Publications

This paper presents a exposition of Putnam’s model theoretic arguments in the context of his broader philosophical position. I argue that Putnam used the arguments not just to undermine metaphysical realism, but to reveal that the philosophical debate between metaphysical realism and internal realism is dialectically problematic in that the metaphysical realist defence cannot “count against” (Putnam in Philosophical Topics: The philosophy of Hilary Putnam 20(1):355, 1992c) the converse position. Putnam’s response is that this is a debate that we should simply undercut.

I examine van Fraassen’s critique of structural realism from the underdetermination of representation. I show that the critique targets a much broader class of positions than structural realism and argue that structural realists should adopt van Fraassen’s own response to the problem, which is to give a pragmatic account of representation.

The primary justification for mathematical structuralism is its capacity to explain two observations about mathematical objects, typically natural numbers. Non-eliminative structuralism attributes these features to the particular _ontology_ of mathematics. I argue that attributing the features to an ontology of structural objects conflicts with claims often made by structuralists to the effect that their structuralist theses are versions of Quine’s ontological relativity or Putnam’s internal realism. I describe and argue for an alternative explanation for these features which instead explains the attributes them to the _mathematical practice_ of representing numbers using more concrete tokens, such as sets, strokes and so on.

According to the popular ‘epistemic virtue account’ (EVA) of theory choice, we should choose between scientific theories on the basis of their epistemic virtues: empirical fit, simplicity, unity etc. More specifically, we should use a rule that aggregates theories’ virtues into a ranking of the overall goodness of the theories. However, an application of Arrow’s impossibility theorem shows that, given plausible premises, there is no rule that can aggregate theories’ virtues into a theory ranking. The EVA-supporter might try to avoid the impossibility result of Arrow’s theorem by asserting that we have more fine-grained distinctions between theories’ epistemic virtues than initially supposed. We show that implausibly fine-grained distinctions between virtue quantities are necessary to escape the impossibility result. This is shown via novel proofs of Arrow’s theorem for cases in which the quantities to be aggregated are measured on any combination of different scales of information, as is typically the case when aggregating epistemic virtues.

Structuralist positions in the philosophy of physics and mathematics have a complicated relationship with Hilary Putnam's model-theoretic arguments. One reason to think that Putnam's permutation argument motivates structuralism is that the hole argument about spacetime, which structuralists about physics take to support their position, has been claimed to be a version of Putnam's permutation argument (Liu, 1996, Rynasiewicz, 1994). I argue against this claim. However, as Demopoulos and Friedman (1985) have claimed, Newman's objection to structuralism is closely analogous to Putnam's argument.