Ombre determinanti

[bertanimauro]

From APUPA created by bertanimauro: bertanimauro/APUPA#5

Se le righe delle matrici sono i coefficienti dei polinomi e l'hyperdeterminant trasforma le righe in altri coefficienti, tali coefficienti sono delle ombre, ossia delle costanti che nascondono polinomi.

Come determinante di laplace. Già notazione di Leibniz di chiamare i coefficenti della matrice a_ij è una forma di ombra. Poi gli a_ij nascondono le incognite e le sottoparti dei determinanti nascondono parti di polinomi e il determinante nasconde un sistema di polinomi

[bertanimauro]

Trovata la matematica di Pierce quando parla dei radicali in traccia2/articolo/TraduzionePassoChiavePeirce.docx . Il file in oggetto è il traccia2/math/Peirce.pdf dove si amplia la logica di Boole ai relatives. Per una teoria su i relatives guardare i tre file relativi all'algebra della logica traccia2/math/peirceOnTheAlgebraOfLogic1.pdf. Forse il riassunto generale applicato alle algebre vettoriali si trova qui traccia2/math/peirceLinearAssociativeAlgebra.pdf .

[bertanimauro]

on Pierce

Beginning with his first paper on the "Logic of Relatives" (1870), Peirce extended the theory of relations that Augustus De Morgan had just recently awakened from its Cinderella slumbers. Much of the mathematics of relations now taken for granted was "borrowed" from Peirce, not always with all due credit; on that and on how the young Bertrand Russell, especially his Principles of Mathematics and Principia Mathematica, did not do Peirce justice, see Anellis (1995).[64] In 1918 the logician C. I. Lewis wrote, "The contributions of C.S. Peirce to symbolic logic are more numerous and varied than those of any other writer—at least in the nineteenth century."[91] Beginning in 1940, Alfred Tarski and his students rediscovered aspects of Peirce's larger vision of relational logic, developing the perspective of relation algebra.

Relational logic gained applications. In mathematics, it influenced the abstract analysis of E. H. Moore and the lattice theory of Garrett Birkhoff. In computer science, the relational model for databases was developed with Peircean ideas in work of Edgar F. Codd, who was a doctoral student[92] of Arthur W. Burks, a Peirce scholar. In economics, relational logic was used by Frank P. Ramsey, John von Neumann, and Paul Samuelson to study preferences and utility and by Kenneth J. Arrow in Social Choice and Individual Values, following Arrow's association with Tarski at City College of New York.

On Peirce and his contemporaries Ernst Schröder and Gottlob Frege, Hilary Putnam (1982)[86] documented that Frege's work on the logic of quantifiers had little influence on his contemporaries, although it was published four years before the work of Peirce and his student Oscar Howard Mitchell. Putnam found that mathematicians and logicians learned about the logic of quantifiers through the independent work of Peirce and Mitchell, particularly through Peirce's "On the Algebra of Logic: A Contribution to the Philosophy of Notation"[85] (1885), published in the premier American mathematical journal of the day, and cited by Peano and Schröder, among others, who ignored Frege. They also adopted and modified Peirce's notations, typographical variants of those now used. Peirce apparently was ignorant of Frege's work, despite their overlapping achievements in logic, philosophy of language, and the foundations of mathematics.

Peirce's work on formal logic had admirers besides Ernst Schröder:

[bertanimauro]

Qui il grafo delle relazioni tra le classi trovate. Da vedere su desktop, no mobile

[bertanimauro]

Lavoro finito con estrapolazione relazioni tra materie. qui il file

[bertanimauro]

Aggiunto il libro di Boole mathematical analysis of logic. (traccia2/math/BooleMathematicalAnalysisOfLogic.pdf). Base per leggere traccia2/math/peirceOnTheAlgebraOfLogic1.pdf. consigliato leggere almeno da pagina 23 a 52

[bertanimauro]

Idea da controllare: Usare algebra di Pierce per derivare concetti su materie in bibliometria.

