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This work gives a new argument for ‘Empirical Philosophy of Mathematical Practice’. It analyses different modalities on how empirical information can influence philosophical endeavours. We evoke the classical dichotomy between “armchair” philosophy and empirical/experimental philosophy, and claim that the latter should in turn be subdivided in three distinct styles:  Apostate speculator ,  Informed analyst , and  Freeway explorer . This is a shift of focus from the source of the information towards its use by philosophers. We present several examples from philosophy of mind/science and ethics on one side and a case study from philosophy of mathematics on the other. We argue that empirically informed philosophy of mathematics is different from the rest in a way that encourages a  Freeway explorer  approach, because intuitions about mathematical objects are often unavailable for non-mathematicians (since they are sometimes hard to grasp even for mathematicians). This consideration is supported by a case study in set theory.

Three Roles of Empirical Information in Philosophy: Intuitions on Mathematics do Not Come for Free