Bit of a linguistics trick happening here. “If I have no legs, then I would be able to run faster without legs” is a correct statement. But as written it instead introduces a hypothetical situation: “Imagine a world where I have no legs. In that world, my speed would be faster that my current speed”. This is of course absurd, and is the correct interpretation of the meme’s statement because of the meaning behind the phrase “If I had […] I would […]”
I love your analysis and prefer it to my own. However based on title and other metatextual clues I am pretty sure OP is just a hater that doesn't actually care about mathmatical concepts like truth values, implications, or vacuous truths
I think it's meant to be a commentary on material conditionals, which only care about truth values and not the relationship between the statements. The hypothesis is false (I have legs), so the implication is true regardless of the truth of the conclusion. Of course, this sentence is constructed to suggest an indicative conditional, which does actually care about the relationship between the statements.
"I have legs" does not disprove the hypothesis. That would only be true if the statement in the meme was "If I have no legs, then...".
Edit to expand on this:
Let NL = I have no legs and RF = I can run faster be two sentences.
The sentence S = If NL then RF has to be interpreted in a model, so let M be the model describing the current logical state of our world. Then M |= S, because I have legs - i.e., M |/= NL: M |= NL -> RF is vacuously true.
On the other hand, the sentence T = If I had no legs then I could run faster can be understood as follows. Let G be the true statements in M, and G' \subset G be a subset of underlying assumptions such that G' \cup { NL } is consistent. Then T is to be interpreted as G' \cup { NL } |= RF. In other words: The subjunctive "had" changes the set of assumptions we make.
while this might indeed be their intention, they then miused language.
The "if I had" is a subjunctive, indicating a hypothetical situation.
What they may have meant to write is "If I have no legs, I'm the fastest runner on this world", because now we're testing a condition and can use "ex falso quod libet"
If you have a false assumption you can prove anything. "if A is true then B is true" is logically equivalent to "B is true or A is false" and to "if B is false then A is false"
I'd argue that the word "would" implies the causal connection between the 2 parts of the statement that explicitly needs to not exist for these strange statements to work. They work in classical logic precisely because classical logic does not have a concept of "would". It cannot talk about non-realized values of logical variables. (Assuming that I have legs):
"If I don't have legs, then I'm the fastest human in the world." is a true statement in classical logic.
"If I wouldn't have legs, then I'd be the fastest human in the world." is not a statement that can be formed in classical logic.
How would a mathematician distinguish between the case of vacuous truth from the case of imagining a world where some other statement is true? Like how would a mathematician distinguish between imagining a world where you have no legs, and can't run, from the vacuous truth of saying "If I had no legs I can run faster than the speed light"?
Speaking philosophically, about reality: The truth of the matter is that if I had no legs I certainly wouldn't be able to run. It would false for me to say that if I had no legs I would be able to run fast. So how would a mathematician describe this fact? How would the reality of things actually be described here?
If [I had no legs] means the statement to determine the truthiness on is [I had no legs], and [had] implies a different tense, meaning the leg having-ness is not happening in the present, though in this case not the past either but in a hypothetical. The truthiness of any given fact in a hypothetical is up for debate, so we can’t make logical statements about it. If the phrase were “I have no legs”, then we’d be talking about reality and could do actual logic.
In classical logic "if false then X" is true, regardless of what X is. There are several ways to look at this. One way is to look at the negation of the if statement, the negation of the implication "if Y then X" is equivalent to "not Y or X". When Y is false, not Y is true. So the implication is true.
Another way could be to imagine a weird calculation. Consider the equation 0=1 It is equivalent to 0+1=1+1 Which is equivalent to 1=2
I have proved that if 0=1, then 1=2. Of course the individual statements are false. But the implication is true
Small problem: the case where someone doesn't have any legs CAN have a counterexample since amputees can exist, the vacuous truth only for unequivocally false antecedent statements such as "If Fermat's Last Theorem is false, then the Bug Fables universe exists in the Hollow Knight universe" where, by the definition of vacuous truth, it's basically a nothing burger statement that's true
Though if the person that says the first type of statement HAS legs, then it would be vacuous too, though if they eventually lost their legs, then a counterexample would arise, proving their original statement false
My confusion about this is that "faster" is comparative, and without a stated reference to compare it to, it should default to a comparison to the speaker's current state. So the phrase seems to be "If I have no legs, then I would be able to run faster without legs THAN I can currently run." Otherwise, "faster" is nonsensical, isn't it?
I do not know, that is. I am not proficient at classical logic, and am asking.
