Riddle: How Many Plums Were on the Tree?

[vikasj007]

A man had not eyes, yet saw plums on a tree. He neither took plums, nor left plums. How many plums were on the tree?

 

[Bartholomew]

One answer:
He saw the plums in his mind's eye; there was no actual tree so no actual plums were on it.

 

[Problem+Solve=Reason]

No plums where there in the first place.

 

[Bartholomew]

No plums where there in the first place.

That doesn't explain how he saw them. It didn't say he saw "all" plums on the tree; it said he saw "plums" on the tree, implying "some plums." That means he saw at least two plums.

 

[DaveC426913]

So, to complete Bart's answer, he saw
as many as he wished to see.

 

[vikasj007]

It didn't say he saw "all" plums on the tree; it said he saw "plums" on the tree, implying "some plums."

though it does not make much of a difference to the answer, but just for you, assume that he saw all the plums that were on that tree.

 

[Bartholomew]

No, you miss the point. If you had said "all" plums it could have meant "no" plums (if there weren't any). Since you just said "plums" it means "some plums," and can't mean "no plums."

 

[vikasj007]

No, you miss the point. If you had said "all" plums it could have meant "no" plums (if there weren't any). Since you just said "plums" it means "some plums," and can't mean "no plums."

yeah, i guess you are right.


and, i said plums, not all plums. (just to avoid any confusion)

 

[DaveC426913]

So, what *is* the answer?

 

[vikasj007]

OK, the answer is 2.

now i will give all of you another chance, see if you can come up with the explanation for this.

 

[Gokul43201]

2 plums fits the second half of the puzzle. He neither took plums, nor left plums. He took a plum leaving behind a plum.

Can't make sense of the first statement, though.

 

[NateTG]

One eye, two eyes.

 

[Gokul43201]

Yes, I must have not eyes ! Or brains !

 

[DaveC426913]

OK, this is going over my head.

We've got a partial answer: there are 2 plums.
The rest of the teaser is about 'why?'

Now, what do the eyes have to do with anything?

 

[Bartholomew]

That's a "trick answer," and technically I don't think it's correct. The English language is illogical here--when you say a man "had not eyes," it's the same as saying the man "had not any eyes," or "did not have any eyes," which convention clearly dictates to mean the man "had zero eyes."

Similarly, if you say he did not take plums, it's the same as saying he didn't take any plums, which convention clearly dictates to mean he took zero plums.

 

[vikasj007]

The English language is illogical here--when you say a man "had not eyes," it's the same as saying the man "had not any eyes," or "did not have any eyes," which convention clearly dictates to mean the man "had zero eyes."

well if you check the question, it says, 'a man not had eyes', and not ' a man had not eyes'.

what it means that a man not had eyes, but he had an eye. i don't think that would be incorrect english.

though i agree, that a general assumption for this phrase is that the man has no eyes, but technically, i don't think it is an incorrect statement for a man who has just one eye.

 

[Gokul43201]

A man had not eyes, yet saw plums on a tree. He neither took plums, nor left plums. How many plums were on the tree?

It says he "had not".

If it did say, "A man not had eyes", then it would definitely be incorrect English, but may be accepted as a logical statement, where 'not' is the logical operator referring to the complement of some set.

 

[vikasj007]

Oh, my mistake

i guess, i just switched places between the two phrases, but i still mean the same.

and logically, my statement(in the original question) is an acceptable statement, and does support the answer.

 

[Bartholomew]

No, it doesn't. Did you read my post?

 

[RandallB]

No, it doesn't. Did you read my post?

Easy Bart the real issue for the teaser is not that we have a "English language" issue.
It is the "language of LOGIC" and the tight rules there.
where having an eye
...will return a false on having eyes.
... Thus true on "not eyes"
...would even return a false on having 'any eyes' (still need two)
but having having 'an eye' or 'any eye'
...would return true on "having vision" or able to see tree.

You can't expect to depend on a spoken language to be exact when "That's Bad" is used to decribe 'the most desirable item'.

Good one vikasj007.

'without wax'
RB

 

[Bartholomew]

where having an eye

Do you mean "not having an eye"? I can't make sense of your post.

In the "language of logic," you'd have to say something like "it is not the case that (there exists some x and some y such that (x is an eye and x belongs to the man and y is an eye and y belongs to the man and it is not the case that y is identical with x))." Logic avoids normal phrasing because normal phrasing has various oddities, such as the one under debate currently.

