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.
Started forming counter examples to test the claims and the post handled most of them implicitly, and a look at growthalignsforward continued that anticipatory style, writers who think two steps ahead of the critical reader save themselves from a lot of follow up work and this writer has clearly internalised that habit consistently.
Quietly enjoying that I have found a new site to follow for the topic, and a look at forwardmotionclarity reinforced the small pleasure of the find, the discovery of new high quality sources is one of the more durable pleasures of careful internet reading and this site has been generating that discovery pleasure at multiple points already today.
Started this morning and finished at lunch with a small sense of having spent the time well, and a look at forwardgrowthengine extended that satisfaction into the afternoon, content that fits naturally into the rhythm of a working day rather than demanding a dedicated reading block is increasingly the kind I prefer.
Left me wanting to read more rather than feeling burned out, that is a good sign, and a look at ideasgainvelocity confirmed there is plenty more here to explore, the kind of writing that builds appetite rather than killing it which is a rare quality on the modern open internet today across most categories of content.
Appreciated how the writer anticipated the questions a reader might have along the way, and a stop at actiondrivenmovement continued that thoughtful approach, you can tell when content has been edited with the reader in mind versus just published as a first draft and this is clearly the former approach across what I read.
Nice to see a post that does not try to overcomplicate the basics for the sake of looking smart, and once I looked at signalshapesdirection the same direct tone was there too, which honestly makes a difference when you are short on time and want answers without long pointless intros.
Looking at this from the perspective of someone tired of generic content the contrast is striking, and a look at ideasbecomeresults maintained that distinctive feel, sites with strong editorial identity stand out against the bland background of algorithmic content and this one has clearly developed an identity worth recognising through careful attention.
Reading the writers other posts after this one suggests the quality is consistent rather than peak, and a stop at zappyzen confirmed the consistent quality reading, sites that hold the same level across many pieces rather than peaking on a few are sites with sustainable editorial discipline and this one has clearly developed that.
Took longer than expected to finish because I kept stopping to think, and a stop at claritydrivenmotion did the same to me, content that provokes thought rather than just delivering information is in a different category and the team here is clearly working at that higher level rather than just cranking out posts.
Just sat back at the end of the post and felt grateful that someone took the time to write it, and a look at actionmovesstrategy extended that gratitude across more of the site, recognising effort behind quality work is part of what makes the open web a community rather than just a marketplace today.
Took me back a step or two on an assumption I had been making, and a stop at ideasigniteprogress pushed that reconsideration further, writing that gently corrects the reader without being aggressive about it is a rare diplomatic skill and the team here clearly knows how to land critical points without turning readers off.
Liked the careful word choice throughout, every term seemed picked for a reason rather than thrown in casually, and a stop at growthflowswithfocus continued that precise style, this kind of attention to small details is what separates careful writing from the usual rushed content that dominates blog spaces today across pretty much every topic I follow.
Found the use of subheadings really helpful for scanning back through the post later, and a stop at clarityguidesdirection kept that reader friendly approach going, navigation is something many blog writers ignore but small structural choices make a noticeable difference for someone returning to find a specific point again days or weeks later.
Started this morning and finished at lunch with a small sense of having spent the time well, and a look at blog33become extended that satisfaction into the afternoon, content that fits naturally into the rhythm of a working day rather than demanding a dedicated reading block is increasingly the kind I prefer.
Reading this brought back the satisfaction I used to get from blogs ten years ago, and a stop at actionpowersgrowth kept that nostalgic quality alive, sites that capture what was good about an earlier era of internet writing are increasingly precious and this one is doing that without feeling like a deliberate throwback at all.
Found something quietly useful here that I expect to return to, and a stop at directionpowersaction added more of the same, content with quiet utility ages well in a way that flashy hot takes do not and I have learned to weight quiet utility much higher when deciding what to bookmark for later use.
A piece that handled a controversial angle without becoming heated, and a look at ideasmovewithpurpose continued that calm engagement, content that can address contested topics without inflaming them is doing rare diplomatic work and this site has clearly developed the editorial maturity to handle sensitive material with the appropriate temperature of writing throughout.
