Timeline for Was the early calculus inconsistent?
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Mar 1, 2014 at 2:02 | comment | added | Alexandre Eremenko | Toby Bartels: you wrote: "scholastic logic, which we would regard even today as perfectly rigorous". Who are "we"? | |
| Mar 23, 2013 at 21:14 | comment | added | Mikhail Katz | I would question the claim that "the word 'consistent' cannot be used here in the sense of modern mathematical logic". Berkeley claimed that the calculus was based on the inconsistency $(dx\not=0)\wedge(dx=0)$. Arguably this is the same meaning as in modern logic. | |
| Mar 21, 2013 at 0:31 | comment | added | Alexandre Eremenko | G. Rodrigues: 1. Yes, mathematics is not a science like physics or geology, but it is on the "opposite side" from theology. In the sense that it is more consistent, and the truth proved mathematically has somehow higher status than a scientific truth. (In what sense statement of theology/divinity can be considered true, I don't know. Or what is the criterion of truth in theology:-) 2. Yes, I am a strong Platonist. And frankly speaking it is hard for me to imagine how a working mathematician can be something else, though I know that some mathematicians profess other views. | |
| Mar 20, 2013 at 15:22 | comment | added | G. Rodrigues | If we identify "Divinity" with theology, then no theologian I know disputes that it is not a science in the modern sense of the empirical sciences. But then, neither is mathematics. They will however claim, or some will, that it is a science in the Aristotelian sense. As far as dealing "with the things that do not exist", your opinion is duly noted, but unless you are a Platonist, mathematicians inevitably deal with objects with no extra-mental existence. And since mathematical objects are abstract, not localized in space-time, empirical considerations are of little avail to him. | |
| Mar 20, 2013 at 5:01 | comment | added | Toby Bartels | Divinity may be a study of things that do not exist (although obviously Berkeley himself believed otherwise), but that goes into the premises, which have always been very questionable. But the mode of reasoning was by scholastic logic, which we would regard even today as perfectly rigorous. | |
| Mar 19, 2013 at 23:20 | comment | added | Joël | "Divinity" for Berkeley in this sentence has the sense of whatever makes that each's person's sensations are consistent with each other's. Call it "matter" if you prefer. | |
| Mar 19, 2013 at 22:56 | history | answered | Alexandre Eremenko | CC BY-SA 3.0 |