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#analogy — Public Fediverse posts

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

  1. Objects, Models, Theories • 2
    inquiryintoinquiry.com/2026/09

    Re: Gödel's Lost Letter • The Graph Of Math
    rjlipton.com/2013/11/15/the-gr

    GLL:
    ❝Kurt Gödel is said to have been a latecomer to appreciating the power of Model Theory. He was of course the greatest architect of Proof Theory, which stands in contrast to Model Theory. Model Theory concerns itself with what could be true, while Proof Theory deals with what can be proved. The latter sounds more definite, but they are supplementary: a statement is capable of being true somewhere precisely when its negation cannot be proved. The question is, where is that somewhere? And when?❞

    What — if anything — is the common sense that connects the different senses of the word “model”, as it has been used over the years in logic, mathematics, and the special sciences? It's a problem I've been running into for several decades now and I think I can trace the roots of it going back as far as Aristotle’s treatment of analogy.

    Resources —

    Functional Logic • Inquiry and Analogy
    oeis.org/wiki/Functional_Logic

    Survey of Abduction, Deduction, Induction, Analogy, Inquiry
    inquiryintoinquiry.com/2025/05

    #Peirce #Logic #Mathematics #Semiotics #Inference #Inquiry #InformationTheory
    #Abduction #Deduction #Induction #MathematicalModels #ModelTheory #MentalModels
    #Analogy #AdaptiveSystems #InquiryDrivenSystems #LearningTheory #TriadicRelations

  2. Objects, Models, Theories • 2
    inquiryintoinquiry.com/2026/09

    Re: Gödel's Lost Letter • The Graph Of Math
    rjlipton.com/2013/11/15/the-gr

    GLL:
    ❝Kurt Gödel is said to have been a latecomer to appreciating the power of Model Theory. He was of course the greatest architect of Proof Theory, which stands in contrast to Model Theory. Model Theory concerns itself with what could be true, while Proof Theory deals with what can be proved. The latter sounds more definite, but they are supplementary: a statement is capable of being true somewhere precisely when its negation cannot be proved. The question is, where is that somewhere? And when?❞

    What — if anything — is the common sense that connects the different senses of the word “model”, as it has been used over the years in logic, mathematics, and the special sciences? It's a problem I've been running into for several decades now and I think I can trace the roots of it going back as far as Aristotle’s treatment of analogy.

    Resources —

    Functional Logic • Inquiry and Analogy
    oeis.org/wiki/Functional_Logic

    Survey of Abduction, Deduction, Induction, Analogy, Inquiry
    inquiryintoinquiry.com/2025/05

    #Peirce #Logic #Mathematics #Semiotics #Inference #Inquiry #InformationTheory
    #Abduction #Deduction #Induction #MathematicalModels #ModelTheory #MentalModels
    #Analogy #AdaptiveSystems #InquiryDrivenSystems #LearningTheory #TriadicRelations

  3. Objects, Models, Theories • 2
    inquiryintoinquiry.com/2026/09

    Re: Gödel's Lost Letter • The Graph Of Math
    rjlipton.com/2013/11/15/the-gr

    GLL:
    ❝Kurt Gödel is said to have been a latecomer to appreciating the power of Model Theory. He was of course the greatest architect of Proof Theory, which stands in contrast to Model Theory. Model Theory concerns itself with what could be true, while Proof Theory deals with what can be proved. The latter sounds more definite, but they are supplementary: a statement is capable of being true somewhere precisely when its negation cannot be proved. The question is, where is that somewhere? And when?❞

    What — if anything — is the common sense that connects the different senses of the word “model”, as it has been used over the years in logic, mathematics, and the special sciences? It's a problem I've been running into for several decades now and I think I can trace the roots of it going back as far as Aristotle’s treatment of analogy.

    Resources —

    Functional Logic • Inquiry and Analogy
    oeis.org/wiki/Functional_Logic

    Survey of Abduction, Deduction, Induction, Analogy, Inquiry
    inquiryintoinquiry.com/2025/05

    #Peirce #Logic #Mathematics #Semiotics #Inference #Inquiry #InformationTheory
    #Abduction #Deduction #Induction #MathematicalModels #ModelTheory #MentalModels
    #Analogy #AdaptiveSystems #InquiryDrivenSystems #LearningTheory #TriadicRelations

