Paradoja de Russell

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Re: Paradoja de Russell

Mensaje sin leerpor Hagamenon » Sab Nov 21, 2009 7:34 pm

goheim escribió:1) la frase es verdadera o es falsa


ya la hemos cagao. con esto no estoy de acuerdo. :mrgreen:

¿por qué razón no han de existir las paradojas? porque lo diga aristóteles no significa que es una ley universal.

goheim escribió:En la paradoja de Russell «el barbero de esta ciudad, que afeita sólo a todos los hombres que no se afeitan a sí mismos, ¿se afeita a sí mismo?», la preconcepción es suponer que todos los hombres se afeitan si o si. Es decir si consideramos que la frase "los hombres que no se afeitan así mismos" significa "los hombres que se afeitan pero no lo hacen ellos mismos" la frase no es una paradoja pues el barbero no se afeita y tendrá una gran barba.


no, no. esto es trampa.
si sustituyo tu frase por la que figura en la oración:
«el barbero de esta ciudad, que afeita sólo a todos los hombres que se afeitan pero no lo hacen ellos mismos, ¿se afeita a sí mismo?»

lo que está claro es que el barbero en la realidad se afeita o no. ahí no hay paradoja. pero la oración sigue siendo exactamente igual de paradójica.

por supuesto, con tal que demos por hecho que el barbero se afeita. si no lo hace, tal como está planteado, no habría paradoja. pero eso es trampa. el barbero sí se afeita, pero, ¿lo hace él u otro?

goheim escribió:La frase "Esto que estoy diciendo" no es ni verdadera ni falsa, luego nunca puede ser mentira ni verdad. Podriamos definirla como una frase neutra.


no, no, no. aquí tb. estás haciendo trampa.

"Esto que estoy diciendo" no se refiere a "Esto que estoy diciendo". porque -----> "Esto que estoy diciendo" apunta a "Esto que estoy diciendo es falso"
si te cargas esto, te cargas la recursividad de la frase, y el cristo mental que provoca.
si te cargas esto, te cargas el problema: muerto el perro se acabó la rabia. :mrgreen:

goheim escribió:"Siempre debe recordarse que una persona muy simple puede llegar a proponer un problema sólo capaz de ser resuelto por mentes hábiles, si es que puede resolverse. Una niña pregunto "¿Puede Dios hacer cualquier cosa? Al recibir respuesta afirmativa, dijo enseguida: "Entonces, ¿puede El hacer una piedra tan pesada que El mismo no pueda levantar? Mucho adultos bien despiertos no encuentran enseguida la respuesta satisfactoria. Sin embargo, la dificultad radica meramente en la absurda, aunque sagaz, manera de plantear la pregunta, la que en realidad lleva a preguntar "¿Puede el Todopoderoso destruir su propia omnipotencia" Es algo similar a esta otra "¿Qué sucedería si un cuerpo móvil irresistible llegara a tomar contacto con un cuerpo incapaz de ser movido?" Aqui tenemos simplemente una contradicción de términos. ya que si existiera tal cosa como un cuerpo incapaz de ser movido, no podría al mismo tiempo existir un cuerpo móvil al que nada pudiera resistirse"


vale, estoy completamente de acuerdo con esto, pero NO es lo que se discute.
por la misma, yo puedo decir que solo tengo que observar al barbero y ver si se afeita a si mismo no. hala! solucionado. no hay paradoja. o se afeita o no. punto.

aunque este problema que se plantea tiene otra solución. a mi, si me pregunta esto la niña, la mando a la uni a estudiar física. :mrgreen:
¿Quién de nosotros no se ha sacrificado ya a sí mismo, por su buena reputación?
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Re: Paradoja de Russell

Mensaje sin leerpor goheim » Sab Nov 21, 2009 9:55 pm

Hagamenon escribió:
goheim escribió:1) la frase es verdadera o es falsa


ya la hemos cagao. con esto no estoy de acuerdo. :mrgreen:

¿por qué razón no han de existir las paradojas? porque lo diga aristóteles no significa que es una ley universal.


Por eso es una preconcepción, porque no es así realmente ...



