That's not the same as "(A implies B) and (A implies not-B)" -- that'd be "(A implies (B and not-B)).
↪Philosophim What do you think of this?
https://en.wikipedia.org/wiki/Barbershop_paradox — flannel jesus
I think, at least in philosophy though maybe there's some other argument this stems from that I'm not aware of, that we should separate out implication from modality -- so when you introduce "possibility" and "necessity" those are entirely different operators from implication. — Moliere
Would that make a difference? 0/1=F/T as I understand it. — Moliere
In the end implication must mean necessary or not necessary, in which case the answer will be different. — Philosophim
↪Philosophim What does "simply a language issue" mean? — Moliere
It is troublesome to talk about these things if one is not using very specific terminology. What does "contradictory" really mean? — Lionino
But OP is asking are the two contradictory with each other?
I think what is being asked here is whether one is the denial of the other. And the answer is no. Putting it in logical tables, denial would be whenever (A → B) yields True (A → ¬B) yields False. — Lionino
NB: Given the way that common speech differs from material implication, in common speech the two speakers would generally be contradicting one another. — Leontiskos
The two statements are not contradictory. They simply imply ~A. — hypericin
A contradiction is of the form "P ^ ~P" — Moliere
A classical definition says that two propositions are contradictory if the denial of either entails the affirmation of the other, and vice versa. So there are materially four different relations, given that each of the two propositions can be denied or affirmed. — Leontiskos
it is not possible to contradict a material implication — Leontiskos
Assume P and suppose Q. If an absurdity results on Q, then P and Q are contradictory. — Leontiskos
It shows that they cannot both be true, but it does not show that they cannot both be false — Leontiskos
it does not show that they cannot both be false, and it does not show that the trueness or falseness of one results from the falseness or trueness of the other — Leontiskos
"The car is wholly green." "No, the car is wholly red."
This is a contradiction classically but not according to symbolic logic — Leontiskos
You think the two propositions logically imply ~A? — Leontiskos
When we talk about contradiction there is a cleavage, insofar as it cannot strictly speaking be captured by logic. It is a violation of logic. — Leontiskos
A -> B. But that's not imply. that's "Necessarily leads to." — Philosophim
((p→q)∧(p→¬q)) and (p→(q∧¬q)) are the same formula — Lionino
Thanks - I concede your point. — Leontiskos
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