  4. Objects, Models, Theories • 2
    inquiryintoinquiry.com/2026/09

    Re: Gödel's Lost Letter • The Graph Of Math
    rjlipton.com/2013/11/15/the-gr

    GLL:
    ❝Kurt Gödel is said to have been a latecomer to appreciating the power of Model Theory. He was of course the greatest architect of Proof Theory, which stands in contrast to Model Theory. Model Theory concerns itself with what could be true, while Proof Theory deals with what can be proved. The latter sounds more definite, but they are supplementary: a statement is capable of being true somewhere precisely when its negation cannot be proved. The question is, where is that somewhere? And when?❞

    What — if anything — is the common sense that connects the different senses of the word “model”, as it has been used over the years in logic, mathematics, and the special sciences? It's a problem I've been running into for several decades now and I think I can trace the roots of it going back as far as Aristotle’s treatment of analogy.

    Resources —

    Functional Logic • Inquiry and Analogy
    oeis.org/wiki/Functional_Logic

    Survey of Abduction, Deduction, Induction, Analogy, Inquiry
    inquiryintoinquiry.com/2025/05

    #Peirce #Logic #Mathematics #Semiotics #Inference #Inquiry #InformationTheory
    #Abduction #Deduction #Induction #MathematicalModels #ModelTheory #MentalModels
    #Analogy #AdaptiveSystems #InquiryDrivenSystems #LearningTheory #TriadicRelations

  5. Objects, Models, Theories • 2
    inquiryintoinquiry.com/2026/09

    Re: Gödel's Lost Letter • The Graph Of Math
    rjlipton.com/2013/11/15/the-gr

    GLL:
    ❝Kurt Gödel is said to have been a latecomer to appreciating the power of Model Theory. He was of course the greatest architect of Proof Theory, which stands in contrast to Model Theory. Model Theory concerns itself with what could be true, while Proof Theory deals with what can be proved. The latter sounds more definite, but they are supplementary: a statement is capable of being true somewhere precisely when its negation cannot be proved. The question is, where is that somewhere? And when?❞

    What — if anything — is the common sense that connects the different senses of the word “model”, as it has been used over the years in logic, mathematics, and the special sciences? It's a problem I've been running into for several decades now and I think I can trace the roots of it going back as far as Aristotle’s treatment of analogy.

    Resources —

    Functional Logic • Inquiry and Analogy
    oeis.org/wiki/Functional_Logic

    Survey of Abduction, Deduction, Induction, Analogy, Inquiry
    inquiryintoinquiry.com/2025/05

    #Peirce #Logic #Mathematics #Semiotics #Inference #Inquiry #InformationTheory
    #Abduction #Deduction #Induction #MathematicalModels #ModelTheory #MentalModels
    #Analogy #AdaptiveSystems #InquiryDrivenSystems #LearningTheory #TriadicRelations

  6. Objects, Models, Theories • 1
    inquiryintoinquiry.com/2026/09

    Happy Birthday, Charles Sanders Peirce❢ — September 10, 1839

    I return once more to a recurring subject.

    Re: Artem Kaznatcheev • Three Types of Mathematical Models
    egtheory.wordpress.com/2013/09

    In speaking of models one tends to find denizens of different disciplines talking at cross purposes to one another. Logicians use the word to describe what may be distinguished as “logical models”, saying a model is whatever satisfies a theory — anything a theory holds true of — and that is the sense used in the logical subject of “model theory”.

    Almost everyone else uses the word to describe what may be called “analogical models”, analogues being things holding enough properties in common with other things that learning about Thing 2 (the analogue system) can teach us about Thing 1 (the object system).

    It is actually quite easy to integrate those two senses of the word “model” into a coherent picture of the whole situation, namely, the triadic relationship among objects, analogues, and theories. We'll get into that further as the discussion proceeds.

    Resources —

    Functional Logic • Inquiry and Analogy
    oeis.org/wiki/Functional_Logic

    Survey of Abduction, Deduction, Induction, Analogy, Inquiry
    inquiryintoinquiry.com/2025/05

    cc: academia.edu/community/VDDKwZ
    cc: researchgate.net/post/Objects_

    #Peirce #Logic #Mathematics #Semiotics #Inference #Inquiry #InformationTheory
    #Abduction #Deduction #Induction #MathematicalModels #ModelTheory #MentalModels
    #Analogy #AdaptiveSystems #InquiryDrivenSystems #LearningTheory #TriadicRelations

  7. Objects, Models, Theories • 1
    inquiryintoinquiry.com/2026/09

    Happy Birthday, Charles Sanders Peirce❢ — September 10, 1839

    I return once more to a recurring subject.

