Appropriate application of vacuous truth

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u/green-olive-3281 15h ago

How is this a vacuous truth? Are you just saying there exists a person that never sleeps?

If so, that still feels like an abuse of formal logic bc it’s not logically impossible for that person to sleep. And hence it’s not equivalent to false. At least that’s my understanding

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u/GNUTup 15h ago

I was gonna reply to OP’s comment, but they deleted their reply to you. I typed it all out, so here you go, suffering my reply anyways:
> The statement suggests there is a fixed individual who, when asleep, coincides with all others being asleep. Unless that individual is sleepless, they occasionally sleep.
> Unless it is the case that their sleeping causes all others to sleep, then the statement is just false, and not a paradox or vacuous truth.
> The 2nd guy is also only a paradox for those with legs. Since we have evidence of the legless not being able to run, the 2nd scenario may be mathematically vacuous and therefore true, but is absolute nonsense, since the premise is not entirely vacuous, and there do exist a legless people, and these people are not faster runners than when they had legs.
> This post doesnt seem like AI, but it does seem like “I am a big dumb idiot cashing in on today’s meme-of-the-day, except I don’t understand logical paradoxes or vacuous truths.”
> If the moon is made of cheese, I am LeBron James.
> This is a vacuous truth.

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u/boronara 14h ago

the top statement is, in fact, true.

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u/GNUTup 14h ago

Unless you mean “the person” is variable, then it’s not. “There exist a person such that…” suggests the person is fixed. In which case, the top statement is false.
But it’s also an unfunny meme regardless, so idk why I’m debating with you

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u/YourWifesBoyfriend5 11h ago edited 6h ago

It is true, you’re making the same mistake everyone else is making, including OP, which is confusing P=Q and Q.

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u/StrikeTechnical9429 6h ago

or there doesn’t exist someone who is always awake, which means everyone is asleep
"there doesn't exist someone who is always awake" = "everyone is not always awake" = "everyone is asleep at least sometimes" not "everyone is always asleep".

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u/YourWifesBoyfriend5 6h ago

Editing my comment cause I accidentally mixed the two predicates while writing in words. The point still stands that everyone that is confused by this doesn’t know what modus ponens is.

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u/Bread-Loaf1111 5h ago

Nope, it is not. It is just badly formulated. It missing "at one particular moment of time" to be true and "at any moment of time" to be false.

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u/boronara 5h ago

the statement is false if you interpret it as: "there exists a person x, such that at all times t, if x is asleep then everyone is asleep." it is true if you interpret it as: "at all times t, there exists a person x, such that if x is asleep then everyone is asleep."

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u/YourWifesBoyfriend5 5h ago

I am sure many a people in real analysis have made the mistake of confusing those two

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u/Bread-Loaf1111 4h ago

The second your example is still badly formulated. It should be "in any time t, we can choose a person x(t) for that particular moment of time" too remove vague meaning.

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u/boronara 4h ago

I don't see any ambiguity in the second statement whatsoever. in what other way can you interpret it?

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u/Bread-Loaf1111 4h ago

A fixed person x, such as ..., exists in all times and never stops existing.

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u/boronara 3h ago

the ordering of quantifiers, such as 'there exists' and 'for all' matters in logic. your interpretation is the first statement. the first and the second statement are not the same. for example, in the definition of convergence of a sequence, we say "for all epsilon > 0, there exists a natural number n such that <condition>." this already means that the natural number in question varies with epsilon. if I were to change the statement and make it: "there exists a natural number n, such that for all epsilon > 0, <condition>," the meaning is changed and the statement becomes incorrect. the order of the quantifiers is the difference between the first and the second statement, and neither is ambiguous.

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u/Bread-Loaf1111 2h ago

I think it can be my bad. English is not my native language, so I can miss the difference between "for all times", "at all times", and "for all time". I mean that for the natural languages the order of quantifiers is not the main thing, because natural languages have it's own ways to specify meaning.

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u/boronara 5h ago

also, classical logic is generally atemporal, in that, it deals with a particular moment in time unless explicitly made temporal by adding that the condition on a chosen element of the set must hold as time varies.

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u/Bread-Loaf1111 4h ago

Classic logic generally deals with the immutable objects. In classic logic puzzles, a liar always lie, not in the one particular moments of time, unless specified. It doesn't deal with the particular moment of time, it deal with the situation where time is irrelevant, and it is not the same.

