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3 ideas
| 2252 | Surely maths is true even if I am dreaming? [Descartes] |
| Full Idea: Surely whether I am asleep or awake, two plus three makes five, and a square does not have more than four sides. | |
| From: René Descartes (Meditations [1641], §1.20) |
| 2430 | I can learn the concepts of duration and number just from observing my own thoughts [Descartes] |
| Full Idea: When I think that I exist now, and recollect that I existed in the past, and when I conceive various thoughts, the number of which I know, then I acquire the ideas of duration and number which I can thereafter transfer to all the other objects I wish. | |
| From: René Descartes (Meditations [1641], §3.44) |
| 9801 | Numbers must be assumed to have identical units, as horses are equalised in 'horse-power' [Mill] |
| Full Idea: There is one hypothetical element in the basis of arithmetic, without which none of it would be true: all the numbers are numbers of the same or of equal units. When we talk of forty horse-power, we assume all horses are of equal strength. | |
| From: John Stuart Mill (System of Logic [1843], 2.6.3) | |
| A reaction: Of course, horses are not all of equal strength, so there is a problem here for your hard-line empiricist. Mill needs processes of idealisation and abstraction before his empirical arithmetic can get off the ground. |