Official R/P Chat Thread III: We hate each other in every thread including this one

[CRyan64]

wait there are 4 people right?

i saw this

Mr. Scott, his sister, his son, and his daughter are tennis players. The following facts refer to the people mentioned:

1. The best player's twin and the worst player are of opposite sex.

2. The best player and the worst player are the same age.

Which one of the four is the best player?

but i didn't see u add son. be back in a bit.

[DizzySmalls]

wait there are 4 people right?

i saw this

Mr. Scott, his sister, his son, and his daughter are tennis players. The following facts refer to the people mentioned:

1. The best player's twin and the worst player are of opposite sex.

2. The best player and the worst player are the same age.

Which one of the four is the best player?

but i didn't see u add son. be back in a bit.

^ Typo on my part, now edited. That appears to be the same question but the foursome now plays Tennis and has a more appealing last name

[theoldnite]

1. Italian
2. Mexican
3. American

Everything else is inedible.

hah i'm a total foodie so i'll eat anything as long as its good, but french, indian, etc >>> mexican >>> merican

wait there are 4 people right?

i saw this

Mr. Scott, his sister, his son, and his daughter are tennis players. The following facts refer to the people mentioned:

1. The best player's twin and the worst player are of opposite sex.

2. The best player and the worst player are the same age.

Which one of the four is the best player?

but i didn't see u add son. be back in a bit.

plot twist - his sister is actually his wife

[DizzySmalls]

hah i'm a total foodie so i'll eat anything as long as its good, but french, indian, etc >>> mexican >>> merican

I don't think I've ever had French food.

I was an impossible eater as a child. I only liked bread and cheese. Eating a cheeseburger was a huge accomplishment in my teen years. I've only really come around to steak in the last year or two.

You name it, I probably didn't like it for most of my life. I ate my first chicken tender ~ age 13 or 14 I think. Bacon was ~11 or 12. Salad at about 19-20. In college people used to force me to eat various fruits I had never tried. Oranges have a terrible texture, only took one bite. Never got around to biting into a pear.

plot twist - his sister is actually his wife

My understanding is that the real plot twist comes in if he impregnated his own mother and gave birth to his own sister. Then the sister could also be a twin with the son or daughter described in the problem.

[CRyan64]

OK Cryan I have been practicing logic puzzles. Please help me simplify my structure here. I am confident that I have the correct answer, but I have too much slop and probably some unnecessary "premises" to reach the conclusion. Also, if I made an error in inference, please let me know (with the full knowledge that I will feel pretty stupid).

This is the problem:

"Mr. Short, his sister, his son, and his daughter, are fond of golf and often play together. The following statements are TRUE of their foursome:

(1) The best player's twin and the worst player are of the opposite sex
(2) The best player and the worst player are the same age

Which one of the foursome is the best player?

Here is what I came up with:


1) The best player's twin is the opposite sex of the worst player (given)
2) The best and worst player are the same age (given)

3) The best player and the best player's twin are the same age (by definition of the word twin)
4) A parent must be older than his children
5) Mr Short is a parent to his son and daughter (by literal definition) and is therefore older
6) Mr. Short's sister is not also described as his daughter, so she cannot be twins to his son or daughter
7) The twins therefore must be of the opposite gender (i.e, Mr Short and His sister, or the son and daughter, are the twins)

8) The best player therefore MUST be the SAME gender AND Age as the worst player, and also have a twin (a third person of the same age)(by P1 and P2)
9) The best player, the best players twin, and the worst player MUST BE THE SAME AGE, and two must also have the same gender (to summarize)

C) Mr Short's daughter is the best player, the son is the twin of the opposite sex, and the worst player is Mr Short's sister

Personally I think maternal incest just might throw a kink in this one and make it unsolvable, so thats why I put in premise 6, although I'm sure a textbook has the decorum not to include that possibility anyhow.

Also, if it isn't difficult or time consuming, could you explain how you would put this into symbols?

