Plutón, Venus, Frege y los misterios del lenguaje natural
Pablo de Lora
Universidad Autónoma de Madrid
Universidad Autónoma de Madrid
Los lenguajes naturales (el que estoy empleando en este momento) adolecen de algunas patologías bien conocidas, aunque no por ello menos desconcertantes cuando se inspeccionan con los anteojos del filósofo.
Tal vez la más célebre sea la vaguedad de los conceptos. Si bien no todos los lógicos estarían de acuerdo, parece natural decir que algo es o no es algo y tertium non datur (esta es la denominada «ley del tercio excluso», una de las leyes más importantes de la lógica de predicados clásica). Los griegos, sin embargo, pronto advirtieron que las cosas no eran tan simples. Es al lógico megárico Eubúlides de Mileto a quien se atribuye el célebre «razonamiento de Sorites», un razonamiento que nos hace concluir que no existen cosas tales como «montones de arena» («sorites» quiere decir montón en griego) o, alternativamente, que un grano de arena constituye un montón de arena, o que, en algunos casos algo no es ni blanco ni negro sino indeterminado (el vulgar «gris» con el que apuntalar nuestra híbrida toma de posición en las discusiones cotidianas). Eubúlides nos pregunta si billones de granos forman un montón de arena, ante lo cual nuestra respuesta será obviamente que sí. Ese mismo montón lo seguirá siendo aunque sustraigamos uno de los granos, y si proseguimos así, granito a granito, llegará un momento en el que un solo grano seguirá siendo un montón (pruebe el lector a proceder a la inversa para concluir que no existen cosas tales como montones de arena). Lo que el razonamiento o paradoja de Sorites muestra es que no es nunca sencillo determinar con nitidez el punto a partir del cual un objeto se convierte en otra cosa, dónde empieza la línea de la gordura, calvicie, altura, etc. En general, los conceptos de los lenguajes naturales son vagos cuando no somos capaces de listar con precisión absoluta todas las condiciones que algo debe reunir para engrosar la denotación del concepto.
En los últimos tiempos, los astrónomos se las han tenido que ver con la engorrosa vaguedad de los lenguajes naturales (ellos tan acostumbrados a la exactitud del lenguaje formalizado por excelencia, la matemática) cuando de definir lo que es un planeta se ha tratado. El resultado, como saben, ha consistido – y permítaseme la ironía- en expulsar a Plutón del planetario. Y ello no sin arduas discusiones semánticas más propias de juristas, seres afanados en determinar con exactitud (¡oh! ilusos) términos tales como «alevosía», que de científicos naturales. Para más inri, la controversia se ha saldado finalmente mediante votación. Algunos malévolos habrán pensado: «curioso método científico éste». En realidad, que Plutón sea o no un planeta no es un asunto científico, sino puramente nominal. ¡Qué más da cómo le cataloguemos! Los nombres comunes son convenciones lingüísticas, y los problemas de vaguedad se resuelven, como no, acudiendo a una precisión dada en un lenguaje no vago como el matemático. Si por definición decimos que un montón de arena debe tener un número X (siendo X un número entre 0 e infinito) de granos, o un objeto tales y cuales dimensiones para ser un planeta, se acabó el problema. La precisión será convencional también, pero nos salva la vida, o, al menos, nos evita estériles discusiones verbales.
