10 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? |
| 20475 | Maybe modal sentences cannot be true or false [Casullo] |
| Full Idea: Some people claim that modal sentences do not express truths or falsehoods. | |
| From: Albert Casullo (A Priori Knowledge [2002], 3.2) | |
| A reaction: I can only imagine this coming from a narrow hardline empiricist. It seems to me obvious that we make true or false statements about what is possible or impossible. |
| 20476 | If the necessary is a priori, so is the contingent, because the same evidence is involved [Casullo] |
| Full Idea: If one can only know a priori that a proposition is necessary, then one can know only a priori that a proposition is contingent. The evidence relevant to determining the latter is the same as that relevant to determining the former. | |
| From: Albert Casullo (A Priori Knowledge [2002], 3.2) | |
| A reaction: This seems a telling point, but I suppose it is obvious. If you see that the cat is on the mat, nothing in the situation tells you whether this is contingent or necessary. We assume it is contingent, but that may be an a priori assumption. |
| 20471 | Epistemic a priori conditions concern either the source, defeasibility or strength [Casullo] |
| Full Idea: There are three suggested epistemic conditions on a priori knowledge: the first regards the source of justification, the second regards the defeasibility of justification, and the third appeals to the strength of justification. | |
| From: Albert Casullo (A Priori Knowledge [2002], 2) | |
| A reaction: [compressed] He says these are all inspired by Kant. The non-epistemic suggested condition involve necessity or analyticity. The source would have to be entirely mental; the defeasibly could not be experiential; the strength would be certainty. |
| 20477 | The main claim of defenders of the a priori is that some justifications are non-experiential [Casullo] |
| Full Idea: The leading claim of proponents of the a priori is that sources of justification are of two significantly different types: experiential and nonexperiential. Initially this difference is marked at the phenomenological level. | |
| From: Albert Casullo (A Priori Knowledge [2002], 5) | |
| A reaction: He cites Plantinga and Bealer for the phenomenological starting point (that some knowledge just seems rationally obvious, certain, and perhaps necessary). |
| 20472 | Analysis of the a priori by necessity or analyticity addresses the proposition, not the justification [Casullo] |
| Full Idea: There is reason to view non-epistemic analyses of a priori knowledge (in terms of necessity or analyticity) with suspicion. The a priori concerns justification. Analysis by necessity or analyticity concerns the proposition rather than the justification. | |
| From: Albert Casullo (A Priori Knowledge [2002], 2.1) | |
| A reaction: [compressed] The fact that the a priori is entirely a mode of justification, rather than a type of truth, is the modern view, influenced by Kripke. Given that assumption, this is a good objection. |
| 20474 | 'Overriding' defeaters rule it out, and 'undermining' defeaters weaken in [Casullo] |
| Full Idea: A justified belief that a proposition is not true is an 'overriding' defeater, ...and the belief that a justification is inadequate or defective is an 'undermining' defeater. | |
| From: Albert Casullo (A Priori Knowledge [2002], n 40) | |
| A reaction: Sounds more like a sliding scale than a binary option. Quite useful, though. |
| 1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
| Full Idea: Archelaus was the first person to say that the universe is boundless. | |
| From: report of Archelaus (fragments/reports [c.450 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 02.Ar.3 |
| 5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |
| Full Idea: Archelaus wrote that life on Earth began in a primeval slime. | |
| From: report of Archelaus (fragments/reports [c.450 BCE]) by Malcolm Schofield - Archelaus | |
| A reaction: This sounds like a fairly clearcut assertion of the production of life by evolution. Darwin's contribution was to propose the mechanism for achieving it. We should honour the name of Archelaus for this idea. |