    Re: Artem Kaznatcheev • Three Types of Mathematical Models
    egtheory.wordpress.com/2013/09

    In speaking of models one tends to find denizens of different disciplines talking at cross purposes to one another. Logicians use the word to describe what may be distinguished as “logical models”, saying a model is whatever satisfies a theory — anything a theory holds true of — and that is the sense used in the logical subject of “model theory”.

    Almost everyone else uses the word to describe what may be called “analogical models”, analogues being things holding enough properties in common with other things that learning about Thing 2 (the analogue system) can teach us about Thing 1 (the object system).

    It is actually quite easy to integrate those two senses of the word “model” into a coherent picture of the whole situation, namely, the triadic relationship among objects, analogues, and theories. We'll get into that further as the discussion proceeds.

    Resources —

    Functional Logic • Inquiry and Analogy
    oeis.org/wiki/Functional_Logic

    Survey of Abduction, Deduction, Induction, Analogy, Inquiry
    inquiryintoinquiry.com/2025/05

    cc: academia.edu/community/VDDKwZ
    cc: researchgate.net/post/Objects_

    #Peirce #Logic #Mathematics #Semiotics #Inference #Inquiry #InformationTheory
    #Abduction #Deduction #Induction #MathematicalModels #ModelTheory #MentalModels
    #Analogy #AdaptiveSystems #InquiryDrivenSystems #LearningTheory #TriadicRelations

  8. Objects, Models, Theories • 1
    inquiryintoinquiry.com/2026/09

    Happy Birthday, Charles Sanders Peirce❢ — September 10, 1839

    I return once more to a recurring subject.

    Re: Artem Kaznatcheev • Three Types of Mathematical Models
    egtheory.wordpress.com/2013/09

    In speaking of models one tends to find denizens of different disciplines talking at cross purposes to one another. Logicians use the word to describe what may be distinguished as “logical models”, saying a model is whatever satisfies a theory — anything a theory holds true of — and that is the sense used in the logical subject of “model theory”.

    Almost everyone else uses the word to describe what may be called “analogical models”, analogues being things holding enough properties in common with other things that learning about Thing 2 (the analogue system) can teach us about Thing 1 (the object system).

    It is actually quite easy to integrate those two senses of the word “model” into a coherent picture of the whole situation, namely, the triadic relationship among objects, analogues, and theories. We'll get into that further as the discussion proceeds.

    Resources —

    Functional Logic • Inquiry and Analogy
    oeis.org/wiki/Functional_Logic

    Survey of Abduction, Deduction, Induction, Analogy, Inquiry
    inquiryintoinquiry.com/2025/05

    cc: academia.edu/community/VDDKwZ
    cc: researchgate.net/post/Objects_

    #Peirce #Logic #Mathematics #Semiotics #Inference #Inquiry #InformationTheory
    #Abduction #Deduction #Induction #MathematicalModels #ModelTheory #MentalModels
    #Analogy #AdaptiveSystems #InquiryDrivenSystems #LearningTheory #TriadicRelations

  9. Objects, Models, Theories • 1
    inquiryintoinquiry.com/2026/09

    Happy Birthday, Charles Sanders Peirce❢ — September 10, 1839

    I return once more to a recurring subject.

    Re: Artem Kaznatcheev • Three Types of Mathematical Models
    egtheory.wordpress.com/2013/09

    In speaking of models one tends to find denizens of different disciplines talking at cross purposes to one another. Logicians use the word to describe what may be distinguished as “logical models”, saying a model is whatever satisfies a theory — anything a theory holds true of — and that is the sense used in the logical subject of “model theory”.

    Almost everyone else uses the word to describe what may be called “analogical models”, analogues being things holding enough properties in common with other things that learning about Thing 2 (the analogue system) can teach us about Thing 1 (the object system).

    It is actually quite easy to integrate those two senses of the word “model” into a coherent picture of the whole situation, namely, the triadic relationship among objects, analogues, and theories. We'll get into that further as the discussion proceeds.

