Reactions: existence and constructivity
In mathematics one deals with various objects. Some theorems are about numbers, others about functions or groups, to name but a few. But even though mathematicians are able to work with these mathematical objects, their ontological status usually cannot be inferred.3 What precisely are these objects mathematicians speak about? Are they pre-existing entities that we discover? Are they creations of the human mind? Or are they nothing more than signs written down on paper? Does, for instance, the number ‘2’ have an existence independently of us? And what about a function like f: x↦x + 1?
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