The aforementioned is declared true and is appropriate and pursuant to the rules of the subreddit, r/truths because of its content being a vacuous truth.
The quantity of hippopotamuses in the set is 0, therefore the pet hippopotamuses belonging to me are nonexistent. It cannot be proven that there exists a contradiction to the claim, because the subject doesn’t exist and therefore the claim is true because nothing dissolves it of being a universal statement and because the premises cannot be met. There is no counterexample that can be found in the set of my pet hippopotamuses which consists of nothing. In other words, there is no instance where at least one of my pet hippopotamuses have not skydived, because I do not have any hippopotamuses at all.
The image attached depicts a hippopotamus that I am not in possession of, nor is it considered my pet.
Does that phrasing not imply a fraction with a denominator of zero?
It does not, no. There are no divisions done here.
all hippopotamuses (h) are that which have skydived (s)
if that statement is true: h = s divide both sides by s: h/s = 1 but if h and s are both 0: 0/0 = 1 (which us not true)
thus the statement is undefined, and although not false, certainly not a truth
That isn't the case, though. They didn't mention anything about portions of their hippopotamuses. They made what is called a logical assertion. The structure of their statement is
∀ x ∈ S, P(x) is true
Where S is the set of all their hippopotamuses, and P(x) is whether hippopotamus x has skydived. As a result of S being the empty set, this means that the P(x) is never checked. No division has occurred, and the condition P(x) is never false. Therefore, this is a vacuous truth.
Gotta love the power of set theory
Can you elaborate? I don’t get what you mean by this. It’s not undefined. It’s a truth.
While I agree with you, I think they were saying that amount of hippopotamus that you had that have skydived is [number that have skydived]/[total], which would be 0/0 in this case
Oh. I see it.
rouxls kaard
when did rouxls kaard say that
That's bc i stole your nonexistent hippotamuses
You monster! Give them back to him.
What if I stole them?
And when I make a post like this I get downvoted...
The Reddit community is weird like that sometimes
Because it’s hard to make an actual vacuous truth. The OP has succeeded in doing so, but most previous posters have not been able to get it right (usually because the size of the group was not 0, or other logical inconsistencies).
I mean just technically true statements in general, not just specifically vacuous truths
OP said:
∀x∊H∩P : s(x)
Where H denotes the set of hippopotamuses, P denotes the set of their pets, and s(x) denotes the property of having skydived at least once.
That statement is equivalent to:
∄x∊H∩P : ¬s(x)
"None of my pet hippopotamuses have not skydived at least once"
They then revealed that no hippopotamus is their pet.
∄x∊H : x∊P <=> H∩P=∅
Which we can put in the previous statement.
∄x∊∅ : ¬s(x)
Which is trivially true, as there exists no x in the empty set.
So their statement is true.
Q. E. D.
r/theydidthemath
10% reading, 90% trust
I want a hippopotamus for Christmas!
Russell's Teapot
How do you know you don’t have any pet hippopotamuses, how do you prove that you just didn’t lose all the memories of having one or more and they’ve all skydived and died and from the trauma you lost all the memories and maybe everyone around you too or they just always kept it a secret to not trigger your tears, hahaha
Try calculating the ratio of hippos that skydived to total hippos lol
So far…
“None of your hippopotamuses have ever skydived.”
So how does this phrase relate in regard to the sub’s rules?
Cap
I have eaten all the elephants I've touched in my life
So what is the hippo's name?
I. Believe this post is nonsensical which is against the rules making your description false
‘Nonsensical’ is subjective and your beliefs mentioned in your comment is irrelevant to the fact that this post contains a vacuous truth.
Your description states that the post follows the rules. Should this post be deemed nonsensical, it would be false for it would break rule 1.
In my opinion, it is a well thought out post.
I do to, however, weather or not this is the case is subjective which is also against the rules
if something doesn't exist it can not perform an action what are you on about lmao, your claim may be logically sound argumentatively, but its actual content is illogical
It’s a vacuous truth, which is still a logical truth.
If you have 0 hippos, and exactly 0 of the hippos you own have ever gone skydiving, then every hippos you have has gone skydiving.
A simpler example is the popular “all my hats are green” being a phrase that doesn’t actually prove the speaker owns any hats. I’d recommend to google vacuous truth.
A vacuous truth is grounded in logic. It not being able to perform an action is irrelevant to it being a truth. It is a truth because you cannot find a counterexample from a nonexistent set, which you can’t find a hippopotamus that hasn’t skydived. To disprove a universal statement, you need to find at least one counterexample to make the “All” collapse. In this you can’t, so it remains true.
not being able to be proved false isn't how truth works what, you cant prove there's not a statue of cookie monster on mars but that doesnt make it true this is so stupid
In logic, all X have property P is true if X is an empty set. It’s called a vacuous truth. Your example does not compare.
I think saying “can’t be proved false” was improper wording on OP’s part, it’s close but not quite accurate:
With a vacuous truth, it is true because the negation is false.
