turned into bot:

https://janitorai.com/characters/58b422c9-db78-4b59-bee8-45b8e9ce65f2_character-eliott-friends-dw-oc

probably "repost"

modus ponens:
N ⊃ ~N
N
therefore, ~N

modus tollens:
N ⊃ ~N
N
therefore, ~N

they look identical. so what now? there's another rule we can apply.

the rule states that a "p ⊃ q" argument is the same as a "~p v q" argument where "v" means "or"

so we can turn N ⊃ ~N into ~N v ~N

this type of statement where the two sides of a proposition are the same is known as a "tautology." and a tautology can always be simplified to it's sole part, which in this case is ~N, which is "I have zero nickels."

So if he had one nickel, he indeed would have zero nickels.

consider the statement "If I had a nickel" as N and "I have zero nickels" as ~N.

the statement "If I had a nickel, I'd have zero nickels" could be written as "N ⊃ ~N" where ⊃ means "if...then"

there are two rules we can apply here, and two which we cannot.

one of them is known as modus ponens, and follows as such:

p ⊃ q
p
therefore, q

another one is known as modus tollens, and follows as such:

p ⊃ q
~q
therefore, ~p

the two rules we cannot do are:

affirming the "then"

p ⊃ q
q
therefore, p

denying the "if"

p ⊃ q
~p
therefore, ~q

now let's apply modus ponens and modus tollens to the argument "N ⊃ ~N"

the collab of the millenium 🔥🔥