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Comment by par1970 | Hacker News Reader

par1970·

> In order to not have to explain everything, almost all lessons are mostly teaching you some axioms, even if they really are disputed, or have caveats, etc. Good teachers make clear where there is an axiom, and where something is just being simplified or assumed for the sake of saving time.

What exactly do you mean by the word “axiom” here?

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Something assumed to be true without proof.

Think of it as one layer of abstraction above the model under discussion. Like a hyperparameter. In later years, students get taught the same topics again, with the hyperparameter tuned to be more realistic.

Something that is taught to be a self-evident or universally recognized truth

Does “self-evident” just mean that anyone who knows the sentence’s meaning can determine that it is true without any need to gather empirical data?

eg, All bachelors are unmarried.

eg, If X is a triangle, then X has three sides.

eg, the world is round or it is not the case that the world is round.

And does “universally recognized” just mean that most people believe the proposition is true?

In this context an axiom is a nonlogical axiom, in other words an assumption, one that is not to be questioned or discussed

Okay. So, in your original comment are you asserting that teachers are mostly telling students to believe propositions without giving any epistemic justification for those propositions?

Yes, as part of teaching one topic, teachers have to tell students to "not worry about" some other related topic and just take it as given fact, even when that's not technically true

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