FOM: wider cultural significance: polylogism

[Stephen G Simpson]

Michael Detlefsen 4 Mar 1999 10:49:36 writes:
 > I would appreciate the reference to von Mises (and/or others in the
 > Austrian school) as well.

My recollection is that von Mises' masterpiece `Human Action' has a
long section about Marx's polylogism and other polylogist theories.
Sorry I can't be more precise right now -- I don't have access to my
personal library this semester.

I do think this whole issue of polylogism (i.e. multiple logics) not
only is interesting with respect to both f.o.m. and wider
scientific/cultural issues, but also points to many tie-ins between
the two.

In f.o.m., we can try to clarify and sort out the merits of several
possible positions vis a vis polylogism.  The extreme forms of these
positions might be caricatured as follows:

  1m. there is only one appropriate logic for f.o.m. (predicate
      calculus?)

  2m. there are many different logics appropriate for different
      aspects of mathematics (second-order logic? dynamic logic?
      temporal logic?) or different f.o.m. programs (intuitionistic
      logic?)

  3m. logic is irrelevant or meaningless for mathematics (Poincare?),
      or, mathematical logic is just another branch of mathematics
      (modern anti-f.o.m. bigots?)

Mares' 04 Mar 1999 10:20:48 posting seems to pertain to 2m.

Once could also consider analogous positions concerning the place of
logic in science and scholarship as a whole:

  1w. there is one science called logic, which serves as a common
      method or background for all other sciences (Aristotlean logic?)

  2w. there are many different logics pertaining to different branches
      of science and scholarship (the logic of physics?  the logic of
      law?) or to different groups of people (proletarian logic?
      bourgois logic?  Aryan logic?  Jewish logic?)

  3w. all logic is baloney (nihilism?)

Of course many of these issues are irrelevant to f.o.m. or, more
accurately, they should not be discussed here on the FOM list except
insofar as they pertain to f.o.m.  However, in terms of the above
6-fold scheme, I see many possible tie-ins between f.o.m. and the
wider cultural context.  For example, some mathematicians and math
educators in the United States are now pushing the idea of
ethnomathematics -- different mathematics for different ethnic groups.
Is this a link between 2m and 2w?

A somewhat different but perhaps related issue is topic-neutrality.
Is logic the same for all branches of mathematics, or not?  Is logic
the same for all scientific subjects, or not?

 > P.S. I think that Martin misstated the labor of theory of value

Maybe we ought to stay away from the labor theory of value and other
economics issues, unless they are shown to have some pretty close
connection with logic, f.o.m., etc.

-- Steve