I would give @Banno the credit of levity here, not snark. It is a philosophical joke, aptly placed in the lounge. The justifiable decision to not pray turns out to backfire and prove God's existence, given a logical translation that is initially plausible. Hanover is reading all sorts of strange things into the OP.

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

I ask you the same:
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.

- This OP should not cause you to despair of logic, lol. As I've noted elsewhere, the material conditional is a disproportionately artificial logical construct. A false antecedent makes a material conditional true, and this is something like a bug or at least dross. Much like a bit of imperfect code, as long as you don't exploit the bug the logic is useful. 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.

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

I get it, but was trying to see if there is a takeaway. My question still stands, what’s the use of symbolic logic if the analysis comes before the logic? I know the classic reason is clarity of presentation. But it would be misleading if it it’s seen as the actual catalyst behind the actual reasoning, like a computer language.

I'd say the main point of the OP was snark, — Hanover

"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.

My question still stands, what’s the use of symbolic logic if the analysts comes before the logic? — schopenhauer1

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. 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.

(There is also a normative use in teaching reasoning skills, for we have some common sense intuitions which are fallacious, and which can be ironed out easily with formal logic. seems to overlook this latter point in his analysis of Aristotle.)

"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

And @Hanover, here we see Banno abandoning his Godless ways:

Snark = Jonah
Bellman = God
Crew = Jonah's shipmates

The Biblical allusion is too obvious to ignore. Banno made light of belief in his OP, and now a strange twist of fate has brought it about that his OP led to his belief, not unlike the subject of the OP. :grin:

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

Sure, but as this exercise shows, the logic can stifle the analysis as well, if not used correctly, or even if used correctly.

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

:up:

I think we should be very careful when we throw around the word "logic", just like the word "rational". I try not to use "rational" too much, because it's often just a coded word for "I'm the one with the correct thinking and you are not, you're just not 'rational'". Similarly, logic can stand in for one's rationale, it can mean a formal logical system like Frege developed, a Hegelian-like totalizing feature of metaphysics, and a whole bunch of things.

- I agree. :up:

Interpretive monism to go with logical monism - the One True Understanding of Lewis Carrol. I prefer Martin Gardiner's analysis.

Besides, I haven't said it three times yet.

- I was interpreting you, not Carroll.

yet — Banno

Yet. (!)

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

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. Even so, two arguments can be symbolically similar but not logically equivalent if their premises or conclusions differ in truth value or meaning. Logical equivalence requires that both arguments have the same truth value in all possible scenarios.

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

This statement is only partially correct. 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.

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

Inductive logic indeed involves drawing general conclusions from specific observations but they can never be proven true the way a deductive argument can. It merely deals in probabilities; the more observations you have the likelier your conclusion.

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.

And yes, in formal logic, premises in syllogisms are assumed to be true for the sake of argumentation.

- :up:

-

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

Teasing this out a bit more, the OP contains an implicit move, "Supposing God does not exist..., I should not pray." The formal translation does not take this route, but the connotation is part of the parlor trick.

The parallel in your own example is, "Supposing I am not a billionaire..., I should not scream."

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.

It's much simpler than that.

¬(P → A) ↔ (P ∧ ¬A), so ¬G → ¬(P → A) means ¬G → (P ∧ ¬A).

The argument is actually "if God does not exist then I pray [and it isn't answered], I don't pray, therefore God exists".

¬G → (P → ¬A) is a more appropriate premise and with it the conclusion no longer follows.

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

"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.

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

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.

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

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.

"All penguins are black" means something very different as an analytic statement versus a synthetic statement. The former holds it true as a matter of definition. The latter as a matter of fact. Necessary versus contingent.

Another hot button issue as an example, "Can a man give birth?"

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

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.

"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 is quite obviously not logically equivalent. The statements "if A then B" and "if C then D" involve different propositional variables (A, B, C, and D). Unless we have additional information about the relationship between these variables, we cannot assume they have any connection. The truth value of "if A then B" is determined solely by the truth values of A and B, while the truth value of "if C then D" depends only on C and D. These are independent of each other.

