Lmst

#DailyDoseOfTgomas #CarNap😴 #oof #GotSoTired #JacketPillow #PrettyComfy #NiceSurprise #NoComplaintsHere #HighRecommend #CarNap #Slog #SelfieBlog #FabulousSelfie #QuirkyBoy #Quirky #Selfie #DailySelfie

Precursors Of Category Theory • 3
• https://inquiryintoinquiry.com/2024/05/27/precursors-of-category-theory-3-a/

❝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
• https://oeis.org/wiki/Precursors_Of_Category_Theory

Propositions As Types Analogy
• https://oeis.org/wiki/Propositions_As_Types_Analogy

Survey of Precursors Of Category Theory
• https://inquiryintoinquiry.com/2024/05/24/survey-of-precursors-of-category-theory-5/

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

Precursors Of Category Theory • 2.3
• https://inquiryintoinquiry.com/2024/05/26/precursors-of-category-theory-2-a/

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
• https://oeis.org/wiki/Precursors_Of_Category_Theory

Propositions As Types Analogy
• https://oeis.org/wiki/Propositions_As_Types_Analogy

Survey of Precursors Of Category Theory
• https://inquiryintoinquiry.com/2024/05/24/survey-of-precursors-of-category-theory-5/

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

Precursors Of Category Theory • 2.2
• https://inquiryintoinquiry.com/2024/05/26/precursors-of-category-theory-2-a/

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

Precursors Of Category Theory • 2.1
• https://inquiryintoinquiry.com/2024/05/26/precursors-of-category-theory-2-a/

❝Thanks to art, instead of seeing one world only, our own, we see that world multiply itself and we have at our disposal as many worlds as there are original artists …❞

— Marcel Proust

When it comes to looking for the continuities of the category concept across different systems and systematizers, we don't expect to find their kinship in the names or numbers of categories, since those are legion and their divisions deployed on widely different planes of abstraction, but in their common function.

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

Precursors Of Category Theory • 1
• https://inquiryintoinquiry.com/2024/05/25/precursors-of-category-theory-1-a/

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. My notes on the project are still very rough and incomplete but I find myself returning to them from time to time.

Preamble —

❝Now the discovery of ideas as general as these is chiefly the willingness to make a brash or speculative abstraction, in this case supported by the pleasure of purloining words from the philosophers: “Category” from Aristotle and Kant, “Functor” from Carnap (“Logische Syntax der Sprache”), and “natural transformation” from then current informal parlance.❞

— Saunders Mac Lane • “Categories for the Working Mathematician”

Resources —

Precursors Of Category Theory
• https://oeis.org/wiki/Precursors_Of_Category_Theory

Propositions As Types Analogy
• https://oeis.org/wiki/Propositions_As_Types_Analogy

Survey of Precursors Of Category Theory
• https://inquiryintoinquiry.com/2024/05/24/survey-of-precursors-of-category-theory-5/

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

Survey of Precursors Of Category Theory • 5
• https://inquiryintoinquiry.com/2024/05/24/survey-of-precursors-of-category-theory-5/

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
• https://oeis.org/wiki/Precursors_Of_Category_Theory

Propositions As Types Analogy
• https://oeis.org/wiki/Propositions_As_Types_Analogy

Blog Series —

Notes On Categories
• https://inquiryintoinquiry.com/2013/02/22/notes-on-categories-1/

Precursors Of Category Theory
1. https://inquiryintoinquiry.com/2013/12/20/precursors-of-category-theory-1/
2. https://inquiryintoinquiry.com/2013/12/30/precursors-of-category-theory-2/
3. https://inquiryintoinquiry.com/2014/01/03/precursors-of-category-theory-3/

Precursors Of Category Theory • Discussion
1. https://inquiryintoinquiry.com/2020/09/13/precursors-of-category-theory-discussion-1/
2. https://inquiryintoinquiry.com/2020/09/21/precursors-of-category-theory-discussion-2/
3. https://inquiryintoinquiry.com/2020/09/25/precursors-of-category-theory-discussion-3/

Categories à la Peirce —

C.S. Peirce • A Guess at the Riddle
• https://inquiryintoinquiry.com/2012/03/21/c-s-peirce-a-guess-at-the-riddle/

Peirce's Categories
1. https://inquiryintoinquiry.com/2015/10/30/peirces-categories-1/
2. https://inquiryintoinquiry.com/2015/10/31/peirces-categories-2/
3. https://inquiryintoinquiry.com/2015/11/04/peirces-categories-3/
•••
19. https://inquiryintoinquiry.com/2020/05/13/peirces-categories-19/
20. https://inquiryintoinquiry.com/2020/05/14/peirces-categories-20/
21. https://inquiryintoinquiry.com/2020/06/25/peirces-categories-21/

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

New on iai news

Nothing: The contradiction at the heart of being
#Heidgger, #Carnap and nothing
by Graham Priest

"Those who fancy themselves only too clever and immediately un- cover a contradiction here, since indeed non-beings cannot ‘be’, are thinking in much too narrow way with their ‘non-contradiction’ as the measure of the essence of beings."

https://iai.tv/articles/nothing-the-contradiction-at-the-heart-of-being-graham-priest-auid-2675

