133 ideas
| 16395 | Kripke separated semantics from metaphysics, rather than linking them, making the latter independent [Kripke, by Stalnaker] |
| 17034 | Analyses of concepts using entirely different terms are very inclined to fail [Kripke] |
| 4955 | Some definitions aim to fix a reference rather than give a meaning [Kripke] |
| 10559 | Kripke's modal semantics presupposes certain facts about possible worlds [Kripke, by Zalta] |
| 15901 | Trying to represent curves, we study arbitrary functions, leading to the ordinals, which produces set theory [Cantor, by Lavine] |
| 13444 | Cantor's Theorem: for any set x, its power set P(x) has more members than x [Cantor, by Hart,WD] |
| 18098 | Cantor proved that all sets have more subsets than they have members [Cantor, by Bostock] |
| 15505 | If a set is 'a many thought of as one', beginners should protest against singleton sets [Cantor, by Lewis] |
| 10865 | The continuum is the powerset of the integers, which moves up a level [Cantor, by Clegg] |
| 10701 | Cantor showed that supposed contradictions in infinity were just a lack of clarity [Cantor, by Potter] |
| 13016 | The Axiom of Union dates from 1899, and seems fairly obvious [Cantor, by Maddy] |
| 14199 | Cantor's sets were just collections, but Dedekind's were containers [Cantor, by Oliver/Smiley] |
| 10437 | Names are rigid, making them unlike definite descriptions [Kripke, by Sainsbury] |
| 4949 | Names are rigid designators, which designate the same object in all possible worlds [Kripke] |
| 4951 | A bundle of qualities is a collection of abstractions, so it can't be a particular [Kripke] |
| 17031 | A name can still refer even if it satisfies none of its well-known descriptions [Kripke] |
| 8957 | Some references, such as 'Neptune', have to be fixed by description rather than baptism [Kripke, by Szabó] |
| 10428 | Proper names must have referents, because they are not descriptive [Kripke, by Sainsbury] |
| 4959 | A name's reference is not fixed by any marks or properties of the referent [Kripke] |
| 10082 | There are infinite sets that are not enumerable [Cantor, by Smith,P] |
| 13483 | Cantor's Paradox: the power set of the universe must be bigger than the universe, yet a subset of it [Cantor, by Hart,WD] |
| 8710 | The powerset of all the cardinal numbers is required to be greater than itself [Cantor, by Friend] |
| 15910 | Cantor named the third realm between the finite and the Absolute the 'transfinite' [Cantor, by Lavine] |
| 15905 | Cantor proved the points on a plane are in one-to-one correspondence to the points on a line [Cantor, by Lavine] |
| 9983 | Cantor took the ordinal numbers to be primary [Cantor, by Tait] |
| 17798 | Cantor presented the totality of natural numbers as finite, not infinite [Cantor, by Mayberry] |
| 9971 | Cantor introduced the distinction between cardinals and ordinals [Cantor, by Tait] |
| 9892 | Cantor showed that ordinals are more basic than cardinals [Cantor, by Dummett] |
| 14136 | A cardinal is an abstraction, from the nature of a set's elements, and from their order [Cantor] |
| 15906 | Cantor tried to prove points on a line matched naturals or reals - but nothing in between [Cantor, by Lavine] |
| 11015 | Cantor's diagonal argument proved you can't list all decimal numbers between 0 and 1 [Cantor, by Read] |
| 15903 | A real is associated with an infinite set of infinite Cauchy sequences of rationals [Cantor, by Lavine] |
| 18251 | Irrational numbers are the limits of Cauchy sequences of rational numbers [Cantor, by Lavine] |
| 15902 | Irrationals and the Dedekind Cut implied infinite classes, but they seemed to have logical difficulties [Cantor, by Lavine] |
| 15908 | It was Cantor's diagonal argument which revealed infinities greater than that of the real numbers [Cantor, by Lavine] |
| 13464 | Cantor proposes that there won't be a potential infinity if there is no actual infinity [Cantor, by Hart,WD] |
