By that I mean that I believe that physical systems can be completely described by constructive mathematics based on intuitionistic logic[2] operating on computable reals[3]. I believe that any other kind of mathematics, e.g. classical logic with axiom of choice can create unphysical models.
That being said, I don't object to classical logic as a purely abstract concept. Everything proved in ZFC is certainly true in ZFC! And I don't think any finitist will contest that.