Why is the concept of odd and even a philosophical illusion?

[RobertSeattle]

I've heard this a hundred times on the AA commerical and I'm still confused. Any 13 year old girls out there that can explain this to me? (And I was a math major!)

[stinkeefresh]

1. that's been driving me crazy too!

someone help!

[Goldmund]

2. ME TOO!!!

Every time that commercial comes up I spent the next 5 minutes thinking about what exactly that means, and then I give up.

[ashling]

3. I was just listening to AA on the computer

and I heard the spot for the first time. Then I looked down at the screen and saw this
How wierd is that?
What the hell are they talking about?

[SheepyMcSheepster]

4. here is what some people had to say about it.

http://humanbacon.blogs.com/human_bacon/2004/04/odd_and_even_ph.html

"As for why evenness and oddness of numbers are a philosophical illusion, one can only think of Thomas Aquinas and his dealings with choice and awareness and such. A decent page to read about Aquinas' thoughts about this can be found here: http://radicalacademy.com/philaquinasmdw6.htm. That's as far as I got with google. If all else fails, call up the ad council and hound them for an answer. That is where you started thinking about all this silly stuff, right?"

[stinkeefresh]

5. I'm starting to think

that this is just something an ad copywriter made up because he thought it sounded complex and intellectual.

I've watched other writers do similar things.

[ProfessorGAC]

6. I Think It's Pretty Simple, Robert

Numbers, in an of themselves, have no particular properties, aside from the ones we assign.

So an odd number is only an odd number, because we decided so. There is nothing intrinsically odd about the number 3, vs. the number 4. Similarly, there is nothing intrinsically even about 6.

It's a philosophical convention that one set or numbers are even and every other value is odd. So, it's just an illusory because the descriptor is just an extrinsic construct and not real.

My take. Not saying i'm right. But, it seems logical.
The Professor

[Goldmund]

9. You can extrapolate the same argument and say...

...that numbers themselves are a philosophical illusion.

If a whole number divided by 2 is a whole number, then that number is even; otherwise it's odd. That's just a definition. It's an "illusion" as much as any definition is an illusion. Are prime numbers an illusion? Imaginary numbers? What about the concept of parallel lines, convex shapes, etc? They are all just definitions.

[ProfessorGAC]

11. I Completely Agree

I am just trying to interpret the intention of the commercial that had Robert in a quandry.

I don't think it's that deep. Just a way to describing the abstract nature of numbers and language. The word "dog" only describes the mental picture of a canine, because we say so, right?

Math and language are human created abstractions, and i think that's all the commercial is trying to say. I'm not validating the concept. Just surmising as to the intent.
The Professor

[GumboYaYa]

25. Numbers are really just degrees of relation.

Someone arbitrarily picked zero as the measuring point and thus arbitrarily created the notion of even and odd numbers.

I think I just restated what the Professor already said.

[gpandas]

21. odd and even: i agree and...

there are way too many people who don't realize that mathmatics is made up so we can explain and quantify phenomena. numbers are made up.

[JVS]

26. I would say that the properties are there, we just need to discover them

For instance the most recently discovered mersenne prime was still a mersenne prime before we knew it was, we just hadn't realized it.

[OC_dem]

7. I've got a degree in

Physics and a minor in Philosophy. I have no clue sorry.

[Jim Sagle]

8. By definition, even numbers are the numbers evenly divisible by 2.

Odd number are the other numbers - the ones NOT evenly divisible by
2.

[Devils Advocate NZ]

12. Your definition is missing something...

3 / 2 = 1.5 + 1.5 = even number

At least by your definition. Slavkomae has given the acurate description "If a whole number divided by 2 is a whole number, then that number is even".

[Westegg]

16. Well, OK, evenly divisible by 2 with the result being a WHOLE number...

...as opposed to a fraction.

[Jim Sagle]

19. Good pick.

[NoPasaran]

10. I'm still having trouble

Digging why the sky is blue, man.
:shrug:

[ChavezSpeakstheTruth]

13. "Why don't you tell me?"

:)

[TrogL]

14. There is no such thing as 'one'

Therefore 'even' and 'odd' is an illusion.

[OC_dem]

15. Depends on

the set of rules your playing by.

[Westegg]

17. We've got ten fingers; we count unit by unit...one by one...

I'm no mathemetician or philosopher, BUT, don't we have a number/counting system based on ten because we have ten fingers, evenly divided (5X5)? And why did we start counting in the first place? Because we wanted to know how many THINGS we had---or the other guy had. How many cows, melons, women, whatever (please don't flame, OK? I'm talking about Primitive Man---a well-known Republican). Some of those things were reasonably divisible---you could chop a melon in half and still have a viable half-melon (though it wouldn't stay fresh as long as a whole one would). But you couldn't do that with a living cow or woman. If you created a fraction of a living creature it was changed in its very essence---going from living to dead. Hence, any group of them were equally divisible only as even numbers, not as odd.

In the end, I suggest to you that odd/even is not a philosphical contruct, rather an entirely practical one, based entirely on our limitations as humans.

[TrogL]

22. By the time you get to the tenth finger, it has aged

You are no longer comparing like things.

[Goldmund]

23. The definitions of odd and even...

...apply no matter what you pick as the base of your numerological system.

It's just an arythmetic definition -- and arythmetic doesn't change if you change your base, only representations of numbers do.

[Selwynn]

18. LOL - the answer can be found in the philosophy of Aquinas

I'll admit freely that though I am a philosopher, I wasn't sure that that commercial was really referring to at first.

However, after thinking about it more, I realize that it has to do with epistemology, i.e. the theory of knowledge or in other words, how we know what we know.

When we say "odd" or "even" we are speaking of a relation. Does that "relation" itself have ontological status? Or is it an illusory product of our linear and casually connecting thinking?

I went looking for a quick down and dirty summary of Aquinas on this, and I found this from the Cambridge Encyclopedia of Philosophy (hell even philosophers look stuff up, in fact I'd argue that we look much more stuff up!)

It has been indicated that the epistemological problem centers upon an inquiry concerning the validity of our spontaneous assertions. This inquiry resolves itself into two problems. First, the motive which leads the mind to establish a relation between a subject and a predicate in a judgment, and secondly, the validity of the respective terms themselves. Thus, when I say that a number is odd or even, or, that water boils at 100 degrees C., I may inquire:

* (a) What leads me to form a mental synthesis of number and odd or even; of water and boiling at 100 degrees C.?
* (b) What is the validity of these terms: number; odd; even; water; boiling? Are they mere mental products or do they refer to objects independently existent in an external world?

[Khephra]

20. "Every number is infinite, there is no difference."

"Uncle Al" Crowley.

[skypilot]

24. Don't lots of thing turn out to be...

..."philosophical illusions" when you delve into philosophy, logic, etc?