UDLCO CRH: Hypatia, the teacher who was killed by a mob due to her Socratic questioning

Date: Tue, 3 Feb 2026, 08:19

Subject: Re: What is a fact? (i.e., What does the English word 'fact' denote?)

Hu2:

And eventually Hypatia leads us to Socratic or Shukracharyatic questioning!

Here's a letter from Hypatia in response to her cousin asking the fearful question and I quote,

"I would advise you to lecture less and ask more. Like me, you live in a time of uncertainty and chaos, when people seek answers that feel easy and bring destruction. Like me, you live in a time when no one is taught to tell truth from falsehood. You cannot force someone to believe facts, but you can guide them to the discovery. If someone believes something dehumanizing, see if you can get them to defend their beliefs with reasons. If you doubt their reasons, ask for the facts they base them on. If you doubt their facts, ask where they got them.

Remember as you do so that you serve both the world and them. The mob that killed me claimed victory. But the death of scholarship that was heralded by my death left everyone vulnerable in the end. They condemned their descendants to the onrushing Dark Age. A century later, the swift and ugly death spreading across the Empire hit an Alexandria devoid of scholars. People died in the street without remedy or even understanding of what happened to them.

CC licence: https://commons.wikimedia.org/wiki/File:Hypatia_(Charles_Mitchell).jpg#mw-jump-to-license

I know that what I ask of you is not easy, but I know that you have the support of a network I never had. You can get your patience not just from the scholars of the past but your fellow warriors. Know that every mind you teach is valuable and omit no opportunity to encourage people to question harmful beliefs – nor any opportunity to learn from another.

In doing so, you join a line of scholars seeking to cast light into the darkest night.

Hypatia of Alexandria

About Hypatia of Alexandria

Likely born somewhere between 350-370 AD in Alexandria to a scholar named Theon and an unnamed woman. Gruesomely murdered by a mob in March of 415 AD. Hypatia was a mathematician and teacher whose work survives imperfectly in the commentaries she and her students wrote about famous treatises. She used the Socratic method to teach Christians and pagans regardless of who was in power and who was oppressed.

Unquoted from: https://badasstours.nl/hypatia-of-alexandria-answers-testifying-in-the-dark/

On Tue, 3 Feb 2026, 05:42 hu1 wrote:

Hu3 says:

“So, a "fact check" amounts to checking how justified a belief held by an individual (or a group of individuals) is!”

I was uncomfortable about the statement implied by this sentence, so I thought about it before I went to sleep yesterday and after I woke up in the morning to find out what I was uncomfortable about. And after going through ways of checking whether something is a fact or not, in terms of the four definitions I had suggested, I came to the conclusion that I agree with hu3.

 

“We are constantly focusing on the notion of truth. What about its counterpart, i.e. falsehood?”

In two-valued logic, if a proposition is not true, it is false, and if it is not false, it is true. Hence, if we establish that the negation of a proposition P is false, then it follows that proposition P is true.  In mathematics, the form of proof in which we establish that a proposition is true by showing that its negation is false is called Reductio ad Absurdum (also called Proof through Contradiction.  )Argumentum ad

 

Interestingly, a conjecture in mathematics is a proposition that has not been proved to be either true or false. So there are three values here, namely, Proved to be True, Proved to be False, and Not Yet Proved to True or False. But “Not yet proved to be true or false” is not the same as “Neither true nor false”. In three valued logic, there are three values, namely, True, False, and Neither, thereby rejecting Aristotle’s Law of Excluded Middle.

In Multivalued Logics, there can be more than three values. The opening para of the Wikipedia entry on many valued logic is:

“Many-valued logic (also multi- or multiple-valued logic) is a propositional calculus in which there are more than two truth values. Traditionally, in Aristotle's logical calculus, there were only two possible values (i.e., true and false) for any proposition. Classical two-valued logic may be extended to n-valued logic for n greater than 2. Those most popular in the literature are three-valued (e.g., Łukasiewicz's and Kleene's, which accept the values true, false, and unknown), four-valued, nine-valued, the finite-valued (finitely-many valued) with more than three values, and the infinite-valued (infinitely-many-valued), such as fuzzy logic and probability logic.”

(https://en.wikipedia.org/wiki/Many-valued_logic)

Of particular interest to me in this what is called tetralemma or catushkoti in Buddhist logic, which has four values: P, not-P, neither P nor not-P, and P and not-P. Modern logicians see this as a precursor to Quantum Logic where a proposition can be true in one context (or one history) and false in another. One way of understanding this is to consider the proposition “The sum of angles is two right angles” This is true in Euclidean geometry and false in spherical geometry, Another example comes form the question “Is light a particle or a wave?”. The answer in Quantum Mechanics is “It is a particle under one experimental conditions and a wave under another”. (Wave-Particle duality.) I see this statement as say “It is true under one set of experimental conditions and not-true under another.”

 

What I have stated above is not a response to what hu3 says, but simply reflections triggered by what he says.

 

“By the logic of our argument, falsehood would also be attributed to beliefs.”

I agree.

 

“By the same account, can we say that for every falsehood, there is some degree of likelihood that it may turn out to be true?”

That follows from what Feynman articulates in his public lecture  at the 1955 autumn meeting of the National Academy of Sciences:

“The scientist has a lot of experience with ignorance and doubt and uncertainty, and this experience is of very great importance, I think. When a scientist doesn’t know the answer to a problem, he is ignorant. When he has a hunch as to what the result is, he is uncertain. And when he is pretty darn sure of what the result is going to be, he is still in some doubt. We have found it of paramount importance that in order to progress we must recognise our ignorance and leave room for doubt. Scientific knowledge is a body of statements of varying degrees of certainty — some most unsure, some nearly sure, but none absolutely  certain. [Emphases mine. Hu1]

 

A General remark:

The English words fact, true, and know share an attitude to total certainty , and hence are not open to doubting and questioning. In contrast, the following formulations avoid total certainty, and hence are open to doubting and questioning:

“I assume that P is a fact”

“I assume that P is true”

“As far as I know, P”

“I am convinced that P is true”

“I believe that P is true”

“P is rationally justified”

“It is reasonable to conclude that P is true”

 

In the climatic moment in the movie Agora, the heroine Hypatia says “You will not, and cannot, doubt what you believe – I must” [Watch the YouTube Video clip “Question your beliefs - Agora” (https://www.youtube.com/watch?v=4N8EFH-qYJ4) ] For me, this axiom is at the heart of what I take to be academic knowledge.