[FOM] Godel numbers, use, and mention

Hartley Slater slaterbh at cyllene.uwa.edu.au
Tue Jun 3 01:33:44 EDT 2003

Sandy Hodges says (FOM Digest Vol 6 Issue 4):

>An observer in the spaceship may say that "Hesperus = Phosphorus" is a
>necessary truth about an object, namely the inner planet, and may say
>that "(E y) ( Names(8502, y) & Names(8503, y) )" is a contingent truth
>(about what, I am not clear.   Certainly you can't "replace the numbers
>with the respective names" in it.   I have no clue what Hartley means by
>that.  But perhaps it states a contingent truth about the numbers 8502
>and 8503.)    Suppose the spaceship observer is correct, and in this
>language two equivalent formulas, "Hesperus = Phosphorus" and "(E y) (
>Names(8502, y) & Names(8503, y) )" are respectively a necessary truth
>and a contingent one.   Should they be distressed by this?   Do any bad
>consequences for them follow from the the fact that their axioms have
>made these two formulas equivalent?

First, here is a clue: I was talking about replacing '8502' with ' 
"Hesperus" ', and '8593' by ' "Phosphorus" '.   Second, there 
certainly is no immediate distress if, as Hodges decrees:

>Their language has no modal operators.

Since then the language users are not capable of formulating facts 
about the distinction between necessary and contingent truths.  But 
most people who do not live in Hodges' spaceship do use a modal 
language, and so are capable of, and concerned about making the 

Barry Hartley Slater
Honorary Senior Research Fellow
Philosophy, School of Humanities
University of Western Australia
35 Stirling Highway
Crawley WA 6009, Australia
Ph: (08) 9380 1246 (W), 9386 4812 (H)
Fax: (08) 9380 1057
Url: http://www.arts.uwa.edu.au/PhilosWWW/Staff/slater.html

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