Respecto al resto, por supuesto que te cargas al perro y a la rabía, no es que sea trampa, es que no se pude hacer una frase sobre la realidad que no se pueda aplicar a dicha realidad. De todas formas ya advertí que era en lenguaje "coloquial"

Como ya dije: La distinción formal entre lenguaje objeto y metalenguaje fue introducida por Alfred Tarski como una solución a las paradojas semánticas como la paradoja del mentiroso. Según Tarski, ningún lenguaje puede contener su propio predicado de verdad y permanecer consistente. Para hablar acerca de la verdad en un lenguaje, y no generar contradicciones, es necesario hacerlo desde un lenguaje distinto, con mayor poder expresivo: el metalenguaje.

De hecho la teoria de los niveles de lenguaje fue establecida por Bertrand Russell en su introducción al Tractatus Logico-Philosophicus de Wittgenstein.Russell que había elaborado la teoría de los tipos a fin de resolver algunas paradojas lógicas, establece que "cada lenguaje tiene una estructura propia respecto a la cual nada puede enunciarse en el propio lenguaje; pero puede haber otro lenguaje que trate de la estructura del primer lenguaje, no habiendo límites en esta jerarquía de lenguajes".

De todas formas yo no soy un experto en metalenguaje XD, eso es más de filósofos, lo que pasa es que Russell era tan matemático como filósofo el muy :z16:
Las matemáticas no mienten, lo que hay son muchos matemáticos mentirosos.
Henry David Thoreau (1817-1862) Escritor, poeta y pensador.
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Re: Paradoja de Russell

Mensaje sin leerpor Hagamenon » Sab Nov 21, 2009 10:17 pm

échale un ojo a esto, que está guay.

es de hofstadter, que es matemático, filósofo, ha trabajado mucho tiempo investigando la cognición aplicada sobre todo a la inteligencia artificial, pianista, hizo el doctorado sobre los estados energéticos de los electrones (creo recordar) usando fractales (autoreferencia), habla tropecientos idiomas, es un artista que te cagas con el dibujo, tradujo Eugene Onegin de Pushkin (libro ruso escrito en verso) y es toda una autoridad en el campo de la traducción y tengo entendido que si se mete un huevo en el culo es capaz de lanzarlo a más de 15 metros. :o :o :o

afortunadamente es un tipo pequeñito y feo :mrgreen: es el equilibrio del universo :ugeek:

contexto: tiene una colección de artículos de carácter científico divulgativo con los que hizo un libro. este es parte de uno de esos artículos. En negrita una persona que presenta un argumento muy similar al tuyo, es decir, las palabras apuntan a cosas del mundo real y no pueden apuntar al apuntar, y la distinción entre la forma y el contenido, y todo ese royo.
a continuación su respuesta rebatiendolo.
¿qué tal tu inglés?
hofstadter escribió:Mr Flash insisted that a sentence cannot say what it shows. The former concerns only its content, which is supposedly independent of how it manifests itself in print, while the latter is a property exclusively of its form, that is, of the physical sentence only when it is in print. This distinction sounds crystal-clear at first, but in reality it is mud-blurry. Here is some of what Flash wrote me:

For a sentence to attempt to say what it shows is to commit an error of logical types. It seems to be putting a round peg into a square hole, whereas it is instead putting a round peg into something which is not a hole at all, square or otherwise. This is a category mismatch, not a paradox. It is like throwing the recipe in with the flour and butter and eggs. The source of the equivocation is an illegitimate use of the term 'this'. 'This' can point to virtually anything, but 'this' cannot point to itself. If you stick out your index finger, you can point to virtually anything; and by curling it you can even point to the pointing finger; but you cannot point to pointing. Pointing is of a higher logical type than the thing which is doing the pointing. Similarly, the referent of 'this sentence' can be virtually anything but that sentence. Sentences of the form exemplified by 'This sentence no verb.' and 'This sentence has a verb.' are not well-formed: they commit fallacies of logical type equivocation. Thus their self-referential character is not genuine and they present no problem as paradoxes.

