Computers are playing an increasingly central role in mathematical practice. What are we to make of the new methods of inquiry? In Section 2, I survey some of the ways that computers are used in mathematics. These raise questions that seem to have a generally epistemological character,

A foolish consistency is the hobgoblin of little minds. – Ralph Waldo Emerson We frequently make judgments about the world. Juries make judgments about whether defendants are guilty. Umpires make judgments about whether pitches are strikes.

Aristotelian, or non-Platonist, realism holds that mathematics is a science of the real world, just as much as biology or sociology are. Where biology studies living things and sociology studies human social relations, mathematics studies the quantitative or structural aspects of things, such as ratios, or patterns, or complexity,

Easwaran has given a definition of transferability and argued that, under this definition, randomized arguments are not transferable. I show that certain aspects of his definition are not suitable for addressing the underlying question of whether or not there is an epistemic distinction between randomized and deductive arguments. Furthermore, I demonstrate that for any suitable definition, randomized arguments are in fact transferable. Kenny Easwaran [Easwaran2008] has recently given a definition of transferability of mathematical proofs and has attempted to use this notion to epistemically differentiate between traditional deductive proofs and certain inductive arguments based on randomized trials (which I will call randomized arguments; more on this below). However, I will show that there are problems with Easwaran’s definition and further demonstrate that, for any suitable definition of the term, transferability does not epistemically distinguish between deductive proofs and randomized arguments. 1

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