Fuark sorry brah, I'm gonna have to devote some time to this. The thing about these puzzles is that all of the information isn't handed to you, so you just have to go ahead and assume that you and the puzzle-maker are on the same page about what it means to be a twin, of the same age, better than x, etc etc. Then what we would have is simply those definitions in conjunction with the premises, and then the conclusion (who the best player is) would already be "contained" in those definitions and premises, and it would then just be a matter of mechanical derivation using the inference rules of your proof system to arrive at it. I started with trying to formalize it and I got this:

∨ ∧ � ↔ → ∀ ∃

1. ∃x∃y∃z∃p [~(x=y) ∧ ~(x=z) ∧ ~(x=p) ∧ ~(y=z) ∧ ~(y=p) ∧ ~(z=p) ∧ ∀s [ s=x ∨ s=y ∨ s=z ∨ s=p]]
(There is exactly 4 individuals.)
2. ∀x∀y∀z [ Bxy ∧ Byz → Bxz]
(Transitivity of the is_better_than relation.)
3. ∀x∀y [Bxy↔~Byx]
(x is better than y iff y is not better than x)
4. ∀x~Bxx
(No individual is better than itself.)
5. ∀x[Mx↔~Fx]
(x is male iff x is not female)
6. ∀x[Txy↔Sxy]
(x is the twin of y iff x is the same age as y]
7. ∀x∀y[Txy↔Tyx]
(Symmetric relation of twin-ness)
8. ∀x~Txx
(No person is the twin of themselves).

...I could go on and on, as I didn't exhaust all the relations that might be needed to deduce the conclusion.

As for the original premises, I''l try your second one, it seems like I formalized it correctly. (Translations...oh lawd they can be cheeky as fuk. Pepper your angus, lol.)
(2) The best player and the worst player are the same age

∀x = for all x
∃x = there exists some x
∧ = conjunction
∨= disjunction
→ = conditional
↔ = biconditional

2. ∃x∃z [[Zx ∧ ∀y(Zy → x=y)] ∧ [Wz ∧ ∀p(Wp → z=p)] ∧ Sxz]
(Zx = 'best player', Wx= 'worst player', Sxy = is the same age as.)


As you can see, these things get tedious as fuk, hence people often instead reason about them informally like you did. I'll look over your stuff tomorrow m8, fawk I'm pooped lmao.

[DizzySmalls]

^^^

[CRyan64]

^^^

Ayy lmao. I hope you find symbolic logic as fun as I do. Doing derivations is so hnnng. They are legit like brain-teaser puzzles like crosswords, soduko etc. But I find you get the added bonus of learning logic at the same time. Truth trees are also extremely useful as you get to test for validity, consistency, counter-examples, etc. Translations are something that I still struggle with tho; it can get extremely cheeky. Fortunately most philosophical arguments are rather simple to formalize.

[Apeus]

Fuark sorry brah, I'm gonna have to devote some time to this. The thing about these puzzles is that all of the information isn't handed to you, so you just have to go ahead and assume that you and the puzzle-maker are on the same page about what it means to be a twin, of the same age, better than x, etc etc. Then what we would have is simply those definitions in conjunction with the premises, and then the conclusion (who the best player is) would already be "contained" in those definitions and premises, and it would then just be a matter of mechanical derivation using the inference rules of your proof system to arrive at it. I started with trying to formalize it and I got this:

∨ ∧ � ↔ → ∀ ∃

1. ∃x∃y∃z∃p [~(x=y) ∧ ~(x=z) ∧ ~(x=p) ∧ ~(y=z) ∧ ~(y=p) ∧ ~(z=p)] ∧ ∀x [ x=a ∨ x=b ∨ x=c ∨ x=d]
(There is exactly 4 individuals - fawk I'll have to check my book later to see if I got this one right.)
2. ∀x∀y∀z [ Bxy ∧ Byz → Bxz]
(Transitivity of the is_better_than relation.)
3. ∀x∀y [Bxy↔~Byx]
(x is better than y iff y is not better than x)
4. ∀x~Bxx
(No individual is better than itself.)
5. ∀x[Mx↔~Fx]
(x is male iff x is not female)
6. ∀x[Txy↔Sxy]
(x is the twin of y iff x is the same age as y]
7. ∀x∀y[Txy↔Tyx]
(Symmetric relation of twin-ness)
8. ∀x~Txx
(No person is the twin of themselves).

...I could go on and on, as I didn't exhaust all the relations that might be needed to deduce the conclusion.

