Abstract
In his classic 1965 article “What Numbers Could Not Be” Benacerraf recounts the parable of Ernie and Johnny, those two children to whom their respective father-tutors presented the terms of Neumann’s progression and those of Zermelo’s progression as being the natural numbers, and who come into conflict when it comes to knowing whether or not 3 belongs to 17. From this, Benacerraf derives the ontological moral that only the structure of progression of the so-called natural numbers counts, while the natural numbers themselves do not exist. He says almost nothing about an ontologically neutral, methodological moral that would enable Ernie and Johnny to “identify” their respective progressions with one another, all the while collaborating harmoniously on the development of arithmetic as a theory of progressions.
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de Rouilhan, P. (2016). Identification and Transportability: Another Moral for Benacerraf’s Parable of Ernie and Johnny. In: Pataut, F. (eds) Truth, Objects, Infinity. Logic, Epistemology, and the Unity of Science, vol 28. Springer, Cham. https://doi.org/10.1007/978-3-319-45980-6_8
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