Bertrand Russell: Why I Am Not a Christian (1927)
https://users.drew.edu/~jlenz/whynot.html
#ycombinator #Bertrand_Russell #philosophy #essays #articles #books #Russell #Bertrand_Russell_Society #Wittgenstein #Carnap #Frege #G_E_Moore #Gottlob_Frege #Ludwig_Wittgenstein #Rudolf_Carnap #Bertrand_Russell_Society_Quarterly #Analytic_Philosophy #Early_Analytic_Philosophy #History_of_Analytic_Philosophy #History_of_Early_Analytic_Philosophy

In IAI news

Carnap vs Heidegger: The metaphysics of nothing
Hearing the sounds of silence
by Roy Sorensen

When #Carnap discusses space, he turns to astronomical experiments that support Albert Einstein’s theory of space that bends near massive bodies such as the sun. When #Heidegger discusses space, he discusses the peasant measuring distance by how many pipefuls of tobacco must be smoked along the way.

https://iai.tv/articles/carnarp-vs-heidegger-the-metaphysics-of-nothing-roy-sorensen-auid-2606

I ask your #aesthetic appreciation for the cover to the 1967 English translation of Rudolf #Carnap's The Logical Structure of the World.

Really effective use of #Helvetica, simple in a way you don't see covers so often any more. It's as if the words themselves make up a kind of logical structure which, however, does not seem so sturdy as the logical positivist would like..

Survey of Precursors Of Category Theory • 4
• http://inquiryintoinquiry.com/2023/08/01/survey-of-precursors-of-category-theory-4/

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
• https://oeis.org/wiki/Precursors_Of_Category_Theory

Propositions As Types Analogy
• https://oeis.org/wiki/Propositions_As_Types_Analogy

Blog Series —

Notes On Categories
• https://inquiryintoinquiry.com/2013/02/22/notes-on-categories-1/

Precursors Of Category Theory
1. https://inquiryintoinquiry.com/2013/12/20/precursors-of-category-theory-1/
2. https://inquiryintoinquiry.com/2013/12/30/precursors-of-category-theory-2/
3. https://inquiryintoinquiry.com/2014/01/03/precursors-of-category-theory-3/

Precursors Of Category Theory • Discussion
1. https://inquiryintoinquiry.com/2020/09/13/precursors-of-category-theory-discussion-1/
2. https://inquiryintoinquiry.com/2020/09/21/precursors-of-category-theory-discussion-2/
3. https://inquiryintoinquiry.com/2020/09/25/precursors-of-category-theory-discussion-3/

Categories à la Peirce —

C.S. Peirce • A Guess at the Riddle
• https://inquiryintoinquiry.com/2012/03/21/c-s-peirce-a-guess-at-the-riddle/

Peirce's Categories
1. https://inquiryintoinquiry.com/2015/10/30/peirces-categories-1/
2. https://inquiryintoinquiry.com/2015/10/31/peirces-categories-2/
3. https://inquiryintoinquiry.com/2015/11/04/peirces-categories-3/
•••
19. https://inquiryintoinquiry.com/2020/05/13/peirces-categories-19/
20. https://inquiryintoinquiry.com/2020/05/14/peirces-categories-20/
21. https://inquiryintoinquiry.com/2020/06/25/peirces-categories-21/

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

From Forbes

Why News Organizations Need Philosophers On The Payroll
Theodore McDarrah

"For #Heidegger, philosophers alone have the tools to deal with ambiguous, metaphysical questions, and #Carnap’s philosophy—anything that needs to be proven— “carries no intrinsic weight in itself.” In other words, verifiable statements should not be a concern to #philosophers."

https://www.forbes.com/sites/teddymcdarrah/2023/07/14/why-news-organizations-need-philosophers-on-the-payroll/?sh=4088e1ca2c4d

Continental Philosophy
(2001) : Critchley, Simon
isbn: 0-19-285359-7
#nihilism #immanuel_kant #german_idealism #scientism #martin_heidegger #obscurantism #carnap #philosophy #my_bibtex

Survey of Precursors Of Category Theory
• https://inquiryintoinquiry.com/2023/04/03/survey-of-precursors-of-category-theory-3/

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.

#CategoryTheory #CombinatoryLogic #LambdaCalculus #RelationTheory
#Aristotle #Kant #Peirce #Schönfinkel #Hilbert #Ackermann #Carnap
#HaskellCurry #WilliamHoward #JoachimLambek #SaundersMacLane
#PropositionsAsTypesAnalogy #CurryHowardIsomorphism #Ulam

@problemicist #logic #Carnap #Toop

An der #Philosophie @UniJena@twitter.com werden Denkschulen des 20. Jahrhunderts untersucht. #Adorno, #Gehlen und #Carnap haben Gemeinsamkeiten, die ein dreijähriges Projekt aufzeigen will, das mit rund 350.000 Euro @DFG_public@twitter.com gefördert wird.

➡️ https://www.uni-jena.de/210108_Denkschulenanalyse

#Carnap is a free and open software framework written in #Haskell for teaching and studying formal languages and #logic.

http://dailynous.com/2018/11/07/new-free-open-source-multi-purpose-multi-system-logic-software/

#carnap

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