There will always be people around who will object in this manner, and in the Brabnerian manner. Such people think it is possible to draw a sharp line between attributes of a printed sentence that can be considered part of its form (e.g., the typeface it is printed in, the number of words it contains, and so on), and attributes that can be considered part of its content (i.e., the things and events and relationships that it refers to).
Now, I am used to thinking about language in terms of how to get a machine to deal with it, since I look at the human brain as a very complex machine that can handle language (and many other things as well). Machines, in trying to make sense of sentences, have access to nothing more than the form of such sentences. The content, if it is to be accessible to a machine, has to be derived, extracted, constructed, or created somehow from the sentence's physical structure, together with other knowledge and programs already available to the machine.
When very simple processing is used to operate on a sentence, it is convenient to label the information thus obtained "syntactic". For instance, it is clearly a syntactic fact about "This sentence no verb." that it contains six vowels. The vowel-consonant distinction is obviously a typographical one, and typographical facts are considered superficial and syntactic. But there is a problem here. With different depths of processing, aspects of different degrees of "semanticity" may be detected.
Consider, for example, the sentence "Mary was sick yesterday." Let's call it Sentence M. Listed below are the results of seven different degrees of processing of Sentence M by a hypothetical machine, using increasingly sophisticated programs and increasingly large knowledge bases. You should think of them as being English translations, for your convenience, of computational structures inside the machine that it can act on and use fluently.

1. Sentence M contains twenty characters.
2. Sentence M contains four English words.
3. Sentence M contains one proper noun, one one adverb, in that order. .
4. Sentence,M contains one human's name, one linking verb, one adjective describing a potential health state of a living being, and one temporal adverb, in that order.
5. The subject of Sentence M is a pointer to an individual named `Mary', the predicate is an ascription of ill health to the individual so indicated, on the day preceding the statement's utterance.
6. Sentence M asserts that the health of an individual named 'Mary' was not good the day before today.
7. Sentence M says that Mary was sick yesterday. verb, one adjective, and

Just where is the boundary line that says, "You can't do that much processing!"? A machine that could go as far as version 7 would have

actually understood-at least in some rudimentary sense-the content of Sentence M. Work by artificial-intelligence researchers in the field of natural language understanding has produced some very impressive results along these lines, considerably more sophisticated than what is shown here. Stories can be "read" and "understood", at least to the extent that certain kinds of questions can be answered by the machine when it is probed for its understanding. Such questions can involve information not explicitly in the story itself, and yet the machine can fill in the missing information and answer the question.
I am making this seeming digression on the processing of language by computers because intelligent people like Mr Flash qFiasco seem to have failed to recognize that the boundary line between form and content is as blurry as that between blue and green, or between human and ape. This comparison is not made lightly. Humans are supposedly able to get at the "content" of utterances, being genuine language-users, while apes are not. But ape-language research clearly shows that there is some kind of in-between world, where a certain degree of content can be retrieved by a being with reduced mental capacity. If mental capacity is equated with potential processing depth, then it is obvious why it makes no sense to draw an arbitrary boundary line between the form and the content of a sentence. Form blurs into content as processing depth increases. Or, as I have always liked to say, "Content is just fancy form." By this I mean, of course, that "content" is just a shorthand way of saying "form as perceived by a very fancy apparatus capable of making complex and subtle distinctions and abstractions and connections to prior concepts".
Flash qFiasco's down-home, commonsense distinction between form and content breaks down swiftly, when analyzed. His charming image of someone making a "category error" by throwing a recipe in with the flour and butter and eggs reveals that he has never had Recipe Cake. This is a delicious cake whose batter is made out of cake recipes (if you use pie recipes, it won't taste nearly as good). The best results are had if the recipes are printed in French, in Baskerville Roman. A preponderance of accents aigus lends a deliciously piquant aroma to the cake. My recommendation to Brabner and qFiasco is: "Let them eat recipes."
¿Quién de nosotros no se ha sacrificado ya a sí mismo, por su buena reputación?
Nietzsche
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Re: Paradoja de Russell

Mensaje sin leerpor Hagamenon » Sab Nov 21, 2009 10:21 pm

y este es un cuento escrito entero de forma auto-referencial. :lol: :lol: :lol: :lol:
David Moser escribió:This Is the Title of This Story, Which Is Also Found Several Times in the Story Itself

