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Full Idea
Both ordinalists and cardinalists, to account for our number words, have to account for the fact that we know so many of them, and that we can 'recognize' numbers which we've neither seen nor heard.
Gist of Idea
We must explain how we know so many numbers, and recognise ones we haven't met before
Source
Paul Benacerraf (Logicism, Some Considerations (PhD) [1960], p.166)
A Reaction
This seems an important contraint on any attempt to explain numbers. Benacerraf is an incipient structuralist, and here presses the importance of rules in our grasp of number. Faced with 42,578,645, we perform an act of deconstruction to grasp it.