The Philosophy of Mathematics Today

By Matthias Schirn | Go to book overview

7
Occam's Razor and Scientific Method

JOHN P. BURGESS


1. OCCAM'S RAZOR AND MODERN NOMINALISM

Entities are not to be multiplied beyond necessity, says the legendary razor of the legendary William of Occam, chief of the legendary medieval nominalists. My topic will be the role of this dictum in the philosophy of the last half-century and the science of the last half-millennium. My topic will thus be history, but it will not be the history of medieval philosophy. I will not be questioning the relation between the modern nominalists and the medieval nominales, or between the legendary William of Occam and the historical William Ockham. Before posing the question that will concern me, some preliminaries will be necessary, which I will try not to multiply beyond necessity.

The modern nominalism that will concern me is that which consists in disbelief in abstract entities. Nominalism is not a unified school of thought. One distinction that can be made among nominalists is between the forthright, who concede their position incompatible with the acceptance of modern mathematics and science, and the evasive, who on one ground or another1--perhaps the mathematicians don't really mean it when they say that there are numbers greater than one hundred that are prime, or perhaps this doesn't really imply that there are (such things as) numbers--deny the incompatibility. The evasive positions require examination; I have partially examined them elsewhere; I do not propose to examine them further here. I will proceed here on the common assumption of the forthright nominalists and all anti-nominalists, that a nominalist must reject current mathematics and science.

Another distinction that can be made among nominalists and antinominalists alike is in their attitude towards attempts in the literature to reconstruct current mathematics and/or science nominalistically. (Such

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This paper appears here in almost exactly the same form in which it was given at the conference 'Philosophy of Mathematics Today'. The few departures are indicated in the notes.
1
In discussion at the conference, Paul Benacerraf warned against trying to enumerate all the possible grounds. His own paper dealt, in part, with related issues.

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