Well GCG I can tell you what I can understand of it but perhaps it is not 100%

In a scientific approach it is practice to allow for a margin of uncertainty

Here is a quote from Natalie Angier, a science journalist, from her book The Canon, "Science is uncertain because scientists really can't prove anything, irrefutably and beyond a neutrino of a doubt, and they don't even try. Instead, they try to rule out competing hypotheses, until the hypothesis they're entertaining is the likeliest explanation, within a very, very small margin of error – the tinier, the better.”

You cannot prove anything in science 100%

This is appropriate, since the scientific experiment is subject to observations where a margin of error cannot be ruled out.

Supports the above. Based on the premise that we are biased.

Furthermore universality cannot be proven with examples. The mathematical theorem has been held up as an example of absolute and universal truth, but the theorem is based on postulates which serve as points of departure for the mathematical system within which the theorem is valid.

Mathematical theorem is sometimes used as evidence support something that is universally true. But Hermes is saying that the mathematical theorem is based on postulate. A postulate is when we assume something as correct.

If "universal" is meant to mean all encompassing and unique, a mathematical theorem may therefore also fail to comply with universal validity.

Hermes is defining universal as all encompassing and unique. That mathematical theorems fail to support the fact of universality I don’t know enough about mathematical postulates to comment.

This still leaves one possibility: the axiom or selfevident truth.

An axiom presupposes proof. That mean an axiom cannot be proven. You need to rely on an axiom to prove something. An axiom is assumed to be true e.g. A thing is itself.

An example from Euclid's *Elements:* If two things area equal to another thing, they are also equal to each other.

Again ‘A thing is itself’ or a cat is a cat.

This might constitute an anomaly in traditional skeptical reasoning: an axiom cannot be proven to be universal.

Statement that I need to research further.

Wikipedia does not distinguish between an axiom and a postulate.

Axiom = Postulate.

This has not always been the case. Is there a distinction? It is hard to fathom a mathematical system where the above Euclidian axiom does not apply.

As far as I understand Hermes is asking is there a distinction between an Axiom and a Postulate. He find it hard to believe.

Is this correct Hermes am I understanding it correct?