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Full Idea
To say that 'if' there are two persons and each person has two eyes there 'will be' four eyes is not a statement of fact, but a statement about the system of numbers which is our own creation.
Gist of Idea
That two two-eyed people must have four eyes is a statement about numbers, not a fact
Source
Charles Sanders Peirce (Scientific Attitude and Fallibilism [1899], II)
Book Ref
Peirce,Charles Sanders: 'Philosophical Writings of Peirce', ed/tr. Buchler,Justus [Dover 1940], p.59
A Reaction
One eye for each arm of the people is certainly a fact. Frege uses this equivalence to build numbers. I think Peirce is wrong. If it is not a fact that these people have four eyes, I don't know what 'four' means. It's being two pairs is also a fact.
14769 | Only imagination can connect phenomena together in a rational way [Peirce] |
14775 | Numbers are just names devised for counting [Peirce] |
14776 | That two two-eyed people must have four eyes is a statement about numbers, not a fact [Peirce] |
14772 | If we decide an idea is inspired, we still can't be sure we have got the idea right [Peirce] |
14771 | Only reason can establish whether some deliverance of revelation really is inspired [Peirce] |
14770 | Reasoning is based on statistical induction, so it can't achieve certainty or precision [Peirce] |
14774 | Innate truths are very uncertain and full of error, so they certainly have exceptions [Peirce] |
14773 | A truth is hard for us to understand if it rests on nothing but inspiration [Peirce] |