Consider: the metaphysical understanding of reality, R, entails both that a) there is a self and b) there is no self. — javra
Those different entailments rely on different interpretations of what is meant by"self' so they are not speaking about the same things. — Janus
Tones even mistakes natural language for his own system — Leontiskos
and normatively interprets natural language in terms of his system — Leontiskos
And to read Flannel Jesus' posts is to realize that he did not intend the OP in any special sense. I see no evidence that he was specifically speaking about material implication. — Leontiskos
an argument with two conditional premises should not be able to draw a simple or singular conclusion (because there is no simple claim among the premises). — Leontiskos
No, as per my previously given example, they are (or at least can be) speaking about, or else referencing, the exact same thing via the term "self" - but from two different perspectives and, hence, in two different respects (both of these nevertheless occurring at the same time). — javra
This is a fairly common sort of argument. Something like: "if everything Tucker Carlson says about Joe Biden is true then it implies that Joe Biden is both demented/mentally incompetent and a criminal mastermind running a crime family (i.e., incompetent and competent, not-B and B) therefore he must be wrong somewhere."
— Count Timothy von Icarus
This actually runs head-on into the problem that I spelled out <here>. Your consequent is simply not a contradiction in the sense that ↪Moliere gave (i.e. the second clear sense of "contradiction" operating in the thread). — Leontiskos
No, "two different perspectives and, hence, in two different respects" just is two different interpretations of the concept or meaning of 'self'. — Janus
I have always had difficulty with argument by supposition. What does it mean to suppose A and then show that ~A follows? — Leontiskos
Tones gave an argument for ~A in which he attempted to prove it directly — Leontiskos
What does it mean to suppose A and then show that ~A follows? This gets into the nature of supposition, how it relates to assertion, and the LEM. — Leontiskos
It also gets into the difference between a reductio and a proof proper. — Leontiskos
The point is one I had already made in a post that Tones was responding to, "You think the two propositions logically imply ~A? It seems rather that what they imply is that A cannot be asserted" — Leontiskos
((a→b)∧(a→¬b))↔¬a is valid — Lionino
That is true if "both props" is understood as (A → B) ^ (A → ¬B) and "imply ¬A" as the proposition being True means A is False — Lionino
The original question was, "Do (A implies B) and (A implies notB) contradict each other?"
On natural language they contradict each other. — Leontiskos
On the understanding of contradiction that I gave in the first post, they do not contradict each other, and their conjunction is not a contradiction. — Leontiskos
1 – We know (a→b)∧(a→¬b) is the same as a→(b∧¬b), and (b∧¬b) is a contradiction. So (a→b)∧(a→¬b) just means A implies a contradiction. If (a→b)∧(a→¬b) is True, A cannot be True, it has to be False. But let's say (a→b)∧(a→¬b) is False, does that mean A is true? That is what the logical tables would say: — Lionino
I would want to say something along the lines of this, "A proposition containing (p∧¬p) is not well formed." — Leontiskos
Similar to what I said earlier, "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
and to try to use the logic at hand to manipulate it results in paradoxes. — Leontiskos
I'm sure others have said this better than I — Leontiskos
principle of explosion is in fact relevant here insofar as it too relies on the incorporation of a contradiction into the interior logical flow of arguments. — Leontiskos
It is formal logic pretending to say something. — Leontiskos
Yep. Worth noting that parsing this correctly shows that the original was incomplete - implied nothing."The car is green" and "The car is red" is not a contradiction. But if we add the premise: "If the car is red then the car is not green," then the three statements together are inconsistent. That's for classical logic and for symbolic rendering for classical logic too. — TonesInDeepFreeze
Taking "implies" as material implication, they are not contradictory but show that A implies a contradiction.Do (A implies B) and (A implies notB) contradict each other? — flannel jesus
I had the same thought when I read that. It's wellformed. It is also invalid: A∧¬AI'd like to see what formation rules you come up with. — TonesInDeepFreeze
If (a→b)∧(a→¬b) is False, ¬A is False, so A can be True or not¹. — Lionino
But (a→b)∧(a→¬b) being False simply means that A does not imply a contradiction, it should not mean A is True automatically. — Lionino
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
"Dogs have four legs, and Lassie has four legs, therefore Lassie is a dog" is not a valid argument. The conclusion ("Lassie is a dog") may be true, but it has not been proved by this argument. It does not "follow" from the premises.
