11 ideas
18085 | Values that approach zero, becoming less than any quantity, are 'infinitesimals' [Cauchy] |
Full Idea: When the successive absolute values of a variable decrease indefinitely in such a way as to become less than any given quantity, that variable becomes what is called an 'infinitesimal'. Such a variable has zero as its limit. | |
From: Augustin-Louis Cauchy (Cours d'Analyse [1821], p.19), quoted by Philip Kitcher - The Nature of Mathematical Knowledge 10.4 | |
A reaction: The creator of the important idea of the limit still talked in terms of infinitesimals. In the next generation the limit took over completely. |
18084 | When successive variable values approach a fixed value, that is its 'limit' [Cauchy] |
Full Idea: When the values successively attributed to the same variable approach indefinitely a fixed value, eventually differing from it by as little as one could wish, that fixed value is called the 'limit' of all the others. | |
From: Augustin-Louis Cauchy (Cours d'Analyse [1821], p.19), quoted by Philip Kitcher - The Nature of Mathematical Knowledge 10.4 | |
A reaction: This seems to be a highly significan proposal, because you can now treat that limit as a number, and adds things to it. It opens the door to Cantor's infinities. Is the 'limit' just a fiction? |
19718 | Indefeasibility does not imply infallibility [Grundmann] |
Full Idea: Infallibility does not follow from indefeasibility. | |
From: Thomas Grundmann (Defeasibility Theory [2011], 'Significance') | |
A reaction: If very little evidence exists then this could clearly be the case. It is especially true of historical and archaeological evidence. |
19717 | Can a defeater itself be defeated? [Grundmann] |
Full Idea: Can the original justification of a belief be regained through a successful defeat of a defeater? | |
From: Thomas Grundmann (Defeasibility Theory [2011], 'Defeater-Defs') | |
A reaction: [Jäger 2005 addresses this] I would have thought the answer is yes. I aspire to coherent justifications, so I don't see justifications as a chain of defeat and counter-defeat, but as collective groups of support and challenge. |
19716 | Simple reliabilism can't cope with defeaters of reliably produced beliefs [Grundmann] |
Full Idea: An unmodified reliabilism does not accommodate defeaters, and surely there can be defeaters against reliably produced beliefs? | |
From: Thomas Grundmann (Defeasibility Theory [2011], 'Defeaters') | |
A reaction: [He cites Bonjour 1980] Reliabilism has plenty of problems anyway, since a generally reliable process can obviously occasionally produce a bad result. 20:20 vision is not perfect vision. Internalist seem to like defeaters. |
19715 | You can 'rebut' previous beliefs, 'undercut' the power of evidence, or 'reason-defeat' the truth [Grundmann] |
Full Idea: There are 'rebutting' defeaters against the truth of a previously justified belief, 'undercutting' defeaters against the power of the evidence, and 'reason-defeating' defeaters against the truth of the reason for the belief. | |
From: Thomas Grundmann (Defeasibility Theory [2011], 'How') | |
A reaction: That is (I think) that you can defeat the background, the likelihood, or the truth. He cites Pollock 1986, and implies that these are standard distinctions about defeaters. |
19713 | Defeasibility theory needs to exclude defeaters which are true but misleading [Grundmann] |
Full Idea: Advocates of the defeasibility theory have tried to exclude true pieces of information that are misleading defeaters. | |
From: Thomas Grundmann (Defeasibility Theory [2011], 'What') | |
A reaction: He gives as an example the genuine news of a claim that the suspect has a twin. |
19714 | Knowledge requires that there are no facts which would defeat its justification [Grundmann] |
Full Idea: The 'defeasibility theory' of knowledge claims that knowledge is only present if there are no facts that - if they were known - would be genuine defeaters of the relevant justification. | |
From: Thomas Grundmann (Defeasibility Theory [2011], 'What') | |
A reaction: Something not right here. A genuine defeater would ensure the proposition was false, so it would simply fail the truth test. So we need a 'defeater' for a truth, which must therefore by definition be misleading. Many qualifications have to be invoked. |
19719 | 'Moderate' foundationalism has basic justification which is defeasible [Grundmann] |
Full Idea: Theories that combine basic justification with the defeasibility of this justification are referred to as 'moderate' foundationalism. | |
From: Thomas Grundmann (Defeasibility Theory [2011], 'Significance') | |
A reaction: I could be more sympathetic to this sort of foundationalism. But it begins to sound more like Neurath's boat (see Quine) than like Descartes' metaphor of building foundations. |
13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
Full Idea: In a single day there lies open to men of learning more than there ever does to the unenlightened in the longest of lifetimes. | |
From: Posidonius (fragments/reports [c.95 BCE]), quoted by Seneca the Younger - Letters from a Stoic 078 | |
A reaction: These remarks endorsing the infinite superiority of the educated to the uneducated seem to have been popular in late antiquity. It tends to be the religions which discourage great learning, especially in their emphasis on a single book. |
20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |
Full Idea: Posidonius defined time thus: it is an interval of motion, or the measure of speed and slowness. | |
From: report of Posidonius (fragments/reports [c.95 BCE]) by John Stobaeus - Anthology 1.08.42 | |
A reaction: Hm. Can we define motion or speed without alluding to time? Looks like we have to define them as a conjoined pair, which means we cannot fully understand either of them. |