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.
Excellent execution from start to finish, the post never loses its rhythm and the points stay sharp, and a quick stop at momentumworks kept the same level going, consistency like this across a site is the marker of a serious operation rather than a casual side project running on autopilot somewhere else.
Now appreciating that the post did not require external context to follow, and a look at growthmovement maintained the same self contained quality, content that respects new visitors by being readable without prerequisites is content with broader accessibility and this site has clearly invested in keeping each piece reader friendly for fresh arrivals.
Honestly this kind of writing is why I still bother to read independent sites, and a look at collectivevaluebond extended that broader reflection, the few sites that justify continued attention to non algorithmic content are sites like this one and finding them periodically is enough to keep my reading habits oriented toward independent rather than aggregated content.
The use of plain language without dumbing down the topic was really well done, and a look at actionunlocksvelocity continued in that same accessible style, this is something many technical writers fail at because they either confuse their readers or condescend to them but here neither problem appears at all which is impressive really.
Halfway through I knew I would finish the post, and a stop at trustedleadersbond also held me through to the end, content that signals its quality early and then sustains it is content with real internal consistency and this site has clearly figured out how to maintain quality from opening sentence through to closing thought.
Bookmark added without hesitation after finishing, and a look at progressigniter confirmed I should bookmark the homepage too rather than just this page, the rare site that earns category level trust rather than just single article approval is the kind I want to rely on across many different topics over time.
Going to come back when I have more time to read carefully, the post deserves more than a quick scan, and a stop at ideatraction reinforced that, this is the kind of site that rewards a slower read which is hard to find in this fast paced corner of the internet but really worthwhile.
This one is staying open in a tab for the rest of the day so I can come back and re read certain parts, and a look at clarityengine suggests I will be doing the same with a few more pages here too, this is going to be a deep dive over the coming hours.
Looking for similar voices elsewhere has come up empty in my recent searches, and a stop at claritydrivenprogress 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 adding a small note in my reading log that this site is one to watch, and a look at directionfeedsenergy reinforced the watch status, the few sites I track deliberately rather than encounter accidentally are sites I expect ongoing returns from and this one has cleared the bar for that elevated tracking based on what I read.
Thanks for putting in the work to make this approachable, plenty of sites cover the same ground but most do it badly, and a quick visit to signalcreatesflow confirmed this one stands apart, simple language and useful examples without anyone trying to sell me anything along the way which I really appreciated.
Even just sampling a few posts the consistency is what stands out, and a look at collectivetrusthub confirmed the broader pattern, sites where every piece I sample lives up to the standard set by the others are sites with serious quality control and this one has clearly invested in whatever editorial process produces that consistency reliably.
Picked up several practical tips that I plan to try out this week, and a look at directioncreatesalignment added a few more I will be testing alongside, content with practical hooks that connect to my actual life is the kind that earns my repeat attention rather than the merely interesting that I forget within a day.
Reading the writers other posts after this one suggests the quality is consistent rather than peak, and a stop at smartpartnershiphub 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.
Left me wanting to read more rather than feeling burned out, that is a good sign, and a look at actionoptimizer 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.
Reading this gave me a small mental break from the heavier reading I had been doing, and a stop at collectivebondhub extended that lighter feel, content that provides relief without becoming trivial is harder to produce than people realise and this site has clearly figured out how to be light without being shallow at all.
Reading this triggered a small change in how I think about the topic going forward, and a stop at actionpowersmovement 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.
Even across multiple posts the writers voice has remained consistent in a way I appreciate, and a stop at ideasbecomeprogress continued that voice, sites that maintain editorial consistency across many pieces have something most sites lack and this one has clearly worked out how to keep its voice steady across what reads as a growing archive.
Generally my comment to other readers about new sites is to wait and see but for this one I would jump to recommend now, and a look at visiontrigger reinforced that early recommendation, the speed at which a site earns my recommendation is itself a quality signal and this one has earned mine quickly clearly.
If I were grading sites on this topic this one would receive high marks, and a stop at growthflowsintentionally continued earning those high marks, the informal grading I do mentally for content sources is something I take seriously even though it is informal and this site has been receiving consistent high marks across multiple sessions today.
Refreshing to read something where the words actually mean something instead of filling space, and a stop at clarityroutehub kept that going, the writing here trusts the reader to follow along without endless repetition or constant reminders of what was already said earlier in the post which I appreciate.
Genuinely useful read, the points are practical and easy to apply right away, and a quick look at trustedconnectionhub confirmed that this site is consistent in that approach, looking forward to digging through the rest of it when I get the chance to sit down properly later in the week or this weekend.
Now recognising the post as a rare example of careful writing on a topic that mostly receives careless treatment, and a stop at strategicunitygroup extended that contrast with the average elsewhere, content that highlights how much the average is settling for low quality is content that has both internal merit and external value as a benchmark.
Genuinely changed how I think about a small piece of the topic, which does not happen often online, and a look at progressunlockedforward added another nudge in the same direction, the kind of writing that earns a small mental shift rather than just confirming what you already thought before reading is a sign of careful thought.
Came in skeptical of the angle and left mostly persuaded, and a stop at strategybuilder pushed me a bit further in the same direction, content that can move a critical reader by argument rather than rhetoric is rare and worth pointing out because it indicates real substance underneath the surface presentation here.
