Still valid. — TonesInDeepFreeze
But the puzzle includes an intensional operator "believe'. — TonesInDeepFreeze
Please not. You're inviting the enthusiasts for modal logic to show off, and end up perpetuating the silly libel of a logicalerrorsubtlety. — bongo fury
an instance of modus ponens. — TonesInDeepFreeze
So the argument above is:
1. (A ∧ B) → C
2. A
3. B → C — Michael
if it is not Reagan who wins, it will be Jimmy Carter — Banno
If modus ponens is valid, then if we believe the premises, then we believe the conclusion (not always in fact - people err - but in principle). And the premises are believed but the conclusion is not. So, still, there's a puzzle. — TonesInDeepFreeze
You end up transitioning to a space of interpretations that excludes juiciness. — fdrake
5 Sc v Wc from 2,3,4 — TonesInDeepFreeze
I don't see a problem. — TonesInDeepFreeze
it reads as if when one asserts ~Jc, one has established (Sc v Wc) assuming the argument is valid. — fdrake
Modus ponens:
If p then q
p
therefore, q
p: A Republican wins the election,
q: If it's not Reagan who wins, it will be Anderson
So:
If A Republican wins the election, then If it's not Reagan who wins, it will be Anderson
and
A Republican wins the election
which, by MP, gives
If it's not Reagan who wins, it will be Anderson.
But if it is not Reagan who wins, it will be Jimmy Carter. So there is a prima facie case that MP reaches a false conclusion from true premises. — Banno
If A Republican wins the election, then If it's not Reagan who wins, it will be Anderson
and
A Republican wins the election
which, by MP, gives
(C) If it's not Reagan who wins, it will be Anderson.
If A Republican wins the election, then If it's not Reagan who wins, it will be Anderson
(R v A) -> (~R -> A)
R v A
therefore we have reason to believe ~R -> A
is not [modus ponens]. — TonesInDeepFreeze
"therefore we have deductive reason to assert" — bongo fury
extensionalism — bongo fury
If it's not Reagan who wins, it will be Anderson. — Banno
the argument as stated can't be interpreted as a modus ponens — fdrake
If modus ponens is valid, then if we believe the premises, then we believe the conclusion (not always in fact - people err - but in principle). And the premises are believed but the conclusion is not. So, still, there's a puzzle. — TonesInDeepFreeze
therefore [modal operator] ~R -> A — TonesInDeepFreeze
If modus ponens is valid, then if we believe the premises, then we believe the conclusion (not always in fact - people err - but in principle). And the premises are believed but the conclusion is not. — TonesInDeepFreeze
This does not prove the invalidity of modus ponens. Rather it shows that modus ponens may fail our expectations of belief. And it does seem to me to be a genuine puzzle. — TonesInDeepFreeze
I think you're erroneously reading in a modal operator — Pfhorrest
In that space of assumptions, (apple, orange) — fdrake
if it's not an orange it must be an apple. not(apple) implies orange holds in that domain — fdrake
if you don't receive an orange, you would need to eliminate the possibility of receiving a banana. You can't do that. — fdrake
What you can do is eliminate the possibility of receiving a banana if you have already assumed, or it is true that you will have received, a roundish fruit. — fdrake
But they can't exclude the banana, so they have no reason to believe (in the OP's terms) that they wouldn't receive a banana (analogously, a democrat, Carter, would win). — fdrake
it's evaluated over the candidates — fdrake
If modus ponens is valid, then if we believe the premises, then we believe the conclusion (not always in fact - people err - but in principle). And the premises are believed but the conclusion is not. — TonesInDeepFreeze
about whether they have good reason to believe them. — Pfhorrest
That's also what logical inferences (like modus ponens) are all about: — Pfhorrest
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