This is the first sentence of this story. This is the second sentence. This is the title of this story, which is also found several times in the story itself. This sentence is questioning the intrinsic value of the first two sentences. This sentence is to inform you, in case you haven't already realized it, that this is a self-referential story, that is, a story containing sentences that refer to their own structure and function. This is a sentence that provides an ending to the first paragraph.
This is the first sentence of a new paragraph in a self-referential story. This sentence is introducing you to the protagonist of the story, a young boy named Billy. This sentence is telling you that Billy is blond and blue-eyed and American and twelve years old and strangling his mother. This sentence comments on the awkward nature of the self-referential narrative form while recognizing the strange and playful detachment it affords the writer. As if illustrating the point made by the last sentence, this sentence reminds us, with no trace of facetiousness, that children are a precious gift from God and that the world is a better place when graced by the unique joys and delights they bring to it.
This sentence describes Billy's mother's bulging eyes and protruding

tongue and makes reference to the unpleasant choking and gagging noises she's making. This sentence makes the observation that these are uncertain and difficult times, and that relationships, even seemingly deep-rooted and permanent ones, do have a tendency to break down.
Introduces. in this paragraph, the device of sentence fragments. A sentence fragment. Another. Good device. Will be used more later.
This is actually the last sentence of the story but has been placed here by mistake. This is the title of this story, which is also found several times in the story itself. As Gregor Samsa awoke one morning from uneasy dreams he found himself in his bed transformed into a gigantic insect. This sentence informs you that the preceding sentence is from another story entirely (a much better one, it must be noted) and has no place at all in this particular narrative. Despite the claims of the preceding sentence, this sentence feels compelled to inform you that the story you are reading is in actuality "The Metamorphosis" by Franz Kafka, and that the sentence referred to by the preceding sentence is the only sentence which does indeed belong in this story. This sentence overrides the preceding sentence by informing the reader (poor, confused wretch) that this piece of literature is actually the Declaration of Independence, but that the author, in a show of extreme negligence (if not malicious sabotage), has so far failed to include even one single sentence from that stirring document, although he has condescended to use a small sentence fragment, namely, "When in the course of human events", embedded in quotation marks near the end of a sentence. Showing a keen awareness of the boredom and downright hostility of the average reader with regard to the pointless conceptual games indulged in by the preceding sentences, this sentence returns us at last to the scenario of the story by asking the question, "Why is Billy strangling his mother?" This sentence attempts to shed some light on the question posed by the preceding sentence but fails. This sentence, however, succeeds, in that it suggests a possible incestuous relationship between Billy and his mother and alludes to the concomitant Freudian complications any astute reader will immediately envision. Incest. The unspeakable taboo. The universal prohibition. Incest. And notice the sentence fragments? Good literary device. Will be used more later.
This is the first sentence in a new paragraph. This is the last sentence in a new paragraph.
This sentence can serve as either the beginning of the paragraph or the end, depending on its placement. This is the title of this story, which is also found several times in the story itself. This sentence raises a serious objection to the entire class of self-referential sentences that merely comment on their own function or placement within the story (e.g., the preceding four sentences), on the grounds that they are monotonously predictable, unforgivably self-indulgent, and merely serve to distract the reader from the real subject of this story, which at this point seems to concern strangulation and incest and who knows what other delightful

topics. The purpose of this sentence is to point out that the preceding sentence, while not itself a member of the class of self-referential sentences it objects to, nevertheless also serves merely to distract the reader from the real subject of this story, which actually concerns Gregor Samsa's inexplicable transformation into a gigantic insect (despite the vociferous counterclaims of other well-meaning although misinformed sentences). This sentence can serve as either the beginning of a paragraph or the end, depending on its placement.
This is the title of this story, which is also found several times in the story itself. This is almost the title of the story, which is found only once in the story itself. This sentence regretfully states that up to this point the self-referential mode of narrative has had a paralyzing effect on the actual progress of the story itself-that is, these sentences have been so concerned with analyzing themselves and their role in the story that they have failed by and large to perform their function as communicators of events and ideas that one hopes coalesce into a plot, character development, etc.-in short, the very raisons d'etre of any respectable, hardworking sentence in the midst of a piece of compelling prose fiction. This sentence in addition points out the obvious analogy between the plight of these agonizingly self-aware sentences and similarly afflicted human beings, and it points out the analogous paralyzing effects wrought by excessive and tortured self-examination.
The purpose of this sentence (which can also serve as a paragraph) is to speculate that if the Declaration of Independence had been worded and structured as lackadaisically and incoherently as this story has been so far, there's no telling what kind of warped libertine society we'd be living in now or to what depths of decadence the inhabitants of this country might have sunk, even to the point of deranged and debased writers constructing irritatingly cumbersome and needlessly prolix sentences that sometimes possess the questionable if not downright undesirable quality of referring to themselves and they sometimes even become run-on sentences or exhibit other signs of inexcusably sloppy grammar like unneeded superfluous redundancies that almost certainly would have insidious effects on the lifestyle and morals of our impressionable youth, leading them to commit incest or even murder and maybe that's why Billy is strangling his mother, because of sentences just like this one, which have no discernible goals or perspicuous purpose and just end up anywhere, even in mid
Bizarre. A sentence fragment. Another fragment. Twelve years old. This is a sentence that. Fragmented. And strangling his mother. Sorry, sorry. Bizarre. This. More fragments. This is it. Fragments. The title of this story, which. Blond. Sorry, sorry. Fragment after fragment. Harder. This is a sentence that. Fragments. Damn good device.
The purpose of this sentence is threefold: (1) to apologize for the unfortunate and inexplicable lapse exhibited by the preceding paragraph; (2) to assure you, the reader, that it will not happen again; and (3) to

