In this paper, I argue against Penelope Maddy's set-theoretic realism by arguing (1) that it is perfectly consistent with mathematical Platonism to deny that there is a fact of the matter concerning statements which are independent of the axioms of set theory, and that (2) denying this accords further that many contemporary Platonists assert that there is a fact of the matter because they are closet foundationalists, and that their brand of foundationalism is in radical conflict with actual mathematical practice.

According to Gilles Deleuze, the underground world of Alice in Wonderland has been strongly associated with animality and embodiment. Thus the need for Alice's eventual climb to the surface and her discovery that everything linguistic happens at that border. Yet, strangely, in spite of the claim that Alice disavows false depth and returns to the surface, it seems that it is precisely in the depths that she finally wakes from her sleepy, stupified surface state and investigates the deep structures, the (...) rules of logic. In this investigation, Alice questions many formal structures, such as causality, identity, reference and the rules of replacement. She discovers that Wonderland does not generate consequential conduct; in fact, it generates no conduct whatsoever! In other words, when it comes to consequences, Wonderland may not be all that wonderful. Yet, we do not live in Wonderland and therefore, our actions have consequences. The question this poses is, why organise language so as to escape causal relations and why choose the little girl as emblematic of this organisation? (shrink)

Among the universal attributes of homo sapiens, several have become established as special fields of study—language, art and music, religion, and political economy. But mathematics, another universal attribute of our species, is still modeled separately by logicians, historians, neuroscientists, and others. Could it be integrated into “mathematics studies,” a coherent, many-faceted branch of empirical science? Could philosophers facilitate such a unification? Some philosophers of mathematics identify themselves with “positions” on the nature of mathematics. Those “positions” could more productively serve as (...) models of mathematics. (shrink)

Kitcher and Aspray distinguish a mainstream tradition in the philosophy of mathematics concerned with foundationalist epistemology, and a ‘maverick’ or naturalistic tradition, originating with Lakatos. My claim is that if the consequences of Lakatos's contribution are fully worked out, no less than a radical reconceptualization of the philosophy of mathematics is necessitated, including history, methodology and a fallibilist epistemology as central to the field. In the paper an interpretation of Lakatos's philosophy of mathematics is offered, followed by some critical discussion, (...) and an extension to a social constructivist position (which might well have been unacceptable to Lakatos). (shrink)