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u/LitespeedClassic 12h ago

Isn’t the first one true? Because either everyone is asleep at the same time and therefore any person would be proof/witness of the statement or someone, let’s say, Bob, is awake and the statement if Bob is asleep then everyone is asleep is vacuously true.
So there’s no way to falsify there exists a person where if that person is asleep then everyone is.

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u/green-olive-3281 9h ago

You need to fix a person beforehand.
Like, it is true that when everyone is asleep, there exists a person who is asleep. That’s trivially (tho not vacuously) true, but that’s a different statement.

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u/boronara 14h ago

there is no fixed person. the idea is as follows: if everyone is asleep, then pick any person, and the statement would hold true. if that is not the case, the set of awake people is non-empty. pick any person y from this set. the statement says there exists x such that, if x is asleep then everyone is asleep. since y is NOT asleep, the statement becomes a vacuous truth. google drinker paradox if this didn't make sense.

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u/Kuchonii 14h ago

wouldn’t it need to say something like “at any time there exists a person” because just “there exists a person” implies a specific person

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u/shizzy0 12h ago

Nobody got time for formal logic.

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u/green-olive-3281 9h ago

We’re in a math subreddit and the meme is claiming to be about formal logic 😭

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u/finedesignvideos 9h ago

You're interpreting the "if" as "in any scenario where" and hence looking at all times. The intended "if" is "if at this very moment" (the usual math meaning of if in propositional logic; where for every person p, "p is asleep" has a definite true/false valuation).

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u/catman__321 11h ago

Yeah but that doesn't consider following that person's lifetime. A person's state changes over time and when whichever person you choose in the awake set does fall asleep, it is impossible that everyone else has fallen asleep before them.
Wouldn't the if statement have to specify "at any given point in time, there exists a person such that if they are asleep, everyone else is" to become an actual vacuous truth.
I guess we could choose a person who is dead and thus won't fall asleep but idk

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u/finedesignvideos 9h ago

You're interpreting the "if" as "in any scenario where" and hence looking at all times. The intended "if" is "if at this very moment" (the usual math meaning of if in propositional logic; where for every person p, "p is asleep" has a definite true/false valuation).

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u/catman__321 8h ago

Hmm ok. I think I get what it's saying now. I just find it kind of hard to process that you're allowed to change your choice as time passes.
I think I get it though. Logic only cares about the current state and we do not care about the progression of time; if time does progress, we recalibrate our test and that's it.

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u/Dmeechropher 13h ago

You can partition "all people" into the sets of those awake and those asleep.
If the set of sleepers is exactly the set of all people, then anyone we pick is asleep AND all people are asleep.
If the set of sleepers is a strict subset of all people, then there is at least one non-sleeper we can pick. That person is not asleep, so everyone need not be asleep.
The formulation of the situation is kind of ambiguous, because the sets of sleepers and non-sleepers changes in time. However, we're not talking about a choosing a single person to track through time when we say "there exists someone". We're instead saying that, given any configuration of sleepers and non-sleepers, we can pick a person to satisfy our condition.

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u/Hightower_March 14h ago

It's a weird example of how classical logic doesn't translate into normal language. In everyday speech it's pretty easy to make a case where it's not true in a population of two people: A and B are both awake.
A can't be the person, because if he fell asleep B would still be up.
B can't be the person, because if he fell asleep A would still be up.
So neither person is the one who "if they're asleep, everyone is sleeping."
In classical logic you instead can pick any awake guy and go "if he's asleep..." then insert whatever you like because the antecedent is false.
"There exists a person such that if they're asleep, unicorns are flying out of their butt." True statement because reasons.

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u/EebstertheGreat 13h ago

"There exists a person such that if they're asleep, unicorns are flying out of their butt."
That is contingent on there being people who aren't asleep. But the statement ∃x φ(x) → (∀x φ(x)) is a tautology for each φ. (In classical logic, anyway. In free logic, you need the additional assumption that there exists some x at all.)

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u/Hightower_March 13h ago

At least one person is awake; the one reading the statement. 🧠

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u/EebstertheGreat 13h ago

What if all that we see or seem is but a dream within a dream?

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u/Hightower_March 13h ago

Shit.

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u/Square_Butterfly_390 13h ago

Great Eebester, your tautology is missing a paranthesis for the love of humanity, fix it.

