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Dec
19
comment Prove $( \lnot C \implies \lnot B) \implies (B \implies C)$ without the Deduction Theorem
So the person who asked the question asked for a shorter proof in terms of the number of uses of modus ponens. I basically find this, and the answer gets downvotes.
Dec
19
comment Prove $( \lnot C \implies \lnot B) \implies (B \implies C)$ without the Deduction Theorem
From what I've seen a first proof, and even often later proofs, is often not one of the shortest proofs possible in terms of the number of detachments/uses of modus ponens in the proof.
Dec
19
revised Prove $( \lnot C \implies \lnot B) \implies (B \implies C)$ without the Deduction Theorem
added 112 characters in body
Dec
19
comment Prove $( \lnot C \implies \lnot B) \implies (B \implies C)$ without the Deduction Theorem
I counted 16 uses of modus ponens.
Dec
17
comment Prove $( \lnot C \implies \lnot B) \implies (B \implies C)$ without the Deduction Theorem
None of those preliminary results are necessary. So, I'm not sure what you meant by "need" here.
Dec
16
revised Prove $( \lnot C \implies \lnot B) \implies (B \implies C)$ without the Deduction Theorem
added 4 characters in body
Dec
15
answered Prove $( \lnot C \implies \lnot B) \implies (B \implies C)$ without the Deduction Theorem
Dec
15
comment Prove $( \lnot C \implies \lnot B) \implies (B \implies C)$ without the Deduction Theorem
@HenningMakholm You're right those aren't Mendelson's axioms, but I don't recall the script he uses, and I'm not even sure I know how to LaTex that script up here, so he hasn't asked for anything provable in Mendelson's system if you want to stick to definitions like that. Also, the user probably isn't using Mendelson's script either. And I am human being and other people who use Polish notation are also. I have no idea why you write in such a way as if I were not one.
Dec
15
comment Prove $( \lnot C \implies \lnot B) \implies (B \implies C)$ without the Deduction Theorem
What does "short proof" and "long proof" mean? The axioms here are CpCqp, CCpCqrCCpqCpr, CCNpNqCCNpqp.
Dec
14
comment Is “It is raining or it is not raining.” a tautology?
@M.Wind The Sorites paradox and vagueness are also issues in logic. Note the reference to "fuzzy logic" in the Wikipedia on vagueness and the sorites paradox. Fuzzy logic, which in the broad sense refers to fuzzy mathematics, has many real-world applications.
Dec
13
comment Is “It is raining or it is not raining.” a tautology?
@M.Wind The observer can also decide that it is neither raining, nor not raining if say we have a few drops of water falling from the sky, but not enough for him/her to classify such as rain.
Dec
13
answered Easy question on Logic and Modes Ponens
Dec
13
comment Easy question on Logic and Modes Ponens
You can't use the deduction theorem in a formal proof, when a formal proof is defined as sequence of formulas which starts with the axioms and ends with the theorem and every step is either an axiom or is provable from the axioms of modus ponens and substitution alone.
Dec
11
revised How to transform expressions in polish-notation
added 94 characters in body
Dec
11
comment Using CP prove the truth of a tautology
The proof of B) can get constructed by substituting Q with P, and P with Q throughout the proof of A).
Dec
9
answered Reverse Polish Notation
Dec
9
answered How to transform expressions in polish-notation
Dec
9
awarded  Caucus
Dec
3
answered How to efficiently determine if any two propositional formulas are equivalent
Dec
1
comment proving $ (A \rightarrow B \vee C )\rightarrow((A\rightarrow B) \vee (A\rightarrow C))$
How do you prove that [(A→(B∨C))→((A→B)∨(A→C))] is not intuitionistically valid?