I think I can formalize your second original premise but I'll have to think about the first one. Honestly tho not totally sure if I formalized it correctly, will have to think about it. (Translations...oh lawd they can be cheeky as fuk. Pepper your angus, lol.)
(2) The best player and the worst player are the same age

∀x = for all x
∃x = there exists some x
∧ = conjunction
∨= disjunction
→ = conditional
↔ = biconditional

2. ∃x∃z [[Zx ∧ ∀y(Zy → x=y)] ∧ [Wz ∧ ∀p(Wp → z=p)] ∧ Sxy]
(Zx = 'best player', Wx= 'worst player', Sxy = is the same age as.)


As you can see, these things get tedious as fuk, hence people often instead reason about them informally like you did. I'll look over your stuff tomorrow m8, fawk I'm pooped lmao.

[GreatOldOne]

Fuark sorry brah, I'm gonna have to devote some time to this. The thing about these puzzles is that all of the information isn't handed to you, so you just have to go ahead and assume that you and the puzzle-maker are on the same page about what it means to be a twin, of the same age, better than x, etc etc. Then what we would have is simply those definitions in conjunction with the premises, and then the conclusion (who the best player is) would already be "contained" in those definitions and premises, and it would then just be a matter of mechanical derivation using the inference rules of your proof system to arrive at it. I started with trying to formalize it and I got this:

∨ ∧ � ↔ → ∀ ∃

1. ∃x∃y∃z∃p [~(x=y) ∧ ~(x=z) ∧ ~(x=p) ∧ ~(y=z) ∧ ~(y=p) ∧ ~(z=p)] ∧ ∀x [ x=a ∨ x=b ∨ x=c ∨ x=d]
(There is exactly 4 individuals - fawk I'll have to check my book later to see if I got this one right.)
2. ∀x∀y∀z [ Bxy ∧ Byz → Bxz]
(Transitivity of the is_better_than relation.)
3. ∀x∀y [Bxy↔~Byx]
(x is better than y iff y is not better than x)
4. ∀x~Bxx
(No individual is better than itself.)
5. ∀x[Mx↔~Fx]
(x is male iff x is not female)
6. ∀x[Txy↔Sxy]
(x is the twin of y iff x is the same age as y]
7. ∀x∀y[Txy↔Tyx]
(Symmetric relation of twin-ness)
8. ∀x~Txx
(No person is the twin of themselves).

...I could go on and on, as I didn't exhaust all the relations that might be needed to deduce the conclusion.

I think I can formalize your second original premise but I'll have to think about the first one. Honestly tho not totally sure if I formalized it correctly, will have to think about it. (Translations...oh lawd they can be cheeky as fuk. Pepper your angus, lol.)
(2) The best player and the worst player are the same age

∀x = for all x
∃x = there exists some x
∧ = conjunction
∨= disjunction
→ = conditional
↔ = biconditional

2. ∃x∃z [[Zx ∧ ∀y(Zy → x=y)] ∧ [Wz ∧ ∀p(Wp → z=p)] ∧ Sxy]
(Zx = 'best player', Wx= 'worst player', Sxy = is the same age as.)


As you can see, these things get tedious as fuk, hence people often instead reason about them informally like you did. I'll look over your stuff tomorrow m8, fawk I'm pooped lmao.

^^^ I really hope you can quickly learn to take to heart what I'm about to say:

It doesn't get any better than English.

You get the same chit in every possible story.



Everyone should be forced to watch that entire clip.

Then turn it into logical symbols.

Then...Hell is complete.

[DizzySmalls]

It doesn't get any better than English.

Can you prove that in symbolic logic please

[CRyan64]

^^^ I really hope you can quickly learn to take to heart what I'm about to say:

It doesn't get any better than English.

You get the same chit in every possible story.

can u esplain? i didn't get the message, lol.

i have a feel its something about you finding deductive logic overrated, and i would absolutely disagree with that, lol.
life changed when i lurned dis stuff, oh lawd how it changed. i realized how trivial validity is in argumentation, how how much more important the analysis of language and the clarification of concepts is. and also learning about what validity is, valid arguments no longer looked like some "formal scary thing" that "only scholars put forth".

