To what extent can constructive mathematics based on intuitionistc logic recover the mathematics needed for spacetime physics? Certain aspects of this important question are examined, both technical and philosophical. 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 Relativity Theory, in particular the singularity theorems of Hawking and Penrose. As they stand, these results appear to elude constructivization. On the philosophical side, it (...) is argued that any mentalist-based radical constructivism suffers from a kind of neo-Kantian apriorism. It would be at best a lucky accident if objective spacetime structure mirrored mentalist mathematics. the latter would seem implicitly committed to a Leibnizian relationist view of spacetime, but is it doubtful if implementation of such a view would overcome the objection. As a result, an anti-realist view of physics seems forced on the radical constructivist. (shrink)

One worrying aspect of contemporary Western Society is the increasing prevalence of instances of ‘Science Denial’ in popular culture. Examples include both cases where well-attested scientific hypotheses are rejected and conversely, where scientifically discredited ideas are stubbornly retained. The paper raises the question whether the kind of argument for an anti-realist conception of empirical scientific theory considered in my contribution to the inaugural issue of this journal could in principle provide intellectual succour for these trends. The discussion proceeds through an (...) examination of the role of ‘takings for granted’ in all reflective enquiry to the conclusion that a trusting acceptance of the general credibility of informants is a precondition for the exercise of individual epistemic responsibility, and that in that context an acceptance of at least the empirical adequacy, if not the truth, realistically understood, of the teachings of scientists in general is rationally non-optional. (shrink)