5 ms·

I'm confused. Or maybe you're confusing AND with OR? How can "A and not A" ever be true, let alone tautologically so? Also see https://en.wikipedia.org/wiki/Law

I'm confused. Or maybe you're confusing AND with OR? How can "A and not A" ever be true, let alone tautologically so? Also see https://en.wikipedia.org/wiki/Law_of_noncontradiction https://en.wikipedia.org/wiki/Law_of_noncontradiction

dfischer 6y ago
Quantum states can be A and not A. Unknown questions are A and not A. There’s interesting alternative logic systems that try to tackle this. We get into interesting territory when using English and then “is” as a statement. Most English is assumed to have a certain value because of to be. English is almost inherently flawed with logic bugs and assumptions. E-Prime may help with this. 1. https://en.wikipedia.org/wiki/Catu%E1%B9%A3ko%E1%B9%ADi https://en.wikipedia.org/wiki/Catu%E1%B9%A3ko%E1%B9%ADi 2. https://en.wikipedia.org/wiki/Jaina_seven-valued_logic https://en.wikipedia.org/wiki/Jaina_seven-valued_logic 3. https://en.wikipedia.org/wiki/Infinite-valued_logic https://en.wikipedia.org/wiki/Infinite-valued_logic
- mehrdadn 6y ago
  Okay but I still don't see how the law of the excluded middle says that "a and not a" is always valid.
  - dash2 6y ago
    Grandparent said that the law doesn't say that "a and not a" is always INvalid. (The law also doesn't say that "a and not a" is sometimes valid. It makes no comment at all, but only claims that "a or not a" is always valid. According to the grandparent. Now I need to lie down for a bit....)
    - Tainnor 6y ago
      Yes, this. The point was that you can reject the law of the excluded middle without getting into the absurdity that would result from accepting "a and not a".
      - mehrdadn 6y ago
        Ahh! Now I see I misread your comment, I see what you were trying to say now.
c3534l 6y ago
[this was misleading]
- mehrdadn 6y ago
  Are you sure you're not confusing AND and OR? https://en.wikipedia.org/wiki/Intuitionistic_logic#Relation_to_classical_logic https://en.wikipedia.org/wiki/Intuitionistic_logic#Relation_... Literally copying from Wikipedia: The system of classical logic is obtained by adding any one of the following axioms: ϕ ∨ ¬ϕ (Law of the excluded middle), ... where ∨ means OR, not AND... right?
  - c3534l 6y ago
    Yes. In classical logic, p OR !p is always true. You have to add these axioms to get classical logic. Intuitionistic logic doesn't have that. p OR !p is not necessarily true in intuitionistic logic.
    - mehrdadn 6y ago
      > A and not A are not necessarily contradictions Nobody was saying p OR !p is necessarily true. The argument was about p AND !p. It really seems to me like you're confusing AND and OR... The intuitionist will accept that "A and not A" cannot be true https://en.wikipedia.org/wiki/Intuitionism#Truth_and_proof https://en.wikipedia.org/wiki/Intuitionism#Truth_and_proof
Tainnor 6y ago
I didn't claim that it could be true, as I did in fact state that I know of no logic that accepts "A or not A". The argument was solely about what the law of the excluded middle is. IOW, law of the excluded middle != law of noncontradiction. Classical logic accepts both of these laws, intuitionism only the second. edit: looking at Wikipedia does seem to indicate that there might be systems of logic where "A and not A" might not be valid (paraconsistent logic), but I haven't really looked into that, and I don't know how much such systems are used.

dfischer 6y ago

Quantum states can be A and not A. Unknown questions are A and not A. There’s interesting alternative logic systems that try to tackle this. We get into interesting territory when using English and then “is” as a statement. Most English is assumed to have a certain value because of to be. English is almost inherently flawed with logic bugs and assumptions. E-Prime may help with this. 1. https://en.wikipedia.org/wiki/Catu%E1%B9%A3ko%E1%B9%ADi https://en.wikipedia.org/wiki/Catu%E1%B9%A3ko%E1%B9%ADi 2. https://en.wikipedia.org/wiki/Jaina_seven-valued_logic https://en.wikipedia.org/wiki/Jaina_seven-valued_logic 3. https://en.wikipedia.org/wiki/Infinite-valued_logic https://en.wikipedia.org/wiki/Infinite-valued_logic

mehrdadn 6y ago
Okay but I still don't see how the law of the excluded middle says that "a and not a" is always valid.
- dash2 6y ago
  Grandparent said that the law doesn't say that "a and not a" is always INvalid. (The law also doesn't say that "a and not a" is sometimes valid. It makes no comment at all, but only claims that "a or not a" is always valid. According to the grandparent. Now I need to lie down for a bit....)
  - Tainnor 6y ago
    Yes, this. The point was that you can reject the law of the excluded middle without getting into the absurdity that would result from accepting "a and not a".
    - mehrdadn 6y ago
      Ahh! Now I see I misread your comment, I see what you were trying to say now.

c3534l 6y ago

[this was misleading]

mehrdadn 6y ago
Are you sure you're not confusing AND and OR? https://en.wikipedia.org/wiki/Intuitionistic_logic#Relation_to_classical_logic https://en.wikipedia.org/wiki/Intuitionistic_logic#Relation_... Literally copying from Wikipedia: The system of classical logic is obtained by adding any one of the following axioms: ϕ ∨ ¬ϕ (Law of the excluded middle), ... where ∨ means OR, not AND... right?
- c3534l 6y ago
  Yes. In classical logic, p OR !p is always true. You have to add these axioms to get classical logic. Intuitionistic logic doesn't have that. p OR !p is not necessarily true in intuitionistic logic.
  - mehrdadn 6y ago
    > A and not A are not necessarily contradictions Nobody was saying p OR !p is necessarily true. The argument was about p AND !p. It really seems to me like you're confusing AND and OR... The intuitionist will accept that "A and not A" cannot be true https://en.wikipedia.org/wiki/Intuitionism#Truth_and_proof https://en.wikipedia.org/wiki/Intuitionism#Truth_and_proof

Tainnor 6y ago

I didn't claim that it could be true, as I did in fact state that I know of no logic that accepts "A or not A". The argument was solely about what the law of the excluded middle is. IOW, law of the excluded middle != law of noncontradiction. Classical logic accepts both of these laws, intuitionism only the second. edit: looking at Wikipedia does seem to indicate that there might be systems of logic where "A and not A" might not be valid (paraconsistent logic), but I haven't really looked into that, and I don't know how much such systems are used.