Category Archives: Abstraction

Precursors Of Category Theory • Discussion 3

Take your place on The Great Mandala As it moves through your brief moment of time. Win or lose now you must choose now And if you lose you’re only losing your life. Peter Yarrow Re: Ontolog Forum • Alex … Continue reading

Posted in Abstraction, Ackermann, Aristotle, C.S. Peirce, Carnap, Category Theory, Hilbert, Kant, Logic, Logic of Relatives, Mathematics, Peirce, Peirce's Categories, Relation Theory, Saunders Mac Lane, Sign Relations, Type Theory | Tagged , , , , , , , , , , , , , , , , | 1 Comment

Precursors Of Category Theory • Discussion 2

Re: Ontolog Forum • Alex Shkotin AS: Looking at “categories, or types” in Precursors Of Category Theory • Hilbert and Ackermann what do you think of to say “Precursors Of Type Theory” as Category Theory is a math discipline?   … Continue reading

Posted in Abstraction, Ackermann, Aristotle, C.S. Peirce, Carnap, Category Theory, Hilbert, Kant, Logic, Logic of Relatives, Mathematics, Peirce, Peirce's Categories, Relation Theory, Saunders Mac Lane, Sign Relations, Type Theory | Tagged , , , , , , , , , , , , , , , , | 1 Comment

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

Precursors Of Category Theory • Discussion 1

Re: FB | Medieval Logic • EB • JA • JA • EB • JA • EB • JA • JA • EB JA:  In the logic of Aristotle categories are adjuncts to reasoning designed to resolve ambiguities and thus … Continue reading

Posted in Abstraction, Ackermann, Aristotle, C.S. Peirce, Carnap, Category Theory, Hilbert, Kant, Logic, Logic of Relatives, Mathematics, Peirce, Peirce's Categories, Relation Theory, Saunders Mac Lane, Sign Relations, Type Theory | Tagged , , , , , , , , , , , , , , , , | 1 Comment

Mathematical Method • Discussion 7

Re: Ontolog Forum • Alex Shkotin Dear Alex, You raised the following point: AS: One important usage of a sign is as an element of a language, especially a formal one, i.e. with a formal grammar. For context you cited … Continue reading

Posted in Abstraction, C.S. Peirce, Essentialism, Hypostatic Abstraction, Logic, Mathematics, Metaphysics, Method, Nominalism, Ockham, Ockham's Razor, Peirce, Pragmatic Maxim, Pragmatism, Realism, Semiotics, Theory | Tagged , , , , , , , , , , , , , , , , | Leave a comment

Mathematical Method • Discussion 6

Re: Ontolog Forum • Alex Shkotin Dear Alex, Thanks for the very apt segue from Jon Barwise — Modern mathematics might be described as the science of abstract objects, be they real numbers, functions, surfaces, algebraic structures or whatever.  Mathematical … Continue reading

Posted in Abstraction, C.S. Peirce, Essentialism, Hypostatic Abstraction, Logic, Mathematics, Metaphysics, Method, Nominalism, Ockham, Ockham's Razor, Peirce, Pragmatic Maxim, Pragmatism, Realism, Semiotics, Theory | Tagged , , , , , , , , , , , , , , , , | Leave a comment

Mathematical Method • Discussion 5

Re: Ontolog Forum • Paul Tyson Dear Paul, “How We Think” is a topic for the descriptive science of psychology, and its ways are legion beyond definitive or exhaustive description. “How We Ought To Think” if we wish to succeed … Continue reading

Posted in Abstraction, C.S. Peirce, Essentialism, Hypostatic Abstraction, Logic, Mathematics, Metaphysics, Method, Nominalism, Ockham, Ockham's Razor, Peirce, Pragmatic Maxim, Pragmatism, Realism, Semiotics, Theory | Tagged , , , , , , , , , , , , , , , , | Leave a comment

Mathematical Method • Discussion 4

Re: Peirce List • Helmut Raulien Dear Helmut, It’s one of the occupational hazards of the classifying mind that one can start out consciously characterizing aspects of real situations and end up unwittingly thinking one’s gotten everything under the sun sorted … Continue reading

Posted in Abstraction, C.S. Peirce, Essentialism, Hypostatic Abstraction, Logic, Mathematics, Metaphysics, Method, Nominalism, Ockham, Ockham's Razor, Peirce, Pragmatic Maxim, Pragmatism, Realism, Semiotics, Theory | Tagged , , , , , , , , , , , , , , , , | Leave a comment

Mathematical Method • Discussion 3

Re: Peirce List • Gary Fuhrman Dear Gary, Auke van Breemen wrote: AvB: It seems to come down to:  never consider the textual production of a scientist only in itself, but also look at the reality the text tries to … Continue reading

Posted in Abstraction, C.S. Peirce, Essentialism, Hypostatic Abstraction, Logic, Mathematics, Metaphysics, Method, Nominalism, Ockham, Ockham's Razor, Peirce, Pragmatic Maxim, Pragmatism, Realism, Semiotics, Theory | Tagged , , , , , , , , , , , , , , , , | Leave a comment

Mathematical Method • Discussion 2

Re: Peirce List • Auke van Breemen AvB: It seems to come down to:  never consider the textual production of a scientist only in itself, but also look at the reality the text tries to explain. Dear Auke, Exactly! We … Continue reading

Posted in Abstraction, C.S. Peirce, Essentialism, Hypostatic Abstraction, Logic, Mathematics, Metaphysics, Method, Nominalism, Ockham, Ockham's Razor, Peirce, Pragmatic Maxim, Pragmatism, Realism, Semiotics, Theory | Tagged , , , , , , , , , , , , , , , , | 2 Comments