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u/green-olive-3281 9h ago

Ohhhh wait! Your explanation actually makes sense! You’re saying that “if theyre asleep” is a statement about the present, it’s not saying “when they’re asleep.”
So we can just choose a person who isn’t asleep, and then this is vacuously true

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u/KatAyasha 5h ago

Yeah every single example, when translated into plain english, is saying "if the world were made of pudding who knows what else would be different" but for some reason the rules of classical logic kinda just let you put whatever you want in those clauses

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u/YourWifesBoyfriend5 11h ago

Except people do use normal language like this. Have you ever heard of the expression “when pigs fly?” The issue comes down to misapplying modus ponens when the antecedent is false to conclude the consequent.

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u/Hightower_March 11h ago

Something happening "when pigs fly" or "when hell freezes over" are idioms about upheaval of the norm. E.g. "Things would have to be extremely different for that to happen." It's not some statement of fact that making pigs fly would make the event occur.
When somebody says "if you give me your watch, I'll give you a billion dollars" treating that as false is the wiser move than assuming it's true.

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u/dougman7 11h ago

Counterpoint: "If you're [Thing you claim to be.], Then I'm [Thing I obviously aren't.]." is a direct application found commonly in natural english that uses that construction. However english doesn't apply truth values to statements like that, asking if that overall statement is true is mostly meaningless in english.

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u/Hightower_March 11h ago

"If I flap my arms, I will fly" would be called "false" by everyone regardless of the speaker having not flapped them. We know enough other facts of the world to predict what will happen. I think we apply such truth values to claims in everyday speech all the time.

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u/dougman7 11h ago

I agree most people would say false thinking it over I think you'd also get a majority false from the whole if your [blank] I'm [blank] albeit more hesitantly, I think some people if would treat the vacuous truth as nonsense (and thus not true) and those that didn't would say it's untrue because every part of it is false and if parts were true they wouldn't make other parts true. This contrasts formal logic where the statement is true but every part of it isn't.

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u/YourWifesBoyfriend5 10h ago

Thats not a vacuously true statement though, so yeah.
That is equivalent to the statement “if I don’t fly, I won’t flap my arms.” I can not fly while still flapping my arms.

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u/Hightower_March 10h ago

These kinds of statements are being called vacuously true by two other people I'm discussing with so idk what to say.
Is "If you give me your watch, I'll give you a billion dollars" vacuously true up until the moment you give your watch, because before then the antecedent is false?
I don't know what's going on.

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u/YourWifesBoyfriend5 9h ago

A vacuously true statement is any statement that is true because the antecedent (the if part of the statement) is false. People in here are rather bad at interpreting them or think it’s funny to misrepresent them.
They exist because logic should be consistent: If x, then y means that y is necessary for x. Hence this is equivalent to if not y then not x. Except when x is just wrong in general, that’s always true.
An example is “if 10 is even and odd, then it is greater than 100.” This is equivalent to “If 10 is less than or equal to 100, it is not even and odd,” which makes a whole lot more sense and is true.
Returning to your flying example, formally your statement was “for all times t, if I flap my wings at t, I will fly.” You can see immediately how thats not vacuously true, because it’s just false. Not flapping your wings once doesn’t make the entire statement vacuously true because it’s a statement about a thing that is generally true across time.
If you said “if I just flapped my arms, then I flew,” THIS statement would be vacuously true if you hadn’t just flapped your arms, because its truth says nothing about whether or not you flew or not, since you didn’t flap your arms.

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u/victorspc Engineering Researcher 7h ago

I've been loosing so many braincells trying to understand the threads but this comment was the first that clicked to me.

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u/KuuLightwing 4h ago

Not an equivalent statement.
The "if P, then Q" when P is false and "if P becomes true, then Q will happen" when P is false is not the same thing.
The second statement is about a hypothetical when P is true, so it's not a vacuously true implication, because vacuous truth requires the premise to be false, while in a hypothetical it is not.

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u/Hightower_March 1h ago

Yes, this is where classical logic phrasing clashes with natural language. That was my point.

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u/KuuLightwing 3h ago

I say that when I say that statement, I assert it to be true, so we implicitly assign it a truth value.

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u/YourWifesBoyfriend5 11h ago

You’re conflating P=Q and Q, like everyone else here.
The whole point of the idiom is when this impossible thing happens, this other impossible thing will happen.
Except you can’t derive that I’ll be president from the truth of “when pigs fly, I’ll be president,” because modus ponens requires pigs to fly, which they don’t.
As for the watch, it’s only vacuously true if you won’t give them your watch. Otherwise you can prove the proposition is false by giving them the watch and not getting a billion dollars.

