FOM: Intuition and Rigor
peterb at dcs.qmul.ac.uk
Thu Feb 14 20:42:48 EST 2002
> Here is a modest list of the successes of intuition over rigor.
> 1. Everything is composed of earth, air, fire and water.
> 2. The sun goes round the earth.
> 3. The earth is flat.
> 4. God exists.
> 5. There is an afterlife.
> 6. For every property F, there is a set of all Fs.
> 7. Peano arithmetic is complete.
> 8. Space is Euclidean.
> 9. There is only one kind of infinity.
> 10. Mind is distinct from matter.
> Neil, I don't know if you intended to imply that all these statements have the same epistemological status. I don't think they do: propositions 1,2,3,6,7,8, and 9 have been disproved, while propositions 4,5, and 10 are open questions. Do you mean to suggest that 4,5, and 10 have also been disproved?
> -- Joe Shipman
What occurred to me was a different kind of diversity: not the issue
of truth or provedness, but rather the prior issue of meaningfulness.
The items in Neil's list offer a variety of senses in which they might
be said to admit truth-values _at all_, or not. In particular, I
wouldn't classify 4,5,10 as open questions: one can't even be agnostic
about things which aren't questions (or which have no greater claim to
questionhood than mere grammatical well-formedness in English). For
some of the other seven, too, there is perhaps a questionhoodness
issue. (One non-point: I see now that I've said "questionhoodness"
where to be more consistent with Joe's reply I perhaps should have
said "statementhoodness" - sorry: no significance in that at all.)
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