8 ideas
| 21355 | The Pre-Socratics are not simple naturalists, because they do not always 'leave the gods out' [Leroi] |
| Full Idea: The problem with making naturalism the hallmark of Pre-Socratic thought ...is that they do not always 'leave the gods out'; the Divine can usually be found lurking somewhere is their cosmologies. | |
| From: Armand Marie LeRoi (The Lagoon: how Aristotle invented science [2014], 007) | |
| A reaction: An important observation. I've been guilty of this simplistic view. We tend to ignore the religious fragments, or we possess so little that we have no idea where religion figured in their accounts. |
| 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? |
| 22179 | Explanatory facts also predict, and predictive facts also explain [Hempel, by Okasha] |
| Full Idea: Hempel said every scientific explanation is potentially a prediction - it would have predicted the phenomenon in question, had it not already been known. But also the information used to make a prediction is potentially an explanation. | |
| From: report of Carl Hempel (Aspects of Scientific Explanation [1965]) by Samir Okasha - Philosophy of Science: Very Short Intro (2nd ed) 3 | |
| A reaction: Sounds too neatly glib to be quite true. If you explain a single event there is nothing to predict. You might predict accurately from a repetitive pattern, with no understanding at all of the pattern. |
| 21507 | Scientific explanation aims at a unifying account of underlying structures and processes [Hempel] |
| Full Idea: What theoretical scientific explanation aims at is an objective kind of insight that is achieved by a systematic unification, by exhibiting the phenomena as manifestations of common underlying structures and processes that conform to testable principles. | |
| From: Carl Hempel (Philosophy of Natural Science [1967], p.83), quoted by Laurence Bonjour - The Structure of Empirical Knowledge 5.3 | |
| A reaction: This is a pretty good statement of scientific essentialism, and structures and processes are what I take Aristotle to have had in mind when he sought 'what it is to be that thing'. Structures and processes give stability and powers. |
| 6755 | For Hempel, explanations are deductive-nomological or probabilistic-statistical [Hempel, by Bird] |
| Full Idea: Hempel proposes that explanations involve covering laws and antecedent conditions; this view (the 'covering law' view) has two versions, the deductive-nomological model and the probabilistic-statistical model of explanation. | |
| From: report of Carl Hempel (Aspects of Scientific Explanation [1965]) by Alexander Bird - Philosophy of Science Ch.2 | |
| A reaction: The obvious problem with this approach, it seem to me, is that the laws themselves need explanation, and I don't see how a law can be foundational unless there is a divine law-giver. Are the laws arbitrary and axiomatic? |
| 17083 | The covering-law model is for scientific explanation; historical explanation is quite different [Hempel] |
| Full Idea: To put forward the covering-law models of scientific explanation is not to deny that there are other contexts in which we speak of explanation. ….That it does not fit explaining the rules of Hanoverian succession is to miss the intent of our model. | |
| From: Carl Hempel (Aspects of Scientific Explanation [1965], p. 412-3), quoted by David-Hillel Ruben - Explaining Explanation Ch 1 | |
| A reaction: Important to get that clear. It then requires a clear demarcation between science and the rest, and it had better not rule out biology because it is having a love affair with physics. |
| 13052 | Hempel rejects causation as part of explanation [Hempel, by Salmon] |
| Full Idea: Hempel explicitly rejects the idea that causality plays any essential explanatory role. | |
| From: report of Carl Hempel (Aspects of Scientific Explanation [1965], p.352) by Wesley Salmon - Four Decades of Scientific Explanation 1.1 | |
| A reaction: Hempel champions the 'covering-law' model of explanation. It strikes me that Hempel is so utterly wrong about this that his views aren't even a candidate for correctness, but then for a long time his views were orthodoxy. |