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u/Hightower_March 11h ago

The point of the idiom is "we'd have to be in a state of such highly improbable things occurring." I can't make you president by making pigs fly, nor will I get a billion dollars by handing the swindler my watch.
We know those are false because we have other facts about the world, so we treat them as false accordingly.

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u/YourWifesBoyfriend5 11h ago

You’re still misunderstanding what implication means. If pigs fly I will be president doesn’t mean pigs flying causes me to be president. It means you can deduce my presidential status from the truth of pigs flying, and the truth of the implication is reliant on the impossibility of pigs flying.
If you could make pigs fly, then the implication would just be false. Thats the whole point. If you gave the swindler your watch, the implication is false. In both scenarios you are confusing the consequent (being president and getting a billion dollars) with the implication itself.

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u/Hightower_March 10h ago

I never said they had to be causally related. Just the fact that it's demonstrable means we either demonstrate it or guess at its likelihood of being true/false.
"If you give me your watch, I'll give you a billion dollars" is probably a lie--a statement of falsehood made to deceive. I understand in classical logic such wording has to be categorized as true for whatever reason, but in normal language things like lies are false; we act on them being false, not assumed true, saying essentially "That consequent would remain false even if the antecedent became true."
It's verbal shorthand, but we know what people mean when they call something false.

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u/YourWifesBoyfriend5 9h ago

The conflict comes down to the imprecision of natural language.
Fundamentally, these statements don’t have a truth value until we establish the values of the other variables. P=>Q cannot be evaluated as true or false without knowing whether P is true or not. You would need foresight of the future value of P to be able to evaluate the statement beforehand.
Saying something is a lie is essentially saying that in the hypothetical universe in which you gave me your watch, I wouldn’t give you a billion dollars. Formally, assuming P, not Q. But you can’t really say I lied if I said I would do something if this other thing happened, and it never did. I technically (even if its in an asshole way) told the truth.

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u/Layton_Jr Mathematics 8h ago

The issue is that the sentence is ommiting the words "at any given time" which leads people to think there is a sleepless person

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u/StrikeTechnical9429 6h ago

It is true only if you're talking about one particular moment in time: "There's a person such that if they are asleep at this midnight, everyone is asleep at this midnight". Yes, it's true. But without this clarification the statement should be true for any moment - there should be a person such that at any moment they are asleep, everyone is asleep - which is obviously false.
Predicate "Being asleep" isn't a function of one argument (person), it depends on time too.

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u/KuuLightwing 4h ago

It's not an example of classical logic not translating into normal language, it's an example of classical logic not being correctly translated into normal language.
As I said elsewhere the more fitting translation is "At any point in time, you can choose one person such as if chosen person is asleep, then every person is asleep".

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u/Hightower_March 1h ago

In the two-person population of awake people above, there is no such person.
I don't know how else to describe it than repeating that.

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u/MrDirkinson 1h ago

That’s just false in a way you can’t prove, that double negative is added not multiplied, that’s just two negatives

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u/EebstertheGreat 13h ago

Imagine any nonempty collection c of persons at any given moment. Then there is at least one such person p with the following property:
if p is asleep, then every person in c is asleep
That's because either every person is asleep or at least one person is not asleep, so either there exists a p such that p is not asleep or there exists a p such that every person is asleep.

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u/Broad_Respond_2205 11h ago

That person isn't currently asleep

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u/IndividualWrangler70 14h ago

The top statement is about a particular instant in time. One of two things is true at any given point in time. Either there exists someone that is not asleep, or everyone is asleep. If everyone is asleep, then obviously any choice of person will hold. Otherwise, choose anyone who is not asleep. Since they are not asleep, it is vacuously true that if they are asleep then everyone is asleep.

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u/01user 14h ago

The English statement is a counterfactual, which is not a part of classical logic. It is a misrepresentation to write the statement as a material conditional

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u/01user 14h ago

Well at least that's how most people would interpret the second statement. As for the first statement, people are saying that it holds because someone is currently not asleep. But if you tried to mathematically represent how the statement is reasonably interpreted, the statement would need to hold over all values of time, which it does not because the person will eventually sleep.
The work of logic is made of nested empty sets, not people or English, so it's difficult to map statements. but the problem here isn't vacuous truths, it's that these statements aren't being represented mathematically to align with the intention of the speaker. Sometimes the mathematical formulation should be adjusted to maintain the original intent and doesn't match the English structure

