Russell Marcus, the Chauncey Truax Post-Doctoral Fellow of Philosophy, delivered a plenary talk at the first Colombian Conference on Logic, Epistemology, and Philosophy of Science in Bogotá, Colombia.  In his paper, “Explanation and Indispensability,” he examined a new explanatory indispensability argument.

The new argument alleges that there are mathematical explanations of physical phenomena which should be taken as grounds for inferring the existence of mathematical objects: the Borsuk-Ulam topological theorem which explains the existence of meteorological antipodes in the Earth’s atmosphere; properties of prime numbers which explain the life-cycles of cicadas; phase-space formulations of mechanics which explain physical phenomena in ways that space-time formulations cannot recover.

Marcus argued that the explanatory argument depends for its plausibility on an equivocation between two senses of ‘explanation’. In the first, metaphysical, sense, the argument is no improvement over the standard, Quinean indispensability argument. In the second, epistemological, sense, such mathematical explanations should not be taken as ontologically serious, just as simple adjectival uses of numbers (such as, "I have five mangoes in the refrigerator") are not.

In the audience were the philosophical luminaries Susan Haack, Michael Bishop and Arnold Koslow, who all gave invited talks at the conference.