Do you intend for this to be a Socratic interview? — TonesInDeepFreeze
Wait a minute. If A is false, then the first premise is:
If not-A, then not (not-A)
You can't change one of the A's to false and not the other one. If A is false, they both have to be false. — frank
Yes, so — TonesInDeepFreeze
An Argument is valid if and only if it would be contradictory for the conclusion to be false if all of the premises are true.[ — Hanover
So the argument is one in which the first premise doesn't say anything. — frank
1. Trivial truth
2. A.
Conclusion: not-A.
That's not valid. — frank
think you need to know what "trivially true" means. — frank
'degenerate' in a non-pejorative sense as often in mathematics — TonesInDeepFreeze
importance in Boolean logic used along the way in switching theory, computation, etc. — TonesInDeepFreeze
Logic is a vast field of study, including all kinds of formal and informal contexts. I would not so sweepingly declare certain formulations otiose merely because one is not personally aware of its uses. — TonesInDeepFreeze
Per the definition of "valid":
An Argument is valid if and only if it would be contradictory for the conclusion to be false if all of the premises are true.[
— Hanover
Assuming all premises in the OP true, the conclusion of not A is shown to be false because a valid conclusion of A was shown. — Hanover
In the only interpretation where both premises are true, there's no way to conclude not-A — frank
A -> ~A
A
therefore ~A
There is no interpretation in which both the premises are true. — TonesInDeepFreeze
The fact that the premises are inconsistent doesn't vitiate that the argument is valid. Actually the fact that the premises are inconsistent entails that the argument is valid.
(2) A conclusion itself is valid if and only if it is true in all interpretations. An argument is valid if and only if there are no interpretations in which the premises are all true and the conclusion is false. — TonesInDeepFreeze
But it's not validity we usually disagree over, but soundness, and inconsistent premises make valid inferences unsound. — Srap Tasmaner
As Banno notes, validity is determined by asking if the conclusion flows from the premises, and so he argues under mp, it does, so it is valid.
The wiki cite adds criteria, namely (1) that the negation of the conclusion cannot also flow from the premises for validity and (2) the premises under any formulation must also reach the same conclusion. — Hanover
The argument:
1. A -> ~A
A
therefore ~A
valid
Another argument:
2. A -> ~A
A
therefore A
valid — TonesInDeepFreeze
Trivial — frank
in argumentation on degenerate cases is often inadvertent or deceptive — Srap Tasmaner
"begging the question," generally considered a fatal problem for an argument. That conditional is legitimate in form, and is generally a theorem, but it is fatal if relied on to make a substantive point or demonstrate a claim. It will only happen inadvertently ― in which case, a good-faith discussant will admit their error ― or with an intent to mislead by sophistry. — Srap Tasmaner
Fundamentally, all we're talking about in this case is arguing from a set a premises which are inconsistent — Srap Tasmaner
necessarily inconsistent. — Srap Tasmaner
But people arguing from inconsistent premises often make inferences that, while in themselves correct, continue to hide their inconsistency. — Srap Tasmaner
The losing party, in one sense, grants that they lost, but continues in the competitive spirit, which means they have to shift ground from whether they "officially" or "technically" lost to whether that was a "real" loss, or whether there had a been a "real" competition in the first place. — Srap Tasmaner
Another argument:
A -> ~A
A
therefore A
valid — TonesInDeepFreeze
A -> ~A
A
therefore ~A
There is no interpretation in which both the premises are true.
— TonesInDeepFreeze
If the antecedent in the conditional is false, then the first premise is true. Now say the second premise is true. Then the conclusion does not follow.
If you insult me one more time, we're done. I'm satisfied with ending this discussion. — frank
Only arguments are valid, and "A, therefore A," is not an argument. Argument, at the very least, involves rational movement. — Leontiskos
↪TonesInDeepFreeze
"Trivial" has a clear meaning in analytical philosophy. — frank
I would encourage you to write out in English the only case where both premises are true — frank
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