home.social

#ackermann — Public Fediverse posts

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

  1. Survey of Precursors Of Category Theory • 6
    inquiryintoinquiry.com/2025/05

    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 the topic is given below, still very rough and incomplete, but perhaps a few will find it of use.

    Background —

    Precursors Of Category Theory
    oeis.org/wiki/Precursors_Of_Ca

    Propositions As Types Analogy
    oeis.org/wiki/Propositions_As_

    Blog Series —

    Notes On Categories
    inquiryintoinquiry.com/2013/02

    Precursors Of Category Theory
    1. inquiryintoinquiry.com/2024/05
    2. inquiryintoinquiry.com/2024/05
    3. inquiryintoinquiry.com/2024/05
    4. inquiryintoinquiry.com/2024/05
    5. inquiryintoinquiry.com/2024/05
    6. inquiryintoinquiry.com/2024/05

    Precursors Of Category Theory • Discussion
    1. inquiryintoinquiry.com/2020/09
    2. inquiryintoinquiry.com/2020/09
    3. inquiryintoinquiry.com/2020/09

    Categories à la Peirce —

    C.S. Peirce • A Guess at the Riddle
    inquiryintoinquiry.com/2012/03

    Peirce's Categories
    1. inquiryintoinquiry.com/2015/10
    2. inquiryintoinquiry.com/2015/10
    3. inquiryintoinquiry.com/2015/11
    •••
    19. inquiryintoinquiry.com/2020/05
    20. inquiryintoinquiry.com/2020/05
    21. inquiryintoinquiry.com/2020/06

    C.S. Peirce and Category Theory
    1. inquiryintoinquiry.com/2021/06
    2. inquiryintoinquiry.com/2021/06
    3. inquiryintoinquiry.com/2021/06
    4. inquiryintoinquiry.com/2021/06
    5. inquiryintoinquiry.com/2021/06
    6. inquiryintoinquiry.com/2021/06
    7. inquiryintoinquiry.com/2021/07
    8. inquiryintoinquiry.com/2021/07

    #Aristotle #Peirce #Kant #Carnap #Hilbert #Ackermann #SaundersMacLane
    #Abstraction #Analogy #CategoryTheory #FunctionalLogic #RelationTheory
    #PrecursorsOfCategoryTheory #PropositionsAsTypes #Semiotics #TypeTheory

  2. Survey of Precursors Of Category Theory • 6
    inquiryintoinquiry.com/2025/05

    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 the topic is given below, still very rough and incomplete, but perhaps a few will find it of use.

    Background —

    Precursors Of Category Theory
    oeis.org/wiki/Precursors_Of_Ca

    Propositions As Types Analogy
    oeis.org/wiki/Propositions_As_

    Blog Series —

    Notes On Categories
    inquiryintoinquiry.com/2013/02

    Precursors Of Category Theory
    1. inquiryintoinquiry.com/2024/05
    2. inquiryintoinquiry.com/2024/05
    3. inquiryintoinquiry.com/2024/05
    4. inquiryintoinquiry.com/2024/05
    5. inquiryintoinquiry.com/2024/05
    6. inquiryintoinquiry.com/2024/05

    Precursors Of Category Theory • Discussion
    1. inquiryintoinquiry.com/2020/09
    2. inquiryintoinquiry.com/2020/09
    3. inquiryintoinquiry.com/2020/09

    Categories à la Peirce —

    C.S. Peirce • A Guess at the Riddle
    inquiryintoinquiry.com/2012/03

    Peirce's Categories
    1. inquiryintoinquiry.com/2015/10
    2. inquiryintoinquiry.com/2015/10
    3. inquiryintoinquiry.com/2015/11
    •••
    19. inquiryintoinquiry.com/2020/05
    20. inquiryintoinquiry.com/2020/05
    21. inquiryintoinquiry.com/2020/06

    C.S. Peirce and Category Theory
    1. inquiryintoinquiry.com/2021/06
    2. inquiryintoinquiry.com/2021/06
    3. inquiryintoinquiry.com/2021/06
    4. inquiryintoinquiry.com/2021/06
    5. inquiryintoinquiry.com/2021/06
    6. inquiryintoinquiry.com/2021/06
    7. inquiryintoinquiry.com/2021/07
    8. inquiryintoinquiry.com/2021/07

    #Aristotle #Peirce #Kant #Carnap #Hilbert #Ackermann #SaundersMacLane
    #Abstraction #Analogy #CategoryTheory #FunctionalLogic #RelationTheory
    #PrecursorsOfCategoryTheory #PropositionsAsTypes #Semiotics #TypeTheory

  3. Survey of Precursors Of Category Theory • 6
    inquiryintoinquiry.com/2025/05

    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 the topic is given below, still very rough and incomplete, but perhaps a few will find it of use.

