9 ideas
| 18261 | A simplification which is complete constitutes a definition [Kant] |
| Full Idea: By dissection I can make the concept distinct only by making the marks it contains clear. That is what analysis does. If this analysis is complete ...and in addition there are not so many marks, then it is precise and so constitutes a definition. | |
| From: Immanuel Kant (Wiener Logik [1795], p.455), quoted by J. Alberto Coffa - The Semantic Tradition from Kant to Carnap 1 'Conc' | |
| A reaction: I think Aristotle would approve of this. We need to grasp that a philosophical definition is quite different from a lexicographical definition. 'Completeness' may involve quite a lot. |
| 9565 | Zermelo made 'set' and 'member' undefined axioms [Zermelo, by Chihara] |
| Full Idea: The terms 'set' and 'is a member of' are primitives of Zermelo's 1908 axiomatization of set theory. They are not given model-theoretic analyses or definitions. | |
| From: report of Ernst Zermelo (works [1920]) by Charles Chihara - A Structural Account of Mathematics 7.5 | |
| A reaction: This looks like good practice if you want to work with sets, but not so hot if you are interested in metaphysics. |
| 3339 | For Zermelo's set theory the empty set is zero and the successor of each number is its unit set [Zermelo, by Blackburn] |
| Full Idea: For Zermelo's set theory the empty set is zero and the successor of each number is its unit set. | |
| From: report of Ernst Zermelo (works [1920]) by Simon Blackburn - Oxford Dictionary of Philosophy p.280 |
| 22275 | Logic gives us the necessary rules which show us how we ought to think [Kant] |
| Full Idea: In logic the question is not one of contingent but of necessary rules, not how to think, but how we ought to think. | |
| From: Immanuel Kant (Wiener Logik [1795], p.16), quoted by Michael Potter - The Rise of Analytic Philosophy 1879-1930 02 'Trans' | |
| A reaction: Presumably it aspires to the objectivity of a single correct account of how we all ought to think. I'm sympathetic to that, rather than modern cultural relativism about reason. Logic is rooted in nature, not in arbitrary convention. |
| 16978 | If conceivability is a priori coherence, that implies possibility [Tahko] |
| Full Idea: Maybe conceivability could be understood as a priori coherence, which implies possibility. | |
| From: Tuomas E. Tahko (The Epistemology of Essence (draft) [2013], 3.2) | |
| A reaction: I'm not quite sure why 'a priori' has to be there. Assessing conceivability just is assessing coherence. That couches it as a rational activity, rather than as a purely imaginary one. Trying to conceive a square circle isn't just daydreaming. |
| 18260 | If we knew what we know, we would be astonished [Kant] |
| Full Idea: If we only know what we know ...we would be astonished by the treasures contained in our knowledge. | |
| From: Immanuel Kant (Wiener Logik [1795], p.843), quoted by J. Alberto Coffa - The Semantic Tradition from Kant to Carnap 1 'Conc' | |
| A reaction: Nice remark. He doesn't require immediat recall of knowledge. You can't be required to know that you know something. That doesn't imply externalism, though. I believe in securely founded internal knowledge which is hard to recall. |
| 16975 | Essences are used to explain natural kinds, modality, and causal powers [Tahko] |
| Full Idea: Essences are supposed to do a lot of explanatory work: natural kinds can be identified in terms of their essences, metaphysical modality can be reduced to essence, the causal power of objects can be explained with the help of essence. | |
| From: Tuomas E. Tahko (The Epistemology of Essence (draft) [2013], 1) | |
| A reaction: Natural kinds and modality are OK with me, but I'm dubious about the third one. If an essence explains something's causal powers, I have no idea what an essence might be. Essence are largely characterised in terms of causal powers. |
| 16976 | Scientific essentialists tend to characterise essence in terms of modality (not vice versa) [Tahko] |
| Full Idea: The conception of essence taken for granted in much of the 'scientific essentialist' literature is that essence can be explained in terms of modality (rather than the other way round). | |
| From: Tuomas E. Tahko (The Epistemology of Essence (draft) [2013], 2.1) | |
| A reaction: [He cites Ellis and Bird] That is, presumably, that they are inclined to say that the essence of gold is a set of necessary properties. Maybe conceptual necessities dictate the properties of gold, and they in turn dictate metaphysical necessities? |
| 16977 | If essence is modal and laws are necessary, essentialist knowledge is found by scientists [Tahko] |
| Full Idea: If essence is conceived in terms of modality and the laws of nature are metaphysically necessary, it seems that the laws of nature constitute essentialist knowledge, so the discovery of essences is mostly due to scientists. | |
| From: Tuomas E. Tahko (The Epistemology of Essence (draft) [2013], 2.1) | |
| A reaction: This seems muddled to me. The idea that the laws themselves are essences is way off target. No one thinks all knowledge of necessities is essentialist. Mumford, for example, doesn't even believe in laws. |