(If I completely missed your message ignore that LOL.)

[GreatOldOne]

Everyone should be forced to watch that entire clip (it's actually quite funny, just on the grounds of observing what an ass that guy is. remarkable, really)

Anyway, try turning everything he says into logical symbols.

Then...Hell is complete.


It's related to something about logic being overrated. That would be...once you come to terms with what logic can do, it provides only facility to despair...given despair. I feel it is more like obfuscation than purification...which is exactly what it is supposed to be doing.

Like in programming. Why work in assembly? That is Hell?

[TheStender]

It doesn't get any better than English.

English doesn't exist.

[CRyan64]

English doesn't exist.

Now that's what I call a

[GreatOldOne]

Can you prove that in symbolic logic please

Yes. Will I? No.

Will I rewrite perfectly good programs in assembly?

No.

[DizzySmalls]

Yes. Will I? No.

Would you believe me if I told you I first typed "can", was going to edit it to will, and then left it as is because I thought you would just respond "no"? lol didn't work

[CRyan64]

It's related to something about logic being overrated. That would be...once you come to terms with what logic can do, it provides only facility to despair...given despair. I feel it is more like obfuscation than purification...which is exactly what it is supposed to be doing.

I can understand that for simple arguments. But theorems that take, say, 10 pages to deduce? Informal reasoning in English would be all sorts of failboat. 1 mistake and u dun goof. You are right that I kinda was like wtf? when I realized that deductive logic isn't concerned with discovering truth, but only of analyzing the form of an argument. But I feel that the tools that you learn are extremely useful. And as a bonus, I actually saw someone online that shared you sentiment, about how symbolic logic is "overrated" and "convoluted". So she decided to assess an argument in English. Her conclusion? She concluded that the argument was invalid when it was actually valid. What went wrong? I detected a flaw in her reasoning once I formalized the argument LOL.

oh and speaking of mathematics. brb a body of a gazillion theorems. i would not want mathematics to be on such a shaky ground as being ensured only by 'informal reasoning'. mathematicians reason informally, but the logicians make sure that their reasoning is sound and that their "theorems" are truly theorems.

[theoldnite]

I don't think I've ever had French food.

I was an impossible eater as a child. I only liked bread and cheese. Eating a cheeseburger was a huge accomplishment in my teen years. I've only really come around to steak in the last year or two.

You name it, I probably didn't like it for most of my life. I ate my first chicken tender ~ age 13 or 14 I think. Bacon was ~11 or 12. Salad at about 19-20. In college people used to force me to eat various fruits I had never tried. Oranges have a terrible texture, only took one bite. Never got around to biting into a pear.


My understanding is that the real plot twist comes in if he impregnated his own mother and gave birth to his own sister. Then the sister could also be a twin with the son or daughter described in the problem.

u wot

only tried oranges once and hasn't tried pears wtf

you gotta get on dat foodie time and eat everything cuzz, stuff will change your life (or at least your waist size )

Fuark sorry brah, I'm gonna have to devote some time to this. The thing about these puzzles is that all of the information isn't handed to you, so you just have to go ahead and assume that you and the puzzle-maker are on the same page about what it means to be a twin, of the same age, better than x, etc etc. Then what we would have is simply those definitions in conjunction with the premises, and then the conclusion (who the best player is) would already be "contained" in those definitions and premises, and it would then just be a matter of mechanical derivation using the inference rules of your proof system to arrive at it. I started with trying to formalize it and I got this:

∨ ∧ � ↔ → ∀ ∃

1. ∃x∃y∃z∃p [~(x=y) ∧ ~(x=z) ∧ ~(x=p) ∧ ~(y=z) ∧ ~(y=p) ∧ ~(z=p)] ∧ ∀x [ x=a ∨ x=b ∨ x=c ∨ x=d]
(There is exactly 4 individuals - fawk I'll have to check my book later to see if I got this one right.)
2. ∀x∀y∀z [ Bxy ∧ Byz → Bxz]
(Transitivity of the is_better_than relation.)
3. ∀x∀y [Bxy↔~Byx]
(x is better than y iff y is not better than x)
4. ∀x~Bxx
(No individual is better than itself.)
5. ∀x[Mx↔~Fx]
(x is male iff x is not female)
6. ∀x[Txy↔Sxy]
(x is the twin of y iff x is the same age as y]
7. ∀x∀y[Txy↔Tyx]
(Symmetric relation of twin-ness)
8. ∀x~Txx
(No person is the twin of themselves).

