Here we go. This is my new claim, still under the premise that I do not know any Jew:
P1) I do not know any Jew who believes in God.
Brilliant! That's a true statement. well done.
Definitely. Thank you.
I can obtain back my original statement by application of just one rule of logic. Namely the rule for negating existential qualifiers.
No, your original statement was false and incomplete. The best you can do is change it to the follwing but even that violates the law of non-contradiction.
All the Jews I VACUOUSLY-know are atheists and not atheists.
To make it complete, the word vacuous must be added, and the negation of atheists must be added.
And therefore, both statements are logically equivalent. Which is a good thing. So, that we basically agree on the same thing.
No, they aren't. When the terms are defined properly:
A Jew is either Atheist or not, but cannot be both: A known Jew is thus defined: J(x):{ Atheist XOR Not-Atheist }
If you don't know any Jews, and if the statement "All the Jews I know are Atheist" is considered true, then "All the Jews I know are not-Atheist" must also be considered true.
This contradicts the definition of a Jew.
"All the Jews I know are atheists" cannot be considered true, it is a contradiction of the definition of a Jew, if no Jews are known.
However! Using the same definition of a known Jew, negating it produces a tautology. This is evident from analyzing the truth table for XOR.
P | Q | P XOR Q
T | T | False
T | F | True
F | T | True
F | F | False
P | Q | Not ( P XOR Q )
T | T | True
T | F | False
F | T | False
F | F | True
In this case, P = Atheist and Q = Not Atheist
Notice, the top row and the bottom row of the truth table for Not-XOR. That's a tautology showing that ( Atheist and Not Atheist ) is true, and (Not Atheist and Atheist ) is true. And this is true for any set and any property and any proposition excluding its identity. This relationship between XOR and ~XOR IS classical logic, and it proves that any positive assertion about a property of an empty set is ALWAYS false. But, any negative assertion about an empty set it true. Again, with the one exception, of self-referential identity. The empty set is empty. Unknown Jews are unknown. etc.
Any property is mutually exclusive with the negation of that property. But the version of logic you are employing repeatedly ignores this and asserts a vacuous-truth about a property without asserting the negation of that property which is also simultaneously vacuously-true. This happens when terms are not defined properly, and sets which are not *actually* empty are modeled as if they are. It doesn't need to be problem, it's good and useful to construct sets that happen to empty, and to consider them like THE empty-set, and to model the empty-set behavior, but any conclusion that is reached MUST accomodate and acknowledge the inherent faults in the model.
If a set is constructed and modeled after THE empty set, and a logical conclusion is developed which indicates that this so-called empty-set has magically filled with any property, then... something has gone horribly wrong. The model was in appropriate, the method is flawed, some incorrect assumption was made along the way... In this case, it's multiple things that have gone wrong.
No. It's a lose-win. You lost and I won.
- You had to change your claim twice
- I have shown that your claim is incomplete omitting "vacuous"
- I have shown that your claim is incomplete omitting the corresponding contradiction
- I have shown that the contradiction is being considered true in violation of the law of non-contradiction in classical logic
- I wrote a formal rigorous sound proof using classical logic establishing these facts
- I have summarized this proof above so that many can understand the faults in your positive assertion
- I have shown the logical difference between evaluating a positive assertion on non-existence compared to a negative assertion on non-existence.
- All of this is supported by Stanford university in its encyclopedia of philosophy in the entry on "Contradiction". It's not just ME saying this.
- Your objection to philosophy is rejected because logic is philosophy, and the law of non-contradiction is "classical logic".
- None of your arguments against my postition have been able to gain traction, all you have been able to bring is Youtubes of people who agree, but none of them address the contradiction of considering something true, when its mutually exclusive corresponding property is simultaneaously considered true.
So that's it. The debate is over. You lost and lost repeatedly. I understand that this idea "the empty-set obtains all" is a widely accepted notion, but, that doesn't make it *actually* true. Believe it or not, AI cautioned me about the oppostion I would encounter challenging it.
