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

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Muntean, Ioan
conference paper description
In a recent book (The Metaphysics within Physics), Tim Maudlin reconstructs metaphysics by taking inspiration from the gauge theories interpreted in the ber 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 rst from metaphysics. The metaphysician questions whether gauge theory represented through ber bundles is apt to reform metaphysics. It needs, I claim, a rmer commitment to realism. Second, she cannot see how Maudlin accommodates the metaphysical "loneliness" of objects in the ber bundle metaphysics and complains that the mathematical structures of the ber 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 ber bundle representation which is deeply divided among two types of bundles, corresponding to dierent ontologies: gauge elds and spacetime dieomorphism. Several possible paths towards more realistic interpretations of the ber bundle are briefy 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.