...I could go on and on, as I didn't exhaust all the relations that might be needed to deduce the conclusion.

I think I can formalize your second original premise but I'll have to think about the first one. Honestly tho not totally sure if I formalized it correctly, will have to think about it. (Translations...oh lawd they can be cheeky as fuk. Pepper your angus, lol.)
(2) The best player and the worst player are the same age

∀x = for all x
∃x = there exists some x
∧ = conjunction
∨= disjunction
→ = conditional
↔ = biconditional

2. ∃x∃z [[Zx ∧ ∀y(Zy → x=y)] ∧ [Wz ∧ ∀p(Wp → z=p)] ∧ Sxy]
(Zx = 'best player', Wx= 'worst player', Sxy = is the same age as.)


As you can see, these things get tedious as fuk, hence people often instead reason about them informally like you did. I'll look over your stuff tomorrow m8, fawk I'm pooped lmao.

[GreatOldOne]

Would you believe me if I told you I first typed "can", was going to edit it to will, and then left it as is because I thought you would just respond no? lol didn't work

Yes.

[GreatOldOne]

I can understand that for simple arguments. But theorems that take, say, 10 pages to deduce? Informal reasoning in English would be all sorts of failboat. 1 mistake and u dun goof. You are right that I kinda was like wtf? when I realized that deductive logic isn't concerned with discovering truth, but only of analyzing the form of an argument. But I feel that the tools that you learn are extremely useful. And as a bonus, I actually saw someone online that shared you sentiment, about how symbolic logic is "overrated" and "convoluted". So she decided to assess an argument in English. Her conclusion? She concluded that the argument was invalid when it was actually valid. What went wrong? I detected a flaw in her reasoning once I formalized the argument LOL.

oh and speaking of mathematics. brb a body of a gazillion theorems. i would not want mathematics to be on such a shaky ground as being ensured only by 'informal reasoning'. mathematicians reason informally, but the logicians make sure that their reasoning is sound and that their "theorems" are truly theorems.

I'm not considering mathematics.

If your theorem takes 10 pages to deduce you have at least a problem.

It's probably wrong.

Or else it is of no practical use.

And supposing it is correct in any case nobody will believe you.

[DizzySmalls]

u wot

only tried oranges once and hasn't tried pears wtf

you gotta get on dat foodie time and eat everything cuzz, stuff will change your life (or at least your waist size )

I just don't much care for fruit, and it's not the top priority to force on myself versus other more nutritious options. Fruit to most people is like a treat anyways, so I figure I'm mostly good without it. I do like bananas, but only in moderation

Also, I don't eat any form of seafood or food that comes from under water. I won't even eat so much as a fishstick lol. I once tried salmon caviar though, and had to strongly suppress my gag reflex. Hell is caviar

[CRyan64]

If your theorem takes 10 pages to deduce you have at least a problem.

It's probably wrong.

Or else it is of no practical use.

And supposing it is correct in any case nobody will believe you.

mathematics brah. mathematics. highly valuable. the value of deductive logic here is that you can assess each atomic inference individually, and, if each inference is valid, then the conclusion necessarily follows. bam, you secured (with as much confidence as we can hope for) the truth of the conclusion.

besides. we have theorem proves and proof checkers if we're extra cautious. now, whether a person is convinced that the proof is legit is another story. but those who are familiar with deductive logic shouldn't have a problem with that.

[GreatOldOne]

mathematics brah. mathematics. highly valuable. the value of deductive logic here is that you can assess each atomic inference individually, and, if each inference is valid, then the conclusion necessarily follows. bam, you secured (with as much confidence as we can hope for) the truth of the conclusion.

besides. we have theorem proves and proof checkers if we're extra cautious. now, whether a person is convinced that the proof is legit is another story. but those who are familiar with deductive logic shouldn't have a problem with that.

I edited and added in, 'i am not considering da maths'.

I should have just left my comment as, 'you realize this is a fallacious argument of course'.

