7 ideas
| 8754 | Logic is dependent on mathematics, not the other way round [Heyting, by Shapiro] |
| Full Idea: Heyting (the intuitionist pupil of Brouwer) said that 'logic is dependent on mathematics', not the other way round. | |
| From: report of Arend Heyting (Intuitionism: an Introduction [1956]) by Stewart Shapiro - Thinking About Mathematics 7.3 | |
| A reaction: To me, this claim makes logicism sound much more plausible, as I don't see how mathematics could get beyond basic counting without a capacity for logical thought. Logic runs much deeper, psychologically and metaphysically. |
| 14637 | Only individuals have essences, so numbers (as a higher type based on classes) lack them [McMichael] |
| Full Idea: Essentialism is not verified by the observation that numbers have interesting essential properties, since they are properties of classes and so are entities of a higher logical type than individuals. | |
| From: Alan McMichael (The Epistemology of Essentialist Claims [1986], Intro) | |
| A reaction: This relies on a particular view of number (which might be challenged), but is interesting when it comes to abstract entities having essences. Only ur-elements in set theory could have essences, it seems. Why? Rising in type destroys essence? |
| 14636 | Essences are the interesting necessary properties resulting from a thing's own peculiar nature [McMichael] |
| Full Idea: Essentialism says some individuals have certain 'interesting' necessary properties. If it exists, it has that property. The properties are 'interesting' as had in virtue of their own peculiar natures, rather than as general necessary truths. | |
| From: Alan McMichael (The Epistemology of Essentialist Claims [1986], Intro) | |
| A reaction: [compressed] This is a modern commentator caught between two views. The idea that essence is the non-trivial-necessary properties is standard, but adding their 'peculiar natures' connects him to Aristotle, and Kit Fine's later papers. Good! |
| 14640 | Maybe essential properties have to be intrinsic, as well as necessary? [McMichael] |
| Full Idea: There is a tendency to think of essential properties as having some characteristic in addition to their necessity, such as intrinsicality. | |
| From: Alan McMichael (The Epistemology of Essentialist Claims [1986], VIII) | |
| A reaction: Personally I am inclined to take this view of all properties, and not just the 'essential' ones. General necessities, relations, categorisations, disjunctions etc. should not be called 'properties', even if they are 'predicates'. Huge confusion results. |
| 14638 | Essentialism is false, because it implies the existence of necessary singular propositions [McMichael] |
| Full Idea: Essentialism entails the existence of necessary singular propositions that are not instances of necessary generalizations. Therefore, since there are no such propositions, essentialism is false. | |
| From: Alan McMichael (The Epistemology of Essentialist Claims [1986], I) | |
| A reaction: This summarises the attack which McMichael wishes to deal with. I am wickedly tempted to say that essences actually have a contingent existence (or a merely hypothetical dependent necessity), and this objection might be grist for my mill. |
| 20653 | Six reduction levels: groups, lives, cells, molecules, atoms, particles [Putnam/Oppenheim, by Watson] |
| Full Idea: There are six 'reductive levels' in science: social groups, (multicellular) living things, cells, molecules, atoms, and elementary particles. | |
| From: report of H.Putnam/P.Oppenheim (Unity of Science as a Working Hypothesis [1958]) by Peter Watson - Convergence 10 'Intro' | |
| A reaction: I have the impression that fields are seen as more fundamental that elementary particles. What is the status of the 'laws' that are supposed to govern these things? What is the status of space and time within this picture? |
| 14639 | Individuals enter into laws only through their general qualities and relations [McMichael] |
| Full Idea: Individuals appear to enter into laws only through their general qualities and relations. | |
| From: Alan McMichael (The Epistemology of Essentialist Claims [1986], VIII) | |
| A reaction: This is a very significant chicken-or-egg issue. The remark seems to offer the vision of pre-existing general laws, which individuals then join (like joining a club). But surely the laws are derived from the individuals? Where else could they come from? |