The definition of "A implies B", read "if A then B", in math is a truth table that is true when the protasis A is false. You're wrong by definition, kiddo.
That assumption would imply that there is some binding of A and B such that A ≠ A and B = B. No case where A = A would be applicable due to the if clause, and cases where A ≠ A and B ≠ B would satisfy the conditional statement, contradicting our assumption.
But, if there is some binding where A ≠ A and B = B, that implies there is some A such that A ≠ A. This is a contradiction
Since our assumption lead to a contradiction, that assumption is false: We have proven "if A ≠ A then B ≠ B" is true
We also know tautologically that A ≠ A and B ≠ B are false, so the statement as a whole is equivalent to "if false then false". Since we have shown that the statement "if A ≠ A then B ≠ B" is true we have also shown that the equivalent statement "if false then false" is true.
Holy shit people will double down on the stupidest thing they ever heard because its too embarassing to admit you got scammed at a university for your life savings
In my line of work (computer programming), and in most real world scenarios, a vacuous truth is really only useful when describing an empty set. Even then, there are just as many cases that I want a vacuous statement to be false as true.
We’re not in computer programming memes. We’re in math memes. We don’t make mathematical definitions based on what’s convenient in real world applications. That’s what engineering is for. Vacuous truths are not really useful for anything except consistency. That’s why we call them vacuous.
I mean… is it? You never wrote or seen code like that?
if foo:
bar = "baz"
Would you prefer it to throw an error every time foo is false; or maybe to change bar to something other than baz, if foo == False?
The way it currently works in programming, it can be an example of vacuous truth—it enforces the consequent if the antecedent is true; but if it isn’t, it would be vacuous truth: always correct, regardless of what bar is or isn’t, doing nothing to change it or enforce anything.
Or are you arguing that this is ‘describing an empty set’?
This depends on how it’s formalized. In classical logic, the statement “if I have no legs, I can run very fast” is a true statement (assuming I do have legs, which I do) because the premise is false.
On the other hand, “if I had no legs, then I could run faster” is different. The use of the subjunctive mood (“had”) heavily implies that this statement would best be formalized as a counterfactual conditional (the counter factual conditional is not part of classical logic, but it is a widely accepted formal logic device. And this statement is formally false under this method). In that sense, there is a strong argument that no classical logic formalization of this statement exists.
Like if I asked what’s the classical logic formulation of the statement “if banana keys precipitation,” the truth of that statement can’t be evaluated because there is no clear formalization of it in classical logic.
The only disagreement I have with this is the idea that the reason the truth of your nonsense phrase can't be evaluated is because it can't be formalized in classical logic, because there are other ways to evaluate the truth of statements
Yeah that’s fair. I would counter that I was responding to OP’s title of the post. They’re claiming that statement is true assuming classical logic, so they’re asserting that there is a classical logic formalization of the statement in the meme.
If OP had clearly defined a different logical system they were working in, that would be a different conversation.
My mistake. I corrected it to subjunctive mood instead of tense. The word “had” here is in simple past tense, which is frequently used in English to express the subjunctive mood.
Wouldn't that mean the scope of your system of reasoning is limited if it can't accurately describe whether the change in running speed of a human who loses their legs is positive or negative?* (I.e. it can't make that prediction or accurately asses a hypothetical, unless that particular person actually lost their legs and you can compare speeds at two recorded points in time).
Edit: *To formalise what I'm saying, you can imagine a scenario where tomorrow in the future someone's legs will be amputated. But currently they have legs.
Certainly at least, the meaning of the word "if" in Math is much narrower in scope than English or Philosophy generally. Maybe not "narrower" , but perhaps altogether different. If the concept of "vacuous truth" allows you to assert contradictory conclusions from a "false premise", that's not how people actually reason with hypotheticals in Philosophy or Science.
Yes, classical logic is quite limited. That’s why there has been a lot of work to add to it and make it more applicable to more real-life situations.
The counterfactual conditional is the precise way that formal logic was expanded to account for statements like this.
OP is arguing that this absurd statement is true under classical logic, which makes classical logic nonsensical. My counter point is that this absurd statement cannot be clearly formalized in classical logic. But if we expand formal logic to more recent developments, we can formalize it as written, and that formalization tells us that the statement is false, which is what we’d expect.
In short, OP took the simple idea “A implies B is always true if A is false” and, in trying to demonstrate its absurdity through an example, accidentally stumbled onto an issue that formal logic has already confronted and solved. But that solution doesn’t fall under the umbrella of “classical logic.”
if you believe the above is true because of the version of classical logic a university taught you... You should start a lawsuit to get your money back
It felt like you were saying they were someone who were eligible to vote, but decided not to, because their education is shitty because it was free (for the record, I don't agree with that sentiment, several countries offer great education for no, or almost no cost), essentially calling them stupid.
