Axioms and self-contradiction
Logic describes a true statement as: “If there is no situation in which all the premises are true and the conclusion is false, then the proof is valid.”
In your opinion, an argument like:
Assumption 1: Kobi and Ofra are engaged, but never married.
Assumption 2: Yossi went to the beach.
Conclusion: Yossi knows how to fly
Is he attacking?
After all, it meets the definition (there really is no way that the premises are true but the conclusion is false – because the first premise is self-contradictory, which makes the premises untrue!) Or was the first sentence with self-contradiction rejected from entering the logical system in the first place?
Discover more from הרב מיכאל אברהם
Subscribe to get the latest posts sent to your email.
Discover more from הרב מיכאל אברהם
Subscribe to get the latest posts sent to your email.
How in God's name does the conclusion follow from the assumptions in Ural's response?
This is a logical formalism. Follow the definition: it is not possible for the premises to be true and the conclusion to be false.
So the argument is valid only because of a lie? When there is a contradiction (which we consider a lie) in the premises, then that teaches me every lie that can be? But the content of the lie must also be valid, right?
Thanks for the quick and kind response at night!
As I wrote, a hidden formality allows for everything to be deduced.
Can the Rabbi please explain how a hidden formality can be used to deduce everything?
It was explained above. I will summarize briefly: A valid argument is one in which it is impossible for its premises to be true and its conclusion to be false. In such a situation, we say that the conclusion follows from the premises.
In any argument in which one of its premises is a contradiction (=never false), it is impossible for its premises to be true. Hence, it is also impossible for its premises to be true and its conclusion to be false.
Hence, its conclusion follows from the premises.
The shy one has not learned. So I will dare to ask how we determine that a certain sentence is a conclusion of the premises that preceded it. Thank you very much for your patience.
Explained. If not, they cannot be true and he is false.
Leave a Reply
Please login or Register to submit your answer