    Background —

    Precursors Of Category Theory
    oeis.org/wiki/Precursors_Of_Ca

    Propositions As Types Analogy
    oeis.org/wiki/Propositions_As_

    Blog Series —

    Notes On Categories
    inquiryintoinquiry.com/2013/02

    Precursors Of Category Theory
    1. inquiryintoinquiry.com/2024/05
    2. inquiryintoinquiry.com/2024/05
    3. inquiryintoinquiry.com/2024/05
    4. inquiryintoinquiry.com/2024/05
    5. inquiryintoinquiry.com/2024/05
    6. inquiryintoinquiry.com/2024/05

    Precursors Of Category Theory • Discussion
    1. inquiryintoinquiry.com/2020/09
    2. inquiryintoinquiry.com/2020/09
    3. inquiryintoinquiry.com/2020/09

    Categories à la Peirce —

    C.S. Peirce • A Guess at the Riddle
    inquiryintoinquiry.com/2012/03

    Peirce's Categories
    1. inquiryintoinquiry.com/2015/10
    2. inquiryintoinquiry.com/2015/10
    3. inquiryintoinquiry.com/2015/11
    •••
    19. inquiryintoinquiry.com/2020/05
    20. inquiryintoinquiry.com/2020/05
    21. inquiryintoinquiry.com/2020/06

    C.S. Peirce and Category Theory
    1. inquiryintoinquiry.com/2021/06
    2. inquiryintoinquiry.com/2021/06
    3. inquiryintoinquiry.com/2021/06
    4. inquiryintoinquiry.com/2021/06
    5. inquiryintoinquiry.com/2021/06
    6. inquiryintoinquiry.com/2021/06
    7. inquiryintoinquiry.com/2021/07
    8. inquiryintoinquiry.com/2021/07

    #Aristotle #Peirce #Kant #Carnap #Hilbert #Ackermann #SaundersMacLane
    #Abstraction #Analogy #CategoryTheory #FunctionalLogic #RelationTheory
    #PrecursorsOfCategoryTheory #PropositionsAsTypes #Semiotics #TypeTheory

  4. Survey of Precursors Of Category Theory • 6
    inquiryintoinquiry.com/2025/05

    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 the topic is given below, still very rough and incomplete, but perhaps a few will find it of use.

    Background —

    Precursors Of Category Theory
    oeis.org/wiki/Precursors_Of_Ca

    Propositions As Types Analogy
    oeis.org/wiki/Propositions_As_

    Blog Series —

    Notes On Categories
    inquiryintoinquiry.com/2013/02

    Precursors Of Category Theory
    1. inquiryintoinquiry.com/2024/05
    2. inquiryintoinquiry.com/2024/05
    3. inquiryintoinquiry.com/2024/05
    4. inquiryintoinquiry.com/2024/05
    5. inquiryintoinquiry.com/2024/05
    6. inquiryintoinquiry.com/2024/05

    Precursors Of Category Theory • Discussion
    1. inquiryintoinquiry.com/2020/09
    2. inquiryintoinquiry.com/2020/09
    3. inquiryintoinquiry.com/2020/09

    Categories à la Peirce —

    C.S. Peirce • A Guess at the Riddle
    inquiryintoinquiry.com/2012/03

    Peirce's Categories
    1. inquiryintoinquiry.com/2015/10
    2. inquiryintoinquiry.com/2015/10
    3. inquiryintoinquiry.com/2015/11
    •••
    19. inquiryintoinquiry.com/2020/05
    20. inquiryintoinquiry.com/2020/05
    21. inquiryintoinquiry.com/2020/06

    C.S. Peirce and Category Theory
    1. inquiryintoinquiry.com/2021/06
    2. inquiryintoinquiry.com/2021/06
    3. inquiryintoinquiry.com/2021/06
    4. inquiryintoinquiry.com/2021/06
    5. inquiryintoinquiry.com/2021/06
    6. inquiryintoinquiry.com/2021/06
    7. inquiryintoinquiry.com/2021/07
    8. inquiryintoinquiry.com/2021/07

    #Aristotle #Peirce #Kant #Carnap #Hilbert #Ackermann #SaundersMacLane
    #Abstraction #Analogy #CategoryTheory #FunctionalLogic #RelationTheory
    #PrecursorsOfCategoryTheory #PropositionsAsTypes #Semiotics #TypeTheory

  5. Survey of Precursors Of Category Theory • 6
    inquiryintoinquiry.com/2025/05

    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 the topic is given below, still very rough and incomplete, but perhaps a few will find it of use.