reiterate the point that these are uncertain and difficult times and that aspects of language, even seemingly stable and deeply rooted ones such as syntax and meaning, do break down. This sentence adds nothing substantial to the sentiments of the preceding sentence but merely provides a concluding sentence to this paragraph, which otherwise might not have one.
This sentence, in a sudden and courageous burst of altruism, tries to abandon the self-referential mode but fails. This sentence tries again, but the attempt is doomed from the start.
This sentence, in a last-ditch attempt to infuse some iota of story line into this paralyzed prose piece, quickly alludes to Billy's frantic cover-up attempts, followed by a lyrical, touching, and beautifully written passage wherein Billy is reconciled with his father (thus resolving the subliminal Freudian conflicts obvious to any astute reader) and a final exciting police chase scene during which Billy is accidentally shot and killed by a panicky rookie policeman who is coincidentally named Billy. This sentence, although basically in complete sympathy with the laudable efforts of the preceding action-packed sentence, reminds the reader that such allusions to a story that doesn't, in fact, yet exist are no substitute for the real thing and therefore will not get the author (indolent goof-off that he is) off the proverbial hook.
Paragraph. Paragraph. Paragraph. Paragraph. Paragraph. Paragraph. Paragraph. Paragraph. Paragraph. Paragraph. Paragraph. Paragraph. Paragraph. Paragraph.
The purpose. Of this paragraph. Is to apologize. For its gratuitous use. Of. Sentence fragments. Sorry.
The purpose of this sentence is to apologize for the pointless and silly adolescent games indulged in by the preceding two paragraphs, and to express regret on the part of us, the more mature sentences, that the entire tone of this story is such that it can't seem to communicate a simple, albeit sordid, scenario.
This sentence wishes to apologize for all the needless apologies found in this story (this one included), which, although placed here ostensibly for the benefit of the more vexed readers, merely delay in a maddeningly recursive way the continuation of the by-now nearly forgotten story line.
This sentence is bursting at the punctuation marks with news of the dire import of self-reference as applied to sentences, a practice that could prove to be a veritable Pandora's box of potential havoc, for if a sentence can refer or allude to itself, why not a lowly subordinate clause, perhaps this very clause? Or this sentence fragment? Or three words? Two words? One?
Perhaps it is appropriate that this sentence gently and with no trace of condescension remind us that these are indeed difficult and uncertain times and that in general people just aren't nice enough to each other, and perhaps we, whether sentient human beings or sentient sentences, should just try harder. I mean, there is such a thing as free will, there has to be, and this sentence is proof of it! Neither this sentence nor you, the reader, is


completely helpless in the face of all the pitiless forces at work in the universe. We should stand our ground, face facts, take Mother Nature by the throat and just try harder. By the throat. Harder. Harder, harder.
Sorry.
This is the title of this story, which is also found several times in the story itself.
This is the last sentence of the story. This is the last sentence of the story. This is the last sentence of the story. This is. Sorry.
¿Quién de nosotros no se ha sacrificado ya a sí mismo, por su buena reputación?
Nietzsche
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Re: Paradoja de Russell

