ABSTRACT This paper reveals David Hilbert’s position in the philosophy of mathematics, circa 1900, to be a form of non-eliminative structuralism, predating his formalism. I argue that Hilbert withstands the pressing objections put to him by Frege in the course of the Frege-Hilbert controversy in virtue of this early structuralist approach. To demonstrate that this historical position deserves contemporary attention I show that Hilbertian structuralism avoids a recent wave of objections against non-eliminative structuralists to the effect that they cannot distinguish (...) between structurally identical but importantly distinct mathematical objects, such as the complex roots of $-1$. (shrink)

I show that the indeterminacy problem for computational structuralists is in fact far more problematic than even the harshest critic of structuralism has realised; it is not a bullet which can be bitten by structuralists as previously thought. Roughly, this is because the structural indeterminacy of logic-gates such as AND/OR is caused by the structural identity of the binary computational digits 0/1 themselves. I provide a proof that pure computational structuralism is untenable because structural indeterminacy entails absurd consequences - namely, (...) that there is only one binary computational digit. I conclude that accounting for individuation is a more important desiderata for a theory of computation than even that of triviality. -/- . (shrink)

Ramsey’s Universals has not been served well by its critics and, as a result, the real and important contentions of Ramsey’s essay are often obscured in discussion of his work. This thesis is intended to form the beginning of an attempt to rectify this by offering an exposition and critique of Ramsey’s essay that is particularly sensitive to the background context and purpose of the essay as a whole and to the subtle structure of the argumentation within it. The construction (...) of the arguments in Universals is so intricate that to assess any of its arguments without placing them in the context of the overall strategy of Ramsey’s essay is to grossly underestimate them. For this reason, most of the labour in this thesis will be directed towards articulating Ramsey’s concerns in his essay and the way in which Ramsey’s arguments are supposed to supplement each other in order to establish his main contentions. These tasks take up the first two chapters. Only then will the third chapter consider one particular argument- the incomprehensible trinity argument- and assess whether it is successful by first identifying the role that the argument is intended to play in the overall structure of Ramsey’s argument and then asking whether or not the argument can be said to fulfil such a role. This final chapter is a mere beginning towards a proper critique of Ramsey’s difficult and subtle argumentation in Universals. Nonetheless it serves as an example of how offering a critique of Ramsey which places his arguments within the context and concerns of the essay as a whole, while it does not immediately vindicate them of all criticism, shows them to be far more subtle and robust than they have been estimated to be. (shrink)