Husserl, Dummett, and the linguistic turn

Michael Dummett famously holds that the “philosophy of thought” must proceed via the philosophy of language, since that is the only way to preserve the objectivity of thoughts while avoiding commitments to “mythological,” Platonic entities. Central to Dummett’s case is his thesis that all thought contents are linguistically expressible. In this paper, I will (a) argue that making the linguistic turn is neither necessary nor sufficient to avoid the problems of psychologism, (b) discuss Wayne Martin’s argument that not all thought-contents are linguistically communicable, and (c) present another, stronger argument, derived from Husserl’s early account of fulfillment, that establishes the same conclusion

Renormalization of the spectral action for the Yang-Mills system

We establish renormalizability of the full spectral action for the Yang-Mills system on a flat 4-dimensional background manifold. Interpreting the spectral action as a higher-derivative gauge theory, we find that it behaves unexpectedly well as far as renormalization is concerned. Namely, a power counting argument implies that the spectral action is superrenormalizable. From BRST-invariance of the one-loop effective action, we conclude that it is actually renormalizable as a gauge theory.Comment: 6 pages; 4 figures; minor correction

Renormalization of gauge fields: A Hopf algebra approach

We study the Connes-Kreimer Hopf algebra of renormalization in the case of gauge theories. We show that the Ward identities and the Slavnov-Taylor identities (in the abelian and non-abelian case respectively) are compatible with the Hopf algebra structure, in that they generate a Hopf ideal. Consequently, the quotient Hopf algebra is well-defined and has those identities built in. This provides a purely combinatorial and rigorous proof of compatibility of the Slavnov-Taylor identities with renormalization.Comment: 24 pages; uses feynm