I would give Banno the credit of levity here, not snark. It is a philosophical joke, aptly placed in the lounge. The justified decision to not pray turns out to prove God's existence, given a logical translation that is initially plausible. Hanover is reading all sorts of strange things into the OP. — Leontiskos
The OP is a fun way of exploiting this bug, among other things. I don't think it is meant to be more than that. — Leontiskos
My question still stands, what’s the use of symbolic logic if the analysts comes before the logic? — schopenhauer1
"Just the place for a Snark!" the Bellman cried,
As he landed his crew with care;
Supporting each man on the top of the tide
By a finger entwined in his hair. — Banno
Well, at the very least it is a useful aid for error-checking, even if it is not infallible. It represents a form of calcified analysis that is useful but limited. And it is useful for conceptualizing extended arguments that are difficult to capture succinctly. There are probably other uses as well. — Leontiskos
There are probably other uses as well. I have fought lots of battles against the folks in these parts who have a tendency to make formal logic an unimpeachable god, so I agree with the sort of objection you are considering. — Leontiskos
The two arguments (mine and the OP) are logically equivalent under deductive logic. They are represented symbolically the exact same. For one to be more ridiculous than the other means you are using some standard of measure other than deductive logic to measure them, which means you see one as a syllogism and the other as something else.' — Hanover
Deductive logic says nothing at all about the world. — Hanover
Inductive logic references drawing a general conclusion from specific observations and it relates to gathering information about the world, not just simply maintaining the truth value of a sentence. To claim that statement of the OP is more logical than mine means that the conclusion of the OP bears some relationship to reality. If that is the case, it is entirely coincidental. — Hanover
The two arguments (mine and the OP) are logically equivalent under deductive logic. — Hanover
Except they're not, because your "So..." is entirely different than the OP's "So..." I explained this <here>. — Leontiskos
Logical equivalence is not determined solely by symbolic representation, especially in light of the interpretive choices made when translating from natural language to formal logical symbols. — Benkei
Deductive logic ensures that if the premises are true, the conclusion must also be true. Obviously when the premises are true, a valid deductive conclusion will say something about the world. — Benkei
Your second argument is not inductively supported because the conclusion is supported by the definition of mammal. It's like saying, all bachelors are single, John is single and therefore a bachelor. There's no probability involved that a single man isn't a bachelor. — Benkei
They are completely different. The implicit connotation in the OP makes perfect sense. Your parallel is perfect nonsense. Not all parlor tricks are created equal. The parlor trick of the OP is a great deal better than your attempt regarding billionaires. Your argument possesses no plausibility because it is so obviously unsound. You are trying to make yourself a billionaire with specious reasoning. The OP is not praying on the supposition that God does not exist. — Leontiskos
"If A then B" is logically equivalent to "if C then D." You're going to have offer a proof that is not the case without equivocating between deductive and inductive logic. I don't see how that can be done. — Hanover
This offers an equivocation of the term "true." The sylIogism "If A then B, A, therefore B" is true. The statement "I am at work today" is true. It's the analytic/synthetic distinction. It's for that reason why a statement can be deductively true and inductively false, which is what the OP showed. Analytic validity says nothing about synthetic validity. — Hanover
The definition of "mammal" was arrived at a posteriori as opposed to "bachelor" which, as you've used it, (i.e. there is no probability a bachelor can be married) is a purely analytic statement. That is, no amount of searching for the married bachelor will locate one. On the other hand, unless you've reduced all definitions to having a necessary element for them to be applicable (which would be an essentialist approach), the term "mammal" could be applied to a non-milk providing animal, assuming sufficient other attributes were satisfied. This might be the case should a new subspecies be found. For example, all mammals give birth to live young, except the platypus, which lays eggs. That exception is carved out because the users of the term "mammal" had other purposes for that word other than creation of a legalistic analytic term. — Hanover
then that is a valid disproof of the logic within the OP — Hanover
There isn't a problem with the logic. The problem is that the premise isn't saying what it superficially seems to be saying. — Michael
The "parlor trick" is just that the antecedent contains the contradiction "¬(P → A) ∧ ¬P". — Michael
I was trying to clear away the enticing parlor trick that made the OP appear plausible so that the error could be revealed. If it can be shown that the use of the logic within the OP will lead to absurd results in other instances, then that is a valid disproof of the logic within the OP. Such is a reductio ad absurdem. — Hanover
My "parlor trick" includes the translation. The formalism is not very difficult to understand. What's fun is the way that the translation is intuitive. Hanover's difficulty is this, "Why did we say, 'So I don't pray'?" The explanations I have been giving answer that question and give an account of why the translation is intuitive. — Leontiskos
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