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Talking About Numbers
Easy Arguments for Mathematical Realism
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For thousands of years philosophers have discussed the question of whether numbers exist. Surprisingly, there are very easy arguments from commonly accepted truths that seem to decide the question. For instance, it is a commonly accepted truth that Obama has two hands. If Obama has two hands, then the number of Obama's hands is two, and, thus, numbers exist. If such arguments were convincing, ontological disputes about the existence of numbers could be decided simply by pointing to Obama's hands! The book offers a defense of the profoundness of traditional ontological questions by showing that...
For thousands of years philosophers have discussed the question of whether numbers exist. Surprisingly, there are very easy arguments from commonly accepted truths that seem to decide the question. For instance, it is a commonly accepted truth that Obama has two hands. If Obama has two hands, then the number of Obama's hands is two, and, thus, numbers exist. If such arguments were convincing, ontological disputes about the existence of numbers could be decided simply by pointing to Obama's hands! The book offers a defense of the profoundness of traditional ontological questions by showing that the easy arguments in question are based on false linguistic assumptions. To do so it engages with recent linguistic research and develops analyses of the pertinent sentences that are of interest far beyond the metaontological question at hand.