FOM: Intuition and Rigor

[Peter Burton]

> 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.)

xx p