 

[RandallB]

Do you mean "not having an eye"?
.

I mean in the "language of logic," :
-- "not having any eyes"
-- "having an eye"
can both be true if there is just one eye.

 

[Bartholomew]

"not having any eyes" and "having an eye" are not statements in the language of logic. They are English statements. I showed you what the language of logic sounds like, and it doesn't sound like that.

 

[vikasj007]

Good one vikasj007.

thanks!

but i think next time i'll try to make sure that my teasers are not that questionable

 

[DaveC426913]

So, what, in fact, is the answer?

 

[Mk]

So, to complete Bart's answer, he saw
as many as he wished to see.

"The blind see what they wish to see"

 

[vikasj007]

So, what, in fact, is the answer?

well as i had already told the answer to this is that there are 2 plums on the tree.

after that we were only disscussing whether the first part of the problem is correct or not.

 

[K.J.Healey]

I believe it is worded correctly for the riddle.
He had not eyes, but did have an eye(1), thus he could see the tree.
He didnt leave "plums" so he could have left 1 or 0, unless you say "0 plums"
He didnt take "plums" so he may have taken 0 or 1, unless you say "0 plums" again.
Therefor he took one, left one, there were 2 on the tree.

I don't think its that difficult, and I believe the English used was correct. The only problem is there could also be 0 plum on the tree.

 

[member 5645]

I believe it is worded correctly for the riddle.
He had not eyes, but did have an eye(1), thus he could see the tree.
He didnt leave "plums" so he could have left 1 or 0, unless you say "0 plums"
He didnt take "plums" so he may have taken 0 or 1, unless you say "0 plums" again.
Therefor he took one, left one, there were 2 on the tree.

I don't think its that difficult, and I believe the English used was correct. The only problem is there could also be 0 plum on the tree.

I wish I could have got to this thread from page one, I figured it out right away.

You are correct, but it says he saw PLUMS on the tree, thus there were more than one plum on the tree.

There were 2, he took one.

 

[DaveC426913]

I'm missing something. Why is 2 the max? Why couldn't there have been 867 plums on the tree?

He still could have taken one or zero, and left one or zero.

 

[Bartholomew]

Healey, why don't you actually respond to the reason the English does not support the answer, rather than simply saying "oh yes it works"?

 

[K.J.Healey]

I'm missing something. Why is 2 the max? Why couldn't there have been 867 plums on the tree?

He still could have taken one or zero, and left one or zero.

I think what we have to assume is that in reality, if you "see plums" (notice the plural) then you see more than 1 plum, and not 0 plums. You can actually see any amount more than one, even 867. The catch is later.

Lets look at it again:
"A man had not eyes, yet saw plums on a tree. He neither took plums, nor left plums. How many plums were on the tree?"

Look at the statement "He neither took plums"
if we are assuming that plums means more than one and not zero, then He didnt take more than one and didnt take zero. Therefor he took one.

Same with "nor left plums"
He didnt leave more than one plum and didnt leave zero. Therefor he left one plum.

Thats one on him, one in the tree. 2 plums.

The hint to how to follow the "plum(s)" part of the riddle lies with "A man had not eyes". If you said "a man had eyes" then it would be that he had a multitude(more than one) and not zero of eye. The negative of that would be to have just one eye.

Bartholomew, I am trying to show why it works using the fundamentals of language and more importantly implicit meaning to plural words. How is that not a scientific approach to validating the given argument?

 

[K.J.Healey]

Oh, and about the logic statements, let's try it.

A man had not eyes, yet saw plums on a tree. He neither took plums, nor left plums. How many plums were on the tree?

if N = the number of eyes(ignoring semantics) (0,1,2,3,4...)
the plural of a word implies a number greater than one.
so Eyes = N, N>1

P = # of plum (0,1,2,3,4...)
Before man takes fruit:
Plums in the tree initial = Pti>1 because it says he sees "plums", once again the plural definition.
after the picking of said fruit.
Man would have Pm<=1 (the negative of plural, or not more than one)
Tree final would have Ptf<=1 (same thing)
Now we could say the tree then may have had 0 plums on it as well as 1.

