#analogy — Public Fediverse posts

[en] Big Tech "kill zones": football transfer market #analogy

"... causal evidence that acquisitions by six major US #technology companies [#GAFAM] and IBM create what we call a “kill zone” in startup industries. Just as Manchester United’s acquisition of Rooney signalled to other clubs that competing for top #talent would be futile, #tech giants’ acquisitions appear to #discourage new #market entrants and reduce venture capital #investment ..."

"... debates about digital sovereignty, the future of the European #startup ecosystem, and whether current #antitrust tools are adequate for the #digital age."

"... the economy becomes less #innovative because ... most promising businesses do not grow enough to challenge market incumbents."

https://www.oii.ox.ac.uk/news-events/when-big-tech-plays-like-man-united-how-kill-zones-threaten-europes-future/

#bigtech #digitalsovereignty

Propositions As Types Analogy • 1
• https://inquiryintoinquiry.com/2013/01/29/propositions-as-types-analogy-1/

One of my favorite mathematical tricks — it almost seems too tricky to be true — is the Propositions As Types Analogy. And I see hints the 2‑part analogy can be extended to a 3‑part analogy, as follows.

Proof Hint ∶ Proof ∶ Proposition
∷
Untyped Term ∶ Typed Term ∶ Type

or

Proof Hint ∶ Untyped Term
∷
Proof ∶ Typed Term
∷
Proposition ∶ Type

See my working notes on the Propositions As Types Analogy —
• https://oeis.org/wiki/Propositions_As_Types_Analogy

#Mathematics #CategoryTheory #ProofTheory #TypeTheory
#Logic #Analogy #Isomorphism #PropositionalCalculus
#CombinatorCalculus #CombinatoryLogic #LambdaCalculus
#Peirce #LogicalGraphs #GraphTheory #RelationTheory

Propositions As Types Analogy • 1
• https://inquiryintoinquiry.com/2013/01/29/propositions-as-types-analogy-1/

One of my favorite mathematical tricks — it almost seems too tricky to be true — is the Propositions As Types Analogy. And I see hints the 2‑part analogy can be extended to a 3‑part analogy, as follows.

Proof Hint ∶ Proof ∶ Proposition
∷
Untyped Term ∶ Typed Term ∶ Type

or

Proof Hint ∶ Untyped Term
∷
Proof ∶ Typed Term
∷
Proposition ∶ Type

See my working notes on the Propositions As Types Analogy —
• https://oeis.org/wiki/Propositions_As_Types_Analogy

#Mathematics #CategoryTheory #ProofTheory #TypeTheory
#Logic #Analogy #Isomorphism #PropositionalCalculus
#CombinatorCalculus #CombinatoryLogic #LambdaCalculus
#Peirce #LogicalGraphs #GraphTheory #RelationTheory

Propositions As Types Analogy • 1
• https://inquiryintoinquiry.com/2013/01/29/propositions-as-types-analogy-1/

One of my favorite mathematical tricks — it almost seems too tricky to be true — is the Propositions As Types Analogy. And I see hints the 2‑part analogy can be extended to a 3‑part analogy, as follows.

Proof Hint ∶ Proof ∶ Proposition
∷
Untyped Term ∶ Typed Term ∶ Type

or

Proof Hint ∶ Untyped Term
∷
Proof ∶ Typed Term
∷
Proposition ∶ Type

See my working notes on the Propositions As Types Analogy —
• https://oeis.org/wiki/Propositions_As_Types_Analogy

#Mathematics #CategoryTheory #ProofTheory #TypeTheory
#Logic #Analogy #Isomorphism #PropositionalCalculus
#CombinatorCalculus #CombinatoryLogic #LambdaCalculus
#Peirce #LogicalGraphs #GraphTheory #RelationTheory

Propositions As Types Analogy • 1
• https://inquiryintoinquiry.com/2013/01/29/propositions-as-types-analogy-1/

One of my favorite mathematical tricks — it almost seems too tricky to be true — is the Propositions As Types Analogy. And I see hints the 2‑part analogy can be extended to a 3‑part analogy, as follows.