Locgical sequence is a simpler conception than causal sequence, because every causal sequence is a logical sequence but not every logical sequence is a causal sequence; and it is no reply to this to say that a logical sequence between two facts implies a causal sequence between some two facts whether the same or differenit. [preso da traccia2/math/peirceOnTheAlgebraOfLogic1.pdf pag 21]

Una citazione è una sequenza causale, quindi una implicazione. Ranganathan cita Hilbert libro Ranganathan catalogato sotto biblioteconomia del 1900 libro Hilbert catalogato sotto geometria fine Ottocento biblioteconomia 1900 implica [influenzata da] geometria fine 1800

Dai libri si trova relazione tra le classi Oppure quandosi mostra un libro si mostrano le materie a cui è legato e cliccando sulle materie escono altri libri di quella materia. Oppure si può navigare sulle influenze tra le materie.

Simile a concetto di functional di Hilbert vedi https://github.com/bertanimauro/Ranganathan_APUPA/issues/2#issuecomment-1047585765

[bertanimauro]

Sono riuscito a cancellare la versione doppia. Ora c'è una sola versione del file aggiornata

Il giorno dom 27 set 2020 alle ore 00:42 luca giusti giustiluca@gmail.com ha scritto:

Ciao Mauro, ho uploadato il file che abbiamo modificato oggi. Come vedi lo ho ricaricato nella versione con un solo underscore all'inizio (quella originale). Ora però non trovo il modo di cancellare la seconda che avevo aggiornato (con que underscore all'inizio).

Luca

Il giorno ven 7 ago 2020 alle ore 13:22 Mauro Bertani < notifications@github.com> ha scritto:

Se le righe delle matrici sono i coefficienti dei polinomi e l'hyperdeterminant trasforma le righe in altri coefficienti, tali coefficienti sono delle ombre, ossia delle costanti che nascondono polinomi.

Come determinante di laplace. Già notazione di Leibniz di chiamare i coefficenti della matrice a_ij è una forma di ombra. Poi gli a_ij nascondono le incognite e le sottoparti dei determinanti nascondono parti di polinomi e il determinante nasconde un sistema di polinomi

[bertanimauro]

Ciao Mauro, ho uploadato il file che abbiamo modificato oggi. Come vedi lo ho ricaricato nella versione con un solo underscore all'inizio (quella originale). Ora però non trovo il modo di cancellare la seconda che avevo aggiornato (con que underscore all'inizio).

Luca

Il giorno ven 7 ago 2020 alle ore 13:22 Mauro Bertani < notifications@github.com> ha scritto:

Se le righe delle matrici sono i coefficienti dei polinomi e l'hyperdeterminant trasforma le righe in altri coefficienti, tali coefficienti sono delle ombre, ossia delle costanti che nascondono polinomi.

Come determinante di laplace. Già notazione di Leibniz di chiamare i coefficenti della matrice a_ij è una forma di ombra. Poi gli a_ij nascondono le incognite e le sottoparti dei determinanti nascondono parti di polinomi e il determinante nasconde un sistema di polinomi

[bertanimauro]

Quel testo di pierce, io non lo ricordo

Il dom 27 set 2020, 09:16 ellegi69 notifications@github.com ha scritto:

Ho guardato su gmail ma non ho ritrovato il testo su Peirce che ti avevo inviato e che mi dicevi ieri sera. Da una prima scorsa mi sembrava molto attinente al sostro lavoro ma non avevo trovato il tempo di leggerlo. Lo hai mica depositato su Github?

[bertanimauro]

Articoli sulle citazioni: Sono partito da una citazione trovata nell'elenco di Gnoli e seguendo le references sono arrivato ad articoli degli anni 50-70 che ipotizzano una struttura della letteratura scientifica che rimanda a lavoro di matematica su spazi multidimensionali metrici. Quello che stiamo facendo noi.

