation Theory, Saunders Mac Lane, Semiotics, Type Theory, Universals | Tagged , , , , , , , , , , , , , , , , , , , , , , | 3 Comments

Relation Theory • Discussion 1

Re: Cybernetics • Arthur Phillips Responding to what I’ll abductively interpret as a plea for relevance from the cybernetic galley, let me give a quick review of where we are in this many-oared expedition. Our reading of Ashby (see Survey … 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 , , , , , , , , , , , , , , , , , , , , , , | Leave a comment

Survey of Relation Theory • 4

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

Ask Meno Questions • Discussion 4

Re: FB | Foundations of Mathematics • Oguzhan Kosar The questions raised under the heading of “Foundations of Mathematics” are generally considered to fall under the “Philosophy of Mathematics”, in particular, critical reflection on the possibility of mathematical knowledge and … Continue reading

Posted in Anamnesis, Arete, C.S. Peirce, Descartes, Education, Epistemology, Eternal Return, Foundations of Mathematics, Infinity, Innate Idea, Inquiry, Inquiry Driven Systems, Inquiry Into Inquiry, Knowledge, Learning, Locke, Logic, Mathematics, Medium = Message, Meno, Peirce, Philosophy of Mathematics, Plato, Pragmata, Pragmatism, Pythagoras, Recollection, Semiotics, Sign Relations, Socrates, Tabula Rasa, Teaching, Triadic Relations, Turing Test, Virtue | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | Leave a comment

¿Shifting Paradigms? • 6

Re: Peter Cameron • Infinity and Foundation C.S. Peirce is one who recognized the constitutional independence of mathematical inquiry, finding at its core a mode of operation tantamount to observation and more primitive than logic itself.  Here is one place … Continue reading

Posted in Algorithms, Boole, C.S. Peirce, Combinatorics, Computation, Foundations of Mathematics, Inquiry, Laws of Form, Leibniz, Logic, Mathematics, Model Theory, Paradigms, Peirce, Proof Theory, Spencer Brown | Tagged , , , , , , , , , , , , , , , | Leave a comment

¿Shifting Paradigms? • 5

Re: Peter Cameron • Infinity and Foundation We always encounter a multitude of problems whenever we try to rationalize mathematics by reducing it to logic, where logic itself is reduced to a purely deductive style.  A number of thinkers have … Continue reading

Posted in Algorithms, Boole, C.S. Peirce, Combinatorics, Computation, Foundations of Mathematics, Inquiry, Laws of Form, Leibniz, Logic, Mathematics, Model Theory, Paradigms, Peirce, Proof Theory, Spencer Brown | Tagged , , , , , , , , , , , , , , , | 3 Comments

Survey of Relation Theory • 3

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 Relation Theory • 2

In this Survey of previous 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 … Continue reading

Posted in Algebra, C.S. Peirce, Combinatorics, Discrete Mathematics, Duality, Dyadic Relations, Foundations of Mathematics, Logic, Logic of Relatives, Mathematics, Model Theory, Peirce, Proof Theory, Relation Theory, Semiotics, Set Theory, Sign Relational Manifolds, Sign Relations, Surveys, Teridentity, Thirdness, Triadic Relations, Triadicity, Type Theory, Visualization | 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, Peirce, Pragmatics, Rhetoric, Semantics, Semiositis, Semiotics, Sign Relations, Syntax, Zeroth Law Of Semiotics | 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 Epimenides, Foundations of Mathematics, Liar Paradox, Logic, Logical Graphs, Paradox, Peirce, Pragmatics, Rhetoric, Semantics, Semiositis, Semiotics, Sign Relations, Syntax, Zeroth Law Of Semiotics | Tagged , , , , , , , , , , , , , , | 4 Comments