Let me repeat the standard proof with more details and structure. I hope that will help you, and help me to understand what is the real issue.
At present, I still don’t know what bothers you.
First, some definitions to reduce minimize typing:
Q = ”I don’t know any Jew”
P = “All the Jews I know are atheists”
~P (negation of P) = “I know at least one Jew who is not an atheist”
C = “I know at least one Jew AND I don’t know any Jew”
Let’s, start:
- Q is true (Premise)
- C is false. It cannot be that I know a Jew, and I know no Jews
- P is either true or false (exclusive or)
- P is true if and only if ~P is false
- ~P is either true or false (exclusive or)
- If ~P were true, then C would be true
- Therefore ~P is false. Because of 6), 5) and 2)
- Therefore P is true. Because of 3), 4) and 7)
So, the conclusion follows from the premises: P is true, and it is therefore the case that “All the Jews I know are atheists”.
The premise is just a fact. Since I know no Jews.
So, you can defeat the necessity of the conclusion, only if you find a step that is fallacious. Or Unjustified.
I cannot exclude a typo, a mistake, or that a step requires more sub steps. And, if you find more of those steps, tell me please only the one with the smallest sequence number, so that we can focus on it, and move to the next.
Failing to do that, will compel you to accept the conclusion. Unless you admit to operate outside the boundaries, and the rules of logic.
So, which one would that be?
Ciao
- viole