    Background —

    Precursors Of Category Theory
    oeis.org/wiki/Precursors_Of_Ca

    Propositions As Types Analogy
    oeis.org/wiki/Propositions_As_

    Blog Series —

    Notes On Categories
    inquiryintoinquiry.com/2013/02

    Precursors Of Category Theory
    1. inquiryintoinquiry.com/2024/05
    2. inquiryintoinquiry.com/2024/05
    3. inquiryintoinquiry.com/2024/05
    4. inquiryintoinquiry.com/2024/05
    5. inquiryintoinquiry.com/2024/05
    6. inquiryintoinquiry.com/2024/05

    Precursors Of Category Theory • Discussion
    1. inquiryintoinquiry.com/2020/09
    2. inquiryintoinquiry.com/2020/09
    3. inquiryintoinquiry.com/2020/09

    Categories à la Peirce —

    C.S. Peirce • A Guess at the Riddle
    inquiryintoinquiry.com/2012/03

    Peirce's Categories
    1. inquiryintoinquiry.com/2015/10
    2. inquiryintoinquiry.com/2015/10
    3. inquiryintoinquiry.com/2015/11
    •••
    19. inquiryintoinquiry.com/2020/05
    20. inquiryintoinquiry.com/2020/05
    21. inquiryintoinquiry.com/2020/06

    C.S. Peirce and Category Theory
    1. inquiryintoinquiry.com/2021/06
    2. inquiryintoinquiry.com/2021/06
    3. inquiryintoinquiry.com/2021/06
    4. inquiryintoinquiry.com/2021/06
    5. inquiryintoinquiry.com/2021/06
    6. inquiryintoinquiry.com/2021/06
    7. inquiryintoinquiry.com/2021/07
    8. inquiryintoinquiry.com/2021/07

    #Aristotle #Peirce #Kant #Carnap #Hilbert #Ackermann #SaundersMacLane
    #Abstraction #Analogy #CategoryTheory #FunctionalLogic #RelationTheory
    #PrecursorsOfCategoryTheory #PropositionsAsTypes #Semiotics #TypeTheory

  6. 𝗔𝗰𝗸𝗲𝗿𝗺𝗮𝗻𝗻 𝗼𝗽𝘃𝗼𝗹𝗴𝗲𝗿 𝗚𝗿𝗼𝗲𝗻𝗲𝘄𝗲𝗴𝗲𝗻 𝗯𝗶𝗷 𝘄𝗶𝗲𝗹𝗲𝗿𝗽𝗹𝗼𝗲𝗴 𝗝𝗮𝘆𝗰𝗼-𝗔𝗹𝗨𝗹𝗮

    Pascal Ackermann zet zijn wielerloopbaan voort bij de Australische ploeg Jayco-AlUla. De Duitse sprinter neemt de plaats in van Dylan Groenewegen, de Nederlander die overstapt naar Unibet Rose Rockets. Ackermann heeft 41 overwinningen op zijn naam staan en komt over van Israel - Premier Tech. Hij...

    rtl.nl/nieuws/sport/artikel/55

    #Ackermann #opvolger #Groenewegen

  7. 𝗔𝗰𝗸𝗲𝗿𝗺𝗮𝗻𝗻 𝗼𝗽𝘃𝗼𝗹𝗴𝗲𝗿 𝗚𝗿𝗼𝗲𝗻𝗲𝘄𝗲𝗴𝗲𝗻 𝗯𝗶𝗷 𝘄𝗶𝗲𝗹𝗲𝗿𝗽𝗹𝗼𝗲𝗴 𝗝𝗮𝘆𝗰𝗼-𝗔𝗹𝗨𝗹𝗮

    Pascal Ackermann zet zijn wielerloopbaan voort bij de Australische ploeg Jayco-AlUla. De Duitse sprinter neemt de plaats in van Dylan Groenewegen, de Nederlander die overstapt naar Unibet Rose Rockets. Ackermann heeft 41 overwinningen op zijn naam staan en komt over van Israel - Premier Tech. Hij...

    rtl.nl/nieuws/sport/artikel/55

    #Ackermann #opvolger #Groenewegen

  8. 𝗔𝗰𝗸𝗲𝗿𝗺𝗮𝗻𝗻 𝗼𝗽𝘃𝗼𝗹𝗴𝗲𝗿 𝗚𝗿𝗼𝗲𝗻𝗲𝘄𝗲𝗴𝗲𝗻 𝗯𝗶𝗷 𝘄𝗶𝗲𝗹𝗲𝗿𝗽𝗹𝗼𝗲𝗴 𝗝𝗮𝘆𝗰𝗼-𝗔𝗹𝗨𝗹𝗮

    Pascal Ackermann zet zijn wielerloopbaan voort bij de Australische ploeg Jayco-AlUla. De Duitse sprinter neemt de plaats in van Dylan Groenewegen, de Nederlander die overstapt naar Unibet Rose Rockets. Ackermann heeft 41 overwinningen op zijn naam staan en komt over van Israel - Premier Tech. Hij...