Without additional information, there's no reason to believe that the truth value of one statement would always match the other for all possible combinations of truth values. It's therefore entirely possible for "if A then B" to be true while "if C then D" is false, or vice versa, depending on the specific truth values of A, B, C, and D.

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

Yes, you're right to point out some equivocation here but the point I was trying to make stands. If the premisses of a deductive argument are true (and I'm assuming a form of correspondence theory) then a valid argument will have a logically true conclusion and necessarily correspond with reality.

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

While scientific terms do evolve, they do function as relatively fixed definitions within the scientific community. The fact that definitions can change doesn't necessarily mean they are probabilistic or inductive in nature during their period of use and "giving milk" is a rather necessary condition in that definition since the name is derived from breasts because of the mammary gland. So no, nice try but nobody has ever used the term for any animal that doesn't produce milk and they never will.

So no, nice try but nobody has ever used the term for any animal that doesn't produce milk and they never will. — Benkei

I don't produce milk?

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.

"it is not the case that if I pray then it will be answered" does not mean "if I pray then it will not be answered". It actually means "I pray and it is not answered".

Using modus tollens, the argument actually amounts to "if I do not pray then God exists, I do not pray, therefore God exists."

Formally:

¬G → ¬(P → A)
∴ ¬G → P
∴ ¬P → G
¬P
∴ G

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

I've agreed that the deductive logic within the OP is valid. I disagree that it's inductively valid. As in your reduction of the argument to:

"if I do not pray then God exists, I do not pray, therefore God exists."

that is deductively correct.

However, "if you do not pray then God exists" is a false statement if treated as a contingency. The reductio, for clarification purposes, was creating an absurdity, as in, "if I don't scream then I will be a billionaire, I do not scream, therefore I am a billionaire."

That is false because everyone knows that my defining characteristics are that I scream and that I am a billionaire.

If you don't produce milk, of what use are your nipples?

The argument is valid but its first premise is false (or at least hasn't been proven to be true).

:lol: Yes, yes, don't be too literal. You do have a mammary gland though.

You do have a mammary gland though. — Benkei

Well, I do, but those with congenital amazia don't. I assume they're still mammals.

I don't know, are they?

The "parlor trick" is just that the antecedent contains the contradiction "¬(P → A) ∧ ¬P". — Michael

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.

-

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

You are failing to recognize the non-equivalence of the two. Whenever the "So" premise is justified the argument works. In the OP it is prima facie justified ("So I do not pray"). In your example it is not ("So I do not scream").

also on bachelors:

How has the term bachelor evolved over time? Perplexity.ai:

The term "bachelor" has evolved significantly since its origins. Initially, in the 12th century, it referred to a "knight bachelor," a young squire training for knighthood. By the 14th century, it expanded to mean "unmarried man" and was also used for junior members of guilds and universities.

In the 13th century, it became associated with academic degrees, particularly the "bachelor's degree," indicating a low-level qualification. Over time, the term has taken on various connotations, including "eligible bachelor" in the Victorian era, referring to a financially and socially desirable unmarried man. Today, it primarily denotes an unmarried man without the historical implications of lower status.
---
So even bachelors are not as analytic as we like to pretend it is. But hey, everything frays at the edges of language. I'm not too worried about it.

And lo, God said "this should freak them scientists out for a century or Two." And verily, it was so.

https://www.britannica.com/story/why-is-the-platypus-a-mammal

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

FYI I edited my post hours ago. Weird that you're seeing the old version.

I've corrected what I was trying to say.

See also this that might be even clearer.

- I understand, but the same point applies to the edited post. You are prescinding from the translation and focusing entirely on the formalism. In fact you are back-engineering a new English sentence to better fit the formalism. Again, my "parlor trick" includes the translation itself. The levity of the OP derives in large part from the initial plausibility of the translation.

Again, Lionino's thread shows in some detail why there are no obvious English translations for ~(P→A).

even bachelors are not as analytic as we like to pretend it is. But hey, everything frays at the edges of language. I'm not too worried about it. — Benkei

That's the Quine argument. https://iep.utm.edu/quine-an/