26 ideas
| 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 |
| 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 |
| 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 |
| 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 |
| 5311 | If observation goes up a level, we expect the laws of the lower level to remain in force [Wilson,EO] |
| Full Idea: When the observer shifts his attention from one level of organisation to the next, as from physics to chemistry, he expects to find obedience to all the laws of the levels below. | |
| From: Edmund O. Wilson (On Human Nature [1978], Ch.1) | |
| A reaction: This seems to state a necessary condition of reduction, but not a sufficient one. Wilson points out that new phenomena emerge at higher levels. This principle is similar to Hume's argument against miracles. You don't easily overthrow basic laws. |
| 5312 | A child first sees objects as distinct, and later as members of groups [Wilson,EO] |
| Full Idea: From a single-minded effort to move objects a child's activity grows into a detached reflection on the movements themselves. The objects are first perceived as distinct entities, and then as members of groups to be classified. | |
| From: Edmund O. Wilson (On Human Nature [1978], Ch.3) | |
| A reaction: This does not, of course, prove anything about the philosophical problems of universals, but it does seem to pinpoint the stage in human development when 'universals' are perceived. The basis seems to be groups or sets, but how do we spot those? |
| 14193 | 'Substance theorists' take modal properties as primitive, without structure, just falling under a sortal [Paul,LA] |
| Full Idea: Some deep essentialists resist the need to explain the structure under de re modal properties, taking them as primitive. One version (which we can call 'substance theory') takes them to fall under a sortal concept, with no further explanation. | |
| From: L.A. Paul (In Defense of Essentialism [2006], §1) | |
| A reaction: A very helpful identification of what Wiggins stands for, and why I disagree with him. The whole point of essences is to provide a notion that fits in with sciences, which means they must have an explanatory role, which needs structures. |
| 14195 | If an object's sort determines its properties, we need to ask what determines its sort [Paul,LA] |
| Full Idea: If the substance essentialist holds that the sort an object belongs to determines its de re modal properties (rather than the other way round), then he needs to give an (ontological, not conceptual) explanation of what determines an object's sort. | |
| From: L.A. Paul (In Defense of Essentialism [2006], §1) | |
| A reaction: See Idea 14193 for 'substance essentialism'. I find it quite incredible that anyone could think that a thing's sort could determine its properties, rather than the other way round. Even if sortals are conventional, they are not arbitrary. |
| 14196 | Substance essentialism says an object is multiple, as falling under various different sortals [Paul,LA] |
| Full Idea: The explanation of material constitution given by substance essentialism is that there are multiple objects. A person is essentially human-shaped (falling under the human sort), while their hunk of tissue is accidentally human-shaped (as tissue). | |
| From: L.A. Paul (In Defense of Essentialism [2006], §1) | |
| A reaction: At this point sortal essentialism begins to look crazy. Persons are dubious examples (with sneaky dualism involved). A bronze statue is essentially harder to dent than a clay one, because of its bronze. If you remake it of clay, it isn't the same statue. |
| 14198 | Absolutely unrestricted qualitative composition would allow things with incompatible properties [Paul,LA] |
| Full Idea: Absolutely unrestricted qualitative composition would imply that objects with incompatible properties and objects such as winged pigs or golden mountains were actual. | |
| From: L.A. Paul (In Defense of Essentialism [2006], §5) | |
| A reaction: Note that this is 'qualitative' composition, and not composition of parts. The objection seems to rule out unrestricted qualitative composition, since you could hardly combine squareness with roundness. |
| 14190 | Deep essentialist objects have intrinsic properties that fix their nature; the shallow version makes it contextual [Paul,LA] |
| Full Idea: Essentialism says that objects have their properties essentially. 'Deep' essentialists take the (nontrivial) essential properties of an object to determine its nature. 'Shallow' essentialists substitute context-dependent truths for the independent ones. | |
| From: L.A. Paul (In Defense of Essentialism [2006], Intro) | |
| A reaction: If the deep essence determines a things nature, we should not need to say 'nontrivial'. This is my bete noire, the confusion of essential properties with necessary ones, where necessary properties (or predicates, at least) can indeed be trivial. |
| 14191 | Deep essentialists say essences constrain how things could change; modal profiles fix natures [Paul,LA] |
| Full Idea: The deep essentialist holds that most objects have essential properties such that there are many ways they could not be, or many changes through which they could not persist. Objects' modal profiles characterize their natures. | |
| From: L.A. Paul (In Defense of Essentialism [2006], Intro) | |
| A reaction: This is the view I like, especially the last bit. If your modal profile doesn't determine your nature, then what does? Think of how you sum up a person at a funeral. Your modal profile is determined by dispositions and powers. |
| 14192 | Essentialism must deal with charges of arbitrariness, and failure to reduce de re modality [Paul,LA] |
| Full Idea: Two objections to deep essentialism are that it falters when faced with a skeptical objection concerning arbitrariness, and the need for a reductive account of de re modality. | |
| From: L.A. Paul (In Defense of Essentialism [2006], Intro) | |
| A reaction: An immediate response to the second objection might be to say that modal facts about things are not reducible. The charge of arbitrariness (i.e. total arbitrariness, not just a bit of uncertainty) is the main thing a theory of essences must deal with. |
| 14197 | An object's modal properties don't determine its possibilities [Paul,LA] |
| Full Idea: I reject the view that an object's de re modal properties determine its relations to possibilia. | |
