[shkkmo]

This had me worried:

"God-given axioms, which is academic lingo for a truth we accept purely by our God-given logic, like: if something is not true then it is false, something cannot exist in an empty set, something logical is logical."

But then I saw this and started laughing:

"Remember when everyone used tables to lay out their HTML? Well, that proved to be a horrible way to do things, because tables are inherently inflexible. It’s a strictly geometric constraint. Now we all use divs and CSS, because we get a much-more flexible CSS engine to define our layout. Postgres and her SQL friends are all table based, just like the <table> of 1999. Don’t be 1999."

[abtinf]

Why did the axioms bit have you worried? OP is pretty much exactly right, except for the part where we accept it by our "logic". Axioms are simply true, end of story; logic does not apply to axioms themselves, only how they can be used in relation to other axioms.

[shkkmo]

Axioms are simply something that you accept as true to build a model. There is no 'simply true, end of story' or 'proven by logic' to axioms.

Many axioms maybe picked because they seem 'obviously true', (or more likely, because they are useful) but that doesn't make their truth simple or make them the result of logic. (For an example take a look at the existence of infinity).

Additionally, the 'axioms' he lists are all what I would generally consider tautologies. (Although you might argue that the first one is actually an axiom of bivalent logic systems).