    rtl.nl/nieuws/sport/artikel/55

    #Ackermann #opvolger #Groenewegen

  9. 𝗔𝗰𝗸𝗲𝗿𝗺𝗮𝗻𝗻 𝗼𝗽𝘃𝗼𝗹𝗴𝗲𝗿 𝗚𝗿𝗼𝗲𝗻𝗲𝘄𝗲𝗴𝗲𝗻 𝗯𝗶𝗷 𝘄𝗶𝗲𝗹𝗲𝗿𝗽𝗹𝗼𝗲𝗴 𝗝𝗮𝘆𝗰𝗼-𝗔𝗹𝗨𝗹𝗮

    Pascal Ackermann zet zijn wielerloopbaan voort bij de Australische ploeg Jayco-AlUla. De Duitse sprinter neemt de plaats in van Dylan Groenewegen, de Nederlander die overstapt naar Unibet Rose Rockets. Ackermann heeft 41 overwinningen op zijn naam staan en komt over van Israel - Premier Tech. Hij...

    rtl.nl/nieuws/sport/artikel/55

    #Ackermann #opvolger #Groenewegen

  10. 𝗔𝗰𝗸𝗲𝗿𝗺𝗮𝗻𝗻 𝗼𝗽𝘃𝗼𝗹𝗴𝗲𝗿 𝗚𝗿𝗼𝗲𝗻𝗲𝘄𝗲𝗴𝗲𝗻 𝗯𝗶𝗷 𝘄𝗶𝗲𝗹𝗲𝗿𝗽𝗹𝗼𝗲𝗴 𝗝𝗮𝘆𝗰𝗼-𝗔𝗹𝗨𝗹𝗮

    Pascal Ackermann zet zijn wielerloopbaan voort bij de Australische ploeg Jayco-AlUla. De Duitse sprinter neemt de plaats in van Dylan Groenewegen, de Nederlander die overstapt naar Unibet Rose Rockets. Ackermann heeft 41 overwinningen op zijn naam staan en komt over van Israel - Premier Tech. Hij...

    rtl.nl/nieuws/sport/artikel/55

    #Ackermann #opvolger #Groenewegen

  11. #idw #Esoterik #Katholiban Dritter Zwischenbericht zu sexuellem #Missbrauch im Bistum #Trier vorgelegt.

    Forschende der Universität decken Fälle in Amtszeiten der Bischöfe #Marx und #Ackermann auf. Außerdem wurde ihr Umgang mit Fällen der vorherigen Amtszeiten beleuchtet. idw-online.de/de/news860665

  12. #idw #Esoterik #Katholiban Dritter Zwischenbericht zu sexuellem #Missbrauch im Bistum #Trier vorgelegt.

    Forschende der Universität decken Fälle in Amtszeiten der Bischöfe #Marx und #Ackermann auf. Außerdem wurde ihr Umgang mit Fällen der vorherigen Amtszeiten beleuchtet. idw-online.de/de/news860665

  13. #idw #Esoterik #Katholiban Dritter Zwischenbericht zu sexuellem #Missbrauch im Bistum #Trier vorgelegt.

    Forschende der Universität decken Fälle in Amtszeiten der Bischöfe #Marx und #Ackermann auf. Außerdem wurde ihr Umgang mit Fällen der vorherigen Amtszeiten beleuchtet. idw-online.de/de/news860665

  14. #idw #Esoterik #Katholiban Dritter Zwischenbericht zu sexuellem #Missbrauch im Bistum #Trier vorgelegt.

    Forschende der Universität decken Fälle in Amtszeiten der Bischöfe #Marx und #Ackermann auf. Außerdem wurde ihr Umgang mit Fällen der vorherigen Amtszeiten beleuchtet. idw-online.de/de/news860665

  15. Niederberg: Forscherpreis für Helios-Pathologen

    Für seine wissenschaftliche Fotografie wird Prof. Dr. Maximilian Ackermann, Pathologe am Helios Universitätsklinikum Wuppertal der Universität Witten/Herde…
    #Wuppertal #Deutschland #Deutsch #DE #Schlagzeilen #Headlines #Nachrichten #News #Europe #Europa #EU #"Helios" #Ackermann #Germany #Herdecke #Karolinska #LennartNilsson #Maximilian #Nordrhein-Westfalen #Pathologe #Preis #Preisträger #prof #Wissenschaftlich
    europesays.com/de/306175/

  16. To check how intelligent an #AI tool is, ask it to compute the #ackermann function of (5,5).

  17. To check how intelligent an tool is, ask it to compute the function of (5,5).

  18. Precursors Of Category Theory • 3
    inquiryintoinquiry.com/2024/05

    ❝Act only according to that maxim by which you can at the same time will that it should become a universal law.❞

    — Immanuel Kant (1785)

    C.S. Peirce • “On a New List of Categories” (1867)

    ❝§1. This paper is based upon the theory already established, that the function of conceptions is to reduce the manifold of sensuous impressions to unity, and that the validity of a conception consists in the impossibility of reducing the content of consciousness to unity without the introduction of it.❞ (CP 1.545).

    ❝§2. This theory gives rise to a conception of gradation among those conceptions which are universal. For one such conception may unite the manifold of sense and yet another may be required to unite the conception and the manifold to which it is applied; and so on.❞ (CP 1.546).

