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References

1. Frege, §27.
2. Frege, §12: "But an intuition in this [Kant's] sense cannot serve as ground of our knowledge of the laws of arithmetic."
3. Frege, §5: "Kant declares [statements such as 2 + 3 = 5] to be unprovable and synthetic, but hesitates to call them axioms because they are not general and because the number of them is infinite. Hankel justifiably calls this conception of infinitely numerous unprovable primitive truths incongruous and paradoxical."
4. Frege, §14: "The fact that [denying the parallel postulate] is possible shows that the axioms of geometry are independent of one another and of the primitive laws of logic, and consequently are synthetic. Can the same be said of the fundamental propositions of the science of number? Here, we have only to try denying any one of them, and complete confusion ensues."
5. Frege 1960, p. 9-12.
6. Shapiro 2000, p. 96: "Frege's Foundations of Arithmetic contains a sustained, bitter assault on Mill's account of arithmetic"
7. Frege 1960, p. 10: "If the definition of each individual number did really assert a special physical fact, then we should never be able to sufficiently admire, for his knowledge of nature, a man who calculates with nine-figure numbers."
8. Shapiro 2000, p. 98: "Frege also takes Mill to task concerning large numbers."
9. Frege 1960, p. 11: "[...] the number 0 would be a puzzle; for up to now no one, I take it, has ever seen or touched 0 pebbles."
10. Frege, §22: "Is it not in totally different senses that we speak of a tree having 1000 leaves and again as having green leaves? The green colour we ascribe to each single leaf, but not the number 1000."
11. Frege, §57: "For example, the proposition 'Jupiter has four moons' can be converted into 'the number of Jupiter's moons is four'"
12. Frege, §63: "Hume long ago expressed such a means: 'When two numbers are so combined as that one has always a unit answering to every unit of the other, we pronounce them equal'"
13. Boolos 1998, p. 154: "Frege defines 0 as the number of the concept: being non-self-identical. Since everything is self-identical, no object falls under this concept. Frege defines 1 as the number of the concept being identical with the number zero. 0 and 0 alone falls under this latter concept."