1. https://arxiv.org/ftp/arxiv/papers/1211/1211.6321.pdf
   • @misc{zhang2012citation, title={Citation content analysis (cca): A framework for syntactic and semantic analysis of citation content}, author={Guo Zhang and Ying Ding and Staša Milojević}, year={2012}, eprint={1211.6321}, archivePrefix={arXiv}, primaryClass={cs.DL} }
2. https://www.researchgate.net/publication/220434629_Mapping_of_science_by_combined_co-citation_and_word_analysis_I_Structural_aspects
   • @article{article, author = {Braam, Robert and Moed, Henk and Raan, Ton}, year = {1991}, month = {05}, pages = {233-251}, title = {Mapping of science by combined co-citation and word analysis. I. Structural aspects}, volume = {42}, journal = {JASIS}, doi = {10.1002/(SICI)1097-4571(199105)42:43.0.CO;2-I} }
3. http://www.jstor.org/stable/284546
   • @article{10.2307/284546, ISSN = {00368539}, URL = {http://www.jstor.org/stable/284546}, author = {Belver C. Griffith and Henry G. Small and Judith A. Stonehill and Sandra Dey}, journal = {Science Studies}, number = {4}, pages = {339--365}, publisher = {Sage Publications, Ltd.}, title = {The Structure of Scientific Literatures II: Toward a Macro- and Microstructure for Science}, volume = {4}, year = {1974} }
4. https://doi.org/10.1002/asi.4630240406
   • @article{doi:10.1002/asi.4630240406, author = {Small, Henry}, title = {Co-citation in the scientific literature: A new measure of the relationship between two documents}, journal = {Journal of the American Society for Information Science}, volume = {24}, number = {4}, pages = {265-269}, doi = {10.1002/asi.4630240406}, url = {https://asistdl.onlinelibrary.wiley.com/doi/abs/10.1002/asi.4630240406}, eprint = {https://asistdl.onlinelibrary.wiley.com/doi/pdf/10.1002/asi.4630240406}, abstract = {Abstract A new form of document coupling called co-citation is defined as the frequency with which two documents are cited together. The co-citation frequency of two scientific papers can be determined by comparing lists of citing documents in the Science Citation Index and counting identical entries. Networks of co-cited papers can be generated for specific scientific specialties, and an example is drawn from the literature of particle physics. Co-citation patterns are found to differ significantly from bibliographic coupling patterns, but to agree generally with patterns of direct citation. Clusters of co-cited papers provide a new way to study the specialty structure of science. They may provide a new approach to indexing and to the creation of SDI profiles.}, year = {1973} }
5. https://www.sciencedirect.com/journal/journal-of-mathematical-psychology/vol/11/issue/4
   • @article{CUNNINGHAM1974335, title = "Monotone mapping of similarities into a general metric space", journal = "Journal of Mathematical Psychology", volume = "11", number = "4", pages = "335 - 363", year = "1974", issn = "0022-2496", doi = "https://doi.org/10.1016/0022-2496(74)90027-3", url = "http://www.sciencedirect.com/science/article/pii/0022249674900273", author = "James P. Cunningham and Roger N. Shepard" }
6. http://128.174.199.77/psychometrika_highly_cited_articles/kruskal_1964a.pdf
   • Multidimensional scaling is the problem of representing n objects: geometrically by n points, so that the interpoint distances correspond in some sense to experimental dissimilarities between objects. In just what sense distances and dissimilarities should correspond has been left rather vague in most approaches, thus leaving these approaches logically incomplete. Our fundamental hypothesis is that dissimilarities and distances are monotonically related. We define a quantitative, intuitively satisfying measure of goodness of fit to this hypothesis. Our technique of multidimensional scaling is to compute that confi~xlration of points which optimizes the goodness of fit. A practical computer program for doing the calculations is described in a compamon paper.
   • TY - JOUR AU - Kruskal, J. B. PY - 1964 DA - 1964/03/01 TI - Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis JO - Psychometrika SP - 1 EP - 27 VL - 29 IS - 1 AB - Multidimensional scaling is the problem of representingn objects geometrically byn points, so that the interpoint distances correspond in some sense to experimental dissimilarities between objects. In just what sense distances and dissimilarities should correspond has been left rather vague in most approaches, thus leaving these approaches logically incomplete. Our fundamental hypothesis is that dissimilarities and distances are monotonically related. We define a quantitative, intuitively satisfying measure of goodness of fit to this hypothesis. Our technique of multidimensional scaling is to compute that configuration of points which optimizes the goodness of fit. A practical computer program for doing the calculations is described in a companion paper. SN - 1860-0980 UR - https://doi.org/10.1007/BF02289565 DO - 10.1007/BF02289565 ID - Kruskal1964 ER -

