All Logic, No Bite

Oh man, that resonates with me. One of the constant frustrations for me was that once you get foundations in a topic, the rest follows, but the foundations are often full of things that are axioms under one metatheory and theorems under another metatheory. When they were axioms, I remember always being comfortable, like "sure I can assume things," but as theorems there's always that bit of "wait hold up you can't just do that without saying more."

The one that I remember most strongly that way was the unique mapping from the empty set/object/whatever as a theorem.

Not in geometry for me, but it was required in my linear algebra, discrete math and computer architecture classes, all of which were required for my CS degree.

I've found that any time you try to generalize about what is or isn't "usually" required in school, there are a lot of exceptions, to say the least. Curriculum is all over the place.

I would say high school geometry is still mostly "syllogistic" and not the formal philosophical / mathematical logic worked out between Kant and Gödel which forms the backbone of modern mathematics. It is good solid logical thinking, and mathematically correct! - but not really what the author means here.

By the traditional translation of if/then sentences to classical logic, it is. If you want to go further down the rabbit hole, several things are debatable here: When people use if/then sentences, do they really mean material implication, where (A -> B) is equivalent to (~A OR B)? Also, people often use the word "or" in a sense that's closer to exclusive OR, as opposed to the inclusive OR that the logical operator indicates. Overall, can the meaning of a sentence with imperative intent be fully captured by a proposition that is just meant to indicate a state of affairs?

"Do finish the house chores" is more naturally taken as a command, so the question is whether it should be assigned a truth value at all. It is linked to some normative claims that would plausibly be truth-valued: "you are permitted to play Minecraft only if you finish the chores", or perhaps "you ought to finish the chores, or you are not permitted to play Minecraft". The former is equivalent to the original sentence only if we take "can't" as expressing lack of permission (which it may not): "if you don't finish house chores, you can't/are not permitted to play Minecraft".

And “If you don’t play Minecraft, you don’t have to finish house chores.”

"xor you can't play Minecraft" is correct :)

you sure?

I think "if you don't you can't" does not preclude other don'ts leading to you can'ts, but "Do or you can't" means that if you Do you can, although in normal vernacular usage you are right that they are interchangeable.