[FOM] Re: Shapiro on natural and formal languages

Timothy Y. Chow tchow at alum.mit.edu
Tue Nov 30 08:25:59 EST 2004

Joe Shipman clarified what he was asking for; to test my understanding, 
let me suggest two candidates:

1. Every finite graph can be embedded in R^3 without crossings.

2. The trefoil knot cannot be unknotted in R^3.

Both of these are visually obvious, and it seems any kind of formalization 
is likely to lose something in the translation.  Do these then qualify?

Vladimir Sazonov questions whether any so-called visual proof is really 
anything more than a heuristic starting point if it's not clear how to
formalize it.  What do you say about #2 above?  This strikes me as an
example of something that is as obviously true as any standard axiom,
yet which I wouldn't call "linguistic" (even if one admits visual 
languages).  It's also not immediately clear how to formalize it, but
formalization seems to reduce the clarity and certainty rather than to
increase it.


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