[bertanimauro]

Algebraizations

An alternate approach to the semantics of first-order logic proceeds via abstract algebra. This approach generalizes the Lindenbaum–Tarski algebras of propositional logic. There are three ways of eliminating quantified variables from first-order logic that do not involve replacing quantifiers with other variable binding term operators:

Cylindric algebra, by Alfred Tarski and colleagues; Polyadic algebra, by Paul Halmos; Predicate functor logic, mainly due to Willard Quine. These algebras are all lattices that properly extend the two-element Boolean algebra.

Tarski and Givant (1987) showed that the fragment of first-order logic that has no atomic sentence lying in the scope of more than three quantifiers has the same expressive power as relation algebra.[18]:32–33 This fragment is of great interest because it suffices for Peano arithmetic and most axiomatic set theory, including the canonical ZFC. They also prove that first-order logic with a primitive ordered pair is equivalent to a relation algebra with two ordered pair projection functions.[19]:803

https://en.m.wikipedia.org/wiki/Two-element_Boolean_algebra

https://en.m.wikipedia.org/wiki/First-order_logic

[bertanimauro]

Frege In general, a concept is a function whose value is always a truth value (139). A relation is a two place function whose value is always a truth value (146).

Frege draws an important distinction between concepts on the basis of their level. Frege tells us that a first-level concept is a one-place function that correlates objects with truth-values (147). First level concepts have the value of true or false depending on whether the object falls under the concept. So, the concept F has the value the True with the argument the object named by 'Jamie' if and only if Jamie falls under the concept F (or is in the extension of F).

ref. https://en.wikipedia.org/wiki/Function_and_Concept ref. Gottlob Frege. Function und Begriff. Vortrag gehalten in der Sitzung vom 9. Januar 1891 der Jenaischen Gesellschaft für Medicin und Naturwissenschaft (Function and Concept. An Address to the Jenaische Gesellschaft für Medizin und Naturwissenschaft on 9 January 1891). Verlag Hermann Pohle, Jena, 1891.

Aggiunto file /Traccia2/math/fregeFunctionAndConcept

[bertanimauro]

Ho guardato su gmail ma non ho ritrovato il testo su Peirce che ti avevo inviato e che mi dicevi ieri sera. Da una prima scorsa mi sembrava molto attinente al sostro lavoro ma non avevo trovato il tempo di leggerlo. Lo hai mica depositato su Github?

Il giorno dom 27 set 2020 alle ore 08:34 luca giusti giustiluca@gmail.com ha scritto:

Sono riuscito a cancellare la versione doppia. Ora c'è una sola versione del file aggiornata

[bertanimauro]

Ok, forse era quello. Ieri sera ho fatto commit del testo di traccia2 modificato. Penso che dobbiamo andare verso un'unione delle due tracce in un unico saggio, alla fine del quale metterei una illustrazione delle sperimentazioni che hai fatto.

