Béziau-13 Questions about Universal Logic- continuación. Preguntas 2 y 3

2. How is it possible to develop a general theory of logics, to

unify logics so various as quantum logic, erotetic logic or fuzzy

logic?

In order to solve such a question, we have to ask, how two different

systems can be considered both as logics, and this naturally leads to ask

what a logic is. That is the central point. The key of the problem.

Even a Girard, a Brady or a Hintikka would admit that, while anything

cannot be considered as a logic, there are different logics, their is not the

only one even if it appears to them as the only true one, as depicting the

reasoning most adequately. In fact their systems are like many other ones,

whether concerning their properties or the technicalities displayed in order

to elaborate them.

Hence, it seems natural to consider what is commonly shared by all

logical systems. Such is the approach of universal logic. Now what does

mean all logical systems: all systems called logical? Recognized as logical?

Or every possible and conceivable systems? What is the criterion according

to which we can say that such a thing is a logic and such another one has

nothing to do with a logic, is only a paralogic or something totally illogical?

Universal logic cannot be a descriptive theory: it cannot claim to describe

what is logical in a variety of systems considered as logics by the

people or the elite. No theory in human science is a purely descriptive one:

it seems impossible to account for an inconsistent variety of various viewpoints,

some of which appear to be completely arbitrary ones, unless some

very special logic is used for this purpose like Bychovsky’s paraconsistent

turbopolar logic.

On the other hand, to develop a theory that would be a purely normative

one, imposing some viewpoint that has just a slight bearing to what

is ordinarily called logic or logics, wouldn’t appear to be satisfactory at all

unless it is some genial view that would give us a new insight, making us

realize that we were entirely mistaken. But if so, the theory would not be a

properly normative one, it will impose the force of a description we didn’t

already know. It cannot be said that the Einsteinian theory is more normative

than the Newtonian one. In any case we have to vacillate between

normative and descriptive. We have to be cautious concerning variety while

having some unitary view that doesn’t reduce to such a variety.

The basic view of universal logic is double, inspired both by Tarski

and Birkhoff. From the late twenties, Tarski suggested its theory of the

consequence operator that is a very general theory of the notion of logical

consequence, making abstraction of the logical operators. He thus made a

jump into abstraction. Laws of logic don’t appear any more as for example

laws concerning negation such as principles of contradiction or excluded

middle, but as laws ruling the notion of consequence: self-deducibility,

monotony, transitivity. However these very laws can be and have actually

been criticized, so that the view is to reject any law, any axiom, and even

those located at a more abstract level. This may appear as totally absurd,

prima facie

.

Then Birkhoff comes into play. He himself developed a general theory

of algebra from a primary notion of algebraic structure not obeying

any axiom, whereas its predecessors sought to unify algebra around such

very general laws as associativity or commutativity. But as he aptly said

himself, such a unification was no more possible to a certain stage, and

especially it was not possible to unify two large trends, algebras studied by

the Noether school, on the one hand, and, on the other hand, the Boolean

trend including the notion of lattice as developed in particular by Birkhoff

himself. Thus Birkhoff developed universal algebra without taking axioms

into account.

Such a surprising approach can be called a conceptual one, as opposed

to an axiomatic one. Category theory is itself more conceptual than

axiomatic. The point is not to produce a large axiomatic system like ZF

set-theory from which everything could be deduced; rather, it is to elaborate

some concepts that could serve to describe the whole of mathematical

phenomena in a unitary fashion.

The approach of universal logic is also a conceptual one, where the

point is to capture the whole logical phenomena, not to be looking for

some axiomatic Graal or genuine laws of thought or reality, from which

everything could be deduced.

3. What is meant exactly by a logic according to universal

logic ? You often refer to Bourbaki, although the latter is often

considered as a suspicious guy by logicians.

According to universal logic, a logic is a certain kind of structure. The

project of universal logic is in the spirit of modern mathematics. As it is

well known, from the 1930’s onward, Nicolas Bourbaki made the proposal

to reconstruct the entire mathematics through the notion of structure.

For Bourbaki, any mathematical object does only make sense from the

perspective of a structure or, better, of a set of structures. The number 4

does not exist in itself and per se, but as connected with other numbers

that form the entire structure of natural numbers. Now its existence is not

confined to the structure of natural numbers, it also extends to the structure

of integers, rational, real numbers, and so on. So such connections between

these various structures also characterize what the number 4 is.