Proof Hint ∶ Proof ∶ Proposition
∷
Untyped Term ∶ Typed Term ∶ Type

or

Proof Hint ∶ Untyped Term
∷
Proof ∶ Typed Term
∷
Proposition ∶ Type

See my working notes on the Propositions As Types Analogy —
• https://oeis.org/wiki/Propositions_As_Types_Analogy

#Mathematics #CategoryTheory #ProofTheory #TypeTheory
#Logic #Analogy #Isomorphism #PropositionalCalculus
#CombinatorCalculus #CombinatoryLogic #LambdaCalculus
#Peirce #LogicalGraphs #GraphTheory #RelationTheory

Propositions As Types Analogy • 1
• https://inquiryintoinquiry.com/2013/01/29/propositions-as-types-analogy-1/

One of my favorite mathematical tricks — it almost seems too tricky to be true — is the Propositions As Types Analogy. And I see hints the 2‑part analogy can be extended to a 3‑part analogy, as follows.

Proof Hint ∶ Proof ∶ Proposition
∷
Untyped Term ∶ Typed Term ∶ Type

or

Proof Hint ∶ Untyped Term
∷
Proof ∶ Typed Term
∷
Proposition ∶ Type

See my working notes on the Propositions As Types Analogy —
• https://oeis.org/wiki/Propositions_As_Types_Analogy

#Mathematics #CategoryTheory #ProofTheory #TypeTheory
#Logic #Analogy #Isomorphism #PropositionalCalculus
#CombinatorCalculus #CombinatoryLogic #LambdaCalculus
#Peirce #LogicalGraphs #GraphTheory #RelationTheory

Survey of Precursors Of Category Theory • 6
• https://inquiryintoinquiry.com/2025/05/05/survey-of-precursors-of-category-theory-6/

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/2024/05/25/precursors-of-category-theory-1-a/
2. https://inquiryintoinquiry.com/2024/05/26/precursors-of-category-theory-2-a/
3. https://inquiryintoinquiry.com/2024/05/27/precursors-of-category-theory-3-a/
4. https://inquiryintoinquiry.com/2024/05/28/precursors-of-category-theory-4-a/
5. https://inquiryintoinquiry.com/2024/05/29/precursors-of-category-theory-5-a/
6. https://inquiryintoinquiry.com/2024/05/30/precursors-of-category-theory-6-a/

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/

C.S. Peirce and Category Theory
1. https://inquiryintoinquiry.com/2021/06/23/c-s-peirce-and-category-theory-1/
2. https://inquiryintoinquiry.com/2021/06/24/c-s-peirce-and-category-theory-2/
3. https://inquiryintoinquiry.com/2021/06/27/c-s-peirce-and-category-theory-3/
4. https://inquiryintoinquiry.com/2021/06/28/c-s-peirce-and-category-theory-4/
5. https://inquiryintoinquiry.com/2021/06/29/c-s-peirce-and-category-theory-5/
6. https://inquiryintoinquiry.com/2021/06/30/c-s-peirce-and-category-theory-6/
7. https://inquiryintoinquiry.com/2021/07/01/c-s-peirce-and-category-theory-7/
8. https://inquiryintoinquiry.com/2021/07/02/c-s-peirce-and-category-theory-8/

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

#ADHD #perimenopause #quidditch #analogy

Images generated with #PixelStudio. Text my own, inspired by a certain fictional game from the HP series. Everyone's experiences are different, this is just me trying to make sense of my struggles.

What does @MillerLite, #MillerGenuineDraft, @millerhighlife, @Molson_Canadian, #MickeysMaltLiquor, #IcehouseBeer & @Leinenkugels have to do with language & rhetoric & making? Find out in our review of @jdpollack’s #Shortcut: http://the-agency-review.com/shortcut #analogy #writing #marketing

Western liberals: "Capitalism is not the problem. The problem is crony capitalism. What we need is 'real' and 'fair' capitalism where large corporations don't have so much of the market share."
'Yeah, bruh! Cancer is not the problem. The problem is stage 4 cancer. What we need is stage 2 cancer.'