    Cued by Kant's idea regarding the function of concepts in general, Peirce locates his categories on the highest levels of abstraction able to provide a meaningful measure of traction in practice. Whether successive grades of conceptions converge to an absolute unity or not is a question to be pursued as inquiry progresses and need not be answered in order to begin.

    Resources —

    Precursors Of Category Theory
    oeis.org/wiki/Precursors_Of_Ca

    Propositions As Types Analogy
    oeis.org/wiki/Propositions_As_

    Survey of Precursors Of Category Theory
    inquiryintoinquiry.com/2024/05

    #Aristotle #Peirce #Kant #Carnap #Hilbert #Ackermann #SaundersMacLane
    #Abstraction #Analogy #CategoryTheory #Diagrams #FoundationsOfMathematics
    #FunctionalLogic #RelationTheory #ContinuousPredicate #HypostaticAbstraction
    #CategoryTheory #PeircesCategories #PropositionsAsTypes #TypeTheory #Universals

  19. Precursors Of Category Theory • 3
    inquiryintoinquiry.com/2024/05

    ❝Act only according to that maxim by which you can at the same time will that it should become a universal law.❞

    — Immanuel Kant (1785)

    C.S. Peirce • “On a New List of Categories” (1867)

    ❝§1. This paper is based upon the theory already established, that the function of conceptions is to reduce the manifold of sensuous impressions to unity, and that the validity of a conception consists in the impossibility of reducing the content of consciousness to unity without the introduction of it.❞ (CP 1.545).

    ❝§2. This theory gives rise to a conception of gradation among those conceptions which are universal. For one such conception may unite the manifold of sense and yet another may be required to unite the conception and the manifold to which it is applied; and so on.❞ (CP 1.546).

    Cued by Kant's idea regarding the function of concepts in general, Peirce locates his categories on the highest levels of abstraction able to provide a meaningful measure of traction in practice. Whether successive grades of conceptions converge to an absolute unity or not is a question to be pursued as inquiry progresses and need not be answered in order to begin.

    Resources —

    Precursors Of Category Theory
    oeis.org/wiki/Precursors_Of_Ca

    Propositions As Types Analogy
    oeis.org/wiki/Propositions_As_

    Survey of Precursors Of Category Theory
    inquiryintoinquiry.com/2024/05

    #Aristotle #Peirce #Kant #Carnap #Hilbert #Ackermann #SaundersMacLane
    #Abstraction #Analogy #CategoryTheory #Diagrams #FoundationsOfMathematics
    #FunctionalLogic #RelationTheory #ContinuousPredicate #HypostaticAbstraction
    #CategoryTheory #PeircesCategories #PropositionsAsTypes #TypeTheory #Universals

  20. Precursors Of Category Theory • 3
    inquiryintoinquiry.com/2024/05

    ❝Act only according to that maxim by which you can at the same time will that it should become a universal law.❞

    — Immanuel Kant (1785)

    C.S. Peirce • “On a New List of Categories” (1867)

    ❝§1. This paper is based upon the theory already established, that the function of conceptions is to reduce the manifold of sensuous impressions to unity, and that the validity of a conception consists in the impossibility of reducing the content of consciousness to unity without the introduction of it.❞ (CP 1.545).

    ❝§2. This theory gives rise to a conception of gradation among those conceptions which are universal. For one such conception may unite the manifold of sense and yet another may be required to unite the conception and the manifold to which it is applied; and so on.❞ (CP 1.546).

    Cued by Kant's idea regarding the function of concepts in general, Peirce locates his categories on the highest levels of abstraction able to provide a meaningful measure of traction in practice. Whether successive grades of conceptions converge to an absolute unity or not is a question to be pursued as inquiry progresses and need not be answered in order to begin.

    Resources —

    Precursors Of Category Theory
    oeis.org/wiki/Precursors_Of_Ca

    Propositions As Types Analogy
    oeis.org/wiki/Propositions_As_

    Survey of Precursors Of Category Theory
    inquiryintoinquiry.com/2024/05

    #Aristotle #Peirce #Kant #Carnap #Hilbert #Ackermann #SaundersMacLane
    #Abstraction #Analogy #CategoryTheory #Diagrams #FoundationsOfMathematics
    #FunctionalLogic #RelationTheory #ContinuousPredicate #HypostaticAbstraction
    #CategoryTheory #PeircesCategories #PropositionsAsTypes #TypeTheory #Universals

  21. Precursors Of Category Theory • 3
    inquiryintoinquiry.com/2024/05

    ❝Act only according to that maxim by which you can at the same time will that it should become a universal law.❞

    — Immanuel Kant (1785)

    C.S. Peirce • “On a New List of Categories” (1867)

    ❝§1. This paper is based upon the theory already established, that the function of conceptions is to reduce the manifold of sensuous impressions to unity, and that the validity of a conception consists in the impossibility of reducing the content of consciousness to unity without the introduction of it.❞ (CP 1.545).

