If you don't understand something, be quiet.
Thank you for wanting to know more. Your lack of ignorance is the only reason why I'm bothering to write this.
In my post, I actually said "If it is raining and
it is not raining, then the moon is made of gouda cheese". So, here's the proof:
Well, first, let's symbolize this...
p = "it's raining"
q = "the moon is made of gouda cheese"
These are the logic symbols required:
* = "and"
v = "or"
~ = "not"
So, this is symbolized as:
If (p*~p) , then q
It's raining and it's not raining, then this implies the moon is made of gouda cheese.
So, here are the rules of logic we'll use:
1: Addition, aka: "from x, we get x v y"
This is like saying "if it's raining, then it's raining or it's not raining." It works for whatever x and y stand for. So long as x was true, it's true.
2: Simplification, aka: "from x * y, we get x, and we get y"
This is like saying "If there's cake and cheese, then there's cake"
3: Disjunctive syllogism, aka: "from x v y, and ~x, we get y"
This is like saying "If you have 1 or 2, and you don't have one, then you have 2"
So, let's prove this:
We have p*~p, and we'll prove q.
From p*~p, we get p, by simplification.
From p, we get p v q, by addition.
From p*~p, we get ~p, by simplification.
From ~p, and p v q, we get q, by disjunctive syllogism.
So, if p*~p, then q.
So, if it's true that it's raining and it's not raining, then the moon is made of gouda cheese. Of course, it's never raining and not raining at the same time, so we don't need to worry about this. This isn't the paradox I was talking about, by the way.
Anyway, proving curry's paradox will take too long here, as it goes into metalogic and metalinguistics, so I'll give up on this.
Really, though, we should have a thread here explaining basic logic, at least. I wonder what people talk about in the logic forum if they don't even know modus ponens. It's gotta be the most basic part of deductive logic there is.
Sorry for going on about this, but it's a bit disappointing is all. Anyway, I'm glad one person was interested in logic, in the logic forum.