    Resources —

    Functional Logic • Inquiry and Analogy
    oeis.org/wiki/Functional_Logic

    Survey of Abduction, Deduction, Induction, Analogy, Inquiry
    inquiryintoinquiry.com/2025/05

    cc: academia.edu/community/VDDKwZ
    cc: researchgate.net/post/Objects_

    #Peirce #Logic #Mathematics #Semiotics #Inference #Inquiry #InformationTheory
    #Abduction #Deduction #Induction #MathematicalModels #ModelTheory #MentalModels
    #Analogy #AdaptiveSystems #InquiryDrivenSystems #LearningTheory #TriadicRelations

  10. Objects, Models, Theories • 1
    inquiryintoinquiry.com/2026/09

    Happy Birthday, Charles Sanders Peirce❢ — September 10, 1839

    I return once more to a recurring subject.

    Re: Artem Kaznatcheev • Three Types of Mathematical Models
    egtheory.wordpress.com/2013/09

    In speaking of models one tends to find denizens of different disciplines talking at cross purposes to one another. Logicians use the word to describe what may be distinguished as “logical models”, saying a model is whatever satisfies a theory — anything a theory holds true of — and that is the sense used in the logical subject of “model theory”.

    Almost everyone else uses the word to describe what may be called “analogical models”, analogues being things holding enough properties in common with other things that learning about Thing 2 (the analogue system) can teach us about Thing 1 (the object system).

    It is actually quite easy to integrate those two senses of the word “model” into a coherent picture of the whole situation, namely, the triadic relationship among objects, analogues, and theories. We'll get into that further as the discussion proceeds.

    Resources —

    Functional Logic • Inquiry and Analogy
    oeis.org/wiki/Functional_Logic

    Survey of Abduction, Deduction, Induction, Analogy, Inquiry
    inquiryintoinquiry.com/2025/05

    cc: academia.edu/community/VDDKwZ
    cc: researchgate.net/post/Objects_

    #Peirce #Logic #Mathematics #Semiotics #Inference #Inquiry #InformationTheory
    #Abduction #Deduction #Induction #MathematicalModels #ModelTheory #MentalModels
    #Analogy #AdaptiveSystems #InquiryDrivenSystems #LearningTheory #TriadicRelations

  11. Icon, Likeness, Likely Story, Likelihood, Probability • 3

    Re: Peirce ListPhyllis Chiasson

    A more complete excerpt and the translator’s notes are very helpful here.

    A probability (εικος) is not the same as a sign (σηµειον).  The former is a generally accepted premiss ;  for that which people know to happen or not to happen, or to be or not to be, usually in a particular way, is a probability :  e.g., that the envious are malevolent or that those who are loved are affectionate.  A sign, however, means a demonstrative premiss which is necessary or generally accepted.1  That which coexists with something else, or before or after whose happening something else has happened, is a sign of that something’s having happened or being.

    An enthymeme is a syllogism from probabilities or signs ;  and a sign can be taken in three ways — in just as many ways as there are of taking the middle term in the several figures :  either as in the first figure or as in the second or as in the third.

    • E.g., the proof that a woman is pregnant because she has milk is by the first figure ;  for the middle term is ‘having milk’.  A stands for ‘pregnant’, B for ‘having milk’, and C for ‘woman’.
    • The proof that the wise are good because Pittacus was good is by the third figure.  A stands for ‘good’, B for ‘the wise’, and C for Pittacus.  Then it is true to predicate both A and B of C ;  only we do not state the latter, because we know it, whereas we formally assume the former.
    • The proof that a woman is pregnant because she is sallow is intended to be by the middle figure ;  for since sallowness is a characteristic of woman in pregnancy, and is associated with this particular woman, they suppose that she is proved to be pregnant.  A stands for ‘sallowness’, B for ‘being pregnant’, C for ‘woman’.

    If only one premiss is stated, we get only a sign ;  but if the other premiss is assumed as well, we get a syllogism,2 e.g., that Pittacus is high-minded, because those who love honour are high-minded, and Pittacus loves honour ;  or again that the wise are good, because Pittacus is good and also wise.

    In this way syllogisms can be effected ;  but whereas a syllogism in the first figure cannot be refuted if it is true, since it is universal, a syllogism in the last figure can be refuted even if the conclusion is true, because the syllogism is neither universal nor relevant to our purpose.3  For if Pittacus is good, it is not necessary for this reason that all other wise men are good.  A syllogism in the middle figure is always and in every way refutable, since we never get a syllogism with the terms in this relation4 ;  for it does not necessarily follow, if a pregnant woman is sallow, and this woman is sallow, that she is pregnant.  Thus truth can be found in all signs, but they differ in the ways which have been described.

