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Does such a symbol exist?

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Does a symbol exist that represents the set of things that cannot be represented by symbols? Any designers out there interested in taking a whack at creating one?

I've recently become fascinated with the exploration languages limitations in communicating it's own limitations.

If anyone knows of writers, philosophers, scientists, or others who explore this space please respond :)

3 comments

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Jun8
This is the classical "who shaves the barber" paradox (http://en.wikipedia.org/wiki/Barber_paradox), which Russell used to show that the approach to set theory at his time can be shown to contradict itself. Then came Godel et al. For a good intorduction to these topics I suggest Godel, Escher, Bach or Labyrinths.
ggchappell
> This is the classical "who shaves the barber" paradox

I don't think it is. Simply because a set contains things that cannot be represented by a symbol, does not mean that the set itself cannot be represented by a symbol. And since it can, the set is not a member of itself. No paradoxes.

Also, I propose to you all that everything can be represented by a symbol. Thus, the set in question is the empty set. And here is the requested symbol:

∅

bricestacey
Genuine question: Can you provide an example or explain what exists that cannot be represented by symbols?