BUT the previous argument gets rid of that possibility because the sum of plums
Pm + Ptf <=2
and
Pti > 1
So Pm+Ptf = Pti
so solve both cases
Pti <=2
Pti >1
Since we are dealing with integers the only possible answer is 2.

 

[DaveC426913]

Same with "nor left plums"
He didnt leave more than one plum and didnt leave zero. Therefor he left one plum.

Got it now.

My interpretation of 'didn't leave plums' is 'didn't put multiple plums back'. The interpretation you are using is 'didn't leave multiple plums on the tree'.

 

[Bartholomew]

Healey, your approach is reasonable if you interpret "he had not eyes" as "he did not have a plural number of eyes." My point which I have explained before is that in English, "he had not eyes" means "he did not have any eyes," or "he had zero eyes."

Incidentally, if you take the literal "non-plural" meaning, "he had not eyes" means "he did not have a plural number of eyes and he did not have zero eyes," since "zero eyes" is a plural number of eyes. So "he had not eyes" means "he had one eye" according to your logic, which is nonsense; if I say "I had not sunglasses" it does not mean I had exactly one "sunglass."

 

[K.J.Healey]

Healey, your approach is reasonable if you interpret "he had not eyes" as "he did not have a plural number of eyes." My point which I have explained before is that in English, "he had not eyes" means "he did not have any eyes," or "he had zero eyes."

Incidentally, if you take the literal "non-plural" meaning, "he had not eyes" means "he did not have a plural number of eyes and he did not have zero eyes," since "zero eyes" is a plural number of eyes. So "he had not eyes" means "he had one eye" according to your logic, which is nonsense; if I say "I had not sunglasses" it does not mean I had exactly one "sunglass."

Are you an English major? When you say "in English, "he had not eyes" means "he did not have any eyes" I see that as a mistake. Positive/negative structure in english is very much like mathematics, and when simplifying a statement you need to consider both the context and the properties of the base word provided. You can correctly say that "he had not" means exactly "he didnt have" but you cannot say that "eyes" means "any eyes". So if I say "I have eyes" does that mean I say "I have any eyes"? No. It means I have a plural of eye.

Also sunglasses has completely different word properties than eyes, becasue the singular for what we consider a set of sunglasses is plural because we shorten "a set/pair of sunglasses" to "sunglasses". So it is still singular of the word "pair".

 

[Bartholomew]

From dictionary.com, "any" (the relevant definition) means "One, some, every, or all without specification." So "eyes" does mean "any eyes." What would you say "any eyes" means?

I'm not sure why it doesn't sound right to say "I have any eyes." Probably that has something to do with grammar rather than the simple meaning of "any."

Okay, replace "sunglasses" with "motorcycles." If I say, "I did not have motorcycles," by the literal meaning, it says, "I did not have 0 or 2 or more motorcycles," so it says, "I had exactly 1 motorcycle," in contradiction to the common sense interpretation of it.

 

[K.J.Healey]

See I see "I did not have motorcycles" to mean I had one motorcycle. Thats my common sense interpertation.

When you talk about "any" and "eyes" and say "eyes does mean "any eyes"" I don't see where you get that. I used dictionary.com too and it says :

PLURAL : # Grammar. Of or being a grammatical form that designates more than one of the things specified.

More than one. So "eyes" is the plural of "eye". There can be no disputing that. That means that there must be "more than one of" eye. If you do not have "more than one of" you have "one or zero of" when talking about positive quantities.

The only argument that slows us down is that "eye" is a tricky word like sunglasses.
If you didnt have any eyes, you would say "I do not have eyes." right? While if you didnt have any bottles of water you would say "I do not have a bottle of water." The way we describe a quantity of certain objects differs and creates problems like these.

I say we just agree that the English language is really messed up.

 

[Bartholomew]

All right, so "plural" was not what I meant. I meant, "of the form 'eyes.''" Zero eyes is of the form "eyes" in this sense. If you say, "he had not eyes," it means, absolutely literally, that he had nothing that can be spoken of as "eyes." "Zero eyes" literally can be spoken of as "eyes," as can "two eyes," or "three eyes," etc.

Anyway, my point is not about the idiosyncracies of interpreting "eyes" literally. My point is about how in the English language, "eyes" means "any eyes" which means "at least one eye." The word "any" means without specification; simply stressing that there are some. "He did not have eyes at all" is equivalent, and again it means, "he had zero eyes."