If (a→b)∧(a→¬b) is False, ¬A is False, so A can be True or not¹.
— Lionino
But (a→b)∧(a→¬b) being False simply means that A does not imply a contradiction, it should not mean A is True automatically.
— Lionino
Isn't this a fairly big problem given that (¬¬A↔A)? — Leontiskos
Isn't this a fairly big problem given that (¬¬A↔A)? I take it that this is the same thing I have pointed out coming out in a different way? Namely the quasi-equivocation on falsity? — Leontiskos
Around a third of folk hereabouts who have an interest in logical issues cannot do basic logic. — Banno
As in the concept/meaning of self as "that which is purple and square" vs. "that which is orange and circular" or any some such? And this in relation to "there both is and is not a self"? — javra
Again, one perspective being the mundane physical world of maya/illusion/magic-trick and the other being that of the ultimate, or else the only genuine, reality to be had: that of literal nondualistic being. — javra
Compare:
((A→(B∧¬B))
∴ ¬A
With:
((A→(B∧¬B))
¬(B∧¬B)
∴ ¬A
With:
((A→(B∧¬B))
¬(B∧¬B)
¬(B∧¬B) = "True"
∴ A does not follow
This demonstrates the analogical equivocity — Leontiskos
What is the definition 'analogical equivocity'? — TonesInDeepFreeze
By saying "'Lassie is a dog; is true", they are adopting Dx as a premise. So, of course...
That's just a matter of defining the words. If 'dead' and 'living' are defined so that they are not mutually exclusive, then of course we don't make the inference. It's silly to claim that sentential logic is impugned with the example.
Isn't this a fairly big problem given that (¬¬A↔A)? — Leontiskos
¬(a→(b∧¬b)) → a — Leontiskos
But let's say (a→b)∧(a→¬b) is False, does that mean A is true? That is what the logical tables would say: — Lionino
and the way material implication works in classical logic is that, if the antecedent is false, the implication is always true — Lionino
If (a→b)∧(a→¬b) is False, ¬A is False, so A can be True or not¹. — Lionino
You seem to be missing the point of the example — Count Timothy von Icarus
That's just a matter of defining the words. If 'dead' and 'living' are defined so that they are not mutually exclusive, then of course we don't make the inference. It's silly to claim that sentential logic is impugned with the example.
...when it comes to vamps it's deadly serious. :death: :death: :death: — Count Timothy von Icarus
I know you want a strict definition, but the wonderful irony is that someone like yourself who requires the sort of precision reminiscent of truth-functional logic can't understand analogical equivocity or the subtle problems that attend your argument for ¬A. As we have seen in the thread, those who require such "precision" tend to have a distaste for natural language itself. — Leontiskos
By saying "'Lassie is a dog; is true", they are adopting Dx as a premise. So, of course,
Ax(Dx -> Fx)
Fs
Dx
Therefore Dx
is valid.
In other words:
All dogs have four legs.
Lassie is a dog.
Therefore Lassie has four legs.
is not valid.
Let a proposition P be A→(B∧¬B)
Whenever P is 1, A is 0.
In natural language, we might say: when it is true that A implies a contradiction, we know A is false.
Now a proposition Q: ¬(A→(B∧¬B))
Whenever Q is 1, A is 1.
Do you think it is correct to translate this as: when it is not true that A implies a contradiction, we know A is true? — Lionino
"if a statement is true, then that statement is implied by any statement whatever." — Count Timothy von Icarus
It is not the case that if A then B&~B implies A. — TonesInDeepFreeze
It is not the case that if A then both B and not-B — TonesInDeepFreeze
Since it is true that Lassie is a dog, "dogs have four legs" implies that Lassie is a dog. In fact, "dogs do not have four legs" also implies that Lassie is a dog! Even false statements, even statements that are self-contradictory, like "Grass is not grass," validly imply any true conclusion in symbolic logic. And a second strange principle is that "if a statement is false, then it implies any statement whatever." "Dogs do not have four legs" implies that Lassie is a dog, and also that Lassie is not a dog, and that 2 plus 2 are 4, and that 2 plus 2 are not 4.
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