1. Physics relies on mathematical principles
2. For the mathematical principles to be justified, they need logical justification
2′. Mathematics reduces to logic
3. Iff physics relies on mathematical principles, then physics relies on logic
C1: If antedent in claim 3. obtains, consequent obtains: physics relies on logic
4. Logic relies on the characterisation of fundamental ontological categories (being, truth, individuals, classes, quantifiers, possibles, etc)
5. Iff logic relies on fundamental categories, then logic relies on metaphysics
6. The antecedent of 5 obtains, therefore the consequent obtains: logic relies on metaphysics
C2: Physics relies on metaphysics in at least one way.
The contraversial premises are 2. 2′, and possibly 4.
This is just a thought. Its not usually my way to be even entertaining logicism!