Il giorno dom 27 set 2020 alle ore 11:12 Mauro Bertani < notifications@github.com> ha scritto:

Se parli invece della matematica di Pierce è nella cartella traccia2

Il dom 27 set 2020, 11:07 Mauro Bertani bertanimauro@gmail.com ha scritto:

Quel testo di pierce, io non lo ricordo

[bertanimauro]

Aggiunto due libri [Peirce Charles Sanders, "Description of a Notation for the Logic of Relatives, Resulting from an Amplification of the Conceptions of Boole's Calculus of Logic", Memoirs of the American Academy of Arts and Sciences , 1873, New Series, Vol. 9, No. 2 (1873), pp. 317-378]

[Peirce Benjamin, "Linear Associative Algebra", American Journal of Mathematics , 1881, Vol. 4, No. 1 (1881), pp. 97-229 link]

Probabile articolo che Pierce cita come fondamentale del 1883 in traccia_2/Capitolo_con_passo_chiave_di_Peirce.docx

[bertanimauro]

Se parli invece della matematica di Pierce è nella cartella traccia2

Il dom 27 set 2020, 11:07 Mauro Bertani bertanimauro@gmail.com ha scritto:

Quel testo di pierce, io non lo ricordo

[bertanimauro]

Nell'articolo nella parte su metodo pustulazionale, nel sottoparagrafo di Peano, l'assioma 4, contraddetto da Russell, risolto, crea la teoria dei tipi. È la classe membro di se stessa? Qui una trattazione più completa. Vedere anche di Frege Basic law 5

[bertanimauro]

Esempio di studio di argomenti trattati da una persona. Unito a classificazione a faccette e messi tutto su una retta si mettono vicino gli autori simili. qui l'esempio delle query. qui alcuni calcoli sulle persone nate nel 1970 che hanno il nome che inizia con la A o la B prese da British bibliografy. Su 450 persone una trentina hanno scritto libri su più di una argomento. Tenendo conto di 10 aspetti e costruendo con la tecnica num1, num2, num3 il numero che rappresenta la persona. Possiamo mettere vicino persone che hanno trattato gli stessi argomenti, andando , mentre salgono i numeri a persone con una conoscenza enciclopedica.

[bertanimauro]

La logica dei level e i reeb graph https://github.com/bertanimauro/Ranganathan_APUPA/issues/3#issuecomment-1047586085 usata nei round elimina il problema della teoria dei tipi di russell perchè stringhe di soggetto create da differenti strutture nei round si trasformano sempre in un punto di uno spazio vettoriale R^3. E' una cosa molto simile a quello che aveva fatto Pierce di unire la logica all'algebra vettoriale per il calcolo delle soluzioni di frasi logiche con variabili. Ma qui si tiene conto anche dei manifold e delle logiche di high level. Non fornisce soluzioni a frasi logiche con variabili ma permette di studiare le logiche di high level come se fossero uno spazio vettoriale R^3 eliminando il paradosso dei tipi e disponendo i tipi su level in funzione della loro complessità. Non ho più una matrice di relazioni ma uno spazio di punti. E quindi si può usare la topologia. Neighborhood.

[bertanimauro]

Type theory

Frege -concept and function- An object is anything that is not a function, so that an expression for it doas not contain an empty place [that has not arguments] Now just as functions are fundamental different from objects, so also functions whose arguments are and must be functions are fundamental different from functions whose argoment are objects and cannot be anything else. I call the latter first level, the former second level

Ernst Zermelo in his (1908) A new proof of the possibility of a well-ordering (published at the same time he published "the first axiomatic set theory")[18] laid claim to prior discovery of the antinomy in Cantor's naive set theory. He states: "And yet, even the elementary form that Russell9 gave to the set-theoretic antinomies could have persuaded them [J. König, Jourdain, F. Bernstein] that the solution of these difficulties is not to be sought in the surrender of well-ordering but only in a suitable restriction of the notion of set"

