20 ideas
| 11064 | Classes can be reduced to propositional functions [Russell, by Hanna] |
| Full Idea: Russell held that classes can be reduced to propositional functions. | |
| From: report of Bertrand Russell (Mathematical logic and theory of types [1908]) by Robert Hanna - Rationality and Logic 2.4 | |
| A reaction: The exact nature of a propositional function is disputed amongst Russell scholars (though it is roughly an open sentence of the form 'x is red'). |
| 6407 | The class of classes which lack self-membership leads to a contradiction [Russell, by Grayling] |
| Full Idea: The class of teaspoons isn't a teaspoon, so isn't a member of itself; but the class of non-teaspoons is a member of itself. The class of all classes which are not members of themselves is a member of itself if it isn't a member of itself! Paradox. | |
| From: report of Bertrand Russell (Mathematical logic and theory of types [1908]) by A.C. Grayling - Russell Ch.2 | |
| A reaction: A very compressed version of Russell's famous paradox, often known as the 'barber' paradox. Russell developed his Theory of Types in an attempt to counter the paradox. Frege's response was to despair of his own theory. |
| 10418 | Type theory seems an extreme reaction, since self-exemplification is often innocuous [Swoyer on Russell] |
| Full Idea: Russell's reaction to his paradox (by creating his theory of types) seems extreme, because many cases of self-exemplification are innocuous. The property of being a property is itself a property. | |
| From: comment on Bertrand Russell (Mathematical logic and theory of types [1908]) by Chris Swoyer - Properties 7.5 | |
| A reaction: Perhaps it is not enough that 'many cases' are innocuous. We are starting from philosophy of mathematics, where precision is essentially. General views about properties come later. |
| 10047 | Russell's improvements blocked mathematics as well as paradoxes, and needed further axioms [Russell, by Musgrave] |
| Full Idea: Unfortunately, Russell's new logic, as well as preventing the deduction of paradoxes, also prevented the deduction of mathematics, so he supplemented it with additional axioms, of Infinity, of Choice, and of Reducibility. | |
| From: report of Bertrand Russell (Mathematical logic and theory of types [1908]) by Alan Musgrave - Logicism Revisited §2 | |
| A reaction: The first axiom seems to be an empirical hypothesis, and the second has turned out to be independent of logic and set theory. |
| 23478 | Type theory means that features shared by different levels cannot be expressed [Morris,M on Russell] |
| Full Idea: Russell's theory of types avoided the paradoxes, but it had the result that features common to different levels of the hierarchy become uncapturable (since any attempt to capture them would involve a predicate which disobeyed the hierarchy restrictions). | |
| From: comment on Bertrand Russell (Mathematical logic and theory of types [1908]) by Michael Morris - Guidebook to Wittgenstein's Tractatus 2H |
| 21718 | Ramified types can be defended as a system of intensional logic, with a 'no class' view of sets [Russell, by Linsky,B] |
| Full Idea: A defence of the ramified theory of types comes in seeing it as a system of intensional logic which includes the 'no class' account of sets, and indeed the whole development of mathematics, as just a part. | |
| From: report of Bertrand Russell (Mathematical logic and theory of types [1908]) by Bernard Linsky - Russell's Metaphysical Logic 6.1 | |
| A reaction: So Linsky's basic project is to save logicism, by resting on intensional logic (rather than extensional logic and set theory). I'm not aware that Linsky has acquired followers for this. Maybe Crispin Wright has commented? |
| 18126 | A set does not exist unless at least one of its specifications is predicative [Russell, by Bostock] |
| Full Idea: The idea is that the same set may well have different canonical specifications, i.e. there may be different ways of stating its membership conditions, and so long as one of these is predicative all is well. If none are, the supposed set does not exist. | |
| From: report of Bertrand Russell (Mathematical logic and theory of types [1908]) by David Bostock - Philosophy of Mathematics 8.1 |
| 18128 | Russell is a conceptualist here, saying some abstracta only exist because definitions create them [Russell, by Bostock] |
| Full Idea: It is a conceptualist approach that Russell is relying on. ...The view is that some abstract objects ...exist only because they are definable. It is the definition that would (if permitted) somehow bring them into existence. | |
| From: report of Bertrand Russell (Mathematical logic and theory of types [1908]) by David Bostock - Philosophy of Mathematics 8.1 | |
| A reaction: I'm suddenly thinking that predicativism is rather interesting. Being of an anti-platonist persuasion about abstract 'objects', I take some story about how we generate them to be needed. Psychological abstraction seems right, but a bit vague. |
| 18124 | Vicious Circle says if it is expressed using the whole collection, it can't be in the collection [Russell, by Bostock] |
| Full Idea: The Vicious Circle Principle says, roughly, that whatever involves, or presupposes, or is only definable in terms of, all of a collection cannot itself be one of the collection. | |
| From: report of Bertrand Russell (Mathematical logic and theory of types [1908], p.63,75) by David Bostock - Philosophy of Mathematics 8.1 | |
| A reaction: This is Bostock's paraphrase of Russell, because Russell never quite puts it clearly. The response is the requirement to be 'predicative'. Bostock emphasises that it mainly concerns definitions. The Principle 'always leads to hierarchies'. |
| 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. |
| 21051 | Check your rationality by thinking of your opinion pronounced by the supreme court [Rawls] |
| Full Idea: To check whether we are following public reason we might ask: how would our argument strike us presented in the form of a supreme court opinion? | |
| From: John Rawls (Political Liberalism [1993], p.254), quoted by Michael J. Sandel - Justice: What's the right thing to do? 10 | |
| A reaction: A very nice practical implementation of Kantian universalisability. How would your opinion sound if it were written into a constitution? |
| 21119 | Power is only legitimate if it is reasonable for free equal citizens to endorse the constitution [Rawls] |
| Full Idea: Exercise of political power is fully proper only when it is exercised in accordance with a constitution the essentials of which all citizens as free and equal may reasonably be expected to endorse in light of principles and ideals acceptable to reason. | |
| From: John Rawls (Political Liberalism [1993], p.217), quoted by Andrew Shorten - Contemporary Political Theory 02 | |
| A reaction: This is not the actual endorsement of Rousseau, or the tacit endorsement of Locke (by living there), but adds a Kantian appeal to a rational consensus, on which rational people should converge. Very Enlightenment. 'Hypothetical consent'. |