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Patrick, 
 
Well, there is no discussion of either intermediate 
cases or of "public functions" in the original 1954 paper, 
which is very short.  He brings in this discussion in the 
1955 paper to respond to critics of his original paper 
who pointed out the existence of the intermediate cases. 
Samuelson fully agrees with the critics that there are 
intermediate cases.  He does not clearly say that those 
functions you mentioned must be or should be provided 
publicly, and he clearly did not say that they were pure 
collective consumption goods, although he probably did 
at the time believe that they should be provided publicly 
as they largely were then. 
 
I continue to disagree that his definition of pure 
collective consumption goods (definitely the clearest 
term) is based on mathematics.  I shall not repeat this 
again, but simply note that the mathematics follows 
from the definition.  Now, you seem to deny the existence 
of such pure collective consumption goods, and that is 
certainly a defensible philosophical and methodological 
position, partly because such goods are by their very 
nature hard to "put one's hands on" (much less assign 
property rights with excludability characteristics to them). 
But, once one allows the possibility for such a good to 
exist, the mathematics follows logically, although again, 
I grant that one can object in general to the use of such 
mathematics or deny the applicability of the mathematics 
because it assumes some kind of nonexistent collectivity 
in the face of methodological individualism.  But, it is not 
the math that is doing the defining. 
 
So, let us confront then the final question, the existence 
of pure collective consumption (or "public") goods. 
Samuelson poses the standard example of national defense. 
Why do you reject this?  I can appreciate that if it is defense 
against a ground attack on certain boundaries of a country 
that it might not be a pure collective consumption good, with 
national defense actually only defending a subset of the 
population.  But, what about deterring against overwhelming 
nuclear attack that would destroy all human life on the planet? 
Is this not a pure collective consumption good? 
 
As a final point I would say that you make to much of 
denying a reality to "public functions."  These are simply 
services and we treat services as being like goods in usual 
economic analysis.  Whether these publicly provided services 
are actually pure (or even intermediate) collective consumption 
goods, or whether they could or should be provided privately, 
is quite another matter. 
 
Barkley Rosser 
 
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