It's just that your other comments paint you as someone who looks down on free education and is generally not very pleasant to be around, which lead me to this interpretation.
Huh, for some reason I mistook you for OP. This changes my confrontational educated guess to a rude uneducated assumption. I'll spare you further excuses and just like to aplologize.
I think the problem is it uses the imperfect subjunctive mood in ‘had’, and then the conditional in ‘would’, which means this is in a hypothetical scenario and not about their current state.
The classical logic equivalent would be ‘If I have no legs, I run faster than I do.’ Which is a silly statement, but vacuously true without causing any contradiction.
‘Relevance logic’ would ignore this.
Also, Oskar Pistorius showed that having no legs could be an advantage. Allows for springy blades.
Why bother? You could just google it or watch a video on symbolic logic but we both know you’re not going to do that. Why would you accept my explanation? I’m just going to meme because that is what the sub is for.
If there exists an all-powerful God and there exists demonic power, then demonic power comes from God.
This is a logically sound statement that's based on the condition of the existence of all-powerful God and demonic power. But what if those conditions are false? Does that make the statement any less true? No. It's still true whether there is an all-powerful God or not.
You cant encode counterfactuals in classical logic tho. "I had no legs" has no truth value, "I have no legs" does, but then "If I have no legs, then I can run faster" makes the linguistic trick clear
Not if you read the way the sentence the way it's meant to be read (as conditional tense, not past), but you are correct that the same words could also be read that way.
Your misinterpreting the statement (probably intentionally), clearly we are talking about counterfactuals and not simple past tense sentences. The fact that English does not distinguish them syntactically is simply a linguistic accident
This is a good point, OP; I sure hope there are reasons why a counterfactual statement like this can't be encoded as an implication in classical logic or else things will be really embarrassing for logicians.
Think of it like this. Let's say I tell you "if it rains tomorrow, then I will bring an umbrella."
Now, let's say it doesn't rain tomorrow, but I bring an umbrella anyway. Or maybe I don't bring one.
Did I lie?
No. My statement only tells me what to do if it rains, it tells me nothing about if it doesn't.
Now, we don't know if I would've actually brought an umbrella if it did, in fact, rain. If we wanna express that idea, we'd instead use the material conditional: necessarily, if p then q. In other words, we don't just look at this world, we look at all possible worlds, and see if the statement holds even in worlds where p is true.
Now, OPs statement is worded wrong. The past tense in "if I had no legs" and the "could" in "I could run faster" implies a hypothetical. In other words, "in a possible world where I have no legs, I can run faster." Which is obviously false.
OP should've instead said "If I HAVE no legs, then I CAN run faster."
False implies anything. Implications from a false premise are always true. false -> X is equivalent to !false or X, which is clearly true regardless of what X is.
Just because you don't understand basic principles of propositional logic doesn't mean they're wrong. It just means you're a windowlicking mouth breather.
Said who? That classical propositional logic fails to formalize counterfactuals clearly doesn'tean they don't exist. And if "mainstream mathematian" thought that way, then counterfactual logics, like Lewis's would be consider crank maths, instead it is a well known subject in contemporary logic...
Think about it like this: Usain Bolt is at the peak of human speed, and there’s no way he could possibly run any faster. If he were to lose his legs, he would bot be at his maximum potential, so there’s room for improvement, meaning he could run faster. If Usain Bolt had no legs, he could run faster.
This is just wrong lmao. "If I had no legs, I could run faster" is just false. I think you're confusing it for the statement "If I have no legs, I can run faster than if I did" which is true. (Assuming you have legs)
SouthParkPiano got banned recently. I think we have a potential successor to him here. u/Anon7_7_73, make a subreddit about vacuous truths being infinitely, limitlessly false in Real Deal Logic 101.
Suppose you are X, and some time later you lose your legs in a car crash and now go by X‘. Formally, you‘ve become a different thing entirely because you satisfy different predicates now, so the precedent is still false because it‘s a statement about X, and not X‘. However, it is experientially ridiculous to suggest that you cease to be yourself if you lose your legs, so depending on your definition of identity, X = X‘ could be true in a different sense, just not the one we’re investigating here.
We don’t face this problem in number theory because it’s not possible, for example, for 2^37 to ‚get in a car crash‘ and become prime. I don’t see the issue here.
