MATHEMATICAL CONSTRUCTIVISM IN SPACETIME

To what extent can constructive mathematics based on intuitionistic lo gic recover the mathematics needed for spacetime physics? Certain aspe cts of this important question are examined, both technical and philos ophical. On the technical side, order, connectivity, and extremization properties of the continuum are reviewed, and attention is called to certain striking results concerning causal structure in General Relati vity Theory, in particular the singularity theorems of Hawking and Pen rose. As they stand, these results appear to elude constructivization. On the philosophical side, it is argued that any mentalist-based radi cal constructivism suffers from a kind of neo-Kantian apriorism. It wo uld be at best a lucky accident if objective spacetime structure mirro red mentalist mathematics. The latter would seem implicitly committed to a Leibnizian relationist view of spacetime, but it is doubtful if i mplementation of such a view would overcome the objection. As a result , an anti-realist view of physics seems forced on the radical construc tivist.