Of all philosophy’s subdisciplines, philosophy of mathematics has been that most resistant to the adoption of empirical methods. The difficulty this poses to experimental philosophy is considerable; and sadly, experimental philosophers have not recognized its seriousness.
We (I) realized (believed) the transformation of philosophy into a respectable, scientific discipline would not be complete so long as this bulwark stood firm. So we stormed this citadel of armchair philosophy, to raze it to the ground. Or capture the fortress. Whichever metaphor you prefer.
We decided to conduct an X-PERIMENT! (a survey). Our mission: to settle once and for all the debate raging among philosophers of mathematics about what numbers really are. We went out into the wild habitat of New York city and surveyed 500 ordinary people. Not like us at all, really.
Here is what we asked them:
‘Is the number two the set containing the set containing the null set as its only member? Or is it the set containing both the null set and the set containing the null set?’
This is what they said:
That should settle it.