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Intuitionism As Generalization
 Philosophia Math
, 1990
"... ms that hold only in computational models. For example, Brouwer proved that every totally defined function on the real line is continuous. A theory where this is provable cannot refer to the classical universe, so we have to consider whether we like its models better than the classical model. But an ..."
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ms that hold only in computational models. For example, Brouwer proved that every totally defined function on the real line is continuous. A theory where this is provable cannot refer to the classical universe, so we have to consider whether we like its models better than the classical model. But any theorem in constructive mathematics is a theorem in classical mathematics, so in this case it is not a question of choosing between models, but of deciding whether it is worthwhile to talk about computational models in addition to the classical model. By comparing mathematical realism with intuitionism from an informal axiomatic point of view, we can steer clear of most of the metaphysical problems involved in analyzing these notions from the ground up, and concentrate on what may be termed the purely mathematical aspects. In particular we won't have to consider whether intuitionists hold that a theorem "isn't true until it's known to be true", as Blais 1 <F