106 ideas
| 11006 | Russell started a whole movement in philosophy by providing an analysis of descriptions [Read on Russell] |
| 15924 | Predicative definitions are acceptable in mathematics if they distinguish objects, rather than creating them? [Zermelo, by Lavine] |
| 17608 | We take set theory as given, and retain everything valuable, while avoiding contradictions [Zermelo] |
| 17607 | Set theory investigates number, order and function, showing logical foundations for mathematics [Zermelo] |
| 10870 | ZFC: Existence, Extension, Specification, Pairing, Unions, Powers, Infinity, Choice [Zermelo, by Clegg] |
| 13012 | Zermelo published his axioms in 1908, to secure a controversial proof [Zermelo, by Maddy] |
| 17609 | Set theory can be reduced to a few definitions and seven independent axioms [Zermelo] |
| 13017 | Zermelo introduced Pairing in 1930, and it seems fairly obvious [Zermelo, by Maddy] |
| 13015 | Zermelo used Foundation to block paradox, but then decided that only Separation was needed [Zermelo, by Maddy] |
| 13020 | The Axiom of Separation requires set generation up to one step back from contradiction [Zermelo, by Maddy] |
| 13486 | Not every predicate has an extension, but Separation picks the members that satisfy a predicate [Zermelo, by Hart,WD] |
| 18944 | Russell's theories aim to preserve excluded middle (saying all sentences are T or F) [Sawyer on Russell] |
| 7758 | 'Elizabeth = Queen of England' is really a predication, not an identity-statement [Russell, by Lycan] |
| 5772 | The idea of a variable is fundamental [Russell] |
| 18941 | Names don't have a sense, but are disguised definite descriptions [Russell, by Sawyer] |
| 4945 | Russell says names are not denotations, but definite descriptions in disguise [Russell, by Kripke] |
| 18942 | Russell says a name contributes a complex of properties, rather than an object [Russell, by Sawyer] |
| 7745 | Are names descriptions, if the description is unknown, false, not special, or contains names? [McCullogh on Russell] |
| 10449 | Logically proper names introduce objects; definite descriptions introduce quantifications [Russell, by Bach] |
| 15159 | The meaning of a logically proper name is its referent, but most names are not logically proper [Russell, by Soames] |
| 2612 | Russell rewrote singular term names as predicates [Russell, by Ayer] |
| 7757 | "Nobody" is not a singular term, but a quantifier [Russell, by Lycan] |
| 18943 | Russell implies that all sentences containing empty names are false [Sawyer on Russell] |
| 6411 | Critics say definite descriptions can refer, and may not embody both uniqueness and existence claims [Grayling on Russell] |
| 10433 | Definite descriptions fail to refer in three situations, so they aren't essentially referring [Russell, by Sainsbury] |
| 1608 | The theory of descriptions eliminates the name of the entity whose existence was presupposed [Russell, by Quine] |
| 7754 | Russell's theory explains non-existents, negative existentials, identity problems, and substitutivity [Russell, by Lycan] |
| 21529 | Russell showed how to define 'the', and thereby reduce the ontology of logic [Russell, by Lackey] |
| 6333 | The theory of definite descriptions reduces the definite article 'the' to the concepts of predicate logic [Russell, by Horwich] |
| 6412 | Russell implies that 'the baby is crying' is only true if the baby is unique [Grayling on Russell] |
| 7743 | Russell explained descriptions with quantifiers, where Frege treated them as names [Russell, by McCullogh] |
| 7310 | Russell avoids non-existent objects by denying that definite descriptions are proper names [Russell, by Miller,A] |
| 12006 | Denying definite description sentences are subject-predicate in form blocks two big problems [Russell, by Forbes,G] |
| 4569 | Russell says apparent referring expressions are really assertions about properties [Russell, by Cooper,DE] |