    ❝§2. This theory gives rise to a conception of gradation among those conceptions which are universal. For one such conception may unite the manifold of sense and yet another may be required to unite the conception and the manifold to which it is applied; and so on.❞ (CP 1.546).

    Cued by Kant's idea regarding the function of concepts in general, Peirce locates his categories on the highest levels of abstraction able to provide a meaningful measure of traction in practice. Whether successive grades of conceptions converge to an absolute unity or not is a question to be pursued as inquiry progresses and need not be answered in order to begin.

    Resources —

    Precursors Of Category Theory
    oeis.org/wiki/Precursors_Of_Ca

    Propositions As Types Analogy
    oeis.org/wiki/Propositions_As_

    Survey of Precursors Of Category Theory
    inquiryintoinquiry.com/2024/05

    #Aristotle #Peirce #Kant #Carnap #Hilbert #Ackermann #SaundersMacLane
    #Abstraction #Analogy #CategoryTheory #Diagrams #FoundationsOfMathematics
    #FunctionalLogic #RelationTheory #ContinuousPredicate #HypostaticAbstraction
    #CategoryTheory #PeircesCategories #PropositionsAsTypes #TypeTheory #Universals

  22. Precursors Of Category Theory • 3
    inquiryintoinquiry.com/2024/05

    ❝Act only according to that maxim by which you can at the same time will that it should become a universal law.❞

    — Immanuel Kant (1785)

    C.S. Peirce • “On a New List of Categories” (1867)

    ❝§1. This paper is based upon the theory already established, that the function of conceptions is to reduce the manifold of sensuous impressions to unity, and that the validity of a conception consists in the impossibility of reducing the content of consciousness to unity without the introduction of it.❞ (CP 1.545).

    ❝§2. This theory gives rise to a conception of gradation among those conceptions which are universal. For one such conception may unite the manifold of sense and yet another may be required to unite the conception and the manifold to which it is applied; and so on.❞ (CP 1.546).

    Cued by Kant's idea regarding the function of concepts in general, Peirce locates his categories on the highest levels of abstraction able to provide a meaningful measure of traction in practice. Whether successive grades of conceptions converge to an absolute unity or not is a question to be pursued as inquiry progresses and need not be answered in order to begin.

    Resources —

    Precursors Of Category Theory
    oeis.org/wiki/Precursors_Of_Ca

    Propositions As Types Analogy
    oeis.org/wiki/Propositions_As_

    Survey of Precursors Of Category Theory
    inquiryintoinquiry.com/2024/05

    #Aristotle #Peirce #Kant #Carnap #Hilbert #Ackermann #SaundersMacLane
    #Abstraction #Analogy #CategoryTheory #Diagrams #FoundationsOfMathematics
    #FunctionalLogic #RelationTheory #ContinuousPredicate #HypostaticAbstraction
    #CategoryTheory #PeircesCategories #PropositionsAsTypes #TypeTheory #Universals

  23. Precursors Of Category Theory • 2.3
    inquiryintoinquiry.com/2024/05

    In the logic of Aristotle categories are adjuncts to reasoning whose function is to resolve ambiguities and thus to prepare equivocal signs, otherwise recalcitrant to being ruled by logic, for the application of logical laws. The example of ζωον illustrates the fact that we don't need categories to “make” generalizations so much as to “control” generalizations, to reign in abstractions and analogies which have been stretched too far.

    References —

    • Aristotle, “The Categories”, Harold P. Cooke (trans.), pp. 1–109 in Aristotle, Volume 1, Loeb Classical Library, William Heinemann, London, UK, 1938.

    • Karpeles, Eric (2008), Paintings in Proust, Thames and Hudson, London, UK.

    Resources —

    Precursors Of Category Theory
    oeis.org/wiki/Precursors_Of_Ca

    Propositions As Types Analogy
    oeis.org/wiki/Propositions_As_

    Survey of Precursors Of Category Theory
    inquiryintoinquiry.com/2024/05

    #Aristotle #Peirce #Kant #Carnap #Hilbert #Ackermann #SaundersMacLane
    #Abstraction #Analogy #CategoryTheory #Diagrams #FoundationsOfMathematics
    #FunctionalLogic #RelationTheory #ContinuousPredicate #HypostaticAbstraction
    #CategoryTheory #PeircesCategories #PropositionsAsTypes #TypeTheory #Universals

  24. Precursors Of Category Theory • 2.3
    inquiryintoinquiry.com/2024/05

    In the logic of Aristotle categories are adjuncts to reasoning whose function is to resolve ambiguities and thus to prepare equivocal signs, otherwise recalcitrant to being ruled by logic, for the application of logical laws. The example of ζωον illustrates the fact that we don't need categories to “make” generalizations so much as to “control” generalizations, to reign in abstractions and analogies which have been stretched too far.