#liberals #neoliberalism #cancer #capitalism #politics #economics #analogy #metaphor #fairness #marketshare #markets #aspiration #perspective #psychology #humannature #huimancondition #philosophy

MARK OF THE BEAST? For those that may have such thoughts ... #religion #security #gov #immigration #law #society #news #opinion #analogy #satire #humor #writing #bookcafe #art_of_review #myth #history #apocallypse #distopian #errtlings #ai #android_dreams #privacy www.bbc.com/news/article...

Switzerland votes on electroni...

Geologic Calendar (Geology ⛰️)

The Geologic Calendar is a scale in which the geological timespan of the Earth is mapped onto a calendrical year; that is to say, the day one of the Earth took place on a geologic January 1 at precisely midnight, and today's date and time is December 31 at midnight. On this calendar, the inferred appearance of the first living sing...

https://en.wikipedia.org/wiki/Geologic_Calendar

#GeologicCalendar #Analogy #Geology #UnitsOfTime #PopularScience #TimeInAstronomy

Geologic Calendar (Geology ⛰️)

The Geologic Calendar is a scale in which the geological timespan of the Earth is mapped onto a calendrical year; that is to say, the day one of the Earth took place on a geologic January 1 at precisely midnight, and today's date and time is December 31 at midnight. On this calendar, the inferred appearance of the first living sing...

https://en.wikipedia.org/wiki/Geologic_Calendar

#GeologicCalendar #Analogy #Geology #UnitsOfTime #PopularScience #TimeInAstronomy

Geologic Calendar (Geology ⛰️)

The Geologic Calendar is a scale in which the geological timespan of the Earth is mapped onto a calendrical year; that is to say, the day one of the Earth took place on a geologic January 1 at precisely midnight, and today's date and time is December 31 at midnight. On this calendar, the inferred appearance of the first living sing...

https://en.wikipedia.org/wiki/Geologic_Calendar

#GeologicCalendar #Analogy #Geology #UnitsOfTime #PopularScience #TimeInAstronomy

Geologic Calendar (Geology ⛰️)

The Geologic Calendar is a scale in which the geological timespan of the Earth is mapped onto a calendrical year; that is to say, the day one of the Earth took place on a geologic January 1 at precisely midnight, and today's date and time is December 31 at midnight. On this calendar, the inferred appearance of the first living sing...

https://en.wikipedia.org/wiki/Geologic_Calendar

#GeologicCalendar #Analogy #Geology #UnitsOfTime #PopularScience #TimeInAstronomy

Geologic Calendar (Geology ⛰️)

The Geologic Calendar is a scale in which the geological timespan of the Earth is mapped onto a calendrical year; that is to say, the day one of the Earth took place on a geologic January 1 at precisely midnight, and today's date and time is December 31 at midnight. On this calendar, the inferred appearance of the first living sing...

https://en.wikipedia.org/wiki/Geologic_Calendar

#GeologicCalendar #Analogy #Geology #UnitsOfTime #PopularScience #TimeInAstronomy

#funny #analogy #coorperation #collaboration #workingtogether

Interpreter and Interpretant • Selection 10.2
• https://inquiryintoinquiry.com/2025/02/11/interpreter-and-interpretant-selection-10-a/
• https://bsky.app/profile/inquiryintoinquiry.bsky.social/post/3lhyet3gfzk2c

In logical terms, the analogy of experience proceeds by inducing a Rule about the validity of a current knowledge base and then by deducing a Fact, the applicability of that knowledge base to a current experience.

Step 1 is Inductive, abstracting a Rule from a Case and a Fact.

• Case : E_past ⇒ E_poss, Chosen events fairly sample Collective events.
• Fact : E_past ⇒ K_pres, Chosen events support the Knowledge regime.
────────────────────────────────────────────────
• Rule : E_poss ⇒ K_pres, Collective events support the Knowledge regime.

Step 2 is Deductive, admitting a Case to a Rule and arriving at a Fact.

• Case : E_pres ⇒ E_poss, Current events fairly sample Collective events.
• Rule : E_poss ⇒ K_pres, Collective events support the Knowledge regime.
────────────────────────────────────────────────
• Fact : E_pres ⇒ K_pres, Current events support the Knowledge regime.