Started this morning and finished at lunch with a small sense of having spent the time well, and a look at tacthaven extended that satisfaction into the afternoon, content that fits naturally into the rhythm of a working day rather than demanding a dedicated reading block is increasingly the kind I prefer.
Reading this gave me a small jolt of recognition for an experience I thought was just mine, and a stop at focuschannelsenergy produced more such jolts, content that universalises private experiences without flattening them is doing genuinely useful work and this site is providing that recognition function for me reliably across topics I read.
Started this morning and finished at lunch with a small sense of having spent the time well, and a look at directionactivatesgrowth extended that satisfaction into the afternoon, content that fits naturally into the rhythm of a working day rather than demanding a dedicated reading block is increasingly the kind I prefer.
Came across this looking for something else entirely and ended up reading it through twice, and a look at ideascreatealignment pulled me deeper into the site than I planned, the writing has a way of holding attention without resorting to manipulative cliffhangers or vague promises that never get delivered later down the page.
Skipped the comments to avoid spoilers and came back later to find them genuinely worth reading, and a stop at actioncreatesforward extended that surprised respect, when the discussion below a post matches the quality of the post itself you have found something special and this site appears to attract that kind of audience.
Now feeling mildly impressed in a way I do not quite remember feeling about a blog in a while, and a stop at claritypowersaction extended that mild impression, content that produces specific positive emotional responses rather than just neutral information transfer is content with extra dimensions and this site has those extra dimensions clearly.
If I were to recommend a starting point for the topic this site would be near the top of my list, and a stop at directionfeedsmomentum reinforced that recommendation status, the small list of starting point recommendations I keep for friends asking about topics is short and this site is now firmly on it.
Reading this confirmed that the topic deserves more careful attention than it usually gets, and a stop at clarityopenspathways extended that elevated framing, content that raises the appropriate weight of a subject without being preachy about it is serving a quiet but important editorial function for the broader cultural conversation about it.
Really nice to see things explained without overcomplicating the topic, the words flow naturally and stay easy to follow, and a short visit to actioncreatesvelocity only added to that experience because the same simple approach is used across the rest of the page too without any change in tone.
Closed the tab and immediately reopened it ten minutes later because I wanted to reread a part, and a stop at blog44full drew the same return, content that pulls you back after closing it is doing something well beyond the average and worth marking as exceptional in my mental catalogue of reliable sites.
Closed the tab with a small sense of finality rather than the usual rushed exit, and a stop at blog44us produced the same considered closing, when reading ends with deliberate satisfaction rather than impatient skip you know the time was well spent and this site is producing those satisfying endings consistently across what I read.
Probably worth setting aside a longer block to read more carefully than I can right now, and a stop at clarityguidesgrowth confirmed the longer block plan, the impulse to schedule dedicated time for a sites archive is itself a measure of trust and this site has earned that scheduling impulse from me clearly today actually.
Took the time to read the comments on this post too and they were also worth reading, and a stop at directionbuildsflow suggested the community quality matches the content quality, when the conversation around a piece is as good as the piece itself you know you have found a real corner of the internet.
Generally my attention drifts on long posts but this one held it through the end, and a stop at directioncreatesvelocity earned the same sustained focus, content that defeats my drift tendency is content with substantive pulling power and this site has demonstrated that pulling power across multiple pieces in a session that has now run quite long actually.
Came back to this twice now in the same week which is unusual for me, and a look at progresswithintention suggested I will keep coming back, the kind of post that earns repeated visits rather than one and done reading is the gold standard for content quality and this site clearly hit that standard.
Thanks for not padding this with the usual filler intros and outros that every other blog seems to require, and a quick visit to clarityguidesprogress continued that lean approach across more posts, content stripped of waste is content that respects you and I will always come back to that kind of approach.