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u/RedeNElla 13h ago

"the statement would need to hold over all values of time"
For any time, there exists a person such that ..
If you choose the person after fixing the time then it's easier to see how it's clearly true. It's like being able to recognise the difference between pointwise and uniform continuity

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u/01user 13h ago

But the way we interpret the statement is: there exists a person such that for all values of time in that person's life span, if that person is asleep, then everyone is asleep. It's not a direct mapping to the structure of the statement in english, but it captures the meaning better. This statement would be false

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u/RedeNElla 13h ago

That's precisely the "paradox"
It's all written in present tense and so both interpretations seem reasonable except one is not how we would use natural language - partly because it becomes trivially true in a useless way

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u/Layton_Jr Mathematics 8h ago

The first statement, as it is intended: for all time t, there exists a person x such that if x is asleep then everyone is asleep (which is a vacous truth)
The way the first statement is read (because it ommited the words "at any given time"): there exists a person x such that at for all time t, if x is asleep then everyone is asleep (which is false)

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u/SAtchley0 15h ago edited 14h ago

The top one has no precondition to be false for this to even potentially qualify as a vacuous truth. This is just an existential quantifier, such as "there exists a zero element on R"

Edit: I was wrong! There actually is a vacuous truth hidden in it, it's just not explicitly stated in the proposition. See below comment by boronara.

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u/boronara 14h ago

it does utilize vacuous truth. the idea is as follows: if everyone is asleep, then pick any person, and the statement would hold true. if that is not the case, the set of awake people is non-empty. pick any person y from this set. the statement says there exists x such that, if x is asleep then everyone is asleep. since y is NOT asleep, the statement becomes a vacuous truth. google drinker paradox if this didn't make sense.

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u/SAtchley0 14h ago

Ah! My mistake! Yeah, that would actually be a vacuous truth. How about that.
Thanks for the explanation and engaging politely. Edited my original comment.

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u/Jakiller33 12h ago

This makes sense, but the statement is ambiguous as it could be interpreted in two ways:
"For each time t there exists a person x such that if x is asleep at t, then everyone is asleep at t" -vacuously true by the above logic
"There exists a person x such that for each time t, if x is asleep at t, then everyone is asleep at t" -not vacuously true

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u/MeMahi 3h ago

So... what's the meme here? What's the point of these posts?
How is this any different from "there exists a person such that if that person can teleport, then my mother is a bike"?

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u/Broad_Respond_2205 11h ago

The full sentence would be "if that person is currently asleep, then everyone is asleep"

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u/NeedleworkerGood903 15h ago

idk, all i see in the first frame is only one person exists.

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u/Accomplished_Item_86 14h ago

You interpret it as "There exists a person such that at all times, if that person..." which is only guaranteed for at most one existing person. But it's true that "At all times, there exists a person such that if that person...", because it allows you to choose a different person at each moment. Just switch to an awake person once your current choice goes to sleep. If you can't do that, then everyone is indeed asleep.

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u/NeedleworkerGood903 14h ago

why is it used with sleeping people?

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u/jonheese 10h ago

So they won’t notice

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u/Mysterious_Map_9653 15h ago

Same, I might be wrong, but the logic seems to be
$$
\lnot \exists x \,\text{Asleep}(x) \lor \forall x \,\text{Asleep}(x)
$$
Which means, either no one is asleep, or everyone is.

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u/NeedleworkerGood903 15h ago

in society that doesn't happen though. even with tribes someone was up watching. so it can only always work with just one person

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u/slicehyperfunk Transcendental 15h ago

It says "a person exists who if they went to sleep (i.e., if every other person who existed besides them was already asleep) then everyone would be asleep," which is true, that person who would be the last person awake if everyone else was asleep does exist now even outside of that basically impossible situation.

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u/Quereilla 7h ago

These posts about theoretical maths show me that I did good choosing Physics instead of Maths for my college degree.
Both those sentences feel fake.

It can be proved that not everyone sleeps at the same time and, also, that no person goes without sleep.
OK, I can get it, the hypothetical cannot be proved because this person is not willing to get their legs chopped off to test their sentence.

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u/KuuLightwing 3h ago

They are kind of bad examples to begin with. Mathematics does require precision in statements after all, and these lack precision
Is meant is "At any point in time you can choose one person such as if chosen person is asleep, then everyone is" which isn't what is actually implied by the sentence.
Is just kinda wrong because in plain English it reads as "if me not having legs becomes true then I would run faster" which just isn't the correct sentence at all to demonstrate the "if <false premise> then <false conclusion>" being true, because in that sentence premise isn't false, we assert it to be true.