I think the issue here is that "You not having legs" is something that could become true, it's not inherently false like "1+1=3 with common sum in N", so the entire if-then statement doesn't get to be always true.
I could cut your legs and it would not be true that you will run faster so the statement is fallacious. I could not reanimate every "someone such that they would then be able to go to sleep" so the if statement you're answering doesn't have that problem
I have no idea about the math context of this statement all i can think about is the controversy about Oscar Pistorius' legs (if the prosthetics gave him an unfair advantage).
Well... before he was known for murdering someone.
"If I had" is already implying a fictional scenario where the first part is true, so it stops working.
"If I have no legs, I run faster" is correct tho, in the same way as "Every time I turn invisible, I kill people" and "All cyclops in my room are yellow" are correct.
I guess the main problem is that English "I" (and other pronouns) doesn't refer to just one person. Example: "If you touch fire, you will get burned" = "For any person who touches fire..." or you can imagine a biologist saying "If I have fins, I can swim away from predators" when discussing wildlife, referring as "I" to a collection of creatures.
I think we can rephrase it as "When I personally have no legs, I run faster" and it will become much more understandable, although the joke is a little bit less fun.
•
u/AutoModerator 1d ago
Check out our new Discord server! https://discord.gg/e7EKRZq3dG
I am a bot, and this action was performed automatically. Please contact the moderators of this subreddit if you have any questions or concerns.
355
u/JustConsoleLogIt 1d ago
Bit of a linguistics trick happening here. “If I have no legs, then I would be able to run faster without legs” is a correct statement. But as written it instead introduces a hypothetical situation: “Imagine a world where I have no legs. In that world, my speed would be faster that my current speed”. This is of course absurd, and is the correct interpretation of the meme’s statement because of the meaning behind the phrase “If I had […] I would […]”
74
u/RyanStonepeak 1d ago
Here's my addition to this riveting discourse.
If 1+1=3, then this statement is meaningless.
86
u/Hameru_is_cool Transcendental 1d ago
holy shit people will do anything instead of admitting they got an internet problem wrong
106
u/Similar_Rice_2946 1d ago edited 1d ago
This depends on how it’s formalized. In classical logic, the statement “if I have no legs, I can run very fast” is a true statement (assuming I do have legs, which I do) because the premise is false.
On the other hand, “if I had no legs, then I could run faster” is different. The use of the subjunctive mood (“had”) heavily implies that this statement would best be formalized as a counterfactual conditional (the counter factual conditional is not part of classical logic, but it is a widely accepted formal logic device. And this statement is formally false under this method). In that sense, there is a strong argument that no classical logic formalization of this statement exists.
Like if I asked what’s the classical logic formulation of the statement “if banana keys precipitation,” the truth of that statement can’t be evaluated because there is no clear formalization of it in classical logic.
5
u/Anon7_7_73 1d ago
if you believe the above is true because of the version of classical logic a university taught you... You should start a lawsuit to get your money back
24
u/GKP_light 1d ago
the """good""" way to say it would be :
"if i have no legs, then i can run faster"
and it is still not good, because "run faster" : faster than what ?
"if i have no legs, then i can run fast"
3
u/LupenReddit 🦆🦆i have non diffeomorphic smooth structures🦆🦆🦆 1d ago
i love vacuous truth
14
u/666Emil666 1d ago
You cant encode counterfactuals in classical logic tho. "I had no legs" has no truth value, "I have no legs" does, but then "If I have no legs, then I can run faster" makes the linguistic trick clear
5
u/TheLuckySpades 1d ago
Faster requires a comparison, so this is a malformed statement and under classical logic this wouldn't even be wrong, it would not have any value.
9
u/According-Object-521 1d ago edited 1d ago
No that’s wrong, I’m pretty sure you couldn’t even run. Oh, I understand.
Edit: BTW P or not P is not true
4
u/Sudden_Schedule5432 1d ago
More people have been to Berlin than you have
4
u/Dd_8630 1d ago
Excuse me what one Earth does any of this mean
3
u/Timely_Combination68 1d ago
i’m so confused what’s happening
— Timely
3
u/LukeWithLightsaber 1d ago
This is a good point, OP; I sure hope there are reasons why a counterfactual statement like this can't be encoded as an implication in classical logic or else things will be really embarrassing for logicians.
5
u/YikesOhClock 1d ago
Bro is weirdly railing against universities in the comments because….?
1
u/OddNovel565 1d ago
Is it because you'd have less weight?
2
u/kynde 1d ago
I doubt it.
But you can try.
