Re: On "logical proofs"

[jrmu@xxxxxxxxxx]

The search for truth, and science in specific, often does not proceed by
proof but by conjecture supported by internal consistency with empirical
evidence.  Proofs usually come later. To give a culinary analogy: To
conjecture correctly is to cook up a delicious idea. To write a rigorous
proof is wash the intellectual dishes.

The first proof of the Pythagorean theorem occurred much later than
Pythagoras. The earliest we have on record was by Euclid, yet the
theorem is named after Pythagoras, not Euclid. Fermat's Last Theorem was
named after Fermat who proposed the conjecture without proof, and not
Andrew Wiles who proved it with rigor 350 years later.

Many of our advances lack proof. Newton was unable to prove how
gravitational force could act at a distance. Do there even exist a
priori proofs for relativity or quantum physics? As I understand it,
these are conjectures consistent with empirical evidence. We can prove
relatively little. We cannot even disprove brain in a vat.

As a side note, how should the theory of education proceed? Should
education teach "absolute truth" as we currently understand it? But our
understanding of nature and science today is almost certainly wrong.
Should it therefore mirror how the human mind actually learns, by
teaching according to successive approximations of the truth? Rather
than teach what we perceive to be generalized universal truth, which is
likely to overwhelm a child and be correct anyway, it may make sense to
teach incorrect models which are easier to grasp.

Humanity first learned to model the cosmos through geocentrism, then
heliocentrism. Only after classical physics was firmly established did
humanity attempt the theory of relativity. The world proceeds first from
atomic theory and only later attempts subatomic particles and quanta.

But if teaching should be done via successive approximations, does this
affirm the usefulness of a noble lie?

As for Laozi and Zhuangzi being irrational and mystical, Zhuangzi lived
in the time of Plato, not the time of Kant or Huemer. It is more fair to
compare Zhuangzi with Plato, who was also quite mystical. Doubtless,
other less influential Taoists later polished the philosophy and
provided clearer arguments for it later on.

-- 
Aaron Lin
jrmu@xxxxxxxxxx
IRCNow (https://ircnow.org)

On Tue, Jun 30, 2026 at 07:09:42AM -0700, jrmu wrote:
> Greetings Zinov and IRCNow-Offtopic,
> 
> I do not think Aquinas and Laotzi/Zhuangzi mean the same thing; at least, not
> so clearly.  There's no way I would have drawn the conclusion about imaginary
> numbers being valid truth from your excerpt of Aquinas.  I believe God is the
> essence of truth/logos, and since mathematics falls under logical truth, I
> suppose what Aquinas and Laozi said are equivalent. The
> Logos in Greek was translated as the Tao in Chinese in many of Bible
> translations, instead of the Word like in English. So, it makes sense that the
> Catholic conception is similar. (Incidentally, this belief
> is why I cannot reject mathematical platonism)
> 
> Yet there's no way I *personally* would have jumped from the Summa Theologica
> to imaginary numbers. I can, however, make that jump from the thesis that "the
> Tao is ineffable".  I don't think the Summa Theologica's ineffability of God is
> a core tenet of Catholicism, but 1) if it were, and 2) were it clearer that
> ineffability applied to mathematical truth, then yes 3) I would consider
> Aquinas prescient.
> 
> Do you have any arguments against my thesis that "the search for truth is what
> leads to a productive culture?" That is my main thesis, not that I'm choosing
> or rejecting analytical philosophy. I might read it eventually, but not for
> now, because for now I want to determine the universe of worthwhile philosophy,
> and I am unwilling to completely rule out Zhuangzi or the Tao Te Ching just
> yet. I have obviously not ruled out analytic philosophy because I downloaded
> all of Russell's books. But this heuristic will let me immediately reject some
> books in the Western Canon like Freud and Nietzsche, since they deny the
> existence of truth.
> 
> As for your approach to philosophy via rationality, is requiring rational
> "proofs" an arbitrary decision?  There may be valid reasons for why
> Laozi/Zhuangzi and others do not approach their philosophy with "proofs":
> 
> 1) They believe the truth to be self-evident (their most likely reasoning)
> 
> This is also done in the West. For example, the declaration of independence
> states: "We hold these truths to be self-evident, that all men are created
> equal". No effort is made whatsoever to justify the beliefs. It does not
> imply the conclusion is wrong.
> 
> 2) The proof is left as an exercise to the reader (since the author finds the
> proof boring and tedious)
> 
> I do this all the time! So did brilliant thinkers like Fermat -- "I have
> discovered a truly marvelous proof of this, which this margin is too narrow to
> contain." Fermat, of course, had no real proof: he just found the task tedious
> and boring.
> 
> 3) It is also entirely possible that the author is a fraud or cult leader
> 
> For Zhuangzi, his reasoning more likely lies with 1) and 2).
> 
> I wonder what benefit step-by-step "logical proofs" offer us. Lucretius' On the
> Nature of Things, for example, offered us many "proofs" of atomism. Many of
> those proofs are now obviously based on 1) incorrect premises and 2) absurd
> inferences logic which lead to 3) incorrect conclusions.
> 
> For example, Lucretius argues that taste and smell are based on how atoms hook
> together. The foul smells and tastes are due to sharp piercing hooks between
> atoms contacting our nose and tongue. This, he explains, is how all sensations
> occur from all things beind made of the same form of matter.
> 
> The 1) premise, the 2) inference, and 3) the conclusion are all wrong.
> 
> Is such a logical "proof" even helpful? Since the entire system of logic
> Lucretius uses is fallacious, how is it any better than Zhuangzi who simply
> omits the proof altogether?
> 
> The vast majority of the "proof-based" philosophical works are just as flawed
> as Lucretius. Bad proofs are not much different from no proofs at all.
> 
> Again, look at Plato's Parmenides and the One and the Many. Comically absurd
> logic arriving at a conclusion that may indeed be correct. In the end, what
> matters is the conclusion is correct.
> 
> It is enough for a mathematician to propose an interesting and *correct*
> conjecture without offering any proof. Goldbach's conjecture is interesting
> despite no proof. I am not obsessed with proofs, I am obsessed with arriving at
> the truth as quickly as possible. Fermat's Last Theorem recently was solved:
> "Together, the two papers are 129 pages long[4][5] and consumed more than seven
> years of Wiles's research time." "Only a small number of people were capable of
> fully understanding at that time all the details of what he had done". What a
> waste of human talent.
> 
> -- 
> Aaron Lin
> jrmu@xxxxxxxxxx
> IRCNow (https://ircnow.org)
> 
>