> Formal logic usually isn’t taught in high school
Have things changed? Last century, this was a key part of (in the US) high school geometry courses. I won't argue that it was as in depth as you'd get in a college course (like you'd be exposed to in a math or philosophy degree program), but it was formal logic and it was taught.
Diogenesian 3 hours ago [-]
This doesn't seem quite right to me:
In the modern academic practice, the question of where a particular idea came from, or whether an axiom is ontologically correct, is considered vacuous and out of scope. For the most part, you’re just handed a rulebook to play someone else’s game.
I very much had the opposite problem with Munkres's Topology or Dummit and Foote's Abstract Algebra: those authors hand you the ontological / scientific justifications for "everyday" ZFC without actually telling you the precise rules. I had to read a formal book on mathematical logic before I really understood point-set topology (at which point my misconceptions were clearly trivial confusion).
To be clear I think the standard intuitive semi-naive set theory is the correct approach for most math students. But it didn't work for me. I needed to see the axioms and formal language.
6gvONxR4sf7o 33 minutes ago [-]
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.
Joker_vD 3 hours ago [-]
> "If you don't finish house chores, you can't play Minecraft"
is equivalent to "Do finish the house chores, or you can't play Minecraft".
jasperry 2 hours ago [-]
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?
playorizaya 2 hours ago [-]
And “If you don’t play Minecraft, you don’t have to finish house chores.”
Diogenesian 2 hours ago [-]
"xor you can't play Minecraft" is correct :)
bryanrasmussen 3 hours ago [-]
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.
Rendered at 16:25:16 GMT+0000 (Coordinated Universal Time) with Vercel.
Have things changed? Last century, this was a key part of (in the US) high school geometry courses. I won't argue that it was as in depth as you'd get in a college course (like you'd be exposed to in a math or philosophy degree program), but it was formal logic and it was taught.
To be clear I think the standard intuitive semi-naive set theory is the correct approach for most math students. But it didn't work for me. I needed to see the axioms and formal language.
The one that I remember most strongly that way was the unique mapping from the empty set/object/whatever as a theorem.
is equivalent to "Do finish the house chores, or you can't play Minecraft".
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.