FOM: Rota AS/IS debugged

Robert Tragesser RTragesser at
Fri Nov 20 06:43:47 EST 1998

        Steve Simpson has mentioned Rota's "As" (as discussed in Rota's 
INDISCRETE THOUGHTS) and Joe Shipman has expressed puzzlement.  I'll 
take a shot at explaining what's at issue and pointing to some 
connections maybe relevant to FOM.  I'll be brief;  there are many 
complexities and subtlties of course. . .  It is [3] below that contains
the important content.

[1] Yes,  the use of 'as' here surely has its roots in the Aristotelian 
'qua', as in:  "Paul Erdo"s qua mathematician",  "Paul Erdo"s qua 
nomad", 'Paul Erdo"s qua worrier about digestion problems".

[2] But the attention Rota pays to "as" and the jobs he makes it do,  
undoubtedly come from Heidegger.  In Heidegger,  the pattern IS AS IS AS
IS AS becomes a kind of trope for the cycle of analysis or other sort of
laying open. It's not worth explaining this.

[3] Rota main philosophical point is that most any thing you choose 
(including mathematical items and such) has a very messy identity 
indeed.  Nothing can be identitfied through a simple identification such
as X is B.  Rather we have 
X as A, X as B, X as C...

These are as it were different slices through X.  None of them is 
priveleged,  none gives "_the_ identity of X".  You might try to think 
that the identity of X is some sort of sum of all the X as Y's,  but 
generally no exhaustive account can be given.  W.r.t. mathematics,  Rota
gives a couple easy examples.  Boolean algebra.  Euclidean space.  There
is no privileged characterization of either of these (characterization =
identification),  but different characterizations for different 
purposes.  There is no expectation of a principle or rule generating all
possible characterizations or guises (as it were),
A Boolean algebra as A,  A Boolean algebra as B, ...
Intension is the main issue -- that which prevents A being (wholly) 
reducible to B,  etc.  The logic of "as" is so to speak the logic of 

        In the case of more concrete things,  such as human beings,
such as those slices through "Paul Erdo"s" above,  the list is not only 
inexhaustible,  but it is dynamic.  And the simple word "as" hides a 
multitude of different "relations" __as__.  Paul Erdo"s is not "as" a 
mathematician in the same way that he is "as" someone from Middle 
Europe,  as he is "as" a worrier about digestion.  
        My thoughts as brain activity
        My thoughts as expressed in these words
These are two mutually irreducible "identities" of my thoughts; with 
quite a different force to "as" in each case.
        An especially important X as C is when X bears the relation of 
Fundierung (crudely,   nonindependence) to C. 

        In any case,  its rather obvious that we are opened here onto a 
vast and mostly uncharted continent of tremendously significant 
phenomena (all identities as messy identities).  Rota has put us ashore,
 and that's about all.  But quite astonishing and unexpected logical 
landscapes emerge,  clearly.

robert tragesser
West(Running)Brook,  Connecticut 06498 

More information about the FOM mailing list