Why use this trick to find God when you can cash in?

If I am not a billionaire, then it is false that if I scream, my screams will be heard. So I do not scream. Therefore I am a billionaire.

This points out the real problem of the syllogism, which is that the premises in the God example are assumed by the reader to be contingent and not necessary and the truth value of the conclusion is then confused as actually saying something about the world as opposed to it just being a logical application of rules. The way it's structured is that you read the conclusion and forget it's just a tautology.

The "So" in "So I do not pray" is a clever twist, as it suggests the speaker has decided to do something to create God, leading the reader down the intended road that the syllogism means something beyond its logical structure.

I'm finding this hard to follow - is your claim that the argument is invalid? It isn't. — Banno

I think it's more addressing that these mean different things:

1. ¬(P→A)
2. P→¬A

And so these mean different things:
3. (¬G→¬(P→A)∧¬P)→G
4. (¬G→(P→¬A)∧¬P)→G

(3) is valid but (4) isn't.

Translating (1) and (2) into ordinary language introduces a problem, because we would translate (1) as "it is not the case that if I pray then it will be answered" and (2) as "if I pray then it will not be answered" which seem to mean the same thing, but (1) and (2) don't mean the same thing.

The "So" in "So I do not pray" is a clever twist, as it suggests the speaker has decided to do something to create God... — Hanover

I want to say that this is off, and that the trick is the ambiguity of, "If God does not exist..." The valid argument looks like this:

1. Suppose God does not exist
2. Therefore, It is false that if I pray, then my prayers will be answered
3. Therefore, I do not pray

But the logical translation makes the "if" a logical condition, not a supposition (i.e. not a condition whose scope extends to (3)). "So I do not pray," is a hanger-on from the alternative English translation which the formal presentation opts out of. ...Of course the idiosyncrasy of the material conditional is also doing a lot of work here.

3. (¬G→¬(P→A)∧¬P)→G — Michael

There is an ambiguity in the order of operations here which echoes my point to . Which has precedence? The '→' or the '∧'? Depending on which, the nature of the falsum arguably changes.

Going back to this:

(As a proof this runs into some of the exact same difficulties that were discussed in this thread.) — Leontiskos

Suppose the '∧' has precedence: (¬G→(¬(P→A)∧¬P))
Then we have (¬G→falsum)

But what happens if the '→' has precedence? : ((¬G→¬(P→A))∧¬P)
Then the same paradox from the previous thread arises, where you have (¬G→¬(verum)), along with the quandary of whether ¬(verum) is the same as falsum (and also whether the consequent should be interpreted as ¬(verum), or as ¬(P→A) conjoined with the recognition that (P→A) happens to be true in this case).

(The difficulty is apparently that falsum is context-independent whereas propositional negation is not. Does the modus tollens require propositional negation, or will falsum also suffice? And then what about ¬(verum), which is a combination of the two?)

(CC: @Lionino, @TonesInDeepFreeze)

Why isn't the conclusion just a non-sequitur?

Why isn't the conclusion just a non-sequitur? — schopenhauer1

Because [page 1]. :razz:

I tried to summarize why <here>.

I don't see how the conclusion can be derived conditionally from the premises- it is tacked on.

(CC: Lionino, — Leontiskos

It seems that Lionino will not sign up ever again, sadly. :sad: I tried to interact with him through PM for the past months, and I hadn't any answer. I wish he could be back.

I don't see how the conclusion can be derived conditionally from the premises- it is tacked on. — schopenhauer1

Do you agree with this:

~P
∴(P→A) — Leontiskos

It seems that Lionino will not sign up ever again, sadly. :sad: — javi2541997

Maybe. He left in frustration but will perhaps change his mind in time. I hope he returns.

The argument in Banno’s post is a link to a logic tree diagram that shows you why it’s valid.

~P
∴(P→A) — Leontiskos

No.

- Then check out 's response.

The argument in Banno’s post is a link to a logic tree diagram that shows you why it’s valid. — Michael

Can you have a non-sequitur critique of a structurally valid statement? Does content matter?

Same question https://thephilosophyforum.com/discussion/comment/939929

Well, I suppose that’s what my first post above does. The (valid) formal logic is an improper translation of the English language sentence.