Bourbaki’s insight consists in reconstructing every mathematical structure

from some “fundamental structures” or “mother structures” through

a crossing process, which gives rise to “cross-structures”. He distinguishes

between three sorts of basic structures, namely: algebraic structures, topological

structures and structures of order, and reconstructs the structure of

real numbers as a crossing between these three fundamental mother structures.

The idea of universal logic is that logical structures are fundamental

ones but departing from the Bourbakian trinity. Note that this is not

in opposition with the insight of the very famous General, given that he

admitted the plausible appearance of other core structures. What does

matter with such a perspective is that we argue against any reduction of

logic to algebra, since logical structures are differing from algebraic ones

and cannot be reduced to them. Universal logic is not universal algebra.

Some logicians are at a loss to understand this because two basic

trends are often contrasted in the history of modern logic, namely: Boolean

and Fregean trends, and one tends to assimilate any mathematization of

logic with the Boolean trend, the notion of Boolean algebra, or algebraic

logic. For some people, any structure is an algebraic structure. Historically,

algebraic structures certainly played a crucial role in promoting the notion

of structure, since someone like Glivenko used this word structure as a

synonym for lattice. But nowadays, such a confusion appears ridiculous

after Bourbaki and category theory.

There is no good reason to say that any logic is an algebra, or algebraic.

For instance, to take such a connective as negation to be a function seems

to be quite arbitrary, given that negation can be equally seen as a relation.

Another pernicious assimilation is that of logical structures with ordering

structures: this leads one to think that the notion of logical consequence

has to be naturally transitive, but this is quite questionable.

In order to avoid any ambiguity, it should be said that the stance of

universal logic is a Neobourbakian and not a Bourbakian one, not only

because Bourbaki did not see logics as fundamental structures but he once

adopted some axiomatic-formalistic stance that is not ours and which is

quite independent of his informal conceptual stance, the stance we are

following was mainly expressed in his famous paper, “L’architecture des

math´ematiques”.

Peguntras sobre Lógica Universal a Jean-Yves Béziau

De a poco ire subiendo las preguntas que le hizo Linda Easthood a Béziau y sus respuestas.
La lógica universal no es principio lo que uno pensaría.... muy interesante!!!

1- . Although your proposal to develop a universal logic is

very appealing, isn’t it a utopian one? Isn’t it an absurd, or even

dangerous thing to believe that it would be possible to develop a

unique logic accounting for everything?

Let us immediately reject some misunderstanding; universal logic, as

I understand it, is not one universal logic. In fact, from the viewpoint of

universal logic the existence of one universal logic is not even possible, and

this is a result that can easily be shown. One might thus say somehow

ironically the following: according to universal logic there is no universal

logic.

Some people in some countries have always tried to elaborate a universal

system that would account for any sort of reasoning, or reasoning

as a whole. Aristotelian logic was depicted itself as a universal one. More

recently, first-order classical logic appeared to some as a universal system

accounting for mathematical reasoning as well as current one, that is, the

one used to buy your bread at the bakery.

But first-order classical logic was also criticized at length, whether

concerning its claim to describe mathematical reasoning or physical, computational,

current, philosophical ones, and the like. Many new logics were

further developed, namely: intuitionistic logic, combinatory logic, linear

logic, quantum logic, erotetic logic, modal logic, paraconsistent logic, polar

logic, relevant logic and so many others, all the more that each of these is

often to be divided into a disparate multiplicity, as in the case of modal

logics.

Among advocates of these logics, some forcefully believe that their

own logic is the best one, that it explains everything, solves everything,

so that their logic is universal, as was formerly the case with Stanis law

Le´sniewski or, more recently, with Jean-Yves Girard and its linear logic,

Jaakko Hintikka and its IF logic, and, even more explicitly, Ross Brady

with its relevant logic he squarely dubbed a “universal logic”.

Such a view is not shared by people working in quantum logic, for

example; indeed, these only want to account for one particular reasoning

related to one particular area, without ever claiming that such is the reasoning

we are using or should use whenever we go at the bakery. Now is

such a view consistent? Are we entitled to say the following: to each area,

to each situation, its own logic, or even to each group of persons, to each

individual, its own logic. So there would be a logic of chemistry, logic of

clouds, logic of sex, logic of women, logic of dogs, the logic of Bouvard and

the logic of P´ecuchet.

Actually, such a relativization of logic is equally absurd as the opposite

stance according to which only one logic could explain everything.