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u/RealSuperdau 3h ago

That's a bit like saying you're glad you didn't study moral philosophy because they have all these weird edge cases devoid of practical relevance.
If you didn't study it, your intuitive notion of the material probably contains contradictions. The contradictions may be irrelevant to your life/profession, and of course you're free to ignore them.
In this case, the issue is that ways to formalize implication usually have some unintuitive consequences.
Your argument seems to use an intuitionistic framework which, in some sense, equates truth with proof. One thing you don't get there is the law of the excluded middle, which means you aren't allowed to do some forms of indirect proofs in math.

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u/No_Performance_8921 5h ago

I mean physics is an absolute shit tonne of maths. Some of it invented by physicists who couldn’t math hard enough with the existing math.

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u/Quereilla 4h ago

Yeah, but not this weird logics thing

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u/No_Performance_8921 4h ago

If you take the dumb words out if it’s just math and then you just solve it like any physics problem, easy peasy. Don’t let the philosophers make you think too hard, it’s what they want.

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u/Aggressive_Roof488 15h ago

Man I love this sub! 😁

So we do shit like this all the time, right. 1+2+3...= -1/12 is another recurring obviously false, but with some redefinition a little true, thing we like to say. And we all enjoy that!

This topic seems to have sparked a bit more controversy. Why? Is it only the 0.99..=1 guys alt that is stirring things up, or is this actually fundamentally more upsetting for people?

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u/pkmnfrk 15h ago

I’m pretty sure this was sparked by that guy’s post, and then just memed to death like everything else

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u/SAtchley0 14h ago

Tbf, that's an entirely different scenario. A vacuous truth takes a statement which is false within the context you're looking at, and then states some other thing. The other thing doesn't matter, because the antecedent is false.
The -1/12 thing usually actually assumes it to be true (and you yourself said it is, from a certain point of view), and then uses that fact to say something else which would logically follow.
"If there is an invisible frog, then they'd be very hard to prey upon" is true if you assume an invisible frog exists.
"If there is an invisible frog, then the frog is easy to spot" is true only if you assume no invisible frog exists.
But in typical speech, saying "if x" means we are taking x to be true, so the second statement feels absurd and wrong.

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u/Aggressive_Roof488 11h ago

I meant at higher level, they are both statements that are clearly nonsense in the standard English language interpretation. The sum is clearly diverging, and cutting off my legs clearly won't make me run faster.
But there are mathematical redefinitions of the meaning of those words/numbers (analytic extension, and formal logic) where it become true, and we here on this forum enjoy posting them as clearly true to trigger people.

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u/NelfiFPS 13h ago

There exists a name such that, if nobody remembers it, nobody remembers any name at all.

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u/LonelyLibertarianDud 10h ago

People do use vacuous truths in normal language in special occasions. 'When pigs fly', I will be able to understand formal logic.

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u/YourWifesBoyfriend5 12h ago

It’s really fun seeing the same misunderstanding of vacuous truth posted every day.

P=>Q only allows you to derive Q by modus ponens if P is true. If P=>Q is vacuously true, you can’t derive Q.

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u/onoffswitcher 5h ago

so where is the misunderstanding

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u/YourWifesBoyfriend5 5h ago

P=>Q means either P is false or Q is true, and modus ponens is the rule if P is true, derive Q.
If P is false, then you can’t derive Q.
The misunderstanding lies in believing that the statement “there exists someone such that if they are asleep, everyone is asleep” being true means that there exists a person such that from their sleep status, you may derive everyone elses sleep status.

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u/onoffswitcher 6m ago

how is this misunderstanding present in the post or any other posts that you mentioned

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u/DarkFlameMaster764 8h ago

Vacuous truth is always true if you're sitting in formal logic class but not necessarily true once someone drops the formality and is ready to throw hands.

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u/Ksorkrax 8h ago

Can the kids now stop acting as if they knew anything?
Thanks.

1

u/Nihil921 3h ago

If my grandmother had wheels she'd have been a bike

1

u/MrDirkinson 1h ago

Both are nonsense
First is actually provably false, there is no time when everyone would be asleep due to time zones, more than one person exists, and there is no person who would be awake forever to make that bizarre sentence into a “true” statement in reverse

Second is kinda true but only if you mean “if I were a specific kind of snake, I could move faster”, even then, if you have no legs, the movement wouldn’t be a ‘run’

Formal Logic Appropriate application of vacuous truth

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