The distinction between mathematical and physical objects has probably played a greater role shaping the philosophy of mathematics than the distinction between observable and theoretical entities has had in defining the philosophy of science. All the major movements in the philosophy of mathematics may be seen as attempts to free mathematics of an abstract ontology or to come to terms with it. The reasons are epistemic. Most philosophers of mathematics believe that the abstractaess of mathematical objects introduces special difficulties in (...) accounting for our ability to know them, to refer to them and even to entertain beliefs about them. These difficulties—supposedly absent even in the case of the most theoretical physical objects—make mathematical objects especially problematic and philosophically unattractive.Few have questioned this epistemic thesis or the ontic distinction it presupposes. LaVerne Shelton (1980) challenged the abstract-concrete distinction some years ago in an unpublished APA address. (shrink)

The practice of describing multiparticle quantum systems in terms of labeled particles indicates that we think of quantum entities as individuatable. The labels, together with particle indistinguishability, create the need for symmetrization or antisymmetrization (or, in principle, higher-order symmetries), which in turn results in “surplus formal structure” in the formalism, formal structure which corresponds to nothing in the real world. We argue that these facts show quanta to be unindividuatable entities, things in principle incapable of supporting labels, and so things (...) which support no factual difference_if two of them are thought of as being switched. When thinking of the metaphysics of quanta, we should eschew the misleading labels of the tensor product Hilbert space formalism and prefer the ontologically more faithful description of the Fock space formalism. This conception eliminates puzzles about the quantum statistics of bosons. (shrink)

Much apprehension has been expressed by philosophers about the method of renormalisation in quantum field theory, as it apparently requires illegitimate procedure of infinite cancellation. This has lead to various speculations, in particular in Teller (1989). We examine Teller's discussion of perturbative renormalisation of quantum fields, and show why it is inadequate. To really approach the matter one needs to understand the ideas and results of the renormalisation group, so we give a simple but comprehensive account of this topic. With (...) this in hand, we explain how renormalisation can and should be understood. One thing that is revealed is that apparently very successful theories such as quantum electro-dynamics cannot be universally true; resolving the tension between success and falsity leads to a picture in which any theory may be viewed as irreducibly phenomenological. We explain how, and argue that the support for this view is tenuous at best. (shrink)

In this paper we critically review the various attempts that have been made to understand quantum field theory. We focus on Teller's (1990) harmonic oscillator interpretation, and Bohm et al.'s (1987) causal interpretation. The former unabashedly aims to be a purely heuristic account, but we show that it is only interestingly applicable to the free bosonic field. Along the way we suggest alternative models. Bohm's interpretation provides an ontology for the theory--a classical field, with a quantum equation of motion. This (...) too has problems; it is not Lorentz invariant. (shrink)

If the general arguments concerning theinvolvement of variation and selection inexplanations of ``fit'' are valid, then variationand selection explanations should beappropriate, or at least potentiallyappropriate, outside the paradigm historisticdomains of biology and knowledge. In thisdiscussion, I wish to indicate some potentialroles for variation and selection infoundational physics – specifically inquantum field theory. I will not be attemptingany full coherent ontology for quantum fieldtheory – none currently exists, and none islikely for at least the short term future. Instead, I wish to (...) engage in some partiallyspeculative interpretations of some interestingresults in this area with the aim ofdemonstrating that variation and selectionnotions might play a role even here. Ifvariation and selection can survive in even asinhospitable and non-paradigmatic a terrain asfoundational physics, then it can surviveanywhere. (shrink)

I discuss issues concerning the philosophical foundations andimplications of quantum field theory, renormalization inparticular. A new understanding of the correspondence principle,an unexpected role of perturbation theory and, most of all, acriterion to reduce the set of consistent theories frominfinitely many to finitely many, are the key concepts of atheoretical set-up that appears to overcome in a natural wayvarious consistency problems of quantum mechanics and offerseveral hints for further developments.