Obviously, there is also one intermediary situation according to which there

are neither only one nor thousand and one logics, but three or four: so is

the middle, not to say mediocre position of people who cut the cake into

three parts saying that there is the reasoning for formal sciences, on the one

hand, the reasoning for empirical sciences, on the other hand, and finally

the natural reasoning for daily life. Behind such a stance we see again the

old contradistinction between inductive logic and deductive logic.

The view of universal logic is that one plausibly can unify the large

kaleidoscopic variety of logics, while preserving their diversity. In the case of

universal logic, as opposed to those who support the view of one universal

logic, unity is entailed by diversity. Universal logic is not a logic but a

general theory of different logics. This general theory is no more a logic

itself than is meteorology a cloud.

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Invitación: Congreso Internacional "Wittgenstein en Español"

Congreso internacional "Wittgenstein en Español"

Congreso internacional "Wittgenstein en Español"

Toledo, del 20 al 23 de junio de 2011

Juegos del lenguaje y Formas de vida

Sin lugar a dudas, los debates suscitados por L. Wittgenstein han estimulado el pensamiento contemporáneo. Nos ofrece recursos para innovar gran parte de las cuestiones analizadas por la filosofía tradicional. Muchos de los planteamientos clásicos, después de un análisis pormenorizado, se han transformado en cuestiones de debate en la que han participado activamente filósofos intelectualmente respetables. Frente a las dudas suscitadas por este pensador, la terminología ha sido revisada y discutida. A menudo, el lector tiene la sensación que después de una lectura atenta de sus argumentos, estamos principiando un nuevo campo de reflexión. Algo semejante ocurre cuando reflexiona acerca de dos términos nucleares del pensamiento contemporánero, a saber: "juego del lenguaje" y "formas de vida".

En un momento de lucidez, L. Wittgenstein anota:

Das Wort »Sprachspiel« soll hier hervorheben, daß das Sprechen der Sprache ein Teil ist einer Tätigkeit, oder einer Lebensform." (Wittgenstein, PU, 23)

"El término "juego del lenguaje" ha de poner de relieve aquí que hablar una lengua forma parte de una actividad o de una forma de vida." (Wittgenstein, IF, 23)

La cita pone de manifiesto que existe una correlación entre el término "juego de lenguaje" y el hecho genuino de que el modo de hablar una lengua es, por un lado, una actividad humana y, sin embargo, también, pone de manifiesto una forma de vida. Ciertamente, podríamos preguntar, qué relevancia desempeña el juego de lenguaje en el condicionamiento de nuestra forma de vida. ¿Existe una relación recíproca entre los "juegos de lenguaje" y las "formas de vida"? ¿Hasta que punto, nuestra forma de vida y la forma de vida de otros individuos viene reflejada en los juegos lingüísticos que usan? ¿Cómo codifica el juego de lenguaje nuestras formas de vida y la de nuestros semejantes? Dar respuestas a cuestiones tan intrigantes nos induce a repasar todo nuestro edificio terminológico

En su corta vida, ambos términos han generado, como mínimo, tres controversias y va en camino de suscitar una nueva disputa en los próximos años. El concepto alemán "Lebensform(en)", que traducido al castellano se denomina "formas de vida", se ha convertido en un problema central de la filosofía. De facto, L. Wittgenstein lo menciona algo más de una veintena de veces en su obra. Sin embargo, la convulsión que ha generado y el modo como es usado ha generado una gran discusión en el ámbito filosófico. En su origen, el concepto "formas de vida" fue analizado desde opciones culturales, antropológicas, psicológicas y lingüísticas. Su cambio de significado permitió múltiples interpretaciones. Por un lado, la interpretación monista ha entrado en conflicto con una visión pluralista del mundo. También los que conciben los modos de vida como modos de coexistencia que sobreviven paralelas han discutido con aquellas posiciones radicales que entienden que la pluralidad de formas de vida desembocan inevitablemente en un conflicto.

Estrechamente vinculado a las formas de vida se discute el término "juegos del lenguaje" (Sprachspiel). Monismo y pluralismo se confunden con las posiciones pragmáticas con el fin de aclarar este ámbito de investigación.

Este congreso pretende analizar de modo sistemático los argumentos desarrollados acerca de este complejo con el fin de reconducir el debate y ubicarlo en el ámbito pertinente.

17000 nuevas palabras de Wittgenstein.

