Posina Venkata Rayudu wrote:
Pictures, by themselves, don't support propositions that take yes-or-no truth-values. A string (a concatenation) of images cannot replace well-formed formulae, assertion.
I dare not speculate as to whether non-Boolean truth-value object of topos has any bearing on Wittgenstein's 'proof against pictures in thinking.'
I would say this. It is often useful to work in the so-called geometric logic: not the full intuitionistic internal logic of toposes but that fragment of it that is stable under pullback along geometric morphisms. For instance, it is closely related to continuity, and reasoning geometrically can give automatic continuity proofs. Geometric logic does not have negation as a logical connective, and consequently you approach a proposition asking not "Is this true or false?", but "What truth do I find in this?" (A concrete example is a computer program that is taking a long time to complete. It may have gone into an infinite loop, but you will never discover this. The question "Does this terminate or not?" is not the useful one in practice; instead you ask "Have I got a result yet?") Somehow (and I don't think I can be any less vague here) this approach to truth feels a more appropriate one for visual imagery, and even for much verbal imagery, such as that of poetry, philosophy or religion. Is the story of the Good Samaritan true or false? Quite probably false: it never happened exactly as stated. But that misses the point that you can still find truth in it. Steve Vickers. 10-Jan-2002 10:02:16 -0400,822;000000000000-00000000