    We must either classify signs in this way, and regard their middle term as an index (τεκµηριον)5 (for the name ‘index’ is given to that which causes us to know, and the middle term is especially of this nature), or describe the arguments drawn from the extremes6 as ‘signs’, and that which is drawn from the middle as an ‘index’.  For the conclusion which is reached through the first figure is most generally accepted and most true.  (Aristotle, Prior Analytics 2.27, 70a3–70b6).

    Translator’s Notes

    1. If referable to one phenomenon only, a sign has objective necessity ;  if to more than one, its value is a matter of opinion.
    2. Strictly an enthymeme.
    3. If the signs of an enthymeme in the first figure are true, the conclusion is inevitable.  Aristotle does not mean that the conclusion is universal, but that the universality of the major premiss implies the validity of the minor and conclusion.  The example (<all> those who have honour, etc.) quoted for the third figure contains no universal premiss or sign, and fails to establish a universal conclusion.
    4. i.e. when both premisses are affirmative.
    5. Signs may be classified as irrefutable (1st figure) and refutable (2nd and 3rd figures), and the name ‘index’ may be attached to their middle terms, either in all figures or (more probably) only in the first, where the middle is distinctively middle.
    6. Alternatively the name ‘sign’ may be restricted to the 2nd and 3rd figures, and may be replaced by ‘index’ in the first.

    Reference

    • Aristotle, “Prior Analytics”, Hugh Tredennick (trans.), pp. 181–531 in Aristotle, Volume 1, Loeb Classical Library, William Heinemann, London, UK, 1938.

    Resource

    cc: Academia.eduCyberneticsLaws of FormMathstodon
    cc: Research GateStructural ModelingSystems ScienceSyscoi

    #Analogy #Aristotle #CSPeirce #IconIndexSymbol #Induction #Inquiry #Likelihood #LikelyStory #Likeness #Logic #Mathematics #Probability #ProbableReasoning #Semiotics #SignRelations
  12. Icon, Likeness, Likely Story, Likelihood, Probability • 2
    inquiryintoinquiry.com/2026/05

    Re: Peirce List • Phyllis Chiasson
    web.archive.org/web/2013121115
    web.archive.org/web/2013121103

    I'm still a bit fuzzy on how Aristotle's account relates to Peirce's usage, though I'm pretty sure Peirce must have taken Aristotle's usage into account, but it does seem that Aristotle drew some sort of distinction here, using a term “tekmerion” which gets translated as “index” to make the following remark later on in that chapter.

    ❝We must either classify signs in this way, and regard their middle term as an index [τεκµηριον] (for the name ‘index’ is given to that which causes us to know, and the middle term is especially of this nature), or describe the arguments drawn from the extremes as ‘signs’, and that which is drawn from the middle as an ‘index’. For the conclusion which is reached through the first figure is most generally accepted and most true.❞ (Aristotle, Prior Analytics, 2.27.70b1–6).

    Reference —

    Aristotle, “Prior Analytics”, Hugh Tredennick (trans.), pp. 181–531 in Aristotle, Volume 1, Loeb Classical Library, William Heinemann, London, UK, 1938.

    Resource —

    Theme One Program • User Guide • Appendix A
    academia.edu/5211369/Theme_One

    #Aristotle #Peirce #IconIndexSymbol #Semiotics #SignRelations
    #Logic #Mathematics #Probability #ProbableReasoning #Induction
    #Inquiry #Analogy #Likelihood #LikelyStory #Likeness #Morphism

  13. Icon, Likeness, Likely Story, Likelihood, Probability • 2

    Re: Peirce ListPhyllis Chiasson

    I’m still a bit fuzzy on how Aristotle’s account relates to Peirce’s usage, though I’m pretty sure Peirce must have taken Aristotle’s usage into account, but it does seem that Aristotle drew some sort of distinction here, using a term “tekmerion” which gets translated as “index” to make the following remark later on in that chapter.

    We must either classify signs in this way, and regard their middle term as an index [τεκµηριον] (for the name ‘index’ is given to that which causes us to know, and the middle term is especially of this nature), or describe the arguments drawn from the extremes as ‘signs’, and that which is drawn from the middle as an ‘index’.  For the conclusion which is reached through the first figure is most generally accepted and most true.  (Aristotle, Prior Analytics, 2.27.70b1–6).

    Reference

    • Aristotle, “Prior Analytics”, Hugh Tredennick (trans.), pp. 181–531 in Aristotle, Volume 1, Loeb Classical Library, William Heinemann, London, UK, 1938.