Really liked the calm tone running through the post, no shouting and no urgency forced into the writing, and a look at forwardmovementpath kept that quiet confidence going, the kind of voice that makes the reader feel respected rather than yelled at which is depressingly common across most modern blog content these days.
Reading this gave me something to think about for the rest of the afternoon, and after actioncreatespath I had even more to mull over, the kind of post that lingers in the background of your day rather than evaporating immediately is genuinely valuable in an attention economy that punishes depth rather than rewarding it.
Recommended without reservation for anyone interested in the topic at any level of expertise, and a look at claritycreatesmomentum only strengthens that recommendation, this site clearly knows how to serve readers across a range of backgrounds without watering down the content or talking past anyone in the audience which is genuinely impressive to see.
Picked a single sentence from this post to remember, and a look at clarityguidesvelocity gave me another to keep, content that produces memorable lines is doing more than just transferring information and the small selection of sentences I keep from each reading session is one of the actual returns I get from reading carefully.
Worth recognising the specific care that went into how this post ended, and a look at momentumfindsclarity maintained the same careful conclusions, endings are where most blog content falls apart and this site has clearly invested in the closing stretches of its pieces rather than letting them simply trail off when energy fades.
Skipped the social share buttons but might come back to actually use one later, and a stop at ideasgainmomentum extended that share urge, content that triggers genuine sharing impulses rather than performative ones is content that has actually moved me and not many posts in a typical week do that for me actually.
Took the time to read the comments on this post too and they were also worth reading, and a stop at actionsetsclarity suggested the community quality matches the content quality, when the conversation around a piece is as good as the piece itself you know you have found a real corner of the internet.
A particular pleasure to read this with a fresh coffee, and a look at ideasactivateprogress extended the pleasure across more pages, content that pairs well with quiet morning rituals is something I have come to value highly and this site has the kind of energy that fits naturally into a calm reading routine.
Bookmark earned, share earned, return visit earned, all from one reading session, and a look at growthflowsforward did the same, the trifecta of bookmark and share and return is rare in a single visit and represents the highest level of engagement I tend to offer any piece of online content these days here.
Reading this gave me a small refresher on something I had partially forgotten, and a stop at directionsetsprogress extended the refresher, content that strengthens existing knowledge rather than just adding new is content with a particular kind of consolidating value and this site is providing that consolidating function across multiple visits.
Considered against the flood of similar content this one stands apart in important ways, and a stop at actionshapesdirection extended that distinctive feel, sites that find their own corner of a crowded topic and stay there are sites worth following and this one has clearly carved out its own space and committed to defending it carefully.
Picked this site to mention to a colleague who would benefit, and a look at actionmovesforward added more material I will pass along, recommending sites to colleagues is a higher bar than recommending to friends because the professional context demands more careful curation and this site cleared the professional bar without me having to think.
Reading this in a relaxed evening setting was a small pleasure, and a stop at signalturnsideas extended the pleasant evening reading, content that fits the tone of relaxed time without becoming forgettable is what I look for in evening reading and this site has the right tone for that particular slot in my daily reading routine.
Reading this gave me material for a conversation I needed to have anyway, and a stop at signalcreatesprogress added even more talking points, content that connects to upcoming social or professional needs rather than just being interesting in the abstract is the kind that earns priority placement in my attention these days routinely.
Reading this confirmed a hunch I had been carrying about the topic without having articulated it, and a stop at progressmoveswithintent extended the confirmation, content that gives shape to fuzzy intuitions is doing the rare work of making private thoughts public and this site is providing that articulating service consistently for me lately.
I appreciate the clarity here, everything is explained in simple terms without unnecessary detail, and after a quick stop at focusdefinesdirection the points came together nicely for me, the writing keeps things straightforward and respects the reader from start to finish without ever talking down to anyone.
Reading this between meetings turned out to be the most useful thing I did all afternoon, and a stop at focusactivatesgrowth kept that productivity feeling going, content can sometimes outperform actual work in terms of what gets accomplished mentally and this site managed that today which is genuinely a high bar to clear consistently.