Mensaje sin leerpor goheim » Sab Nov 21, 2009 11:16 pm

Hacerme leer esto a estas horas :z15:

La primera interesante, una opinión más. Pero como te comenté antes no es mi opinión en particular es la opción a la que matemáticos y filósofos han llegado y que yo comparto en parte. Si quieres mi punto de vista te lo daré:

Es obvio que las paradojas existen, sino no existiría siquiera dicha palabra, aunque esto no sea condición suficiente ni necesaria. Pero estas paradojas deben evitarse fijando unas bases sólidas sobre las que asentarse de tal forma que eliminemos dichas paradojas, a fin de llegar a un resultado válido ya sea en el mundo real o en el matemático. Como comedura de coco no están mal, ...pero yo no puedo evitarla deformación profesional :sick: Por ejemplo en la paradoja del mentiroso original:

"Todos los cretenses son mentirosos" dicho por Epiménides que era de Creta

Se debe partir de la base de que los cretenses dicen siempre la verdad o siempre mienten.

Mi mente hace lo siguiente (si soy un poco friki):

Si los cretenses siempre mienten o dicen la verdad -> la frase es mentira o es verdad
Epiménides es cretense -> siempre dice la verdad o siempre miente
luego "Todos los cretenses son mentirosos" puede ser verdadera o puede ser mentira

1) Si la frase es verdadera -> "Todos los cretenses son mentirosos" es verdadera -> Epiménides miente pues es cretense.-> la frase no puede ser verdadera -> contradicción


2) Si la frase es falsa -> "Todos los cretenses son mentirosos" es mentira -> Epiménides por ser cretense puede mentir o no (ya que el hecho de que la frase sea mentira no implica que Epiménides no haya mentido).

a) Si Epiménides dice la verdad ->la frase es verdadera -> contradicción
b) Si Epiménides siempre miente -> la frase es mentira -> coincidencia

-> Epiménides miente y la frase es mentira, es decir no todos los cretenses mientes, sólo Epiménides y algunos más :sad4: (si estoy enfermo)

En cuanto al segundo texto, me ha parecido muy lioso, pero divertido al mismo tiempo
Las matemáticas no mienten, lo que hay son muchos matemáticos mentirosos.
Henry David Thoreau (1817-1862) Escritor, poeta y pensador.
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Re: Paradoja de Russell

Mensaje sin leerpor Hagamenon » Sab Nov 21, 2009 11:24 pm

goheim escribió:En cuanto al segundo texto, me ha parecido muy lioso, pero divertido al mismo tiempo


esa es la idea. si te paras un poco a pensarlo es bastante divertido. y lioso.

ya conocía la paradoja de epiménides. hofstadter la menciona varias veces, y el mismo es un auténtico maestro jugando con el lenguaje.


un saludo
¿Quién de nosotros no se ha sacrificado ya a sí mismo, por su buena reputación?
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Re: Paradoja de Russell

Mensaje sin leerpor Agustín » Mar Nov 24, 2009 5:07 pm

:sad4:

(¿Por qué habré leído este hilo?)
Imagen

¡RA, RA, RA!... mén
Desde que me asocié soy mejor persona... ¿Y tú a qué esperas?
http://www.iniciativaatea.org/asociarse.php
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Re: Paradoja de Russell

Mensaje sin leerpor Morzillo » Mar Nov 24, 2009 9:14 pm

Hagamenon, ¿por qué no puede haber paradojas? por la propia definición de lo que es una paradoja, es algo que no puede pasar, es algo contradictorio. Algo no puede ser verdadero y al mismo tiempo no ser verdadero. Por lo que significa NO, si no es verdadero, no es verdadero!!! cuac!!!
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Re: Paradoja de Russell

Mensaje sin leerpor Hagamenon » Mar Nov 24, 2009 9:46 pm

Morzillo escribió:Hagamenon, ¿por qué no puede haber paradojas? por la propia definición de lo que es una paradoja, es algo que no puede pasar, es algo contradictorio. Algo no puede ser verdadero y al mismo tiempo no ser verdadero. Por lo que significa NO, si no es verdadero, no es verdadero!!! cuac!!!


vale, vale. las paradojas no existen :salut: :salut: :salut: :salut:


por los cojones :lol:
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