Tag Archives: Propositions As Types Analogy

Survey of Precursors Of Category Theory • 6

Posted on May 5, 2025 by Jon Awbrey

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

Posted in Abstraction, Ackermann, Analogy, Aristotle, C.S. Peirce, Carnap, Category Theory, Foundations of Mathematics, Hilbert, Hypostatic Abstraction, Kant, Logic, Mathematics, Propositions As Types Analogy, Relation Theory, Saunders Mac Lane, Semiotics, Type Theory, Universals | Tagged , , , , , , , , , , , , , , , , , , | 2 Comments

Survey of Precursors Of Category Theory • 5

Posted on May 24, 2024 by Jon Awbrey

A few years ago I began a sketch on the “Precursors of Category Theory”, tracing the continuities of the category concept from Aristotle, to Kant and Peirce, through Hilbert and Ackermann, to contemporary mathematical practice.  A Survey of resources on … 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 , , , , , , , , , , , , , , , , , , , , , , | 10 Comments

Peirce’s Law • 7

Posted on October 25, 2023 by Jon Awbrey

Equational Form (concl.) The following animation replays the steps of the proof. Reference Peirce, Charles Sanders (1885), “On the Algebra of Logic : A Contribution to the Philosophy of Notation”, American Journal of Mathematics 7 (1885), 180–202.  Reprinted (CP 3.359–403), (CE 5, 162–190). … Continue reading →

Posted in C.S. Peirce, Equational Inference, Laws of Form, Logic, Logical Graphs, Mathematics, Peirce, Peirce's Law, Proof Theory, Propositional Calculus, Propositions As Types Analogy, Semiotics, Spencer Brown, Visualization | Tagged , , , , , , , , , , , , , | 9 Comments

Peirce’s Law • 6

Posted on October 24, 2023 by Jon Awbrey

Equational Form (cont.) Using the axioms and theorems listed in the entries on logical graphs, the equational form of Peirce’s law may be proved in the following manner. Reference Peirce, Charles Sanders (1885), “On the Algebra of Logic : A … Continue reading →

Posted in C.S. Peirce, Equational Inference, Laws of Form, Logic, Logical Graphs, Mathematics, Peirce, Peirce's Law, Proof Theory, Propositional Calculus, Propositions As Types Analogy, Semiotics, Spencer Brown, Visualization | Tagged , , , , , , , , , , , , , | 9 Comments

Peirce’s Law • 5

Posted on October 23, 2023 by Jon Awbrey

Equational Form A stronger form of Peirce’s law also holds, in which the final implication is observed to be reversible, resulting in the following equivalence. The converse implication is clear enough on general principles, since holds for any proposition Representing … Continue reading →

Posted in C.S. Peirce, Equational Inference, Laws of Form, Logic, Logical Graphs, Mathematics, Peirce, Peirce's Law, Proof Theory, Propositional Calculus, Propositions As Types Analogy, Semiotics, Spencer Brown, Visualization | Tagged , , , , , , , , , , , , , | 9 Comments

Peirce’s Law • 4

Posted on October 22, 2023 by Jon Awbrey

Proof Animation The following animation replays the steps of the proof. Reference Peirce, Charles Sanders (1885), “On the Algebra of Logic : A Contribution to the Philosophy of Notation”, American Journal of Mathematics 7 (1885), 180–202.  Reprinted (CP 3.359–403), (CE 5, 162–190). Resources … Continue reading →

Posted in C.S. Peirce, Equational Inference, Laws of Form, Logic, Logical Graphs, Mathematics, Peirce, Peirce's Law, Proof Theory, Propositional Calculus, Propositions As Types Analogy, Semiotics, Spencer Brown, Visualization | Tagged , , , , , , , , , , , , , | 9 Comments

Peirce’s Law • 3

Posted on October 21, 2023 by Jon Awbrey

Graphical Proof Using the axiom set given in the articles on logical graphs, Peirce’s law may be proved in the following manner. Reference Peirce, Charles Sanders (1885), “On the Algebra of Logic : A Contribution to the Philosophy of Notation”, … Continue reading →

Posted in C.S. Peirce, Equational Inference, Laws of Form, Logic, Logical Graphs, Mathematics, Peirce, Peirce's Law, Proof Theory, Propositional Calculus, Propositions As Types Analogy, Semiotics, Spencer Brown, Visualization | Tagged , , , , , , , , , , , , , | 9 Comments

Peirce’s Law • 2

Posted on October 20, 2023 by Jon Awbrey

Graphical Representation Representing propositions in the language of logical graphs, and operating under the existential interpretation, Peirce’s law is expressed by means of the following formal equivalence or logical equation. Reference Peirce, Charles Sanders (1885), “On the Algebra of Logic … Continue reading →

Posted in C.S. Peirce, Equational Inference, Laws of Form, Logic, Logical Graphs, Mathematics, Peirce, Peirce's Law, Proof Theory, Propositional Calculus, Propositions As Types Analogy, Semiotics, Spencer Brown, Visualization | Tagged , , , , , , , , , , , , , | 9 Comments

Peirce’s Law • 1

Posted on October 19, 2023 by Jon Awbrey

A Curious Truth of Classical Logic Peirce’s law is a propositional calculus formula which states a non‑obvious truth of classical logic and affords a novel way of defining classical propositional calculus. Introduction Peirce’s law is commonly expressed in the following … Continue reading →

Posted in C.S. Peirce, Equational Inference, Laws of Form, Logic, Logical Graphs, Mathematics, Peirce, Peirce's Law, Proof Theory, Propositional Calculus, Propositions As Types Analogy, Semiotics, Spencer Brown, Visualization | Tagged , , , , , , , , , , , , , | 9 Comments

Peirce’s Law

Posted on October 18, 2023 by Jon Awbrey

A Curious Truth of Classical Logic Peirce’s law is a propositional calculus formula which states a non‑obvious truth of classical logic and affords a novel way of defining classical propositional calculus. Introduction Peirce’s law is commonly expressed in the following … Continue reading →

Posted in C.S. Peirce, Equational Inference, Laws of Form, Logic, Logical Graphs, Mathematics, Peirce, Peirce's Law, Proof Theory, Propositional Calculus, Propositions As Types Analogy, Semiotics, Spencer Brown, Visualization | Tagged , , , , , , , , , , , , , | 9 Comments