Otro ilustre déficit de los lenguajes naturales que les quiero presentar es la ambigüedad, el fenómeno consistente en que un mismo término cuenta con distintos significados («banco», «puro»). En esos casos, es el contexto donde el término aparece el que nos aclarará su significado. ¿Y el fenómeno inverso? ¿Existen términos o proposiciones distintas con el mismo significado? La respuesta es obviamente sí, si pensamos en Venus, un planeta (de momento) al que durante muchos siglos los seres humanos se han referido con dos expresiones diferentes «la estrella matutina» y «la estrella vespertina» pues creían que de dos objetos distintos se trataba. Desde tiempo ha sabemos que son la misma, así que podemos concluir que:
(1)Venus=estrella matutina
(2)Venus=estrella vespertina
(2)Venus=estrella vespertina
Estos enunciados de identidad supusieron un buen quebradero de cabeza para quien pasa por ser el padre de la lógica matemática contemporánea: Gottlob Frege. La razón es, de nuevo, simple y su solución también conocida y harto discutida. De acuerdo con una vieja distinción debida a Kant, las proposiciones (tales como «Venus es la estrella matutina») pueden ser analíticas o sintéticas. La verdad de las primeras es «definicional», se basa en los significados de los términos empleados. Así, para comprobar que «solterón es el varón no casado», no tengo que desarrollar labor empírica alguna, cosa que sí me es exigida en cambio cuando me las veo con una proposición «sintética» tal como «Venus no contiene agua en su superficie». De las dos oraciones anteriores (1) y (2) yo puedo fácilmente concluir (3) Venus=Venus y (4) la estrella matutina= la estrella vespertina. Esas oraciones son equivalentes, pero su carácter no es el mismo. (3) es una proposición analítica, pero (4) no lo es. (3) no me informa de nada y (4) sí. Esta es la razón por la cual Frege (y después Russell), haciéndose eco de una larga tradición que se remonta a Platón, concluye que los nombres propios como «Venus» o «Shakespeare» sólo denotan (carecen de intensión o connotación), pues en otro caso nos veríamos obligados a admitir que existen enunciados de identidad («Venus es Venus» o «Shakespeare es Shakespeare») de naturaleza contingente (y parece que «Venus es Venus» es una verdad necesaria) o proposiciones sintéticas tales como «Venus es la estrella matutina» o «Shakespeare es el autor de Hamlet» de naturaleza necesaria (y parece que en ambos casos tales proposiciones son verdaderas a posteriori, el fruto de la investigación en el mundo).
En «Über Sinn und Bedeutung» («Sobre el sentido y la referencia», su célebre artículo de 1892) Frege nos ha legado además otra forma de concebir las relaciones de identidad que tanto a lógicos como a matemáticos conduce por las calles de la amargura. De acuerdo con el lógico alemán, expresiones tales como «estrella vespertina=estrella matutina» o «2×2=8-4» tienen la misma referencia («Venus», «4») pero distinto significado. ¿Cómo es ello posible? Porque en estos casos hemos de considerar que el mismo objeto (la referencia de las expresiones o su denotación) es presentado de modos diversos. A ese «presentar» a los objetos de distinto modo Frege lo llama «sentido» (Sinn). Corolario: los términos (de los lenguajes naturales o artificiales) expresan su sentido y denotan su referencia y ambas cosas (sentido y referencia) conjuntamente conforman su significado.
Frege fue el máximo inspirador de una corriente filosófica que no ha hecho gran fortuna: el logicisimo. Junto con otros célebres matemáticos (como David Hilbert) anhelaba poder reducir toda la matemática a unos cuantos axiomas lógicos. Para muchos filósofos de otras disciplinas, el espíritu fregeano ha permeado en la forma de un cierto estilo a la hora de afrontar los problemas filosóficos, una actitud que tiene que ver con la inquisición acerca del sentido en el que las palabras son empleadas en el discurso filosófico o vulgar. Muchos pensamos que en numerosas ocasiones la tarea filosófica prioritaria – y para algunas única- es desvelar esos «modos de ser presentados los objetos o ideas», analizar el lenguaje natural con el que nos referimos al mundo y a nosotros mismos, pues la experiencia nos revela que, como en el caso de Venus, no pocos puzzles metafísicos son sólo aparentes; no pocas de las dificultades anunciadas a bombo y platillo no son tales sino «pseudoproblemas» y no pocos de los misterios filosóficos son tan sólo el resultado de haber llenado con hojarasca semántica el patio de nuestros pensamientos.
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