The Fiber Bundle at the Gates of Metaphysics. Challenging Maudlin’s Proposal

In a recent book (The Metaphysics within Physics), Tim Maudlin reconstructs metaphysics by taking inspiration from the gauge theories interpreted in the fiber bundle framework. I call his project the “fiber bundle metaphysics”. Primarily targeted not to Humean Supervenience, but to any metaphysics employing the relation of resemblance among objects (D. Lewis, D. Armstrong), Maudlin’s project is novel and promising. I critically analyze the arguments by identifying several objections stemming first from metaphysics. The metaphysician questions whether gauge theory represented through fiber bundles is apt to reform metaphysics. It needs, I claim, a firmer commitment to realism. Second, she cannot see how Maudlin accommodates the metaphysical “loneliness” of objects in the fiber bundle metaphysics and complains that the mathematical structures of the fiber bundle metaphysics are weakly discernible only. A second class of objections stems from the physics of gauge theories. I see a “conventional” solution to Maudlin’s path-dependency argument against Lewis’s “pure metaphysical relations”: other invariants of affine connections can play the role of internal properties and relations. I raise an objection and address it regarding the duality of the fiber bundle representation which is deeply divided among two types of bundles, corresponding to different ontologies: gauge fields and spacetime diffeomorphism. Several possible paths towards more realistic interpretations of the fiber bundle are briefly discussed. Finally, I bring in the provlem of locality, separability and I emphasize some criticisms. My conclusion is that Mauldin’s project is assuring, but not powerful enough to reform metaphysics.