“All my pet hippos have skydived” can be written as a logical statement where h = “Hippopotamus”, P = “Set of thing that are my pets”, and S = “Set of things that have gone skydiving”. With that, the sentence is
“For all h in P, h is in S” (For all hippos that are my pets, that hippo has gone skydiving)
The negation of that statement is:
“There exists some h in P such that h is not in S” (There is at least one hippo that is my pet and has not gone skydiving)
OP has no pet hippos. Therefore, it is not true that there exists at least one pet hippo of his that hasn’t skydived. The negation is false, which means the original statement is true — for all 0 of his pet hippos, every single one has skydived.
Vacuous truths allow you to say literally anything you want about all elements of an empty set, and it will always be logically true, just not useful. This follows from the rules of formal logic. Saying you can’t prove it false is close to what we’re talking about, but not quite right — it’s not so much that you can’t prove it false, and more so that, if it was false, then the negation of that statement must be true, and we can prove that the negation is not true, so the statement must not be false
Vacuous truths are real truths, the phrase ”all phones in this room have a green wallpaper” is true if there are no phones in the room as there is no phone that doesn’t have a green wallpaper, similarly the phrase ”none of the phones in this room have a green wallpaper” is simultaneously true as there are no phones that does have a green wallpaper.
We are not ”proving” these by showing that the opposite isn’t true (as it can also be true in this case), a simpler way to think of these statements is like this:
”for all x in this room, if x is a phone it has a green wallpaper”
if there are n hippopotamuses, then n things have to skydive for it to be true.
there are zero hippopotamuses, therefore zero things have to skydive for it to be true.
This is double-sided. Can YOU prove this with 100% certainty? No, you cannot. This post violates the rules.
Yes you can. I have 0 hippos. I have 0 hippos that have ever gone skydiving. Therefore, every hippo I own has gone skydiving. It’s a “vacuous truth,” and is rooted in logic.
Except you cant prove you got 0 hippos. Its same as saying "im a guy"
According to rule four, this post doesn’t meet any of the immediate criteria for an untrue post. You don’t need to prove there isn’t a fully-formed onion embedded perfectly-intact within the sun to know that there isn’t one. You can’t entirely prove any negative in reality, but there are many negatives we know to be true.
Youre comparing that to owning a hippo, something thats statistically proven to ve done multiple times before
I have already proven that the claim is correct, within the condition that I do not have a pet hippopotamus.
Thats a sentence that cant be proven. When i say "i am a billionaire", i do not prove that i am one.
Read the body/description. I explained that it’s a vacuous truth.
No, for such truth you need to firstly prove you have no hippos.
"All Polar bears on uranus have jumped atleast once" is true, because it can be proven uranus has no Polar bears. In your statement we cannot prove you got no hippos
I’ve mentioned that I have no hippos and it’s what makes the claim true. I can prove it. There is an extremely small part of the population that owns a hippo as a pet and what’s considered a pet can be subjective. I don’t.
Well read the rules then, because statements you cant 100% prove are not allowed, you shouldve bringed a statistic or Clear proof that you dont own a hippo.
This post still violates the rules, checkmate
The claim is true according to the condition that I don’t own a hippopotamus. You did not capture my king so there is no checkmate.
And you didnt prove the condition, which directly breaks the subreddits rules
you need to prove you have zero hippos. For all we know you have three hippos and only one of them has gone skydiving. Just stating that you have no hippos is not proof.
For example, I can say that I have 4 cats. Even if I do actually own 4 cats, it is still against the rules of this subreddit unless I post actual proof of me owning 4 cats.
Then there can be no post on here that doesn't violate the rules, to moderate in this way is foolish.
How could you prove you own them? A picture certainly wouldn’t work, because they could be anybody’s cats. In fact, no picture, video, or source at all could verify you own four cats because you could’ve doctored the image, used AI, or hacked into some kind of pet owner’s database. This subreddit is propped up partially by any given user’s claim about themselves usually being accepted as true unless obviously false.
[deleted]
My bro got downvoted from on purpose 💔💔💔😭😭😭🥀🥀🥀
Ok but that also means none of your hippopotamuses has ever skydived, since 0 out of them did that
No. That implies I have at least one hippopotamus, which I don’t.
All my hippopotamuses have skydived because you can’t find a counterexample in an empty set and therefore you can’t prove that they haven’t skydived.
Bro has NOT studied formal logic 👏😭. Bro doesn’t know what a universal quantifier is 👏😭. 👏😭 bro doesn’t know the statement can be represented as ∀x(IsPetHippo(x)⟹HasSkydived(x)) 👏😭 bro doesn’t know that (A⟹B) is equivalent to (¬AVB) therefore if all A is false due to there being no hippos,∀x(A(x)⟹B(x)) is true 👏😭
Too many symbols, dumb this down so a goldfish would understand
"If you stick a fork in an electrical outlet, you will get hurt."
This is true.
However, yesterday I didn't stick a fork in an electrical outlet, and then I jumped up and down on some legos for a while. Barefoot. Somehow, I still got hurt.
The formal sentence "If A then B" is not the same as "A causes B," or "B is true if and only if A is true." However, in natural language, we often do mean this (or something similar). So what's going on is that implication in formal logic - called the "material conditional" - doesn't always line up with our intuitive ideas about implication in natural language. This is indeed an issue, ranging from "annoying" to "philosophically fundamental" depending on who you talk to, and there's a lot written about it. However, within the context of formal logic, we use the material conditional.
