if you phrase "A -> B" as "from A follows B", then if A is false, you can say "A -> anything", from A anything follows — flannel jesus
no - the consequent can only be affirmed as true IF the antecedent is first affirmed as true. It's THAT that is not the case here. — flannel jesus
But the difficulties of material implication do not go away here. — Leontiskos
You are thinking of negation in terms of symbolic logic — Leontiskos
in which case the contradictory proposition could be, "Lizards are purple and they are not smarter." — Leontiskos
Yet in natural language when we contradict or negate such a claim, we are in fact saying, "If lizards were purple, they would not be smarter." — Leontiskos
The negation must depend on the sense of the proposition, and in actuality the sense of real life propositions is never the sense given by material implication. — Leontiskos
I know of no context in which that sentence is a contradiction. — TonesInDeepFreeze
There are two separate matters: negation and material implication. — TonesInDeepFreeze
Given the way that common speech differs from material implication, in common speech the two speakers would generally be contradicting one another. — Leontiskos
The question at hand is, "What is the contradiction of 'If lizards were purple then they would be smarter'?" — Leontiskos
You are thinking of negation in terms of symbolic logic, in which case the contradictory proposition could be, "Lizards are purple and they are not smarter." — Leontiskos
The negation of a material conditional will be different from the negation of an if-then statement in natural language — Leontiskos
I don't think that's a coincidence at all. — flannel jesus
You changed the sentence. Here is what you wrote: — TonesInDeepFreeze
"If lizards were purple then they would be smarter" is not a contradiction — TonesInDeepFreeze
I was there giving an answer to the question at hand. — Leontiskos
I give up. Go read Lionino's first post on the first page. — Leontiskos
You don't even understand what is being said. — Leontiskos
Again, a contradiction is a statement and its negation. If there is a contradiction then you could show that both a statement and its negation are implied.
Again:
"if lizards are purple, then they would be smarter" and "if lizards are purple, then they would not be smarter" is not a contradiction.
— TonesInDeepFreeze
But the difficulties of material implication do not go away here. You are thinking of negation in terms of symbolic logic, in which case the contradictory proposition equates to, "Lizards are purple and they are not smarter." — Leontiskos
I take 'the contradictory statement is P' to mean that P is a contradiction, as a contradictory statement is a contradiction. — TonesInDeepFreeze
But maybe you mean it is a contradicting statement. — TonesInDeepFreeze
And if you think they do contradict each other, does that mean they can't both be true at the same time? — flannel jesus
I already corrected your misinterpretation — Leontiskos
I'm glad you finally figured this out — Leontiskos
To help you, Janus' point about natural language is something like this:
Supposing A, would B follow?
Bob: Yes
Sue: No
Now Sue has contradicted Bob. The question is, "What has Sue claimed?" — Leontiskos
They imply ~A.
— TonesInDeepFreeze
Then give your proof. — Leontiskos
Here is the alternative notion of contradiction that you are overlooking:
“opposite assertions cannot be true at the same time” (Metaph IV 6 1011b13–20)
— Aristotle on Non-contradiction | SEP — Leontiskos
It's not a misinterpretation. To say that P is contradictory is to say that P is a contradiction. — TonesInDeepFreeze
First, take out 'would' since subjunctives unnecessarily complicate. — TonesInDeepFreeze
Sue claimed "It is not the case that B follows from the supposition A" — TonesInDeepFreeze
The reason we keep material implication is because we like truth functionality. — Leontiskos
Here's some help for you from the dictionary:
Merriam-Webster - Contradictory
(Adjective): involving, causing, or constituting a contradiction
| contradictory statements
| The witnesses gave contradictory accounts of the accident.
(Noun): a proposition so related to another that if either of the two is true the other is false and if either is false the other must be true — Leontiskos
First, take out 'would' since subjunctives unnecessarily complicate.
— TonesInDeepFreeze
It's like talking to a computer. "Get rid of that natural language, you're confusing our processes!" — Leontiskos
You're still involved in ambiguity. In order to know what Sue denied we must know what Bob affirmed. As noted in my original post, your interpretation will involve Sue in the implausible claims that attend the material logic of ~(A → B), such as the claim that A is true and B is false. Sue is obviously not claiming that (e.g. that lizards are purple). The negation (and contradictory) of Bob's assertion is not ~(A → B), it is, "Supposing A, B would not follow." — Leontiskos
I don't think so. Or I would like to know of a system or approach that supports it.
I mean we all have places we come from and thoughts we start at, but if you walk into the chemistry department and start talking alchemy someone might correct you. — Moliere
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