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A math professor was giving a talk and stated that "given a false premise one can prove anything is true". A member of the audience then interrupted with "Ok th

A math professor was giving a talk and stated that "given a false premise one can prove anything is true". A member of the audience then interrupted with "Ok then, 1 + 1 = 3, now prove that you are the pope." The professor thought for a moment and began, "If 1 + 1 = 3 then 1 = 2 and since the pope and I are two then the pope and I are one."

btilly 14y ago
That is a clever professor. See http://en.wikipedia.org/wiki/Principle_of_explosion http://en.wikipedia.org/wiki/Principle_of_explosion for the usual lines of reasoning that get used.
pella 14y ago
Bertrand Russell is the Pope "The story goes that Bertrand Russell, in a lecture on logic, mentioned that in the sense of material implication, a false proposition implies any proposition. ..." http://www.nku.edu/~longa/classes/mat385_resources/docs/russellpope.html http://www.nku.edu/~longa/classes/mat385_resources/docs/russ...
- chris_wot 14y ago
  Russell's paradox?
  - derleth 14y ago
    Cute, but that's something different again.
    - chris_wot 14y ago
      My bad... This is new to me. What is the difference?
      - derleth 14y ago
        Russell's Paradox is the statement "Does the set of all sets that don't contain themselves contain itself?" (Parse that as "The set of (all sets that don't contain themselves)".) Now, obviously, the set of all sets contains itself, and in naïve set theory that isn't a problem: In naïve set theory, a set is just an unordered collection of any objects you can define; a set that contains itself poses no logical problems in an of itself. However, once you define the set of "all sets that don't contain themselves", you run into an immediate problem: If it does not contain itself, it must, in which case it cannot, and so on, in a neat infinite recursion. This is a real paradox, also known as a falsidical paradox, and a real paradox indicates a deep problem with the set of axioms it was derived from. (Banach-Tarski is not a real paradox by my definition; it is merely called a paradox because it is a counter-intuitive result.) Russell's Paradox blew naïve set theory out of the water; later set theories, such as Zermelo-Fraenkel (more commonly just called ZF), were very careful to not allow sets to contain themselves.
crntaylor 14y ago
In case anyone is interested, the non-witty answer would go like this: Clearly, 1+1=2, which is not 3, so ¬(1+1=3) (by usual rules of addition). But also 1+1=3 (by assumption). Since 1+1=3, then either I am the pope, or 1+1=3. But we know that ¬(1+1=3), which means that I must be the pope.

btilly 14y ago

That is a clever professor. See http://en.wikipedia.org/wiki/Principle_of_explosion http://en.wikipedia.org/wiki/Principle_of_explosion for the usual lines of reasoning that get used.

pella 14y ago

Bertrand Russell is the Pope "The story goes that Bertrand Russell, in a lecture on logic, mentioned that in the sense of material implication, a false proposition implies any proposition. ..." http://www.nku.edu/~longa/classes/mat385_resources/docs/russellpope.html http://www.nku.edu/~longa/classes/mat385_resources/docs/russ...

chris_wot 14y ago
Russell's paradox?
- derleth 14y ago
  Cute, but that's something different again.
  - chris_wot 14y ago
    My bad... This is new to me. What is the difference?
    - derleth 14y ago
      Russell's Paradox is the statement "Does the set of all sets that don't contain themselves contain itself?" (Parse that as "The set of (all sets that don't contain themselves)".) Now, obviously, the set of all sets contains itself, and in naïve set theory that isn't a problem: In naïve set theory, a set is just an unordered collection of any objects you can define; a set that contains itself poses no logical problems in an of itself. However, once you define the set of "all sets that don't contain themselves", you run into an immediate problem: If it does not contain itself, it must, in which case it cannot, and so on, in a neat infinite recursion. This is a real paradox, also known as a falsidical paradox, and a real paradox indicates a deep problem with the set of axioms it was derived from. (Banach-Tarski is not a real paradox by my definition; it is merely called a paradox because it is a counter-intuitive result.) Russell's Paradox blew naïve set theory out of the water; later set theories, such as Zermelo-Fraenkel (more commonly just called ZF), were very careful to not allow sets to contain themselves.

crntaylor 14y ago

In case anyone is interested, the non-witty answer would go like this: Clearly, 1+1=2, which is not 3, so ¬(1+1=3) (by usual rules of addition). But also 1+1=3 (by assumption). Since 1+1=3, then either I am the pope, or 1+1=3. But we know that ¬(1+1=3), which means that I must be the pope.