If: 1. A is A. 2. A is not not-A. does it imply that: 1. B is B. 2. B is not not-B ?
(take a moment to think about it). (continuation below)
While this is a complete blasphemy, it illustrates an important point. Sometimes, subtle switches between induction and deduction are used in a mystical manner, either deliberatly or while being careless.
In any case, if you want to learn more about the mathematical and logical nature of many jokes, I can wholeheartedly recommend to read John Allen Paulos' book "Mathematics and Humor".
Shlomi Fish wrote: > If: > 1. A is A. > 2. A is not not-A. > does it imply that: > 1. B is B. > 2. B is not not-B > ?
> (take a moment to think about it). > (continuation below)
Shlomi, A occurs as a bound variable to a quantifier that is implied but not written. Substitution the bound variable A with the bound variable B does not change anything.
> In any case, if you want to learn more about the mathematical and > logical nature of many jokes, I can wholeheartedly recommend to read > John Allen Paulos' book "Mathematics and Humor".
Paulos is brilliant. His books on "Innumeracy" were among the most overlooked and important social commentary in recent history. And what a fascinating, absorbing author he is.
> > In any case, if you want to learn more about the mathematical and > > logical nature of many jokes, I can wholeheartedly recommend to read > > John Allen Paulos' book "Mathematics and Humor".
> Paulos is brilliant. His books on "Innumeracy" were among the most > overlooked and important social commentary in recent history. And what a > fascinating, absorbing author he is.
Yes, I have read "Innumeracy", which is a very good book. The book "Whence Numeracy" is also very nice, especially for people who are not professional mathematicians.
> > If: > > 1. A is A. > > 2. A is not not-A. > > does it imply that: > > 1. B is B. > > 2. B is not not-B > > ?
> > (take a moment to think about it). > > (continuation below)
> Shlomi, A occurs as a bound variable to a quantifier > that is implied but not written. Substitution the bound > variable A with the bound variable B does not change > anything.
> Have I missed something?
I know one should not explain jokes, but I hope you'll understand:
How do you know that what is true for A is also true for B? ;-)
> > How do you know that what is true for A is also true for B? ;-)
> A occurs as a bound variable to an implied universal quantifier. > What the first statement says is : For ALL A, A is A and A is not not A > So plugging in B where A occurs does not change a thing.
Yeah--I think that's why he put the smiley.
> If the name of a particular entity were placed in the statement, > you might have a point. BTW, what is funny about this?
This reminds me of another joke. An algebra teacher is discussing a problem with a student. The teacher says, "Now, suppose x is the speed at which the train is traveling ..." And the student says, "But teacher, suppose x isn't the speed at which the train is traveling?"
> This reminds me of another joke. An algebra teacher is discussing a problem > with a student. The teacher says, "Now, suppose x is the speed at which the > train is traveling ..." And the student says, "But teacher, suppose x isn't > the speed at which the train is traveling?"
Very nice. I'll add it to one of my fortune files. In any case, if you wish to read some of my other humurous bits (or my more lengthy stories) you can consult my homepage:
In article <deca99a9.0110230410.707df...@posting.google.com>, Shlomi Fish
<shlo...@vipe.technion.ac.il> wrote: > If: > 1. A is A. > 2. A is not not-A. > does it imply that: > 1. B is B. > 2. B is not not-B
A=B. Whatever symbol used, things are what they are. -- ============================================== Reason is the basic method of human survival. AYN RAND ------------------------------------------------------------------------- Radically systematic radical metaphysics: Existence 2 http://home.att.net/~sdgross ------------------------------------------------------------------------- Stephen Grossman Fairhaven, MA, USA sdgr...@att.net ===============================================