| From: L.A. Paul (In Defense of Essentialism [2006], §3) | |
| A reaction: You'll have to read Paul to see why, but I flat disagree with her on this. The whole point of accepting such properties is to determine the modal profile of the thing, and hence see how it can fit into and behave in the world. |
| 14189 | 'Modal realists' believe in many concrete worlds, 'actualists' in just this world, 'ersatzists' in abstract other worlds [Paul,LA] |
| Full Idea: A 'modal realist' believes that there are many concrete worlds, while the 'actualist' believes in only one concrete world, the actual world. The 'ersatzist' is an actualist who takes nonactual possible worlds and their contents to be abstracta. | |
| From: L.A. Paul (In Defense of Essentialism [2006], Intro) | |
| A reaction: My view is something like that modal realism is wrong, and actualism is right, and possible worlds (if they really are that useful) are convenient abstract fictions, constructed (if we have any sense) out of the real possibilities in the actual world. |
| 5309 | Beliefs are really enabling mechanisms for survival [Wilson,EO] |
| Full Idea: Beliefs are really enabling mechanisms for survival. | |
| From: Edmund O. Wilson (On Human Nature [1978], Ch.1) | |
| A reaction: How does he know this proposition which he asserts so confidently? Obvious counterexamples seem to be utterly trivial beliefs, and self-destructive beliefs. What is the evolutionary value of low self-esteem? Still, you see his point. |
| 5310 | Philosophers study the consequences of ethics instead of its origins [Wilson,EO] |
| Full Idea: Philosophers examine the precepts of ethical systems with reference to their consequences and not their origins. | |
| From: Edmund O. Wilson (On Human Nature [1978], Ch.1) | |
| A reaction: He is interested in biological origins, but it strikes me that every moral theory has some account of the origins of morality, be it pure reason, or the love of pleasure, or human nature, or eternal ideas, or the will of God, or selfish desires. |
| 5313 | The rules of human decision-making converge and overlap in a 'human nature' [Wilson,EO] |
| Full Idea: The rules followed in human decision-making are tight enough to produce a broad overlap in the decisions taken by all individuals, and hence a convergence powerful enough to be labelled 'human nature'. | |
| From: Edmund O. Wilson (On Human Nature [1978], Ch.3) | |
| A reaction: This is a nice empirical criterion for asserting the existence of human nature, and it seems right to examine decisions, rather than more thoughtless or conformist behaviour. Existentialists dream of new possibilities, but the old ways always seem best… |
| 5316 | We undermine altruism by rewarding it, but we reward it to encourage it [Wilson,EO] |
| Full Idea: By sanctifying altruism in order to reward it we make it less true, but by that means we promote its recurrence in others. | |
| From: Edmund O. Wilson (On Human Nature [1978], Ch.7) | |
| A reaction: So is my preference for not rewarding (or even noticing) altruism an anti-social tendency. The very conspicuous charity of sponsorship seems somehow inferior to the truly anonymous gift. Or super-altruism is very public, to encourage it in others? |
| 5318 | Pure hard-core altruism based on kin selection is the enemy of civilisation [Wilson,EO] |
| Full Idea: Pure hard-core altruism based on kin selection is the enemy of civilisation. | |
| From: Edmund O. Wilson (On Human Nature [1978], Ch.7) | |
| A reaction: By 'hard-core' he means suicidally self-sacrificing, rather than extensive. This seems a good thesis. It strikes me that the development of civil society is often impeded by family loyalty, such as in the case of the Mafia. |
| 5317 | The actor is most convincing who believes that his performance is real [Wilson,EO] |
| Full Idea: The actor is most convincing who believes that his performance is real. | |
| From: Edmund O. Wilson (On Human Nature [1978], Ch.7) | |
| A reaction: This is a key element of social contract theory. It shows why natural selection of truly altruistic traits might be beneficial to individuals, provided they are surrounded by possible recipricators. We trust those who are genuine and sincere. |
| 5308 | The only human purpose is that created by our genetic history [Wilson,EO] |
| Full Idea: No species, ours included, possesses a purpose beyond the imperatives created by its genetic history. | |
| From: Edmund O. Wilson (On Human Nature [1978], Ch.1) | |
| A reaction: This invites the question of what that purpose is perceived to be. Some people feel an imperative to play the piano all day, so presumably genetic history has created that feeling. Presumably we can also choose a purpose, even extinction. |
| 5314 | Cultural evolution is Lamarckian and fast, biological evolution is Darwinian and slow [Wilson,EO] |
| Full Idea: Cultural evolution is Lamarckian and very fast, whereas biological evolution is Darwinian and usually very slow. | |
| From: Edmund O. Wilson (On Human Nature [1978], Ch.4) | |
| A reaction: An intriguing point, given how discredited Lamarckian evolution is. It links with the Dawkins idea of 'memes' - cultural ideas which spread very fast. Is biological evolution suddenly about to become Lamarckian, as culture influences biology? |
| 5315 | Over 99 percent of human evolution has been in the hunter-gatherer phase [Wilson,EO] |
| Full Idea: Selection pressures of hunter-gatherer existence have persisted for over 99 percent of human genetic evolution. | |
| From: Edmund O. Wilson (On Human Nature [1978], Ch.4) | |
| A reaction: This seems a key point to bear in mind when assessing human nature. Hunter-gathering isn't just one tendency in our genetics; it more or less constitutes everything we are. |
| 5320 | It is estimated that mankind has produced 100,000 religions [Wilson,EO] |
| Full Idea: Since the first recorded religion (in Iraq 60,000 years ago) it is estimated that mankind has produced in the order of one hundred thousand religions. | |
| From: Edmund O. Wilson (On Human Nature [1978], Ch.8) | |
| A reaction: If asked to guess the number, I would probably have said '200'! This staggering figure seems to argue both ways - it suggest a certain arbitrariness in the details of religions, but an extremely intense drive to have some sort of religious belief. |