No good deed goes unpunished.

[Stizzel]

Fuark sorry brah, I'm gonna have to devote some time to this. The thing about these puzzles is that all of the information isn't handed to you, so you just have to go ahead and assume that you and the puzzle-maker are on the same page about what it means to be a twin, of the same age, better than x, etc etc. Then what we would have is simply those definitions in conjunction with the premises, and then the conclusion (who the best player is) would already be "contained" in those definitions and premises, and it would then just be a matter of mechanical derivation using the inference rules of your proof system to arrive at it. I started with trying to formalize it and I got this:

∨ ∧ � ↔ → ∀ ∃

1. ∃x∃y∃z∃p [~(x=y) ∧ ~(x=z) ∧ ~(x=p) ∧ ~(y=z) ∧ ~(y=p) ∧ ~(z=p)] ∧ ∀x [ x=a ∨ x=b ∨ x=c ∨ x=d]
(There is exactly 4 individuals - fawk I'll have to check my book later to see if I got this one right.)
2. ∀x∀y∀z [ Bxy ∧ Byz → Bxz]
(Transitivity of the is_better_than relation.)
3. ∀x∀y [Bxy↔~Byx]
(x is better than y iff y is not better than x)
4. ∀x~Bxx
(No individual is better than itself.)
5. ∀x[Mx↔~Fx]
(x is male iff x is not female)
6. ∀x[Txy↔Sxy]
(x is the twin of y iff x is the same age as y]
7. ∀x∀y[Txy↔Tyx]
(Symmetric relation of twin-ness)
8. ∀x~Txx
(No person is the twin of themselves).

...I could go on and on, as I didn't exhaust all the relations that might be needed to deduce the conclusion.

I think I can formalize your second original premise but I'll have to think about the first one. Honestly tho not totally sure if I formalized it correctly, will have to think about it. (Translations...oh lawd they can be cheeky as fuk. Pepper your angus, lol.)
(2) The best player and the worst player are the same age

∀x = for all x
∃x = there exists some x
∧ = conjunction
∨= disjunction
→ = conditional
↔ = biconditional

2. ∃x∃z [[Zx ∧ ∀y(Zy → x=y)] ∧ [Wz ∧ ∀p(Wp → z=p)] ∧ Sxy]
(Zx = 'best player', Wx= 'worst player', Sxy = is the same age as.)


As you can see, these things get tedious as fuk, hence people often instead reason about them informally like you did. I'll look over your stuff tomorrow m8, fawk I'm pooped lmao.

I'm not sure what's tedious about it. I did this all in my head.

[CRyan64]

I'm not sure what's tedious about it. I did this all in my head.

I meant the formalization of all concepts. Informally reasoning about it probably isn't too hard. This is where I agree with GOO. Formalizing something like this is probably overkill.

...but I like to just cuz I think its fun lolz

[Stizzel]

I meant the formalization of all concepts. Informally reasoning about it probably isn't too hard. This is where I agree with GOO. Formalizing something like this is probably overkill.

...but I like to just cuz I think its fun lolz

lol I was being sarcastic brah. Anyway you philoso****s need to put down your pocket protectors, go to a strip club and have a lap dance.

[DizzySmalls]

lol I was being sarcastic brah. Anyway you philoso****s need to put down your pocket protectors, go to a strip club and have a lap dance.

That's always sounded unappealing to me. Not my idea of fun.

[GreatOldOne]

That's always sounded unappealing to me. Not my idea of fun.

I've only been to a strip club a couple of times.

One time...it turns out the neighbors kid is the bouncer.

Such a 'downer'.

Lulz.

[DizzySmalls]

I've only been to a strip club a couple of times.

One time...it turns out the neighbors kid is the bouncer.

Such a 'downer'.

Lulz.

lol what would lead you to a strip club? Bachelor party or something?

[PaulG]

That's always sounded unappealing to me. Not my idea of fun.

Extremely unappealing. I get turned off by nasty sexually empowered feminist hoes that age faster then a California grape in the sun. Unless they're non hippie and classy sun worshipers. Women need to be stress free and compete with other females on their principles and beauty. This can only be done with the support beam of a man.



Would rather just goto a friends for a classy dinner party.