Tag Archives: Foundations of Mathematics

Ask Meno Questions • Discussion 4

Re: Facebook Discussion • 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 how we come … Continue reading

Posted in Anamnesis, C.S. Peirce, Descartes, Education, Epistemology, Foundations of Mathematics, Infinity, Inquiry, Inquiry Driven Systems, Intelligent Systems, Knowledge, Knowledge Representation, Learning, Learning Theory, Logic, Mathematics, Meno, Peirce, Philosophy, Philosophy of Mathematics, Plato, Pragmata, Pragmatism, Recollection, Semiotics, Socrates, Tabula Rasa, Teaching, Theorem Proving, Triadicity, 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 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 , , , , , , , , , , , , , , , , , , , , , , , , | Leave a 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 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