References —

Awbrey, J.L., and Awbrey, S.M. (1995), “Interpretation as Action : The Risk of Inquiry”, Inquiry : Critical Thinking Across the Disciplines 15(1), 40–52.
• https://www.pdcnet.org/inquiryct/content/inquiryct_1995_0015_0001_0040_0052
• https://www.academia.edu/57812482/Interpretation_as_Action_The_Risk_of_Inquiry

Dewey, J. (1910), How We Think, D.C. Heath, Boston, MA. Reprinted (1991), Prometheus Books, Buffalo, NY.
• https://www.gutenberg.org/files/37423/37423-h/37423-h.htm

Resources —

Survey of Abduction, Deduction, Induction, Analogy, Inquiry
• https://inquiryintoinquiry.com/2024/02/27/survey-of-abduction-deduction-induction-analogy-inquiry-4/

Survey of Semiotics, Semiosis, Sign Relations
• https://inquiryintoinquiry.com/2024/01/26/survey-of-semiotics-semiosis-sign-relations-5/

#Peirce #Logic #Semiotics #Semiosis #SignRelations
#JohnDewey #Interpreter #Interpretant #Pragmatism
#Abduction #Deduction #Induction #Analogy #Inquiry

Interpreter and Interpretant • Selection 10.1
• https://inquiryintoinquiry.com/2025/02/11/interpreter-and-interpretant-selection-10-a/
• https://bsky.app/profile/inquiryintoinquiry.bsky.social/post/3lhyet3gfzk2c

Transfer —

Returning to the scene of Dewey's “Sign of Rain” example, let's continue examining how the transfer of knowledge through the analogy of experience works in that case.

By way of a recap, we began by considering a fragment K_pres of the reasoner's knowledge base which is logically equivalent to a conjunction of two rules.

• K_pres ⇔ (B ⇒ A) ∧ (B ⇒ D).

K_pres may be thought of as a piece of knowledge or item of information allowing for the possibility of certain conditions, expressed in the form of a logical constraint on the present universe of discourse.

Next we found it convenient to express all logical statements in terms of their models, that is, in terms of the primitive circumstances or elements of experience over which they hold true.

• Let E_past be the chosen set of experiences, or the circumstances in mind under “past experience”.

• Let E_poss be the collective set of experiences, or the prospective total of possible circumstances.

• Let E_pres be the current experience, or the circumstances immediately present to the reasoner.

If we think of the knowledge base K_pres as referring to the “regime of experience” over which it is valid, then the sets of models involved in the analogy may be ordered according to the relationships of set inclusion or logical implication existing among them.

Figure 4 shows the subsumption relations involved in the analogy of experience.

Figure 4. Analogy of Experience
• https://inquiryintoinquiry.files.wordpress.com/2025/02/analogy-of-experience.png

#Peirce #Logic #Semiotics #Semiosis #SignRelations
#JohnDewey #Interpreter #Interpretant #Pragmatism
#Abduction #Deduction #Induction #Analogy #Inquiry

Me right now feels very much like, in computer terms, that I’m running out of paging memory.

#dubious #analogy #burnout

Interpreter and Interpretant • Selection 9.2
• https://inquiryintoinquiry.com/2025/01/27/interpreter-and-interpretant-selection-9-a/

Transfer —

In logical terms, the analogy of experience proceeds by inducing a Rule about the validity of a current knowledge base and then by deducing a Fact, the applicability of that knowledge base to a current experience.

Step 1 is Inductive, abstracting a Rule from a Case and a Fact.

• Case : E_past ⇒ E_poss, Chosen events fairly sample Collective events.
• Fact : E_past ⇒ K_pres, Chosen events support the Knowledge regime.
────────────────────────────────────────────────
• Rule : E_poss ⇒ K_pres, Collective events support the Knowledge regime.

Step 2 is Deductive, admitting a Case to a Rule and arriving at a Fact.

• Case : E_pres ⇒ E_poss, Current events fairly sample Collective events.
• Rule : E_poss ⇒ K_pres, Collective events support the Knowledge regime.
────────────────────────────────────────────────
• Fact : E_pres ⇒ K_pres, Current events support the Knowledge regime.

