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

Baynesr at comcast.net Baynesr at comcast.net
Mon May 31 11:57:50 EDT 2010

Reichenbach argues for a contingent a priori BASED on 
Kantian principles. He does not require a theory of rigid 
designation. (I don't criticize the theory of rigid designation, 
only ideas related to its application). 

The difference between 'one degree' and 'one meter' has 
to do with how a constant is introduced, and may entail 
some needed clarification of the nature of constants in 
mathematics. Any real number, c, can be regarded as 
the value of a "constant function": 


In the case of something like 

f(x) = 5 

We might want to say that '5' is uniquely identified as a 
value of the successor function where 'x' is 4. The rules of 
arithmetic *require* all such numbers to be 5. The value 
is determined by the rules of arithmetic. This is, also, true 
of 'one degree'; that is, the reference of 'one degree' is 
determined by the rules of geometry, not our choice of 
circles. In the case of 'one meter' by contrast 
the reference is not determined by the rules of 
geometry (or any other a priori rules) and there is 
nothing constant about the value of 'one meter' as there is 
in the case of 'five'. So we have a sharp distinction 
between 'one meter' and '5', or 'one meter' and 'one degree'. 
It is not a priori that the meter stick is the length it is. It is 
a priori that a circle has the degrees it has (any circle). 
It should be added that we can translate degrees to 
another metric, and sometimes for the purpose of 
calculation must; for example to compute the length 
of an arc based on the radius we have to convert to 
radians from degrees. No such comparison is possible 
in the conversion of feet to inches! No computation 
requires feet rather than inches, for example. 

My discussion in the book relates to the scopal properties 
involved in a logical characterization of this diffference. 
I won't give the "secret" away until the book is easily 



----- Original Message ----- 
From: "Roger Bishop Jones" <rbj at rbjones.com> 
To: hist-analytic at simplelists.com 
Sent: Monday, May 31, 2010 9:28:07 AM GMT -06:00 US/Canada Central 
Subject: sticks, circles and the contingent a priori 

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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