    References —

    • Aristotle, “The Categories”, Harold P. Cooke (trans.), pp. 1–109 in Aristotle, Volume 1, Loeb Classical Library, William Heinemann, London, UK, 1938.

    • Karpeles, Eric (2008), Paintings in Proust, Thames and Hudson, London, UK.

    Resources —

    Precursors Of Category Theory
    oeis.org/wiki/Precursors_Of_Ca

    Propositions As Types Analogy
    oeis.org/wiki/Propositions_As_

    Survey of Precursors Of Category Theory
    inquiryintoinquiry.com/2024/05

    #Aristotle #Peirce #Kant #Carnap #Hilbert #Ackermann #SaundersMacLane
    #Abstraction #Analogy #CategoryTheory #Diagrams #FoundationsOfMathematics
    #FunctionalLogic #RelationTheory #ContinuousPredicate #HypostaticAbstraction
    #CategoryTheory #PeircesCategories #PropositionsAsTypes #TypeTheory #Universals

  25. Precursors Of Category Theory • 2.3
    inquiryintoinquiry.com/2024/05

    In the logic of Aristotle categories are adjuncts to reasoning whose function is to resolve ambiguities and thus to prepare equivocal signs, otherwise recalcitrant to being ruled by logic, for the application of logical laws. The example of ζωον illustrates the fact that we don't need categories to “make” generalizations so much as to “control” generalizations, to reign in abstractions and analogies which have been stretched too far.

    References —

    • Aristotle, “The Categories”, Harold P. Cooke (trans.), pp. 1–109 in Aristotle, Volume 1, Loeb Classical Library, William Heinemann, London, UK, 1938.

    • Karpeles, Eric (2008), Paintings in Proust, Thames and Hudson, London, UK.

    Resources —

    Precursors Of Category Theory
    oeis.org/wiki/Precursors_Of_Ca

    Propositions As Types Analogy
    oeis.org/wiki/Propositions_As_

    Survey of Precursors Of Category Theory
    inquiryintoinquiry.com/2024/05

    #Aristotle #Peirce #Kant #Carnap #Hilbert #Ackermann #SaundersMacLane
    #Abstraction #Analogy #CategoryTheory #Diagrams #FoundationsOfMathematics
    #FunctionalLogic #RelationTheory #ContinuousPredicate #HypostaticAbstraction
    #CategoryTheory #PeircesCategories #PropositionsAsTypes #TypeTheory #Universals

  26. Precursors Of Category Theory • 2.3
    inquiryintoinquiry.com/2024/05

    In the logic of Aristotle categories are adjuncts to reasoning whose function is to resolve ambiguities and thus to prepare equivocal signs, otherwise recalcitrant to being ruled by logic, for the application of logical laws. The example of ζωον illustrates the fact that we don't need categories to “make” generalizations so much as to “control” generalizations, to reign in abstractions and analogies which have been stretched too far.

    References —

    • Aristotle, “The Categories”, Harold P. Cooke (trans.), pp. 1–109 in Aristotle, Volume 1, Loeb Classical Library, William Heinemann, London, UK, 1938.

    • Karpeles, Eric (2008), Paintings in Proust, Thames and Hudson, London, UK.

    Resources —

    Precursors Of Category Theory
    oeis.org/wiki/Precursors_Of_Ca

    Propositions As Types Analogy
    oeis.org/wiki/Propositions_As_

    Survey of Precursors Of Category Theory
    inquiryintoinquiry.com/2024/05

    #Aristotle #Peirce #Kant #Carnap #Hilbert #Ackermann #SaundersMacLane
    #Abstraction #Analogy #CategoryTheory #Diagrams #FoundationsOfMathematics
    #FunctionalLogic #RelationTheory #ContinuousPredicate #HypostaticAbstraction
    #CategoryTheory #PeircesCategories #PropositionsAsTypes #TypeTheory #Universals

  27. Precursors Of Category Theory • 2.3
    inquiryintoinquiry.com/2024/05

    In the logic of Aristotle categories are adjuncts to reasoning whose function is to resolve ambiguities and thus to prepare equivocal signs, otherwise recalcitrant to being ruled by logic, for the application of logical laws. The example of ζωον illustrates the fact that we don't need categories to “make” generalizations so much as to “control” generalizations, to reign in abstractions and analogies which have been stretched too far.

    References —

    • Aristotle, “The Categories”, Harold P. Cooke (trans.), pp. 1–109 in Aristotle, Volume 1, Loeb Classical Library, William Heinemann, London, UK, 1938.

    • Karpeles, Eric (2008), Paintings in Proust, Thames and Hudson, London, UK.