References —

Awbrey, J.L., and Awbrey, S.M. (1995), “Interpretation as Action : The Risk of Inquiry”, Inquiry : Critical Thinking Across the Disciplines 15(1), 40–52.
• https://www.pdcnet.org/inquiryct/content/inquiryct_1995_0015_0001_0040_0052
• https://www.academia.edu/57812482/Interpretation_as_Action_The_Risk_of_Inquiry

Dewey, J. (1910), How We Think, D.C. Heath, Boston, MA. Reprinted (1991), Prometheus Books, Buffalo, NY.
• https://www.gutenberg.org/files/37423/37423-h/37423-h.htm

Resources —

Survey of Abduction, Deduction, Induction, Analogy, Inquiry
• https://inquiryintoinquiry.com/2024/02/27/survey-of-abduction-deduction-induction-analogy-inquiry-4/

Survey of Semiotics, Semiosis, Sign Relations
• https://inquiryintoinquiry.com/2024/01/26/survey-of-semiotics-semiosis-sign-relations-5/

#Peirce #Logic #Semiotics #Semiosis #SignRelations
#JohnDewey #Interpreter #Interpretant #Pragmatism
#Abduction #Deduction #Induction #Analogy #Inquiry

Interpreter and Interpretant • Selection 9.1
• https://inquiryintoinquiry.com/2025/01/27/interpreter-and-interpretant-selection-9-a/

Transfer —

Let's examine how the transfer of knowledge through the analogy of experience works in the case of Dewey's “Sign of Rain” example.

For concreteness, consider a fragment K_pres of the reasoner's knowledge base which is logically equivalent to a conjunction of two rules.

• K_pres ⇔ (B ⇒ A) ∧ (B ⇒ D).

K_pres may be thought of as a piece of knowledge or item of information allowing for the possibility of certain conditions, expressed in the form of a logical constraint on the present universe of discourse.

It is convenient to have the option of expressing all logical statements in terms of their models, that is, in terms of the primitive circumstances or elements of experience over which they hold true.

• Let E_past be the chosen set of experiences, or the circumstances in mind under “past experience”.

• Let E_poss be the collective set of experiences, or the prospective total of possible circumstances.

• Let E_pres be the current experience, or the circumstances immediately present to the reasoner.

If we think of the knowledge base K_pres as referring to the “regime of experience” over which it is valid, then the sets of models involved in the analogy may be ordered according to the relationships of set inclusion or logical implication existing among them.

#Peirce #Logic #Semiotics #Semiosis #SignRelations
#JohnDewey #Interpreter #Interpretant #Pragmatism
#Abduction #Deduction #Induction #Analogy #Inquiry

Interpreter and Interpretant • Selection 8
• https://inquiryintoinquiry.com/2025/01/24/interpreter-and-interpretant-selection-8-a/

Transfer —

What exactly gives the acquisition of a knowledge base its distinctively inductive character? It is evidently the “analogy of experience” involved in applying what we've learned in the past to what confronts us in the present.

Whenever we find ourselves approaching a problem with the thought, “If past experience is any guide …” we can be sure the analogy of experience has come into play. We are seeking to find analogies between past experience as a totality and present experience as a point of application.

From a statistical point of view what we mean is this — “If past experience is a fair sample of possible experience then knowledge gained from past experience may usefully apply to present experience”. It is that mechanism which allows a knowledge base to be carried across gulfs of experience which remain indifferent to the effective contents of its rules.

Next we'll examine how the transfer of knowledge through the analogy of experience works out in the case of Dewey's “Sign of Rain” example.

References —

Awbrey, J.L., and Awbrey, S.M. (1995), “Interpretation as Action : The Risk of Inquiry”, Inquiry : Critical Thinking Across the Disciplines 15(1), 40–52.
• https://www.pdcnet.org/inquiryct/content/inquiryct_1995_0015_0001_0040_0052
• https://www.academia.edu/57812482/Interpretation_as_Action_The_Risk_of_Inquiry

Dewey, J. (1910), How We Think, D.C. Heath, Boston, MA. Reprinted (1991), Prometheus Books, Buffalo, NY.
• https://www.gutenberg.org/files/37423/37423-h/37423-h.htm

#Peirce #Logic #Semiotics #Semiosis #SignRelations
#JohnDewey #Interpreter #Interpretant #Pragmatism
#Abduction #Deduction #Induction #Analogy #Inquiry