| 11009 | Russell's theory must be wrong if it says all statements about non-existents are false [Read on Russell] |
| 21549 | The theory of descriptions lacks conventions for the scope of quantifiers [Lackey on Russell] |
| 12796 | Non-count descriptions don't threaten Russell's theory, which is only about singulars [Laycock on Russell] |
| 7532 | Denoting is crucial in Russell's account of mathematics, for identifying classes [Russell, by Monk] |
| 11988 | Russell's analysis means molecular sentences are ambiguous over the scope of the description [Kaplan on Russell] |
| 6061 | Existence is entirely expressed by the existential quantifier [Russell, by McGinn] |
| 13487 | In ZF, the Burali-Forti Paradox proves that there is no set of all ordinals [Zermelo, by Hart,WD] |
| 18178 | For Zermelo the successor of n is {n} (rather than n U {n}) [Zermelo, by Maddy] |
| 13027 | Zermelo believed, and Von Neumann seemed to confirm, that numbers are sets [Zermelo, by Maddy] |
| 9627 | Different versions of set theory result in different underlying structures for numbers [Zermelo, by Brown,JR] |
| 14562 | A process is unified as an expression of a collection of causal powers [Mumford/Anjum] |
| 14541 | Events are essentially changes; property exemplifications are just states of affairs [Mumford/Anjum] |
| 18775 | Russell showed that descriptions may not have ontological commitment [Russell, by Linsky,B] |
| 7533 | The Theory of Description dropped classes and numbers, leaving propositions, individuals and universals [Russell, by Monk] |
| 14553 | Weak emergence is just unexpected, and strong emergence is beyond all deduction [Mumford/Anjum] |
| 6063 | Russell can't attribute existence to properties [McGinn on Russell] |
| 14538 | Powers explain properties, causes, modality, events, and perhaps even particulars [Mumford/Anjum] |
| 14555 | Powers offer no more explanation of nature than laws do [Mumford/Anjum] |
| 14557 | Powers are not just basic forces, since they combine to make new powers [Mumford/Anjum] |
| 14583 | Dispositionality is a natural selection function, picking outcomes from the range of possibilities [Mumford/Anjum] |
| 14536 | We say 'power' and 'disposition' are equivalent, but some say dispositions are manifestable [Mumford/Anjum] |
| 14584 | The simple conditional analysis of dispositions doesn't allow for possible prevention [Mumford/Anjum] |
| 14582 | Might dispositions be reduced to normativity, or to intentionality? [Mumford/Anjum] |
| 18777 | If the King of France is not bald, and not not-bald, this violates excluded middle [Linsky,B on Russell] |
| 14542 | If statue and clay fall and crush someone, the event is not overdetermined [Mumford/Anjum] |
| 14535 | Pandispositionalists say structures are clusters of causal powers [Mumford/Anjum] |
| 14561 | Perdurantism imposes no order on temporal parts, so sequences of events are contingent [Mumford/Anjum] |
| 14579 | Dispositionality is the core modality, with possibility and necessity as its extreme cases [Mumford/Anjum] |
| 14580 | Dispositions may suggest modality to us - as what might not have been, and what could have been [Mumford/Anjum] |
| 14552 | Relations are naturally necessary when they are generated by the essential mechanisms of the world [Mumford/Anjum] |
| 14578 | Possibility might be non-contradiction, or recombinations of the actual, or truth in possible worlds [Mumford/Anjum] |
| 14549 | Maybe truths are necessitated by the facts which are their truthmakers [Mumford/Anjum] |
| 14585 | We have more than five senses; balance and proprioception, for example [Mumford/Anjum] |
| 14576 | Smoking disposes towards cancer; smokers without cancer do not falsify this claim [Mumford/Anjum] |
| 14551 | If causation were necessary, the past would fix the future, and induction would be simple [Mumford/Anjum] |
| 14571 | The only full uniformities in nature occur from the essences of fundamental things [Mumford/Anjum] |
