FOM: Hersh-Gardner and Institution(s)
Vaughan R. Pratt
pratt at cs.Stanford.EDU
Thu Nov 13 09:21:37 EST 1997
>From: Bill Tait <wtait at ix.netcom.com>
>We may distinguish between
>changing the institution and changing institutions: the institution
>as it is now is immutable by definition (the institution de re, as
>the scholastics would have called it). What changes is not that;
>rather we may abandon that institution for another---we change
>institution_s_. (We change the institution de dicto). For example,
>number theory won't change; we may only abandon it for something else
>(which, of course, may come to be called `number theory'). Maybe,
>with this distinction, the strong feelings of rightness on the part
>of both Hersh and Gardner become explicable.
This is the point of my example
When 7+5 no longer makes 12, 8+6 will no longer make 14.
(Nov. 2, Hersh-Gardner). Neil Tennant's entirely reasonable remarks
about the difficulty of changing one without influencing the other
bears out the immutability of the institution of arithmetic. When the
institution is abandoned, 7+5=12 becomes not so much false as unknown.
But I'm not sure I'd go along with the idea that one changes
institutions only by replacement. Is each of the ongoing changes to
the institution of marriage implemented by replacing the institution or
merely by modifying it?
The advantage of the latter viewpoint is that one can then rank
institutions by their rigidity. Arithmetic, at least of the countable
sets of numbers, seems an intrinsically more rigid institution than
marriage. The institutions associated with the various uncountable
sets of numbers more closely resemble marriage in that regard.
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