Archaeoethnologica: Ecology of a Tool - Book / Ecologia de uma Ferramenta -Livro

+INFO in: https://archaeoethnologica.blogspot.com/2024/09/ecologia-de-uma-ferramenta.html

#Archaeology #Ethnoarchaeology #axe #stoneaxe #Oceania #PapuaNewGuinea #materialculture #ethnography #inmaterial #books #socialstructure #prehistory #symolism #tools #Anthropology #axesymbolism #genderroles #comparatism #analogy #ethnographicanalogy

Archaeoethnologica: Ecology of a Tool - Book / Ecologia de uma Ferramenta -Livro

+INFO in: https://archaeoethnologica.blogspot.com/2024/09/ecologia-de-uma-ferramenta.html

#Archaeology #Ethnoarchaeology #axe #stoneaxe #Oceania #PapuaNewGuinea #materialculture #ethnography #inmaterial #books #socialstructure #prehistory #symolism #tools #Anthropology #axesymbolism #genderroles #comparatism #analogy #ethnographicanalogy

Archaeoethnologica: Ecology of a Tool - Book / Ecologia de uma Ferramenta -Livro

+INFO in: https://archaeoethnologica.blogspot.com/2024/09/ecologia-de-uma-ferramenta.html

#Archaeology #Ethnoarchaeology #axe #stoneaxe #Oceania #PapuaNewGuinea #materialculture #ethnography #inmaterial #books #socialstructure #prehistory #symolism #tools #Anthropology #axesymbolism #genderroles #comparatism #analogy #ethnographicanalogy

Archaeoethnologica: Ecology of a Tool - Book / Ecologia de uma Ferramenta -Livro

+INFO in: https://archaeoethnologica.blogspot.com/2024/09/ecologia-de-uma-ferramenta.html

#Archaeology #Ethnoarchaeology #axe #stoneaxe #Oceania #PapuaNewGuinea #materialculture #ethnography #inmaterial #books #socialstructure #prehistory #symolism #tools #Anthropology #axesymbolism #genderroles #comparatism #analogy #ethnographicanalogy

"Even #GodwinLaw ’s namesake, Mike #Godwin, wrote... that he agrees the Hitler #analogy is not just apt but necessary. He cited Trump’s #authoritarian instincts for consolidating state power in a single leader; dehumanizing political enemies as "vermin"; & claiming that #immigrants were “poisoning the blood of our country,” an infamous #Hitler talking point.

...Vance himself, who in 2016 referred to #Trump as “America’s Hitler.”"
https://www.washingtonpost.com/opinions/2024/09/24/trump-hitler-rhetoric-comparison/

#GOP #Politics #Violence #News #USA #US

Mechanical Logic Gates With Amplification https://hackaday.com/2024/09/20/mechanical-logic-gates-with-amplification/ #digitallogic #electronics #leverlogic #mechanical #amplifier #logicgate #teaching #Science #analogy #capstan #analog #pulley

Mechanical Logic Gates With Amplification https://hackaday.com/2024/09/20/mechanical-logic-gates-with-amplification/ #digitallogic #electronics #leverlogic #mechanical #amplifier #logicgate #teaching #Science #analogy #capstan #analog #pulley

Mechanical Logic Gates With Amplification https://hackaday.com/2024/09/20/mechanical-logic-gates-with-amplification/ #digitallogic #electronics #leverlogic #mechanical #amplifier #logicgate #teaching #Science #analogy #capstan #analog #pulley

Mechanical Logic Gates With Amplification https://hackaday.com/2024/09/20/mechanical-logic-gates-with-amplification/ #digitallogic #electronics #leverlogic #mechanical #amplifier #logicgate #teaching #Science #analogy #capstan #analog #pulley

Mechanical Logic Gates With Amplification - One of the hardest things about studying electricity, and by extension electronics... - https://hackaday.com/2024/09/20/mechanical-logic-gates-with-amplification/ #digitallogic #electronics #leverlogic #mechanical #amplifier #logicgate #teaching #science #analogy #capstan #analog #pulley