| 14570 | Nature is not completely uniform, and some regular causes sometimes fail to produce their effects [Mumford/Anjum] |
| 14569 | It is tempting to think that only entailment provides a full explanation [Mumford/Anjum] |
| 14568 | A structure won't give a causal explanation unless we know the powers of the structure [Mumford/Anjum] |
| 14556 | Strong emergence seems to imply top-down causation, originating in consciousness [Mumford/Anjum] |
| 4567 | Russell argued with great plausibility that we rarely, if ever, refer with our words [Russell, by Cooper,DE] |
| 5810 | Referring is not denoting, and Russell ignores the referential use of definite descriptions [Donnellan on Russell] |
| 16385 | A definite description 'denotes' an entity if it fits the description uniquely [Russell, by Recanati] |
| 5774 | Denoting phrases are meaningless, but guarantee meaning for propositions [Russell] |
| 5775 | In 'Scott is the author of Waverley', denotation is identical, but meaning is different [Russell] |
| 16987 | By eliminating descriptions from primitive notation, Russell seems to reject 'sense' [Russell, by Kripke] |
| 4570 | Russell assumes that expressions refer, but actually speakers refer by using expressions [Cooper,DE on Russell] |
| 16349 | Russell rejected sense/reference, because it made direct acquaintance with things impossible [Russell, by Recanati] |
| 7313 | 'Sense' is superfluous (rather than incoherent) [Russell, by Miller,A] |
| 7767 | The theory of definite descriptions aims at finding correct truth conditions [Russell, by Lycan] |
| 21726 | In graspable propositions the constituents are real entities of acquaintance [Russell] |
| 14566 | Causation by absence is not real causation, but part of our explanatory practices [Mumford/Anjum] |
| 14577 | Causation may not be transitive. Does a fire cause itself to be extinguished by the sprinklers? [Mumford/Anjum] |
| 14563 | Causation is the passing around of powers [Mumford/Anjum] |
| 14587 | We take causation to be primitive, as it is hard to see how it could be further reduced [Mumford/Anjum] |
| 14533 | Causation doesn't have two distinct relata; it is a single unfolding process [Mumford/Anjum] |
| 14558 | A collision is a process, which involves simultaneous happenings, but not instantaneous ones [Mumford/Anjum] |
| 14559 | Does causation need a third tying ingredient, or just two that meet, or might there be a single process? [Mumford/Anjum] |
| 14565 | Sugar dissolving is a process taking time, not one event and then another [Mumford/Anjum] |
| 14567 | Privileging one cause is just an epistemic or pragmatic matter, not an ontological one [Mumford/Anjum] |
| 14537 | Coincidence is conjunction without causation; smoking causing cancer is the reverse [Mumford/Anjum] |
| 14573 | Occasionally a cause makes no difference (pre-emption, perhaps) so the counterfactual is false [Mumford/Anjum] |
| 14572 | Is a cause because of counterfactual dependence, or is the dependence because there is a cause? [Mumford/Anjum] |
| 14574 | Cases of preventing a prevention may give counterfactual dependence without causation [Mumford/Anjum] |
| 14539 | Nature can be interfered with, so a cause never necessitates its effects [Mumford/Anjum] |
| 14550 | We assert causes without asserting that they necessitate their effects [Mumford/Anjum] |
| 14546 | Necessary causation should survive antecedent strengthening, but no cause can always survive that [Mumford/Anjum] |
| 14575 | A 'ceteris paribus' clause implies that a conditional only has dispositional force [Mumford/Anjum] |
| 14548 | There may be necessitation in the world, but causation does not supply it [Mumford/Anjum] |
| 14554 | Laws are nothing more than descriptions of the behaviour of powers [Mumford/Anjum] |
| 14564 | If laws are equations, cause and effect must be simultaneous (or the law would be falsified)! [Mumford/Anjum] |
| 5773 | The ontological argument begins with an unproven claim that 'there exists an x..' [Russell] |