17.000 nuevas palabras mecanografiadas y manuscritas y un puñado de ecuaciones matemáticas; ésa es la nueva veta de pensamiento de Ludwig Wittgenstein que Arthur Gibson, profesor de la Universidad de Cambridge, presentó ayer, después de haber trabajado con el hallazgo durante los últimos tres años.
La aparición del archivo es un auténtico acontecimiento en el claustrofóbico mundo de los estudios de Wittgenstein, el filósofo más impactante del siglo XX, según lo califica el diario 'The Guardian' en la noticia del hallazgo.
Según Gibson, los nuevos textos de Wittgenstein desaparecieron durante la II Guerra Mundial, cuando Wittgenstein (vienés y judío, exiliado en Cambridge), se empleó en un hospital porque consideraba insoportable la idea de dar clase mientras se producían los combates.
Gibson ha explicado el valor de su archivo en 'The Guardian': "Me quedé asombrado cuandoencontré el archivo. Lo increíble es que se trata de un archivo completo, inédito hasta ahora. Nos intoduce en el proceso de pensamiento de Wittgenstein, es como si el lector pudiera hurgar en su mente".

El hallazgo demuestra que Francis Skinner no sólo era su secretario; también era su gran interlocutor.

Parte de esas 17.000 palabras fueron dictadas por Wittgenstein a Francis Skinner, su colaborador más íntimo y, probablemente, su amante. De hecho, la sorprendente muerte de Skinner (que tuvo complicaciones leves derivadas de su poliomelitis y fue víctima de la negligencia de los médicos) fue la causa de que se perdiera el archivo.
Wittgenstein, en estado de 'shock', envió los documentos a otro alumno por correo porque quería deshacerse de ellos. Y así permanecieron hasta que, en 1975, su depositario de los entregó a la Mathematical Association. El motivo, un cuaderno de cuadros comprado en Noruega lleno de fórmulas y anotaciones matemáticas. El cuaderno, en realidad, es uno de los grandes tesoros del archivo hallado, ya que enfrenta a Wittgenstein con el Pequeño Teorema de Fermat, de 1635. Sin embargo, la Mathematical Association carecía de archiveros profesionales, no supo valorar el documento y lo devolvió sin apenas tocarlo.
Además, cuaderno incluye algunas notas "narrativas" manuscritas por el propio Wittgenstein. En ellas, se demuestra que Francis Skinner no sólo fue el secretario del filósofo, sino que también fue su interlocutor más valioso.
"Este archivo demuestra que aún hay ideas revolucionarias e impredecibles que aún nos esperan en la Filosofía de Wittgenstein, aunque hasta ahora hubiéramos creído incorrectamente, que ya la habíamos entendido," dijo Gibson.

Invitación: Encuentro Internacional sobre "Argumentación: el estado del arte"

Durante los días 4-6 de mayo tendrá lugar en Madrid un Encuentro Internacional sobre "Argumentación: el estado del arte", con arreglo al programa colgado en los Documentos de esta misma Comunidad, pueden verse los archivos:
Encuentro sobre Argumentación_Programa.pdf  y  Tríptico1.doc
La asistencia es libre y agradeceremos la presencia de todos los interesados.
Los actos se celebrarán el día 4, de 10:15 a 14 en el Salón de Actos de Filosofía de la Universidad Autónoma de Madrid; los días 5 y 6, de 9:30 a 14 en la Sala de Grados de Filosofía de la UNED (Humanidades, c/ Senda del del Rey, 7): y el día 6 por la tarde, a partir de las 17:00 en el Salón de actos del Centro Asociado de Madrid-UNED: "Escuelas Pías" (c/ Tribulete, 14.

INTERNATIONAL

WORKSHOP

"Argumentation:

The state of the art”

Organizing committee:

Luis Vega (UNED)

Paula Olmos Gómez (UC3M)

Roberto Feltrero, (UNED)

Invitación IX Coloquio Compostelano de Lógica y Filosofía Analítica.

Estimad@s Tod@s:
Es un placer invitaros a la sesión del XI Coloquio Compostelano de Lógica y Filosofía Analítica que tendrá lugar el próximo jueves 28 de abril de 2011 a las 16.30h. en el seminario 330 de la Facultad de Filosofía.
Nuestro invitado es el profesor Janusz Maciaszek de la Universidad de Lodz, Polonia.
El profesor Maciaszek disertará sobre "La temprana filosofía del lenguaje  de Kazimierz Ajdukiewicz".
Adjunto texto en inglés aunque el profesor Maciaszek habla español.
Un saludo,
Concha Martínez Vidal
Departamento de Lóxica e Filosofía Moral
Facultade de Filosofía
Praza de Mazarelos s/n
15782 Santiago de Compostela
Tele. 881812530 Fax: 881812542