an actual example — TonesInDeepFreeze
The premises are consistent and the conclusions are not.
The conclusion is not true under all interpretations. Sometimes it's A and sometimes it's not A. — Hanover
I'm not sure what post you are responding to — Leontiskos
The move is always to a meta-level. What is the game? What is the competition? What is logic? Our world has a remarkable tendency to try to avoid those questions altogether, usually for despair of finding an answer. — Leontiskos
You are confusing consequence or inference with identity. — Leontiskos
Under what definition of "valid" is the argument in the OP valid? — frank
lright, so you're substituting the conclusion of the OP from A to A &~A, which can simply be represented by an F, for false. — Hanover
The opposite of (A & ~ A) is (A v ~ A), which is a tautology
So, if I can prove from the OP that (A v ~ A) flows, then the argument is invalid — Hanover
Negating the conclusion and showing it leads to a contradiction from the same premises proves invalidity. — Hanover
I'm sure there are more convoluted ways to go about it, but does that satisfy your objection? — Hanover
An argument is valid if and only if there are no interpretations in which all the premises are true and the conclusion is false. — TonesInDeepFreeze
P1. A -> ~ A
P2. A
1. A&~A (1,2)
2. ~A (1)
3. ~A v A ( 2 disjunctive introduction)
Still not valid, considering the contradiction allows me to prove anything I want, even that T is F. — Hanover
Just trying to think of real world examples of a formula like "A → ~A", likely dressed up enough to be hard to spot. Excluding reductio, where the intent is to derive this form. What I want is an example where this conditional is actually false, but is relied upon as a sneaky way of just asserting ~A.
I suppose accusations of hypocrisy are nearby. "Your anti-racism is itself a form of racism." "Your anti-capitalism materially benefits you." "Your piety is actually vanity." — Srap Tasmaner
A→B
B→~A
A
∴ B — Leontiskos
In this case there are no interpretations in which all the premises are true. Perforce, there are no interpretations in which all the premises are true and the conclusion is false. So the argument is valid. — TonesInDeepFreeze
An argument is valid if and only if there are no interpretations in which all the premises are true and the conclusion is false.
In this case there are no interpretations in which all the premises are true. Perforce, there are no interpretations in which all the premises are true and the conclusion is false. So the argument is valid. — TonesInDeepFreeze
I imagine you finally had to retire to the insane asylum. Enjoy the rocking chair. — frank
Yes. I edited that post. It's just weird that any argument that can't have all true premises is going to be valid. — frank
As I said, in this particular regard, I'm merely applying the definitions of ordinary formal logic. — TonesInDeepFreeze
TonesInDeepFreeze contention that they are the same — Leontiskos
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