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#categorytheory — Public Fediverse posts

Live and recent posts from across the Fediverse tagged #categorytheory, aggregated by home.social.

  1. Charlotte Aten @[email protected] ·

    While teaching a course on algebraic theories last semester I mentioned at some point that the familiar bicomplete categories Top and Poset were not algebraic, but were topological. A student asked about this later on and I found that the #Wikipedia page on «topological category» pointed to categories enriched in Top, not categories with a forgetful functor to Set which is topological. While I have lost a lot of faith in Wikipedia recently, I am pleased to report that en.wikipedia.org/wiki/Topologi is now a disambiguation page.

    #math #mathematics #topology #algebra #CategoryTheory

    #categorytheory #algebra #topology #mathematics #math #wikipedia
  2. JxHxBxR @[email protected] ·

    In the mountains, I love exploring nature and climbing any little hidden corner.

    My academic interests include mathematics (#mathematics) and mathematical logic ( #mathematicallogic #logic), particularly model theory ( #modeltheory), category theory ( #categorytheory), higher-order logic and metalogic ( #metalogic), as well as the philosophy of mathematics and logic ( #philosophyofmathematics #philosophyoflogic), epistemology and ontology of them.

    #introduction

    #logic #philosophyoflogic #introduction #mathematicallogic #modeltheory #categorytheory
  3. Jon Awbrey @[email protected] ·

    Peirce's 1885 “Algebra of Logic” • Discussion 2
    • inquiryintoinquiry.com/2024/04

    Re: FB | Daniel Everett

    One thing I've been trying to understand for a very long time is the changes in Peirce's writing about math and logic from 1865 to 1885. If there's anything I've learned from reading Peirce in the often dim light of intellectual history it is to be wary of progressivist assumptions — but unlike many of his other fans I apply that caution also within the body of his own work. Long story short, from 1865 to 1885 I see progress on several fronts but also bits of backsliding from his more prescient early insights. So it's a puzzle … and it will take more study to ravel out the reasons why.

    Resources for reconciling Peirce's two accounts —
    1. The 1870 account of logical involution
    2. The 1885 account of universal quantification

    Peirce's 1870 “Logic of Relatives” • Selection 12 • The Sign of Involution
    • inquiryintoinquiry.com/2014/06
    Comments —
    (1) inquiryintoinquiry.com/2014/06
    (2) inquiryintoinquiry.com/2014/06
    (3) inquiryintoinquiry.com/2014/06
    (4) inquiryintoinquiry.com/2014/06
    (5) inquiryintoinquiry.com/2014/06

    Peirce's 1885 “Algebra of Logic” • Selections
    (1) inquiryintoinquiry.com/2024/03
    (2) inquiryintoinquiry.com/2024/03
    (3) inquiryintoinquiry.com/2024/03
    (4) inquiryintoinquiry.com/2024/04

    Peirce, C.S. (1885), “On the Algebra of Logic : A Contribution to the Philosophy of Notation”, American Journal of Mathematics 7, 180–202.
    • jstor.org/stable/2369451

    #Peirce #Logic #AlgebraOfLogic #LogicOfRelatives #RelationTheory #CategoryTheory
    #Semiotics #PredicateCalculus #Quantification #LogicalInvolution #ComputerScience

    #computerscience #logicalinvolution #quantification #predicatecalculus #semiotics #categorytheory
  4. Jon Awbrey @[email protected] ·

    Peirce's 1885 “Algebra of Logic” • Discussion 1
    • inquiryintoinquiry.com/2024/04

    Re: FB | Daniel Everett

    DE:
    ❝One of the most important papers in the history of logic. “On the Algebra of Logic” was the first to introduce the term “quantifier”.

    ❝Peirce, C.S. (1885), “On the Algebra of Logic : A Contribution to the Philosophy of Notation”, American Journal of Mathematics 7, 180–202.
    • jstor.org/stable/2369451 ❞

    As far as quantification by any other word goes, Peirce had already introduced a more advanced and “functional” concept of quantification in his 1870 “Logic of Relatives”. The subsequent passage to Fregean styles of first order logic would turn out to be a retrograde movement toward syntacticism (a species of nominalism), as seen in the general run of what fol‑lowed in the fol‑lowing years.

    See ☞ Peirce's 1870 “Logic of Relatives”
    • inquiryintoinquiry.com/2019/09

    Especially ☞ “The Sign of Involution”
    • inquiryintoinquiry.com/2014/06

    The connection between logical involution and universal quantification which Peirce put to use in his 1870 Logic of Relatives will turn up again a century later with the application of category theory to computer science and both of those in turn to logic. Just one more time Peirce was that far ahead of it.

    See ☞ Lambek and Scott (1986), Introduction to Higher Order Categorical Logic, Cambridge University Press.
    • oeis.org/wiki/User:Jon_Awbrey/

    #Peirce #Logic #AlgebraOfLogic #LogicOfRelatives #RelationTheory #CategoryTheory
    #Semiotics #PredicateCalculus #Quantification #LogicalInvolution #ComputerScience

    #logicalinvolution #quantification #predicatecalculus #semiotics #relationtheory #logicofrelatives