Monday, August 14, 2023

An Exoteric (and Admittedly Dissatisfying) Approach to the "Liar's Paradox" and Its Significance

 

My favorite aspect of philosophy is how some time-honored problem that supposedly defines the parameters of the human condition can be rephrased in such a way that defies our ability to predict.  I like to think of philosophy as a unique conversation that probably will never stop: wherever there is unbounded curiosity, there will be the same kinds of conversations.

One such example, the much discussed “Liar’s Paradox”

The Liar Paradox - Stephen Read - Bing video

a problem that is universally appreciated from the intentionally obscure Zen Koans to Sancho Panza of Cervantes' imagination (For students of literature, Panza famously approaches the Paradox at the bridge in the castle gallows by hanging the “bad” half of the man who lied and allowing the “good” half to live!)

While often amusing and at times bewitching, these semantic "insolubles" are rather troubling, Pr. Read points out.  

How are we to resolve the postcard that says two opposing things on either side (see the video)?  More pressingly, what do paradoxes ultimately suggest about truth and its opposite?  Are we to believe as do some ancient sages that “truth” and “false” are transitory distinctions that rest upon what people are willing to believe in any moment?  Epistemically, can we step into the same river of Truth twice?

Eubulides  (4th century BCE) is the first in recorded history to write about these concerns, we are told, but this issue has not been resolved since his days.  

The problem instead has just migrated to other geographies of the intellect, including the logical foundation of mathematics itself.

Since then, many such puzzles are increasingly sophisticated and formal in the past century (with the hope that a mathematical approach would lend clarity), but we forget that we often use “paradox” in non-technical ways too:

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4214609/

This article above by the NIH tries to resolve a “stress-eating paradox”: namely, that “stress can lead to BOTH hyperphagia AND hypophagia.”  

You don’t need to know Greek that stressed-out people can obviously either eat too much or too little— the common element being a deviation from their dietetic norm (and presumably, the happy medium that is health).

In practice (where it counts most), this case of over- or under-eating suggests that paradoxes usually belie oversimplifications.  That hyperphagia and hypophagia can result from stress might seem contradictory (and thus unhelpful pseudo-“knowledge”) only if you assume everyone’s bodies and genetic makeup, environment, or what have you were the same.  However, once you recognize a multitude of variables that shape outcomes, including hunger, then apparent “paradoxes” are really just a misunderstanding of the situation.  To use a ten-dollar word, it’s the sign of reductionism.  Paradoxes usually indicate that one’s model of this slice of reality is probably a bit too simple.

Now, if this is true of medicine, then what of paradoxes at their more abstract?  How should we encounter or anticipate them in general?  

Medieval minds typically understood paradoxes as symptomatic of unsound approaches to reasoning per se.  One camp even believed that paradoxes were non-propositions that had grammatical content without any logical assertion behind them: to use a more modern example, try to imagine “colorless green ideas.”  Instinctively, you must realize that you can’t.  In this instance, you are abusing grammar to say something semantically nonsensical.  The Liar's Paradox, according to certain medieval thinkers, is committing a similar kind of abuse but not on the grammatical level, but on the logical level of propositions.

This medieval approach to the problem is similar to how modern philosophers approach tautologies.  If the liar in our paradox asserted “p and ~p”, then that is similar to a weatherman saying “tomorrow, it will either rain or not.”  That much is true because, well, it is always true (regardless of either facts or situations): how could it be otherwise?  Now, if something is always true (say, that “a being is something that exists”), then it doesn’t NEED to be said.  It is, in short, unrelated to our concerns and unproductive to say the least.  It tries to use logic in ways that it should not be used. It fails to track onto reality at the level of propositions, or assertive statements of fact (as opposed to mere sentences).  It is fundamentally unserious.  What moderns have said about tautologies applies to what the Cassationists said about paradoxes.

Of greater consequence: The supposed “liar” in the “Liar’s Paradox” is also *necessarily* incapable of lying just as he is incapable of telling the truth.  He enjoys neither the virtue of truthfulness (gaining the confidence of others) nor the vice of deceit (that is, temporarily tricking others for some gain), but nonetheless puts to test society’s willingness to tolerate useless speech.  Logic is a tool that he is choosing not merely to implement for personal gain, but to misuse completely and openly. While unrelated to truth and falsity, this netherworld in between is indeed a problem if taken as a broader statement about reality (as opposed to being what the medievals treated it as: namely, a teaching tool).

To be a good liar by contrast is to be consistent in the lie (ironically, by respecting all other truths, the lie is better preserved!  And leaving them in place so as to seem convincing); aside from this task, a good liar aims to mask the contradiction between statement and fact as best as he can.  This is why a society should appreciate evidence that ties fact to statement both in courtrooms and beyond.  To not care about evidence in itself as it relates to propositions of various kinds is a sign of an ideologically sick society that has broadly rendered truth into a means more so than an end.

That is why it is encouraging to see a society where “liar” is a grievous insult.  Indeed, one could say that the more grievous, the healthier the society.

So, all that said, where do we find ourselves today?  Would our leaders even blink at being called out for their dishonesty?  The casual reader might think there are far worse indictments given what we know of the dealings of certain politicians.

Even so, more so than poverty, more so than material inequality, bigotry, or persecution, the spiritual measure of a nation is its concern for the truth.  Without a concern for the truth, none of those other problems can be taken seriously.  And yet, America is the ecumenical birthplace of “pragmatism.”  It is a place that prides itself on "doing" rather than "thinking."   It is a place that has also been flexible with, perhaps even indifferent to, ultimate concerns.

In post-sectarian Atlantic World, perhaps that was expedient when Protestants and Catholics were killing each other.  Certainly, it was understandable.  But was it right to live as if one had no metaphysics?  For the time being, I don't know how to approach the answer to such a question, but what I can say is that it is categorically untrue because it is impossible to live as if one had no ultimate concerns.  A human life is a testament to what it ultimately values and maintains to be the Truth (capital "T" intended).


An Exoteric (and Admittedly Dissatisfying) Approach to the "Liar's Paradox" and Its Significance

  My favorite aspect of philosophy is how some time-honored problem that supposedly defines the parameters of the human condition can be rep...