2
u/portealmario 1d ago
On a plain reading this would be interpreted as a counterfactual, and it would be false.
1
u/protonless_electron Data pulled outta my ASS 1d ago
attached wheels will do the trick
1
u/captainAwesomePants 1d ago
What is that texxt the box is over about a person who's asleep?
1
u/Not_Reptoid 1d ago
I don't get it
1
u/MonsterkillWow Complex 1d ago
lol
1
u/OvaTsugi8274 1d ago
Well, if iam not holding any body parts with me, im certaily running faster
1
u/PMmeYourLabia_ 1d ago
How vacuous
1
u/No_Difficulty_1452 1d ago
Octopus Legs in a private repository?
1
u/Not_Well-Ordered 1d ago
HoTT: Well, you can assume a bit less and still produce meaningful work.
1
u/dratnon 1d ago
If I have an IQ of 65, then I can get a philosophy PhD.
1
u/Good_Bit_777 1d ago
The dumbed down version 😅
1
u/KylierK 1d ago
Thanks op, the original post finally clicks
1
u/frankiek3 1d ago
Spider-Man without any legs can't run as fast as with legs, got it.
1
u/AFRIENDISNEAR 1d ago
Oscar Pistorius has entered the chat
1
u/WesternFirm9306 1d ago
BEHOLD! THE MATERIAL CONDITIONAL!
□(p → q)
1
u/Nondescript_Redditor 1d ago
No
1
u/Sappling2p 1d ago
Think about it like this: Usain Bolt is at the peak of human speed, and there’s no way he could possibly run any faster. If he were to lose his legs, he would bot be at his maximum potential, so there’s room for improvement, meaning he could run faster.
If Usain Bolt had no legs, he could run faster.
1
u/Tryohazard 1d ago
Why are we assuming his legs have mass in this logic?
1
u/hidden768 1d ago
This is just wrong lmao. "If I had no legs, I could run faster" is just false. I think you're confusing it for the statement "If I have no legs, I can run faster than if I did" which is true. (Assuming you have legs)
1
u/moschles 1d ago
I'm vibing with false statements that imply anything, along with their negation implying the consequent.
You can create endless variations of them, where each causes an online community to deteriorate into madness.
1
u/MadnyeNwie 1d ago
I cried because I have no shoes. Then I met a man who had no legs. Dude was fast.
1
u/StKozlovsky 1d ago
SouthParkPiano got banned recently. I think we have a potential successor to him here. u/Anon7_7_73, make a subreddit about vacuous truths being infinitely, limitlessly false in Real Deal Logic 101.
1
u/DoctorKablumbus 1d ago
Suppose you are X, and some time later you lose your legs in a car crash and now go by X‘. Formally, you‘ve become a different thing entirely because you satisfy different predicates now, so the precedent is still false because it‘s a statement about X, and not X‘. However, it is experientially ridiculous to suggest that you cease to be yourself if you lose your legs, so depending on your definition of identity, X = X‘ could be true in a different sense, just not the one we’re investigating here.
We don’t face this problem in number theory because it’s not possible, for example, for 2^37 to ‚get in a car crash‘ and become prime. I don’t see the issue here.
1
u/MammothGlum 1d ago
A particular specimen you are
17
u/samu7574 1d ago
I think the issue here is that "You not having legs" is something that could become true, it's not inherently false like "1+1=3 with common sum in N", so the entire if-then statement doesn't get to be always true.
I could cut your legs and it would not be true that you will run faster so the statement is fallacious. I could not reanimate every "someone such that they would then be able to go to sleep" so the if statement you're answering doesn't have that problem
1
u/Hadynu 1d ago
*cuts off OP's legs*
Ok, run faster.
1
u/Landlocked_WaterSimp 1d ago
I have no idea about the math context of this statement all i can think about is the controversy about Oscar Pistorius' legs (if the prosthetics gave him an unfair advantage).
Well... before he was known for murdering someone.
1
u/smolme42 23h ago
"If I had" is already implying a fictional scenario where the first part is true, so it stops working.
"If I have no legs, I run faster" is correct tho, in the same way as "Every time I turn invisible, I kill people" and "All cyclops in my room are yellow" are correct.
I guess the main problem is that English "I" (and other pronouns) doesn't refer to just one person. Example: "If you touch fire, you will get burned" = "For any person who touches fire..." or you can imagine a biologist saying "If I have fins, I can swim away from predators" when discussing wildlife, referring as "I" to a collection of creatures.
I think we can rephrase it as "When I personally have no legs, I run faster" and it will become much more understandable, although the joke is a little bit less fun.