Mechanical Logic Gates With Amplification - One of the hardest things about studying electricity, and by extension electronics... - https://hackaday.com/2024/09/20/mechanical-logic-gates-with-amplification/ #digitallogic #electronics #leverlogic #mechanical #amplifier #logicgate #teaching #science #analogy #capstan #analog #pulley

Mechanical Logic Gates With Amplification - One of the hardest things about studying electricity, and by extension electronics... - https://hackaday.com/2024/09/20/mechanical-logic-gates-with-amplification/ #digitallogic #electronics #leverlogic #mechanical #amplifier #logicgate #teaching #science #analogy #capstan #analog #pulley

Mechanical Logic Gates With Amplification - One of the hardest things about studying electricity, and by extension electronics... - https://hackaday.com/2024/09/20/mechanical-logic-gates-with-amplification/ #digitallogic #electronics #leverlogic #mechanical #amplifier #logicgate #teaching #science #analogy #capstan #analog #pulley

Mechanical Logic Gates With Amplification - One of the hardest things about studying electricity, and by extension electronics... - https://hackaday.com/2024/09/20/mechanical-logic-gates-with-amplification/ #digitallogic #electronics #leverlogic #mechanical #amplifier #logicgate #teaching #science #analogy #capstan #analog #pulley

Here's the next core concept video on John Wisdom's classic essay "Gods", this one focusing on the one portion people tend to read, talk about, and put into philosophy of religion anthologies, the parable of the invisible gardener

https://youtu.be/moTIQxLzQ6w
#Video #Wisdom #Religion #Philosophy #Falsification #Parable #Analogy

Here's episode 5 of Mind & Desire, released first to paid Substack subscribers, now published publicly. What analogies can we make to research and study in philosophy? One of my gotos is picking black raspberries

https://gregorybsadler.substack.com/p/mind-and-desire-episode-5-a-similitude
#Podcast #Philosophy #Analogy #Similitude

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/2025/05/05/survey-of-precursors-of-category-theory-6/

#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/

C.S. Peirce and Category Theory
1. https://inquiryintoinquiry.com/2021/06/23/c-s-peirce-and-category-theory-1/
2. https://inquiryintoinquiry.com/2021/06/24/c-s-peirce-and-category-theory-2/
3. https://inquiryintoinquiry.com/2021/06/27/c-s-peirce-and-category-theory-3/
4. https://inquiryintoinquiry.com/2021/06/28/c-s-peirce-and-category-theory-4/
5. https://inquiryintoinquiry.com/2021/06/29/c-s-peirce-and-category-theory-5/
6. https://inquiryintoinquiry.com/2021/06/30/c-s-peirce-and-category-theory-6/
7. https://inquiryintoinquiry.com/2021/07/01/c-s-peirce-and-category-theory-7/
8. https://inquiryintoinquiry.com/2021/07/02/c-s-peirce-and-category-theory-8/

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

In the conclusion of part 3 of the Prolegomena, Immanuel Kant discusses deism and theism, Hume's critique of both, analogy, and deism as only involving "symbolic anthropomorphism"

https://soundcloud.com/gregorybsadler/immanuel-kant-prolegomena-deism-theism-and-anthropomorphism
#Podcast #Kant #Hume #Prolegomena #Deism #Theism #Analogy #Philosophy

I just published episode 5 of the Mind & Desire podcast to paid Substack subscribers and Patreon supporters. It goes public a month or two down the line. Interested in hearing it now? Here's the Substack page https://gregorybsadler.substack.com/p/mind-and-desire-episode-5-a-similitude
#Philosophy #Analogy #Podcast #Similitude

If I drive 10km/h for 5 min, then increase my speed by 10%, continue for the next 5 min, speed up by 10% again, how far have I gone after 2 hours? How is it different if I speed up 10% after every passed km? #analogy #exponentialGrowth #interestrates #riddle #math

Survey of Inquiry Driven Systems • 6
• https://inquiryintoinquiry.com/2024/02/28/survey-of-inquiry-driven-systems-6/

This is a Survey of work in progress on Inquiry Driven Systems, material I plan to refine toward a more systematic treatment of the subject.

An “inquiry driven system” is a system having among its state variables some representing its state of information with respect to various questions of interest, for example, its own state and the states of potential object systems. Thus it has a component of state tracing a trajectory though an “information state space”.