Now in Aristotelian logic, a true conclusion logically follows from, or is proved by, or is "implied" by, or is validly inferred from, only some premises and not others. The above argument about Lassie is not a valid argument according to Aristotelian logic. Its premises do not prove its conclusion. And common sense, or our innate logical sense, agrees. However, modern symbolic logic disagrees. One of its principles is that "if a statement is true, then that statement is implied by any statement whatever."
Logicians have an answer to the above charge, and the answer is perfectly tight and logically consistent. That is part of the problem! Consistency is not enough.[/quote]Logician: So, class, you see, if you begin with a false premise, anything follows.
Student: I just can't understand that.
Logician: Are you sure you don't understand that?
Student: If I understand that, I'm a monkey's uncle.
Logician: My point exactly. (Snickers.)
Student: What's so funny?
Logician: You just can't understand that.[/quoye]
Quite so.
My point is that it is a vacuous instance of validity — Leontiskos
((a→b)∧(a→¬b))↔¬a is valid
— Lionino
My point is that it is a vacuous instance of validity — Leontiskos
As I claimed above, there is no actual use case for such a proposition — Leontiskos
and I want to say that propositions which contain (b∧¬b) are not well formed. — Leontiskos
They lead to an exaggerated form of the problems that ↪Count Timothy von Icarus has referenced. We can argue about material implication, but it has its uses. I don't think propositions which contain contradictions have their uses. — Leontiskos
This is perhaps a difference over what logic is. Is it the art of reasoning and an aid to thought, or just the manipulation of symbols? — Leontiskos
ones I have in mind are good at manipulating symbols, but they have no way of knowing when their logic machine is working and when it is not. They take it on faith that it is always working and they outsource their thinking to it without remainder. — Leontiskos
the only person on these forums who has shown a real interest in what I would call 'meta-logic' is — Leontiskos
A parallel equivocation occurs here on 'false' and 'absurd' or 'contradictory'. Usually when we say 'false' we mean, "It could be true but it's not." In this case it could never be true. It is the opposite of a tautology—an absurdity or a contradiction. — Leontiskos
Usually when we say 'false' we mean, "It could be true but it's not." — Leontiskos
Every time we make an inference on the basis of a contradiction a metabasis eis allo genos occurs (i.e. the sphere of discourse shifts in such a way that the demonstrative validity of the inference is precluded). Usually inferences made on the basis of a contradiction are not made on the basis of a contradiction “contained within the interior logical flow” of an argument. Or in other words, the metabasis is usually acknowledged to be a metabasis. As an example, when we posit some claim and then show that a contradiction would follow, we treat that contradiction as an outer bound on the logical system. — Leontiskos
We do not incorporate it into the inferential structure and continue arguing. — Leontiskos
could also put this a different way and say that while the propositions ((A→(B∧¬B)) and (B∧¬B) have truth tables, they have no meaning. They are not logically coherent in a way that goes beyond mere symbol manipulation. — Leontiskos
((A→(B∧¬B))
∴ ¬A
Viz.:
Any consequent which is false proves the antecedent
(B∧¬B) is a consequent which is false
∴ (B∧¬B) proves the antecedent — Leontiskos
In this case the middle term is not univocal. It is analogical (i.e. it posses analogical equivocity). Therefore a metabasis is occurring. — Leontiskos
A = There are vampires.
B = Vampires are dead.
Not-B = Vampires are living.
As you can clearly judge, this truth table works with Ts straight across the top, since vampires are members of the "living dead." Fools who think logic forces them to affirm ~A — Count Timothy von Icarus
I think Kreeft is involved in word games here — Leontiskos
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