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.
Better than most of the writing I have come across on this topic recently, simpler and more direct, and a look at ideamotionlab continued in that same way, a real outlier in a crowded space full of repetitive content that says little while taking up a lot of reader time today which is unfortunate.
Now feeling the small relief of finding writing that does not condescend, and a stop at businessbondnetwork extended that respect for readers, content that treats its audience as capable adults rather than as people to be managed produces a different reading experience and this site has clearly chosen the respectful approach across all pieces.
A piece that handled multiple complications without becoming confused, and a look at growthalignment continued that organisational clarity, holding multiple threads in a single piece without losing any of them is a sign of skilled writing and this site has clearly developed the editorial discipline to manage complexity without sacrificing readability throughout.
One of the more thoughtful posts I have read recently on this topic, and a stop at actionintelligence added even more weight to that impression, this is genuinely good content that holds its own against far better known sites in the same space without trying to imitate any of them at all which I appreciate.
Solid recommendation from me to anyone working in the area, the perspective here is grounded, and a look at collaborativegrowthcircle adds even more useful angles, the kind of site that becomes a reference rather than just a one time read which is a higher bar than most blogs ever reach today on the modern web.
Really appreciate that the writer did not overstate the importance of the topic to make the post feel weightier, and a quick visit to unitypathbond maintained the same modest framing, content that is honest about its own scope rather than inflating itself is the kind I trust and return to repeatedly over time.
Thanks for keeping things clear and to the point, that is honestly hard to find online these days, and after reading through focusdefinesdirection the message stayed consistent which makes me trust the information being shared more than I usually do on similar pages that cover this same kind of topic.
Closed the post with a small satisfied sigh, and a stop at forwardmotionactivated produced the same gentle exhale, content that ends well is content that respects the rhythm of reading and the writers here have clearly thought about how their pieces close rather than just trailing off when they run out of things to say.
A piece that exhibited the kind of patience that good writing requires, and a look at trustedbondcircle continued that patient quality, hurried writing is easy to spot and this site reads as having been written without time pressure which produces a different feel than the rushed content that dominates much of the modern blog space.
Reading this confirmed that my time researching the topic in other places had not been wasted, and a stop at futurepartnershub extended the confirmation, when independent sources agree that is a useful signal and this site is one of the more reliable sources I have found for cross checking what I read elsewhere on similar subjects.
One of the more thoughtful posts I have read recently on this topic, and a stop at directionalshift added even more weight to that impression, this is genuinely good content that holds its own against far better known sites in the same space without trying to imitate any of them at all which I appreciate.
Well done, the kind of post that makes you slow down and actually read instead of skimming for keywords, and a look at focuscreatesmovement kept me reading carefully too, that is a sign of writing that has been crafted rather than churned out for an algorithm to see today and tomorrow.
Started this morning and finished at lunch with a small sense of having spent the time well, and a look at claritymomentum 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.
Looking for similar voices elsewhere has come up empty in my recent searches, and a stop at focusbuildsvelocity extended the search frustration, the rare site that does what no other does in quite the same way is precious and this one has clearly developed a particular approach that I have not been able to find duplicates of.
Now setting up a small reminder to revisit the site on a slow day, and a stop at actiondirection confirmed the reminder was a good idea, planning return visits is a small organisational act that signals trust in ongoing quality and this site has earned that planned return through consistent performance across the pieces I have read so far.
Polished and informative without feeling overproduced, that is the sweet spot, and a look at claritybuildsprogress hit it again, you can tell when a site has been built with care versus thrown together for the sake of having something to put online and this is clearly the former approach taken by the team.
A piece that built up gradually rather than front loading its main points, and a look at directionalmap maintained the same gradual structure, content that trusts the reader to reach conclusions through accumulating reasoning is more persuasive than content that announces conclusions and then defends them and this site uses the persuasive approach.
Excellent post, balanced and well organised without showing off, and a stop at focuschannelsenergy continued in that same vein, this site has clearly figured out the formula for content that works for readers rather than for search engine ranking signals which is harder than it sounds today and worth real recognition from anyone.
Vague feelings of recognition kept surfacing as I read because the writing names things I have been thinking, and a look at trustedalliancenet produced more of those recognition moments, content that gives shape to private intuitions is content that makes me feel less alone in my own thinking and this site has that effect.
Different feel from the algorithmically optimised posts that dominate the topic, and a stop at signalactivatesgrowth reinforced that human touch, you can tell when a site is being run by someone who reads what they publish versus someone just hitting submit and moving on quickly to the next assignment without checking the result.
Felt like I was reading something written by someone who actually thinks about the topic rather than reciting it, and a look at strategyprogression reinforced that impression, the difference between recited content and considered content is huge and this site clearly belongs to the latter category which I appreciate as a careful reader looking for substance.
Reading this gave me a quiet moment of intellectual pleasure that I had not been expecting, and a stop at momentumstructure extended that pleasure across more pages, the unexpected reward of stumbling into careful writing is one of the small ongoing pleasures of reading the open web and this site is delivering it reliably.
Now feeling confident enough in this site to use it as a reference point for evaluating others on the same topic, and a look at ideamapper continued the comparison friendly quality, sites that serve as quality benchmarks for their topic are precious and this one has clearly become a benchmark for me on this particular subject area.
The headings made navigating the post simple even when I needed to find a specific section quickly, and a look at actiondrivenprogress continued the same thoughtful structure, small details like clear headings show that someone is actually thinking about how the reader uses the page rather than just filling it for length alone.
Reading this triggered a small change in how I think about the topic going forward, and a stop at visiondrivenpartnership reinforced that subtle shift, the rare content that actually moves my thinking rather than just confirming or filling it is the kind I most value and this site is providing that kind of impact today.