    Resource

    cc: Academia.eduCyberneticsLaws of FormMathstodon
    cc: Research GateStructural ModelingSystems ScienceSyscoi

    #Analogy #Aristotle #CSPeirce #IconIndexSymbol #Induction #Inquiry #Likelihood #LikelyStory #Likeness #Logic #Mathematics #Probability #ProbableReasoning #Semiotics #SignRelations
  14. Icon, Likeness, Likely Story, Likelihood, Probability • 1
    inquiryintoinquiry.com/2026/05

    Here's a likely locus classicus for “icon” in its logical sense —

    ❝A probability (εικος) is not the same as a sign (σηµειον). The former is a generally accepted premiss; for that which people know to happen or not to happen, or to be or not to be, usually in a particular way, is a probability:

    ❝For example, that the envious are malevolent or that those who are loved are affectionate.

    ❝A sign, however, means a demonstrative premiss which is necessary or generally accepted. That which coexists with something else, or before or after whose happening something else has happened, is a sign of that something’s having happened or being.❞ (Aristotle, Prior Analytics, 2.27.70a3–10).

    Reference —

    Aristotle, “Prior Analytics”, Hugh Tredennick (trans.), pp. 181–531 in Aristotle, Volume 1, Loeb Classical Library, William Heinemann, London, UK, 1938.

    Resource —

    Theme One Program • User Guide • Appendix A
    academia.edu/5211369/Theme_One

    #Aristotle #Peirce #IconIndexSymbol #Semiotics #SignRelations
    #Logic #Mathematics #Probability #ProbableReasoning #Induction
    #Inquiry #Analogy #Likelihood #LikelyStory #Likeness #Morphism

  15. Icon, Likeness, Likely Story, Likelihood, Probability • 1

    Here’s a likely locus classicus for “icon” in its logical sense —

    A probability (εικος) is not the same as a sign (σηµειον).  The former is a generally accepted premiss;  for that which people know to happen or not to happen, or to be or not to be, usually in a particular way, is a probability:  e.g., that the envious are malevolent or that those who are loved are affectionate.  A sign, however, means a demonstrative premiss which is necessary or generally accepted.  That which coexists with something else, or before or after whose happening something else has happened, is a sign of that something’s having happened or being.  (Aristotle, Prior Analytics, 2.27.70a3–10).

    Reference

    • Aristotle, “Prior Analytics”, Hugh Tredennick (trans.), pp. 181–531 in Aristotle, Volume 1, Loeb Classical Library, William Heinemann, London, UK, 1938.

    Resource

    Related Discussion

    #Analogy #Aristotle #CSPeirce #IconIndexSymbol #Induction #Inquiry #Likelihood #LikelyStory #Likeness #Logic #Mathematics #Probability #ProbableReasoning #Semiotics #SignRelations
  16. 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

  17. Functional Logic • Inquiry and Analogy • Preliminaries
    inquiryintoinquiry.com/2023/06

    Functional Logic • Inquiry and Analogy
    oeis.org/wiki/Functional_Logic

    This report discusses C.S. Peirce's treatment of analogy, placing it in relation to his overall theory of inquiry. We begin by introducing three basic types of reasoning Peirce adopted from classical logic. In Peirce's analysis both inquiry and analogy are complex programs of logical inference which develop through stages of these three types, though normally in different orders.

    Note on notation. The discussion to follow uses logical conjunctions, expressed in the form of concatenated tuples \(e_1 \ldots e_k,\) and minimal negation operations, expressed in the form of bracketed tuples \(\texttt{(} e_1 \texttt{,} \ldots \texttt{,} e_k \texttt{)},\) as the principal expression-forming operations of a calculus for boolean-valued functions, that is, for propositions. The expressions of this calculus parse into data structures whose underlying graphs are called “cacti” by graph theorists. Hence the name “cactus language” for this dialect of propositional calculus.

    Resources —

    Logic Syllabus
    oeis.org/wiki/Logic_Syllabus

    Boolean Function
    oeis.org/wiki/Boolean_function

    Boolean-Valued Function
    oeis.org/wiki/Boolean-valued_f

    Logical Conjunction
    oeis.org/wiki/Logical_conjunct

    Minimal Negation Operator
    oeis.org/wiki/Minimal_negation

    #Peirce #Logic #Abduction #Deduction #Induction #Analogy #Inquiry
    #BooleanFunction #LogicalConjunction #MinimalNegationOperator
    #LogicalGraph #CactusLanguage #PropositionalCalculus