9861 | The same thing is both one and an unlimited number at the same time [Plato] |
21963 | It is possible that an omnipotent God might make one and two fail to equal three [Descartes] |
16928 | Mathematics cannot be empirical because it is necessary, and that has to be a priori [Kant] |
12411 | Mill is too imprecise, and is restricted to simple arithmetic [Kitcher on Mill] |
5656 | Empirical theories of arithmetic ignore zero, limit our maths, and need probability to get started [Frege on Mill] |
14776 | That two two-eyed people must have four eyes is a statement about numbers, not a fact [Peirce] |
8633 | There is no physical difference between two boots and one pair of boots [Frege] |
9577 | The naïve view of number is that it is like a heap of things, or maybe a property of a heap [Frege] |
17697 | The existence of an arbitrarily large number refutes the idea that numbers come from experience [Hilbert] |
5399 | Maths is not known by induction, because further instances are not needed to support it [Russell] |
17806 | It is untenable that mathematics is general physical truths, because it needs infinity [Curry] |
10735 | Abstraction from objects won't reveal an operation's being performed 'so many times' [Geach] |
8884 | The phenomenal concept of an eleven-dot pattern does not include the concept of eleven [Sosa] |
18201 | General principles can be obvious in mathematics, but bold speculations in empirical science [Parsons,C] |
17614 | The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy] |
9610 | Numbers are not abstracted from particulars, because each number is a particular [Brown,JR] |
9612 | There is an infinity of mathematical objects, so they can't be physical [Brown,JR] |
10131 | If mathematics is not about particulars, observing particulars must be irrelevant [George/Velleman] |
10005 | Arithmetic doesn’t simply depend on objects, since it is true of fictional objects [Hofweber] |