Interesting logic question

[traz]

I can see it being either one. Instinctively I thought #1, and I think that's far more intuitive.

[felson]

[ QUOTE ]
[ QUOTE ]
if i were taking a logic test, i would say #2. if i came across this sentence in a medical guide, obv i would assume that the author meant to write the opposite.

[/ QUOTE ]

I could care less what you assume the author meant to write.

[/ QUOTE ]

nh

[kinda]

#1 obv

[Arito]

[ QUOTE ]
it took me so long to figure out how the hell people were answering #2. but now i get it!!

[/ QUOTE ]

Yeah same here, it's like one of those "I see a vase! / I see two faces!" thing.

[felson]

the double negative in the OP produces a literal meaning that makes no sense, so we naturally convert it to a single negative.

"i can't get no satisfaction." -->
"i can't get any satisfaction" vs "i am forced to get some satisfaction"

[VickreyAuction]

no head injury is too small to ignore --->
all head injuries are too big to ignore

that's how I interpreted it.

[DcifrThs]

[ QUOTE ]
i'm glad we're getting a dispersion of beliefs here.

i'll weigh in later on tonight or tomorrow on both threads... as well as the results from the two posts and why i made them.

Barron

[/ QUOTE ]

well i think the results have levelled off enough to reveal the issue.

i was having dinner with my dad when his friend asked me this question and i thought about it for a sec and immediately answered "of course, treat all head injuries." he then asked "really?? are you SURE?" and i though tabout it and rephrased the question to get at the answer. my instinct to guess "treat'em all" is interesting and thought many would share it.

the issue can be clearly seen by an analogous statement:

"no gun is too small to be banned."

therefore, you should ban all guns!

No X is too small to be Y'd implies that you should Y all Xs.

this phrase comes from Alice in Wonderland by Lewis Carroll.

Alice hits her head and the queen of hearts tells her not to worry about it. alice says the injury is small and the queen then says "no head injury is too small to be ignored."

it is interesting b/c if i posted "No gun is too small to be banned" everybody would say, "sure, you should ban all guns"

but because the brain seems to want to protect itself, it a priori thinks that all head injuries shoudl be treated and thus concludes that no head injury is too small to be ignored means that you should treat them all...

at least thats how i think about it.

i was further curious to see whether more mathematically oriented people would get the syntax more easily than average people, thus SMP vs. OOT.

in fact, it came out that way and SMP (though fewer responses) was close to evenly split whereas OOT was dramatically tilted towards the incorrect answer of treating all head injuries.

thanks for all the input guys,
Barron

[sebbb]

"no head injury is too small to ignore"

Let x be the size of the headache.

Let f(x)=1 if we don't ignore the headache
f(x)=0 if we do

I'm gonna suppose that there exists a specific headache size s such that:

if x>=s f(x)=1
if x<s f(x)=0



The opposite of "no head injury is too small to ignore" (A) is "there exists a head injury of size 'a' that is too small to ignore" (not A)


not-A implies that any head injury of size x<a shouldn't be ignored (since they are even smaller, so they are also too small to ignore). So we don't ignore any headache (since headaches of size >a aren't ignored either).

Also "we don't ignore any headache" => not A

So (not A)<=>"we don't ignore any headache"

A is the opposite of "we don't ignore any headache"


Conclusion:

"no head injury is too small to ignore" is the opposite of "treat all head injuries". But it doesnt mean "ignore all head injuries". It just means that there are some injuries that we treat, others that we don't.

[mason55]

p = a head injury
q = a size that can be ignored

there are no P that are not Q

which means all P are Q
which means "all head injuries are of a size that can be ignored"

ignore all head injuries

QED

[bawcerelli]

i'm not buying it