Eodnhoj7 wrote:
derr...let me point out what I said above: ...
My apologies I let your terminology affect me.
In classical Propositional Logic(PL)(which I presume is what you're mangling) there is no 'If P exists'. The standard semantics are True and False so the formula is read as 'if P is true'. What do you mean by 'if P exists'?
"The negation of negative P results in P.
This is double negation of intuitionist logic.
-(-P)-->P
That is it.... ...
Is it, how strange as intuitionistic propositional logic(IPL) is distinguished from classical propositional logic(CPL)in that it does not accept double negation as an axiom, so what is this intuitionist logic you are talking about?
Still, in CPL (--P -> P) reads as "If it is not the case that it is not the case that P is true then P is true" and as this is a tautology, as what it effectively says is (P -> P), then I agree it is always true and valid whether P is true or false.
You do understand what the variables are referring to in PL don't you or have you forgotten or never learnt this, they stand for declarative sentences.
If P exists if and only if (P-->P) and P-->Q, then (P-->P)-->Q.
Real simple.
Not really, real simple is P, P->Q ∴ Q which is called modus ponens in PL.
What you've said is, (P <-> (P v ¬P)^(P->Q)) ->((P v ¬P)->Q) which is false where P is false and Q is true.
But you'll still have to say what "P exists" means?
Nope.
If Q is not P, as Q is a variation of P, then (P-->Q)-->(P-->-P).
But if you are going to use variables for the negation of a proposition then you can't really mix and match them as all you are really saying in the above is (P -> Q) -> (P -> Q) or more accurately (P -> ¬P) -> (P -> ¬P) which again is a tautology so true regardless of whether P is true or false.
You have no idea about anything, I bet you have no idea of your kids are really your own
. ...
What father ever really does but unless they are a paranoid schizophrenic or suspect infidelity and request a DNA test they are still the parent of the child. Still, not an issue that'll ever be bothering you.
You really should be concentrating on improving your English if you wish to display your claimed IQ .
Manifest means display, etc...do you want me to teach you the alphabet too?
You mean vocabulary or lexicon.
I will break it down.
((P-->Q) --> (P-->-P)) <--> (-P=Q)
I've already told you, "=" is not logical operator in PL. If you are going to use it then please provide a truth table for "=".
((P-->P)-->Q) --> ((P-->P)-->-P)
As I've already told you above, you are deluding yourself if you think you can use "¬" and a variable for "¬P" in the same formula. You have to drop one of them as it's fooling you into thinking they are different objects.
No different than saying 1 orange plus 1 orange equals 2 oranges, but orange is one set of objects
So 1+1= 1(2)
P-->P therefore P and -P
You can throw an & sign in instead of ",".
-(-P) --> [P <--> ((P-->P)<-->(P<--P))] --> [{(P-->P) --> {Q} <-->(-P<-->((P-->P)-->(P,-P))}]
This is such a mess so I can't tell which operator is the main one, is it this one,
-(-P) --> [P <--> ((P-->P)<-->(P<--P))] --> [{(P-->P) --> {Q} <-->(-P<-->((P-->P)-->(P,-P))}]
or this one?
-(-P) --> [P <--> ((P-->P)<-->(P<--P))] --> [{(P-->P) --> {Q} <-->(-P<-->((P-->P)-->(P,-P))}]
Or one of the others.
Not that it'll make much of a difference as I guess it'll be subject to the same issues as all the rest.