Mathematics, Models, and Modality: Selected Philosophical Essays - Burgess, John P (Cambridge University Press, 2013)
Galileo and Kepler and Descartes and other seventeenth-century worthies, that it is possible to get behind all human representations to a God’s-eye view of ultimate reality as it is in itself. When they affirm that mathematical objects transcending space and time and causality exist, and mathematical truths transcending human verification obtain, they are affirming that such objects exist and such truths obtain as part of ultimate metaphysical reality (whatever that means). Naturalist realists, by contrast, affirm only (what even some self-described anti-realists concede) that the existence of such objects and obtaining of such truths is an implication or presupposition of science and scientifically informed common sense, while denying that philosophy has any access to exterior, ulterior, and superior sources of knowledge from which to ‘‘correct’’ science and scientifically informed common sense. The naturalized philosopher, in contrast to the alienated philosopher, is one who takes a stand as a citizen of the scientific community, and not a foreigner to it, and hence is prepared to reaffirm while doing philosophy whatever was affirmed while doing science, and to acknowledge its evident implications and presuppositions