I think I understand, it's saying like Something that causes Something else =/= Something else only happens by the Something?
So for example, hunger causes pain but pain is not always because of hunger?
for normals pls....
If you have 0 hippos, AND you have 0 hippos that have ever gone skydiving, it follows that every hippo you own has gone skydiving. It’s a “vacuous truth.”
i see
correct. all have skydived and none have skydived
https://preview.redd.it/42i5o71xdr6g1.jpeg?width=1200&format=pjpg&auto=webp&s=ba6ab2e85673075f39be6f3b94727f40457c25a2
Most posts on r/truths are prima facie. You may attempt to disprove my claim but I guarantee you, it will not succeed. I’ve already proven my claim which appears in the body/description of the post.
Yeah, this is just dumb. You can spin it however you want, but something that does not exist cannot perform an action, therefore the truth is that you’ve never had a hippo that skydived. Your post is the definition of a lie.
the gimmick is that its a specific type of truth, where this logic is literally the point
There are no “types” of truth. In this instance, the thing is true or it is false, and the absence of existence of a thing means that it is entirely impossible for said thing to have performed an action, making this entire post a roundabout lie.
No, it makes it a vacuous truth, which is a valid type of truth statement in formal logic.
OP owns zero hippos. Every element of the set “hippos owned by OP” have skydived. This is true because there are no elements of the set “hippos owned by OP”, so it is the case that all 0 elements hold to this rule.
To actually explain using formal logic, it is a necessarily true statement because its negation is false.
The negation of “For all elements in the set of “hippos that are OP’s pet”, that element is also in the set of “Things that have gone skydiving”” would be
“There exists at least one element in the set of “hippos that are OP’s pet” that is not also in the set of “Things that have gone skydiving””
It is not true that there is at least one hippo that is both OP’s pet and has not gone skydiving, because OP does not own any hippos. The negation of OP’s statement is False. So, by the necessary rules of formal logic, OP’s statement must be true.
The key is that OP is using a universal quantifier on an empty set. If the statement was “My pet hippo has gone skydiving”, then it wouldn’t be a true statement because that means OP owns a skydiving hippo. By using the universal quantifier “All of my pet hippos”, then you are allowed to make technically true claims about an empty set… All 0 of OP’s pet hippos have, in fact, gone skydiving, for the simple reason that there is not a single counterexample of a pet hippo owned by OP that has not gone skydiving
Classical logic is just long-winded lies, then, because the one and actual truth is that if it does not exist, it can not perform an action, meaning that no hippos skydived regardless of roundabout logic.
No, you’re just not understanding that final step between what you’re saying and what OP is saying.
“If it does not exist, it can not perform an action, meaning that no hippos skydived”
Correct. This is true.
“ALL of my pet hippos have skydived.”
Like you said, the hippos do not exist. So it is true that all 0 of the hippos have skydived.
Let me put it to you this way, to explain vacuous truth: let’s say we have a room, and you can put people in the room. You also have a button that turns on a light. The light checks to see if the people in the room are male or female. If all of the people in the room are men, it turns green. If even one person in the room is female, it turns red. So, put two men in the room, the light is green. Put two women in the room, it turns red. Put 50 men and one woman in the room, it turns red. Now, if you take everybody out of the room… what color should the light turn? We already said that it turns red if it detects even one female person in the room. Does it detect any females?
The light has to turn green, because it has not met the condition to turn red. It is the case that, in the empty room, all people in the room are male, because there is not at least one person in the room that is female. The light must be either green or red, and the condition for it turning red has not been met, so by process of elimination it must be green.
That’s how vacuous truths work in formal logic. Every statement is either true or false. OP’s statement cannot be false, because the necessary condition for it being false (owning at least one pet hippo that has not gone skydiving) has not been met. So, since it can’t be False, it must be true.
Again, this is a consequence of OP making a claim about every element of a set that contains no elements. An individual claim (“My pet hippo has gone skydiving”) would not be true. But it is true that, for every nonexistent element of his set, each element has the stated property… because there does not exist any element that does not have the stated property, as there are no elements.
Classical logic doesn’t equal truth; It’s a way of rationalizing that doesn’t necessarily have any bearing on reality. A statement can be asserted through unsound logic, that doesn’t make it a truth.
That statement doesn’t actually mean anything lol.
Classical logic (I assume you mean formal logic) isn’t truth, it’s a way of breaking down statements into atomic units that can then create true or false premises, and formalizes universal relationships about those premises based on the rules of logic. It’s math, but for truth values.
When you say “a statement can be asserted through unsound logic, that doesn’t make it a truth”… well, formal logic is sound logic. It is the definition of sound logic, because it literally is logic, rigorously defined.
I’m not really sure exactly what you’re trying to say here, but if it’s along the lines of “I don’t care if this is a true statement according to logic, I think it’s a lie because it doesn’t sound right to me”…. I mean, sorry my dude, but the rules of formal logic are a much better baseline of truth than your subjective interpretation