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View submission: What makes an argument valid?
My logic is a bit rusty, but I wonder if a bit more context on what's happening underneath the hood would help. The crucial move is 2+2=5 is *necessarily* false. So we can do a bit of craziness using a contradiction.
1. 2+2=5
2. ¬(2+2=5)
3.(2+2=5) ∧ ¬(2+2=5)
4. (2+2=5) ∨ The moon is made of cheese
5. The moon is made of cheese
Annotations.
1. This is one of our premises
2. The little ¬ symbol means "not". In other words, this line is asserting that 2+2 does not equal 5. This is provable using ordinary facts about arithmetic.
3. The little ∧ symbol means "and". Basically this line combines together line 1 and 2 into the statement that 2+2 does equal 5, and 2+2 does not equal 5. Logicians call this "conjunction introduction". This line is kind of fluff, but it clearly shows that we've arrived at a contradiction.
4. The little ∨ symbol means "or". Basically I've used my premise and added on a statement, either (2+2=5) or The moon is made of cheese or both. Logicians call this disjunction introduction.
5. To get at the conclusion, I essentially said, either the 2+2=5 or the moon is made of cheese, and it we know form line two that ¬(2+2=5). So the only way for the or statement to be true is if the moon is made from cheese. This is called a disjunctive syllogism.
In fact, you can prove anything from a contradiction in something called the Principle of Explosion. A *necessarily* false statement is functionally a contradiction because you are assuming one part (2+2=5 in this case), but you can prove it's negation (otherwise it wouldn't be necessarily false), and this lets you form a contradiction. Then, from a contradiction, you can prove anything.
u/ConceptOfHangxiety I wonder if this addresses you question
There's nothing here!