Robert Brandom, a prominent American philosopher in the analytic tradition, addresses the justification for modus ponens reasoning through his inferentialist theory of meaning and understanding. Brandom's approach is rooted in the idea that the meaning and content of linguistic expressions are essentially determined by their inferential roles, that is, by the patterns of inference that they are involved in.

According to Brandom, the justification for modus ponens reasoning lies in the inferential proprieties that govern the logical constants and their use in our linguistic practices. In other words, the validity of modus ponens is not an external constraint imposed on our reasoning, but rather an implicit norm that is built into the very meaning of the conditional (represented by the '→' symbol) and our practice of using it.

Brandom would argue that the meaning of the conditional 'p → q' is constituted by the material inferential proprieties that govern its use. Specifically, asserting 'p → q' commits one to the inference from 'p' to 'q'. This is not merely a descriptive claim about how people reason, but a normative one about how one ought to reason if one is to count as grasping the meaning of the conditional.

In Brandom's view, the validity of modus ponens is not a separate principle that needs to be justified; rather, it is built into the very meaning of the conditional. By asserting 'p → q' and 'p', one has already undertaken commitments that, by the inferential proprieties governing the conditional, entail the commitment to 'q'. This is not an external constraint but an internal requirement for grasping the meaning of the conditional and using it correctly.

Brandom's approach suggests that the justification for modus ponens reasoning is not to be found in some external foundation or self-evident principle, but rather in the implicit norms and inferential proprieties that are constitutive of our linguistic practices and our grasp of the meanings of logical constants like the conditional. In this sense, the validity of modus ponens is not something that needs to be independently justified but is rather a constitutive feature of our logical and linguistic practices themselves.