Same question — schopenhauer1

Same answer: ,

Well, I suppose that’s what my first post above does. The (valid) formal logic is an improper translation of the English language sentence. — Michael

:up:

Does this whole exercise imply something about logic's usefulness with natural language? :chin:.

If there is a step before logical notation that is needed to translate, what is THIS?

Interpretation.

Can you have a non-sequitur critique of a structurally valid statement? Does content matter? — schopenhauer1

That was the point of my post. https://thephilosophyforum.com/discussion/comment/939830 . You can say any ridiculous thing you want as long as you treat the statements as meaningless premises that are reducible to symbols. If you treat the premises as contingent statements that have a truth value of their own based upon empirical information or whatever you use to decide if a statement about the world is valid, then you end up with non-sequitur issues, but those non-sequiter issues are not deductive logic fallacies, but are inductive ones.

Deductively, the conclusion of the OP follows. Inductively not. That's the interesting part of the OP.

- Sure and Lionino's thread delved into this in some detail.

-

- No, I don't think so. The OP is nowhere near as "ridiculous" as your argument about billionaires. The English argument of the OP makes sense in a way that you haven't recognized. I don't see that any of this has to do with deduction vs. induction.

No, I don't think so. The OP is nowhere near as "ridiculous" as your argument about billionaires. The English argument of the OP makes sense in a way that you haven't recognized. I don't see that any of this has to do with deduction vs. induction. — 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.'

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.

Deductive logic says nothing at all about the world.

(1) All dogs are cats, all cats are rats, therefore all dogs are rats. That is true, except for the fact that dogs aren't cats and cats aren't rats.

(2) All dogs are mammals and all mammals provide milk to their young; therefore, all dogs provide milk to their young. That is true, both deductively and inductively.

(1) and (2) are represented the exact same way deductively and are therefore both true deductively. (1) is inductively false and (2) is inductively true.

In a syllogism, the premise is a given. In an informal statement, it is a contigency.

That's what the OP plays upon.

If you treat the premises as contingent statements that have a truth value of their own based upon empirical information or whatever you use to decide if a statement about the world is valid, then you end up with non-sequitur issues, but those non-sequiter issues are not deductive logic fallacies, but are inductive ones. — Hanover

Yep, makes sense. So I guess what's the bigger picture? We can do funny things with symbolic logic seems a bit arbitrary. We need more than symbolic logic to say anything meaningful seems a truism. So what then?

If God does not exist, then it is false that if I pray, then my prayers will be answered. — Banno

I, (or perhaps just this post,) am the answer to all you godless people's prayers.

Therefore the quoted premise is false.

Yes, indeed.

If god does not exists, our prayers would be answered by Un, and hence it is false that if there is no god your prayers will not be answered.

If Un is not distracted by Hanover's screams, of course.

@Leontiskos @Hanover

I guess the silence speaks for itself :meh:

I guess the silence speaks for itself :meh: — schopenhauer1

Hanover's trying to tell us something?

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>.

Deductive logic says nothing at all about the world. — Hanover

Sure it does.

(1) All dogs are cats, all cats are rats, therefore all dogs are rats. That is true, except for the fact that dogs aren't cats and cats aren't rats. — Hanover

It is unsound, and that is why it fails to be informative. It is not uninformative because it is deductive.

(1) and (2) are represented the exact same way deductively and are therefore both true deductively. — Hanover

You're flubbing the difference between soundness and validity. A premise being true does not make it inductive.

The crux is that this claim of yours is entirely false:

the speaker has decided to do something to create God — Hanover

So I guess what's the bigger picture? — schopenhauer1

I'd say the main point of the OP was snark, hitting back at those ancient proofs for the existence of God that can't seem to go away. It points out that attempts to bootstrap something from from logic alone lead to whatever foolishness you desire.

I'd say the main point of the OP was snark, hitting back at those ancient proofs for the existence of God that can't seem to go away. It points out that attempts to bootstrap something from from logic alone lead to — Hanover

:up:

At what realm do you suppose symbolic logic makes sense besides mathematic proofs? Just philosophy journals as a way to gain street cred, that one knows the game?

Edit: I ask because clearly the reasoning and analysis matters more than turning the argument into symbolic logic. If anything, exercises like this show this.