Please follow the above link for the full set of resources.
Articles treating the more central ideas are linked below.

Elements —

Prospects for Inquiry Driven Systems
• https://oeis.org/wiki/User:Jon_Awbrey/Prospects_for_Inquiry_Driven_Systems

Introduction to Inquiry Driven Systems
• https://oeis.org/wiki/Introduction_to_Inquiry_Driven_Systems

Background —

Functional Logic • Inquiry and Analogy
• https://oeis.org/wiki/Functional_Logic_%E2%80%A2_Inquiry_and_Analogy

Functional Logic • Quantification Theory
• https://oeis.org/wiki/Functional_Logic_%E2%80%A2_Quantification_Theory

Functional Logic • Higher Order Propositions
• https://oeis.org/wiki/Functional_Logic_%E2%80%A2_Higher_Order_Propositions

Developments —

Inquiry Driven Systems • Inquiry Fields
• https://oeis.org/wiki/Inquiry_Driven_Systems_%E2%80%A2_Inquiry_Fields

Inquiry Driven Systems • Inquiry Into Inquiry
• https://oeis.org/wiki/Inquiry_Driven_Systems_%E2%80%A2_Overview

Applications —

Conceptual Barriers to Creating Integrative Universities
• https://www.academia.edu/1266492/Conceptual_Barriers_to_Creating_Integrative_Universities

Interpretation as Action • The Risk of Inquiry
• https://www.academia.edu/57812482/Interpretation_as_Action_The_Risk_of_Inquiry

An Architecture for Inquiry • Building Computer Platforms for Discovery
• https://www.academia.edu/1270327/An_Architecture_for_Inquiry_Building_Computer_Platforms_for_Discovery

Exploring Research Data Interactively • Theme One : A Program of Inquiry
• https://www.academia.edu/1272839/Exploring_Research_Data_Interactively._Theme_One_A_Program_of_Inquiry

#Peirce #Inquiry #InquiryDrivenSystems #InformationStateSpace
#Semiotics #SignRelations #Interpretation #SystemsEngineering
#Abduction #Deduction #Induction #Analogy #DynamicsOfInquiry

Survey of Abduction, Deduction, Induction, Analogy, Inquiry • 4
• http://inquiryintoinquiry.com/2024/02/27/survey-of-abduction-deduction-induction-analogy-inquiry-4/

This is a Survey of blog and wiki posts on three elementary forms of inference, as recognized by a logical tradition extending from Aristotle through Charles S. Peirce. Particular attention is paid to the way these inferential rudiments combine to form the more complex patterns of analogy and inquiry.

Please follow the above link for the full set of resources.
Articles and blog series on the core ideas are linked below.

Project Reports —

Functional Logic • Inquiry and Analogy
• https://oeis.org/wiki/Functional_Logic_%E2%80%A2_Inquiry_and_Analogy

Prospects for Inquiry Driven Systems
• https://oeis.org/wiki/User:Jon_Awbrey/Prospects_for_Inquiry_Driven_Systems

Introduction to Inquiry Driven Systems
• https://oeis.org/wiki/Introduction_to_Inquiry_Driven_Systems

Information = Comprehension × Extension
• https://oeis.org/wiki/Information_%3D_Comprehension_%C3%97_Extension

Inquiry Driven Systems • Inquiry Into Inquiry
• https://oeis.org/wiki/Inquiry_Driven_Systems_%E2%80%A2_Overview

Blog Surveys —

Survey of Inquiry Driven Systems
• https://inquiryintoinquiry.com/2023/04/23/survey-of-inquiry-driven-systems-5/

Survey of Pragmatic Semiotic Information
• https://inquiryintoinquiry.com/2023/07/23/survey-of-pragmatic-semiotic-information-7/

Survey of Theme One Program
• https://inquiryintoinquiry.com/2024/02/26/survey-of-theme-one-program-6/

#Peirce #Logic #Abduction #Deduction #Induction #Analogy #Inquiry
#FunctionalLogic #DifferentialLogic #DynamicsOfInquiry #Semiotics
#InformationEqualsComprehensionTimesExtension #InquiryDrivenSystem