[hist-analytic] sticks, circles and the contingent a priori

Roger Bishop Jones rbj at rbjones.com
Mon May 31 10:28:07 EDT 2010

On Monday 31 May 2010 14:23, you wrote:

> The distinction I was drawing is not, I don't believe
>  anyway, a distinction between physical and nonphysical
>  quantities. I can use degrees in figuring out physical,
>  spatial, relations in real time; such as how far an
>  airplane will travel if it is a certain bearing and
>  velocity. The issue concerns how we introduce units of
>  quantity, not whether the quantities are physical or
>  not. No matter which rotation we are talking about we
>  get the same values, e.g. for the trigonometric
>  functions. But if we pick a different stick we get a
>  different "meaning" of 'one meter'. 'One degree' is not
>  dependent on any particular circle; but 'one meter'
>  depends on one particular stick. That is the critical
>  asymmetry.

Well I think I understand your point, and I still think that 
the difference you are pointing to here can be accounted for 
by the fact that the former is and the latter is not a 
standard for a physical quantity, and that the notion of 
dimension is helpful in distinguishing whether something is 
a physical quantity or not.

An alternative way of thinking of it is that measures for 
angles are definable in a pure mathematical context, in much 
the same way that the number pi is definable in that way 
(also defined in terms of circles but dependent on no 
particular circle).

>  Now I don't discuss this in the book; but I
>  do take Kripke to task for what I believe is an
>  equivocation that leads to the erroneous belief that
>  there is a contingent a priori in any non-Kantian sense.
>  I point out on this matter that Kripke is anticipated by
>  Reichenbach, among other things.

Oh, well I misunderstood you there.

Are you now saying that there are contingent a priori truths 
in the sense of Kant? (and that this isn't just a different 
equivocation?).  I knew about the synthetic a priori in Kant 
(arithmetic and geometry for example), but not the 
contingent a priori (arithmetic and geometry still being 

Are you saying that Reichenbach anticipated Kripke's error?


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