Why do you say that axioms require faith?
Discussion
Axioms allow you to choose which statements are true in a formally defined system (like ZF set theory or euclidian geometry). Examples like the axiom of choice or parallel postulate require faith in their truth value for any of the statements that follow those axioms to be true.
Any system of reasoning requires some statements be true, and axioms are those bedrock statements that are taken as truths because we require no proof for them. We require no proof because we have faith they are true.
Does it require an axiom for simple observations? For example, every time I release my pencil from my hand it always falls toward the earth.
Sometimes seemingly simple or obvious things are not so obvious
https://en.m.wikipedia.org/wiki/Parallel_postulate
Parallel postulate seems obvious but non-euclidian geometry does not have such an axiom. Projective geometry also has no parallel postulate requirement.
https://en.m.wikipedia.org/wiki/Axiom_of_choice
Axiom of choice in a finite world makes sense. With infinities you get the Banach-Tarski paradox
https://en.m.wikipedia.org/wiki/Banach%E2%80%93Tarski_paradox
When using mathematical precision to investigate ideas some faith is required that your axioms hold true, because alternative axiomatic systems exist that are also non contradictory.
Think of it like axioms as defining the boundaries of a mathematical reality, and you can have different axioms that create different realities.
What alternative axiom exists that can explain why this pencil falls toward the earth every single time I release it from my hand?
You first need to grasp the concept of an axiom before you apply it (incorrectly)
Is the law of gravity an axiom?
It’s more of a fundamental principle of mechanics. It’s not self-evident. It is empirically derived, and subject to revision.
Apparently there are no axioms within physics like there are in mathematics:
-a number is equal to itself
-transitive law. a=b, b=c, then a=c
-axiom of empty set
Axioms are accepted as true without proof. They’re not necessarily absolute truths, universal, or immutable and may only apply within a given context.
Disclaimer: I summarized the above after using 2 different LLMs.
I appreciate your honesty 😂
Way too many people just copy and paste the entire LLM response shamelessly 😂
I have my suspicion of a certain person on nostr that does this. But I couldn’t really confirm it when I put the text into an AI detector.
I’m pretty sure all AI detectors are unreliable. Could be unaware of a new good one. I remember a story about a school falsely punishing a student with a legit essay or something.
On social media, it gets super obvious when their response is long and worded super formally in contrast to their other brief and dumb replies lol