After reading several posts back to back the consistent voice across them is impressive, and a stop at bondedcapitalpartners continued that voice consistency, sites that maintain a single coherent voice across many pieces by potentially many writers represent serious editorial discipline and this one has clearly developed the institutional consistency needed for that.
Quality writing that respects the reader’s intelligence without overloading them, and a quick look at forwardmotionengine reflected that approach, a balanced thoughtful site that earns trust by being consistent rather than by shouting about how trustworthy it is which is the usual approach online sadly across most content categories.
Reading this triggered a small but real correction in something I had assumed, and a stop at strategyhub extended that corrective effect, content that updates my beliefs through evidence rather than rhetoric is content with intellectual integrity and this site has earned that label consistently across the pieces I have read so far today.
Liked the way the post handled the final paragraph, no neat bow but no abrupt cutoff either, and a stop at bondedstrength continued that thoughtful ending pattern, endings are hard and most blog writers either over engineer them or skip them entirely and this site has clearly figured out a sustainable middle approach.
Quality writing that respects the reader’s intelligence without overloading them, and a quick look at longtermvaluebond reflected that approach, a balanced thoughtful site that earns trust by being consistent rather than by shouting about how trustworthy it is which is the usual approach online sadly across most content categories.
Liked the post enough to read it twice and the second read found new things, and a stop at signalactivatesgrowth similarly rewarded the second look, content with hidden depths that only reveal themselves on careful rereading is the rare kind that earns lasting respect rather than fleeting first impressions only briefly held.
Skipped the comments section but might come back to read it, and a stop at progressblueprint hinted at a quality reader community, sites where the comments are worth reading separately from the post are increasingly rare and signal a particular kind of audience that has grown around the editorial vision over time gradually.
Compared to the usual results for this kind of search this site stands well above the average, and a quick visit to strategicconnectionbond kept the standard high, you can tell within seconds whether a site is going to waste your time or actually deliver and this one clearly delivers without any false starts.
Solid recommendation from me to anyone working in the area, the perspective here is grounded, and a look at signalfeedsmomentum adds even more useful angles, the kind of site that becomes a reference rather than just a one time read which is a higher bar than most blogs ever reach today on the modern web.
Liked the post enough to read it twice and the second read found new things, and a stop at directionalintelligence similarly rewarded the second look, content with hidden depths that only reveal themselves on careful rereading is the rare kind that earns lasting respect rather than fleeting first impressions only briefly held.
Now adding the writer to a small mental list of voices I want to follow, and a look at claritybuilderhub reinforced that follow intention, the few writers whose work I actively track are writers who have demonstrated sustained quality and this writer has clearly demonstrated that sustained quality across the pieces I have sampled here today.
Looking through other posts here the consistency is what makes the site valuable rather than any single piece, and a stop at longtermtrustnetwork extended that consistency observation, sites whose value lies in the ongoing pattern rather than in standout posts are sites I trust more deeply and this one has clearly built that kind of trust.
Bookmark earned, share earned, return visit earned, all from one reading session, and a look at directionchannelsprogress 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.
Now noticing that the post benefited from being neither too short nor too long for its content, and a look at growthmoveswithstructure continued that calibration of length, sites that match length to content rather than padding to hit some target are sites that respect both their material and their readers and this site does both.
Genuine reaction is that I will probably think about this on and off for a few days, and a look at growthflowswithclarity added fuel to that, the best content lingers in your head after you close the tab rather than evaporating immediately and this site clearly knows how to write that kind of memorable content.
Quietly the post solved something I had been turning over without quite knowing how to phrase the question, and a look at actionmomentum extended that quiet solving, content that addresses unformulated needs is content with reader insight and this site has demonstrated that insight at a high rate across the pieces I have read recently.
Following a few of the internal links revealed more posts of similar quality, and a stop at directionalprocess added more to that growing pile, sites where internal links lead to more good content rather than to more of the same recycled material are sites with depth and this one has clearly built that depth carefully.
Skimmed first and then went back to read carefully, and the careful read paid off in places I had missed, and a stop at actionpathfinder got the same treatment, the rare site whose content rewards a second pass is content I want more of in my regular rotation rather than disposable single read articles.
Spent a few minutes here and came away with a clearer picture of the topic, the writing keeps things simple without dumbing them down, and after a stop at actioncreatesforwardpath the rest of the points lined up neatly which is something I appreciate when I am short on time and need answers fast.
In the middle of an otherwise scattered day this post landed as a moment of focus, and a stop at unitytrustbond extended that focused feeling across more pages, content that anchors a fragmented day rather than contributing to the fragmentation is content with real centring effect and this site is providing that anchoring function for me.
Quietly building a case in my head for why this site deserves more attention than it currently seems to receive, and a look at focusbuildsresults reinforced the case, the gap between quality and recognition is a recurring frustration in independent online content and this site is one of the cases that seems particularly egregious to me today.
Felt mildly happier after reading, which sounds silly but is true, and a look at focusguidesmovement extended that small mood lift, content that improves rather than degrades my mental state is content I want more of and the cumulative effect of reading sites that lift versus sites that drag is real over time.
Bookmark added in three places to make sure I do not lose the link, and a look at bondedstability got the same redundant treatment, sites I am afraid to lose are the rare keepers and this is clearly one of them based on what I have read so far across this and a couple of related posts.
Now I want to find more sites like this but I suspect they are rare, and a look at actionconstructor extended that thought, the few sites that meet this quality bar are precious specifically because they are rare and finding others like them is one of the ongoing projects of careful internet curation across the years.
Now feeling that this site is the kind I want to make sure does not disappear, and a look at momentumplanning reinforced that quiet protective feeling, the rare sites whose disappearance would actually matter to me are the sites I want to support through return visits and recommendations and this one has joined that small protected list.