8 ideas
| 19426 | 'Nominal' definitions just list distinguishing characteristics [Leibniz] |
| Full Idea: A 'nominal' definition is nothing more than an enumeration of the sufficient distinguishing characteristics. | |
| From: Gottfried Leibniz (Reflections on Knowledge, Truth and Ideas [1684], p.284) | |
| A reaction: Not wholly clear. Are these actual distinguishing characteristics, or potential ones? Could DNA be part of a human's nominal definition (for an unidentified corpse, perhaps). |
| 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? |
| 19424 | Knowledge needs clarity, distinctness, and adequacy, and it should be intuitive [Leibniz] |
| Full Idea: Knowledge is either obscure or clear; clear ideas are either indistinct or distinct; distinct ideas are either adequate or inadequate, symbolic or intuitive; perfect knowledge is that which is both adequate and intuitive. | |
| From: Gottfried Leibniz (Reflections on Knowledge, Truth and Ideas [1684], p.283) | |
| A reaction: This is Leibniz's expansion of Descartes's idea that knowledge rests on 'clear and distinct conceptions'. The ultimate target seems to be close to an Aristotelian 'real definition', which is comprehensive and precise. Does 'intuitive' mean coherent? |
| 19427 | True ideas represent what is possible; false ideas represent contradictions [Leibniz] |
| Full Idea: An idea is true if what it represents is possible; false if the representation contains a contradiction. | |
| From: Gottfried Leibniz (Reflections on Knowledge, Truth and Ideas [1684], p.287) | |
| A reaction: Odd in the analytic tradition to talk of a single idea or concept (rather than a proposition or utterance) as being 'true'. But there is clearly a notion of valid or legitimate or useful concepts here. Hilbert said true just meant non-contradictory. |
| 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. |
| 19425 | In the schools the Four Causes are just lumped together in a very obscure way [Leibniz] |
| Full Idea: In the schools the four causes are lumped together as material, formal, efficient, and final causes, but they have no clear definitions, and I would call such a judgment 'obscure'. | |
| From: Gottfried Leibniz (Reflections on Knowledge, Truth and Ideas [1684], p.283) | |
| A reaction: He picks this to illustrate what he means by 'obscure', so he must feel strongly about it. Elsewhere Leibniz embraces efficient and final causes, but says little of the other two. This immediately become clearer as the Four Modes of Explanation. |
| 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. |