In 1923, Ludwig Wittgenstein proposed to "dispose" of Russell's paradox as follows: The reason why a function cannot be its own argument is that the sign for a function already contains the prototype of its argument, and it cannot contain itself. For let us suppose that the function F(fx) could be its own argument: in that case there would be a proposition F(F(fx)), in which the outer function F and the inner function F must have different meanings, since the inner one has the form O(fx) and the outer one has the form Y(O(fx)). Only the letter 'F' is common to the two functions, but the letter by itself signifies nothing. This immediately becomes clear if instead of F(Fu) we write (do) : F(Ou) . Ou = Fu. That disposes of Russell's paradox. (Tractatus Logico-Philosophicus, 3.333)

Thus, simple TT (type theory) and ZFC could now be regarded as systems that 'talk' essentially about the same intended objects. The main difference is that TT relies on a strong higher-order logic, while Zermelo employed second-order logic, and ZFC can also be given a first-order formulation. The first-order 'description' of the cumulative hierarchy is much weaker, as is shown by the existence of denumerable models (Skolem paradox), but it enjoys some important advantages."

In mathematics, logic, and computer science, a type system is a formal system in which every term has a "type" which defines its meaning and the operations that may be performed on it.

In a system of type theory, a term is opposed to a type. For example, 4, 2+2, and 2*2 are all separate terms with the type {nat} for natural numbers. Traditionally, the term is followed by a colon and its type, such as 2:{nat} - this means that the number 2 is of type {nat} . Beyond this opposition and syntax, only few can be said about types in this generality, but often, they are interpreted as some kind of collection (not necessarily sets) of the values that the term might evaluate to. It is usual to denote terms by e and types by \tau . How terms and types are shaped depends on the particular type system and is made precise by some syntax and additional restrictions of well-formedness.

[bertanimauro]

Interpretation Unlike propositional logic, where every language is the same apart from a choice of a different set of propositional variables, there are many different first-order languages. Each first-order language is defined by a signature. The signature consists of a set of non-logical symbols and an identification of each of these symbols as a constant symbol, a function symbol, or a predicate symbol. In the case of function and predicate symbols, a natural number arity is also assigned. The alphabet for the formal language consists of logical constants, the equality relation symbol =, all the symbols from the signature, and an additional infinite set of symbols known as variables.

For example, in the language of rings, there are constant symbols 0 and 1, two binary function symbols + and ·, and no binary relation symbols. (Here the equality relation is taken as a logical constant.)

Again, we might define a first-order language L, as consisting of individual symbols a, b, and c; predicate symbols F, G, H, I and J; variables x, y, z; no function letters; no sentential symbols.

Given a signature σ, the corresponding formal language is known as the set of σ-formulas. Each σ-formula is built up out of atomic formulas by means of logical connectives; atomic formulas are built from terms using predicate symbols. The formal definition of the set of σ-formulas proceeds in the other direction: first, terms are assembled from the constant and function symbols together with the variables. Then, terms can be combined into an atomic formula using a predicate symbol (relation symbol) from the signature or the special predicate symbol "=" for equality (see the section "Interpreting equality" below). Finally, the formulas of the language are assembled from atomic formulas using the logical connectives and quantifiers.

Interpretations of a first-order language To ascribe meaning to all sentences of a first-order language, the following information is needed.

• A domain of discourse[3] D, usually required to be non-empty (see below).
• For every constant symbol, an element of D as its interpretation.
• For every n-ary function symbol, an n-ary function from D to D as its interpretation (that is, a function Dn → D).
• For every n-ary predicate symbol, an n-ary relation on D as its interpretation (that is, a subset of Dn).
• An object carrying this information is known as a structure (of signature σ), or σ-structure, or L-structure (of language L), or as a "model".

