The logical high ground here is yours; I'm just pointing out that the linguistics isn't always so simple. — Srap Tasmaner
Where in the world did I say that or anything that could be interpreted as that. I think your materialistic interpretation is a category error. — TheMadFool
It's exactly the opposite. Violating PB is admitting a multivalued logic that I described. Violating LEM is a contradiction. — TheMadFool
Is this a bad example?:s — TheMadFool
What would a TRIvalent system look like? — TheMadFool
2. In LEM what is the ''middle'' that is ''excluded''? — TheMadFool
According to Wikipedia a trivalent logic has three truth values, true, false, and an indeterminate third value. The third value appears to be best described as "unknown — Metaphysician Undercover
The excluded middle is anything other than "is" or "is not". Either the apple is red, or the apple is not red, and the LEM insists that there is no "middle", between being red and being not red. — Metaphysician Undercover
Is ''the apple is red'' AND ''the apple is not red'' also excluded [by LEM]? — TheMadFool
1. If it is then why? Also raises another issue viz. why have the law of noncontradiction? It seems to be a corollary of LEM. — TheMadFool
2. If it isn't then it leads us to a contradiction and also, why? — TheMadFool
No, since disjunction is inclusive. — Nagase
Actually, the situation is probably the reverse. Assuming classical principles, such as double negation and reductio ad absurdum, it's possible to prove LEM from LNC. — Nagase
So, if LEM doesn't exclude [P & ~P] what is this ''middle'' that's being ''excluded''? — TheMadFool
That is to say LEM and LNC are logically equivalent. — TheMadFool
So, what I can't get is what you mean when to my question ''Is ''the apple is red'' AND ''the apple is not red'' also excluded [by LEM]?'' you said ''No, since disjunction is inclusive.''???!!! — TheMadFool
LEM literally says "either p or ~p", not "either p or ~p, but not both". — Nagase
For example, if P is the proposition:
Socrates is mortal.
then the law of excluded middle holds that thelogical disjunction:
Either Socrates is mortal, or it is not the case that Socrates is mortal.
is true by virtue of its form alone. That is, the "middle" position, that Socrates is neither mortal nor not-mortal, is excluded by logic, and therefore either the first possibility (Socrates is mortal) or its negation (it is not the case that Socrates is mortal) must be true. — Wikipedia
Is ''the apple is red'' AND ''the apple is not red'' also excluded? — TheMadFool
2. If it isn't then it leads us to a contradiction and also, why? — TheMadFool
So it is excluded ''that neither Socrates is mortal nor Socrates is not mortal'' — TheMadFool
That means it is excluded that (P & ~P). That's the LNC: ~(P & ~P). — TheMadFool
What is denied by LEM is that there is a third option, that the apple is neither red nor not red. — Metaphysician Undercover
Do you see the difference between LEM and LNC? One says that two opposing statements cannot both be true, the other that two opposing statements cannot both be false. — Metaphysician Undercover
In logic the expression ''neither...nor...'' has a specific translation:
Apple is red = R
Neither the apple is red nor the apple is not red = Apple is not red AND not apple is not red = the apple is not red AND the apple is red = ~R & R = R & ~R
The ''middle'' that is ''excluded'' is the contradiction R & ~R. — TheMadFool
Can you expand on this a bit. Sorry for the trouble. — TheMadFool
Bold emphasis mine.
So it is excluded ''that neither Socrates is mortal nor Socrates is not mortal''
Let P = Socrates is mortal
That means it is excluded that (P & ~P). That's the LNC: ~(P & ~P).
So, LEM isn't the inclusive OR at all. — TheMadFool
I've started warming to the general idea of dialectic — Srap Tasmaner
That's because falsehood is the same as truth of the negation. In truth, LEM only states that A OR NOT(A) is always true, while it is PB which states that either A is true or NOT(A) is true. — Tristan L
As I understand it, PB states that there are only two (bivalence) truth values viz. true and false — TheMadFool
the LEM states that (p v ~p) [...] — TheMadFool
[...] which simply means that given a proposition, either the proposition itself is true or its negation is true. — TheMadFool
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