Wednesday, April 16, 2008

Meta-Definition

Suppose we define a horse's tail to be a leg. How many legs does a horse have?

This question is part of a joke, but I decided to turn it into a real question... What do you think the answer should be?!

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This question is part of a joke that goes like this:
A mathematician, scientist, and engineer are each asked: "Suppose we define a horse's tail to be a leg. How many legs does a horse have?" The mathematician answers "5"; the scientist "1"; and the engineer says "But you can't do that!"


The joke is basically to ridicule engineers, as they are stereotyped to not have a great command of the concepts of hypothesizes and inferencing. But the joke includes another implicit stereotyping of the difference between mathematicians and scientists.

In the field of mathematics, new definitions and theories are usually inclusive of all the definitions and theories that preceded it. Hence, a mathematician would consider a new definition to be inclusive of previous definitions. There is actually another joke about this specific idea:
Mathematics is the art of giving the same name to different things.

Hence, the mathematician's answer is 5!

In the field of science, usually new theories replace older theories, thats why the scientist's answer assumes that the new definition abolishes the older definition. Hence the scientist answered 1!

My answer to this question is "5"... It was actually my first reaction, and also after some thought I think its most convincing. The argument is that: The question doesn't specify whether or not the conventional concept of a leg is still called a leg. First of all, we can agree that the question does not specify; Which is -after all- why the answer is debatable. But the first rule that comes to the mind is that the best answer is the one with the least problematic assumptions. As a rule of the thumb, when something is not explicitly stated to have changed, then leave it as it is. We shouldn't assume something to change when the question doesn't explicitly state that it was changed.
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Update: Added an explained answer

9 comments:

riseofaphoenix said...

One leg I guess.

Tala said...

well the statement is missing so many things..

why did you assume that i know what a tail looks like and what a leg looks like?

you cant assign one name for two different things, this is misleading!

and suppose i knew what a leg is and what a tail is, if i assigned the definition leg to be what we know as a tail;taking the shape of a tail, i should tell you what happened to what we agreed to be a leg because automatically its no longer a leg

Devil's Mind said...

Tala, you can assume that a horse in conventional terminology has 4 legs and 1 tail.

Your arguments do make sense, and are in fact necessary to make a definite answer.

For now, just tell us what your first instinct told you... Remember, the question was originally part of a joke, so the subtle differences are part of the joke!

Devil's Mind said...

"you cant assign one name for two different things, this is misleading! " - Explain to us, why you think so...

Tala said...

i wrote a long reply and it disappeard, so im going again..

when i first read it, i said one leg relying that i know what a tail is that ive seen a horse and it has one tail i didnt take into account whats the new definition is called "leg" or "fill the blank"

now, why should i not assign one name to two different things, assume i agreed that a tail is a leg. now the horse, has 1 leg and 4legs, reverse this claim and say " draw in your mind a leg" "draw me a horse that has a leg" "draw me a horse with 5 legs" this is interference! the purpose of definition is to communicate clearly the pictures in our heads, not the reality. reality is the evidence to whats in our heads when we want to describe our minds. (im still thinking)

another thing, is that if i asked the person who wrote this what is this pointing to a tail and he said "a leg" then i pointed to a leg and he said "a leg" then what he sees in the tail and the leg to be a leg is something else!

so i believe the correct answer for this question is one or more because i dont know what he sees in a tail that makes it a leg.

Anonymous said...

i guess five legs...after all defining the tail as a leg doesn't necessarly mean that the original legs arent legs anymore but it states that the tail is also a leg...:)

The Observer said...

4 leg legs and 1 leg tail :P

Well it depends if we keep the definition of legs to be legs as well or we change them to be something else.

Devil's Mind said...

"Well it depends if we keep the definition of legs to be legs as well or we change them to be something else." - But does the question mention anything about changing the definition of the (conventional) legs to something beside legs?!

I think that the fact that we are discussing whether a conventional leg is still a leg or not, demonstrates that the question did not state anything about changing the definition of conventional legs to something beside legs. [Because if it did state anything about it, there would be no space left for argumentation!]

Tala said...

a week is past sir :D