Just nice to read something that does not feel like it was assembled from a content brief, and a stop at claritymapping kept that handcrafted feel going, you can tell when a real human with real understanding is behind the words versus a templated piece churned out for an algorithm to find.
Liked that the post left some questions open rather than pretending to settle everything, and a stop at actionfuelsmomentum continued that intellectual honesty, content that respects the limits of its own claims is more trustworthy than content that overreaches and this site has clearly figured out which positions it can defend confidently.
Now noticing the post fit a particular gap in my reading without my having articulated the gap before, and a look at signalclarifiesdirection extended that gap filling effect, content that meets needs I had not consciously formulated is content with reader insight and this site has clearly developed that anticipatory editorial sense across many pieces.
A piece that did not lecture even when it had clear positions, and a look at businessrelationshiphub maintained the same teaching without preaching tone, finding the line between informing and lecturing is hard and most sites land on the wrong side of it but this one has clearly figured out how to inform without becoming preachy.
Now feeling the quiet pleasure of finding writing that takes itself seriously without being self serious, and a stop at progressmovessteadily extended that subtle pleasure, the gap between earnest and pretentious is fine and this site has clearly chosen to land on the earnest side without slipping over into pretentious which is impressive.
Now setting up a small reminder to revisit the site on a slow day, and a stop at growthmovesstrategically 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.
During a quiet evening reading session this provided just the right depth without being heavy, and a stop at directionfuelsgrowth maintained the same evening appropriate weight, content with depth that does not exhaust the reader is content with editorial calibration and this site has clearly figured out how to be substantial without being demanding all the time.
Worth marking the moment when reading this clicked into something useful for my own work, and a look at smartgrowthbond extended that practical click, content that connects to my actual life rather than just being interesting is content with the highest kind of value and this site is generating that connection at a high rate.
A piece that demonstrated competence without performing it, and a look at intentionalvector maintained the same self assured but unshowy register, the gap between competence and performance of competence is one I track and this site has clearly chosen to demonstrate rather than perform which I find much more persuasive as a reader.
Will be passing this along to a few people who would benefit from the perspective shared here, and a stop at directionalsystems only added to what I will be sharing, this kind of generous content deserves to circulate widely rather than getting buried in some search engine algorithm tweak that pushes it down the rankings.
A thoughtful piece that did not strain to be thoughtful, and a look at ideasgaintraction continued that effortless quality, when thinking shows up in writing without the writer drawing attention to it you know you are reading something genuinely considered rather than something performing the appearance of consideration which is also common online.
Probably this is one of the better quiet successes on the open web at the moment, and a look at actiondrivesprogress reinforced that quiet success quality, sites that are doing well without making a noise about doing well are the sites I most respect and this one has clearly chosen the quiet success path consistently throughout.
Walked away in a slightly better mood than when I started reading, that says something about the writing, and a stop at elitebusinessbond kept that going, content that leaves you feeling more capable rather than overwhelmed is the kind I keep coming back to again and again over the years and across many topics.
Thanks for taking the time to write this, it is clear that some thought went into how each point would land, and after I went through progressalignment I had a better grip on the topic, real value without the usual marketing noise people have to put up with online when searching for answers.
Felt mildly happier after reading, which sounds silly but is true, and a look at visionexecution 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.
Worth flagging this post as worth a careful read rather than a casual skim, and a stop at collaborativegrowthcircle earned the same careful approach, the few sites that warrant slower reading are sites I now treat differently from the daily content stream and this one has clearly moved into that elevated treatment category.
Reading this prompted a small redirection in something I was working on, and a stop at progressflowsbyfocus extended that redirecting influence, content that affects my actual work rather than just my thinking has the highest practical impact and this site is providing that level of influence for me at a sustainable rate apparently.
Reading this with my morning coffee turned into reading the related posts with my morning coffee, and a stop at progressadvancescleanly stretched the morning further, content that pulls breakfast into a reading session rather than just accompanying it is content that has earned a higher claim on my attention than the average article does.
Compared to the usual results for this kind of search this site stands well above the average, and a quick visit to longtermvaluebond 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.
However many similar pages I have read this one taught me something new, and a stop at focusdesign added more new material, content that contributes genuinely fresh information rather than recycling what is already widely available is content with real informational value and this site is providing that informational freshness at a notable rate.
Without comparing too aggressively to other sources this one stands out for the right reasons, and a look at collaborativepowergroup continued that distinctive quality, content that distinguishes itself through substance rather than style tricks is content with lasting differentiation and this site has clearly chosen substance based differentiation as its core editorial strategy.
My friends would appreciate a few of these posts and I will be sending links accordingly, and a look at progressmoveswithclarity added more pages to my share queue, content that earns shares to specific people in specific contexts is content with social utility and this site is generating those targeted shares from me consistently lately.
Will be back, that is the simplest way to say it, and a quick visit to clarityunlocksvelocity reinforced the decision, this site has earned a spot in my regular rotation alongside a few other reliable places I check when I want something genuinely informative without all the usual modern web noise getting in the way.
Skipped a meeting reminder to finish the post, and a stop at focuschannel held me past another reminder, when content beats meetings the writer is doing something extraordinary because meetings have institutional support behind them and yet good writing can still occasionally win that competition for attention which I find heartening today.
Honestly impressed by the consistency of voice across what I have read so far, and a quick visit to trustedrelationshipnet continued that consistent feel, when a site reads like one careful person rather than a committee the experience is more rewarding for the reader who notices these subtle editorial details over time.