The information specified in the interpretation provides enough information to give a truth value to any atomic formula, after each of its free variables, if any, has been replaced by an element of the domain. The truth value of an arbitrary sentence is then defined inductively using the T-schema, which is a definition of first-order semantics developed by Alfred Tarski. The T-schema interprets the logical connectives using truth tables, as discussed above. Thus, for example, φ & ψ is satisfied if and only if both φ and ψ are satisfied.

This leaves the issue of how to interpret formulas of the form ∀ x φ(x) and ∃ x φ(x). The domain of discourse forms the range for these quantifiers. The idea is that the sentence ∀ x φ(x) is true under an interpretation exactly when every substitution instance of φ(x), where x is replaced by some element of the domain, is satisfied. The formula ∃ x φ(x) is satisfied if there is at least one element d of the domain such that φ(d) is satisfied.

An extensional definition of a concept or term formulates its meaning by specifying its extension, that is, every object that falls under the definition of the concept or term in question.

For example, an extensional definition of the term "nation of the world" might be given by listing all of the nations of the world, or by giving some other means of recognizing the members of the corresponding class. An explicit listing of the extension, which is only possible for finite sets and only practical for relatively small sets, is a type of enumerative definition

REF: interpretation

[bertanimauro]

JOURNAL ARTICLE Matrix Development of the Calculus of Relations Irving M. Copilowish The Journal of Symbolic Logic Vol. 13, No. 4 (Dec., 1948), pp. 193-203 (11 pages) Published By: Association for Symbolic Logic https://doi.org/10.2307/2267134 https://www.jstor.org/stable/2267134

[bertanimauro]

La base delle stringhe di soggetto è la logica del primo ordine a più variabili.

We have here a function whose value is always a truth-value. We called such functions of one argument concepts. we call such functions of two arguments relations.

Frege, Gottlob. Function und Begriff: Vortrag, gehalten in der Sitzung vom 9. Januar 1891 der Jenaischen Gesellschaft für Medicin und Naturwissenschaft. Рипол Классик, 1891. Frege, Gottlob, Peter Thomas Geach, and Max Black. Translations from the philosophical writings of Gottlob Frege. Oxford: Basil Blackwell, 1952.

[bertanimauro]

De Morgan Let X and Y be term, and L a relation in which X may or may not stand to Y, let X..LY signify the assertion of a relation, and X.LY its denial. This separation of relation and judgment is an important step towards the treatement of syllogistic inference.

The supreme law of syllogism of three terms, the law which govern all of possible case, and which every variety of expression must be brought before inference can be made, is this; any relation of X to Y compound with any relation of Y to Z, give a relation of X to Z (compound ratio of magnitude of Euclide)

Let the premise X.LY, Z..MY . These premises are identical to X..lY and Y..M^-1Z of which all the inference is X..lM^-1Z

When by the word syllogism we are agree to mean a composition of two relations into one, we open the field in such a manner that the invention of the middle term, and the component relations which give the compound relation of the conclusion, is seen to costitute the act of mind, which ia always occurring in the effort of the reasoning power.

It is to algebra that we must look for the most habitual use of logical form. Not that onymatic relations are found in frequent occurrance: but so soon as the syllogism is consider under the aspect of combination of relations, it became clear that there is more of syllogism, and more of its variety, in algebra than in other subject whatever, though the matter of relations, pure quantity, is itself a small variety

Ref: de Morgan, A. "On the Logic of Syllogism: IV; and on the Logic of Relations,“transactions of the cambridge Philosophical Society”, 10: 331-358; ora in A. de Morgan." On the Syllogism and Other Logical Writings (1860): 208-246.

[bertanimauro]

Ok.

Il lun 28 set 2020, 09:33 ellegi69 notifications@github.com ha scritto:

Ok, forse era quello. Ieri sera ho fatto commit del testo di traccia2 modificato. Penso che dobbiamo andare verso un'unione delle due tracce in un unico saggio, alla fine del quale metterei una illustrazione delle sperimentazioni che hai fatto.