    Resources —

    Precursors Of Category Theory
    oeis.org/wiki/Precursors_Of_Ca

    Propositions As Types Analogy
    oeis.org/wiki/Propositions_As_

    Survey of Precursors Of Category Theory
    inquiryintoinquiry.com/2024/05

    #Aristotle #Peirce #Kant #Carnap #Hilbert #Ackermann #SaundersMacLane
    #Abstraction #Analogy #CategoryTheory #Diagrams #FoundationsOfMathematics
    #FunctionalLogic #RelationTheory #ContinuousPredicate #HypostaticAbstraction
    #CategoryTheory #PeircesCategories #PropositionsAsTypes #TypeTheory #Universals

  28. Precursors Of Category Theory • 2.2
    inquiryintoinquiry.com/2024/05

    Aristotle —

    ❝Things are equivocally named, when they have the name only in common, the definition (or statement of essence) corresponding with the name being different. For instance, while a man and a portrait can properly both be called animals (ζωον), these are equivocally named. For they have the name only in common, the definitions (or statements of essence) corresponding with the name being different. For if you are asked to define what the being an animal means in the case of the man and the portrait, you give in either case a definition appropriate to that case alone.

    ❝Things are univocally named, when not only they bear the same name but the name means the same in each case — has the same definition corresponding. Thus a man and an ox are called animals. The name is the same in both cases; so also the statement of essence. For if you are asked what is meant by their both of them being called animals, you give that particular name in both cases the same definition.❞ (Aristotle, Categories, 1.1a1–12).

    Translator's Note. ❝Ζωον in Greek had two meanings, that is to say, living creature, and, secondly, a figure or image in painting, embroidery, sculpture. We have no ambiguous noun. However, we use the word ‘living’ of portraits to mean ‘true to life’.❞

    #Aristotle #Peirce #Kant #Carnap #Hilbert #Ackermann #SaundersMacLane
    #Abstraction #Analogy #CategoryTheory #Diagrams #FoundationsOfMathematics
    #FunctionalLogic #RelationTheory #ContinuousPredicate #HypostaticAbstraction
    #CategoryTheory #PeircesCategories #PropositionsAsTypes #TypeTheory #Universals

  29. Precursors Of Category Theory • 2.2
    inquiryintoinquiry.com/2024/05

    Aristotle —

    ❝Things are equivocally named, when they have the name only in common, the definition (or statement of essence) corresponding with the name being different. For instance, while a man and a portrait can properly both be called animals (ζωον), these are equivocally named. For they have the name only in common, the definitions (or statements of essence) corresponding with the name being different. For if you are asked to define what the being an animal means in the case of the man and the portrait, you give in either case a definition appropriate to that case alone.

    ❝Things are univocally named, when not only they bear the same name but the name means the same in each case — has the same definition corresponding. Thus a man and an ox are called animals. The name is the same in both cases; so also the statement of essence. For if you are asked what is meant by their both of them being called animals, you give that particular name in both cases the same definition.❞ (Aristotle, Categories, 1.1a1–12).

    Translator's Note. ❝Ζωον in Greek had two meanings, that is to say, living creature, and, secondly, a figure or image in painting, embroidery, sculpture. We have no ambiguous noun. However, we use the word ‘living’ of portraits to mean ‘true to life’.❞

    #Aristotle #Peirce #Kant #Carnap #Hilbert #Ackermann #SaundersMacLane
    #Abstraction #Analogy #CategoryTheory #Diagrams #FoundationsOfMathematics
    #FunctionalLogic #RelationTheory #ContinuousPredicate #HypostaticAbstraction
    #CategoryTheory #PeircesCategories #PropositionsAsTypes #TypeTheory #Universals

  30. Precursors Of Category Theory • 2.2
    inquiryintoinquiry.com/2024/05

    Aristotle —

    ❝Things are equivocally named, when they have the name only in common, the definition (or statement of essence) corresponding with the name being different. For instance, while a man and a portrait can properly both be called animals (ζωον), these are equivocally named. For they have the name only in common, the definitions (or statements of essence) corresponding with the name being different. For if you are asked to define what the being an animal means in the case of the man and the portrait, you give in either case a definition appropriate to that case alone.

    ❝Things are univocally named, when not only they bear the same name but the name means the same in each case — has the same definition corresponding. Thus a man and an ox are called animals. The name is the same in both cases; so also the statement of essence. For if you are asked what is meant by their both of them being called animals, you give that particular name in both cases the same definition.❞ (Aristotle, Categories, 1.1a1–12).

    Translator's Note. ❝Ζωον in Greek had two meanings, that is to say, living creature, and, secondly, a figure or image in painting, embroidery, sculpture. We have no ambiguous noun. However, we use the word ‘living’ of portraits to mean ‘true to life’.❞

    #Aristotle #Peirce #Kant #Carnap #Hilbert #Ackermann #SaundersMacLane
    #Abstraction #Analogy #CategoryTheory #Diagrams #FoundationsOfMathematics
    #FunctionalLogic #RelationTheory #ContinuousPredicate #HypostaticAbstraction
    #CategoryTheory #PeircesCategories #PropositionsAsTypes #TypeTheory #Universals