11 ideas
| 8132 | We now have a much more sophisticated understanding of logical form in language [Burge] |
| Full Idea: The second half of the twentieth century has seen the development of a vastly more sophisticated sense of logical form, as applied to natural languages. | |
| From: Tyler Burge (Philosophy of Mind: 1950-2000 [2005], p.462) | |
| A reaction: Burge cites this as one of the three big modern developments (along with the critique of logical positivism, and direct reference/anti-individualism). Vagueness may be the last frontier for this development. |
| 13489 | Von Neumann treated cardinals as a special sort of ordinal [Neumann, by Hart,WD] |
| Full Idea: Von Neumann's decision was to start with the ordinals and to treat cardinals as a special sort of ordinal. | |
| From: report of John von Neumann (On the Introduction of Transfinite Numbers [1923]) by William D. Hart - The Evolution of Logic 3 | |
| A reaction: [see Hart 73-74 for an explication of this] |
| 12336 | A von Neumann ordinal is a transitive set with transitive elements [Neumann, by Badiou] |
| Full Idea: In Von Neumann's definition an ordinal is a transitive set in which all of the elements are transitive. | |
| From: report of John von Neumann (On the Introduction of Transfinite Numbers [1923]) by Alain Badiou - Briefings on Existence 11 |
| 18180 | Von Neumann numbers are preferred, because they continue into the transfinite [Maddy on Neumann] |
| Full Idea: Von Neumann's version of the natural numbers is in fact preferred because it carries over directly to the transfinite ordinals. | |
| From: comment on John von Neumann (On the Introduction of Transfinite Numbers [1923]) by Penelope Maddy - Naturalism in Mathematics I.2 n9 |
| 18179 | For Von Neumann the successor of n is n U {n} (rather than {n}) [Neumann, by Maddy] |
| Full Idea: For Von Neumann the successor of n is n U {n} (rather than Zermelo's successor, which is {n}). | |
| From: report of John von Neumann (On the Introduction of Transfinite Numbers [1923]) by Penelope Maddy - Naturalism in Mathematics I.2 n8 |
| 15925 | Each Von Neumann ordinal number is the set of its predecessors [Neumann, by Lavine] |
| Full Idea: Each Von Neumann ordinal number is the set of its predecessors. ...He had shown how to introduce ordinal numbers as sets, making it possible to use them without leaving the domain of sets. | |
| From: report of John von Neumann (On the Introduction of Transfinite Numbers [1923]) by Shaughan Lavine - Understanding the Infinite V.3 |
| 8126 | Anti-individualism says the environment is involved in the individuation of some mental states [Burge] |
| Full Idea: Anti-individualism is the view that not all of an individual's mental states and events can be type-individuated independently of the nature of the entities in the individual's physical or social environment environment. | |
| From: Tyler Burge (Philosophy of Mind: 1950-2000 [2005], p.453) | |
| A reaction: While the Twin Earth experiment emphasises the physical environment, Burge has been responsible for emphasising the social environment. The suspicion is that the whole concept of 'individual' minds will collapse on this view. |
| 8127 | Broad concepts suggest an extension of the mind into the environment (less computer-like) [Burge] |
| Full Idea: Certain thought experiments made trouble for standard functionalism, which limits input/output to the surface of an individual; proposals to extend this into the environment reduces the reliance on a computer paradigm, but increases complexity. | |
| From: Tyler Burge (Philosophy of Mind: 1950-2000 [2005], p.454) | |
| A reaction: [He has the Twin Earth experiment in mind] The jury is out on this, but it looks a bit of a slippery slope. Accounts of action and responsibility need a fairly sharp concept of an individual. Externalism begins to look like just a new scepticism. |
| 8129 | Anti-individualism may be incompatible with some sorts of self-knowledge [Burge] |
| Full Idea: The idea of anti-individualism raised problems about self-knowledge. The question is whether anti-individualism is compatible with some sort of authoritative or privileged warrant for certain types of self-knowledge. | |
| From: Tyler Burge (Philosophy of Mind: 1950-2000 [2005], p.457) | |
| A reaction: [See under 'Nature of Minds' for 'Anti-individualism'] The thought is that if your mind is not entirely in your head, you can no longer be an expert on it. It might go the other way: obviously we can be self-experts, so anti-individualism is wrong. |
| 8131 | Some qualities of experience, like blurred vision, have no function at all [Burge] |
| Full Idea: There appear to be qualitative aspects of experience that have no function in the life of the organism. They constitute dysfunction or noise. Blurriness in a visual experience is an example. | |
| From: Tyler Burge (Philosophy of Mind: 1950-2000 [2005], p.460) | |
| A reaction: The best account of blurred vision would seem to be adverbial - I see 'in a blurred way' (nay, blurredly). Hence maybe blurred vision is functional, but it just isn't functioning very well. |
| 20713 | God must be fit for worship, but worship abandons morally autonomy, but there is no God [Rachels, by Davies,B] |
| Full Idea: Rachels argues 1) If any being is God, he must be a fitting object of worship, 2) No being could be a fitting object of worship, since worship requires the abandonment of one's role as an autonomous moral agent, so 3) There cannot be a being who is God. | |
| From: report of James Rachels (God and Human Attributes [1971], 7 p.334) by Brian Davies - Introduction to the Philosophy of Religion 9 'd morality' | |
| A reaction: Presumably Lionel Messi can be a fitting object of worship without being God. Since the problem is with being worshipful, rather than with being God, should I infer that Messi doesn't exist? |