| 10112 | The naturals won't map onto the reals, so there are different sizes of infinity [Cantor, by George/Velleman] |
| 17889 | CH: An infinite set of reals corresponds 1-1 either to the naturals or to the reals [Cantor, by Koellner] |
| 8733 | The Continuum Hypothesis says there are no sets between the natural numbers and reals [Cantor, by Shapiro] |
| 13447 | Cantor: there is no size between naturals and reals, or between a set and its power set [Cantor, by Hart,WD] |
| 10883 | Cantor's Continuum Hypothesis says there is a gap between the natural and the real numbers [Cantor, by Horsten] |
| 13528 | Continuum Hypothesis: there are no sets between N and P(N) [Cantor, by Wolf,RS] |
| 9555 | Continuum Hypothesis: no cardinal greater than aleph-null but less than cardinality of the continuum [Cantor, by Chihara] |
| 15893 | Cantor's theory concerns collections which can be counted, using the ordinals [Cantor, by Lavine] |
| 18174 | Cantor extended ordinals into the transfinite, and they can thus measure infinite cardinalities [Cantor, by Maddy] |
| 18173 | Cardinality strictly concerns one-one correspondence, to test infinite sameness of size [Cantor, by Maddy] |
| 10232 | Property extensions outstrip objects, so shortage of objects caused the Caesar problem [Cantor, by Shapiro] |
| 18176 | Pure mathematics is pure set theory [Cantor] |
| 8631 | Cantor says that maths originates only by abstraction from objects [Cantor, by Frege] |
| 14896 | Kripke's metaphysics (essences, kinds, rigidity) blocks the slide into sociology [Kripke, by Ladyman/Ross] |
| 17647 | Kripke individuates objects by essential modal properties (and presupposes essentialism) [Kripke, by Putnam] |
| 16995 | Given that a table is made of molecules, could it not be molecular and still be this table? [Kripke] |
| 17047 | If we imagine this table made of ice or different wood, we are imagining a different table [Kripke] |
| 5450 | For Kripke, essence is origin; for Putnam, essence is properties; for Wiggins, essence is membership of a kind [Kripke, by Mautner] |
| 17055 | Atomic number 79 is part of the nature of the gold we know [Kripke] |
| 16997 | An essential property is true of an object in any case where it would have existed [Kripke] |
| 17045 | De re modality is an object having essential properties [Kripke] |
| 17030 | Important properties of an object need not be essential to it [Kripke] |
| 16955 | Kripke says internal structure fixes species; I say it is genetic affinity and a common descent [Kripke, by Dummett] |
| 16996 | Given that Nixon is indeed a human being, that he might not have been does not concern knowledge [Kripke] |
| 13971 | Kripke claims that some properties, only knowable posteriori, are known a priori to be essential [Kripke, by Soames] |
| 12100 | An essence is the necessary properties, derived from an intuitive identity, in origin, type and material [Kripke, by Witt] |
| 16991 | No one seems to know the identity conditions for a material object (or for people) over time [Kripke] |
| 11867 | If we lose track of origin, how do we show we are maintaining a reference? [Kripke, by Wiggins] |
| 12018 | Kripke argues, of the Queen, that parents of an organism are essentially so [Kripke, by Forbes,G] |
| 17046 | Could the actual Queen have been born of different parents? [Kripke] |
| 8274 | Socrates can't have a necessary origin, because he might have had no 'origin' [Lowe on Kripke] |
| 17036 | Identity statements can be contingent if they rely on descriptions [Kripke] |
| 17038 | If Hesperus and Phosophorus are the same, they can't possibly be different [Kripke] |
| 11880 | Kripke says his necessary a posteriori examples are known a priori to be necessary [Kripke, by Mackie,P] |
| 4797 | Instead of being regularities, maybe natural laws are the weak a posteriori necessities of Kripke [Kripke, by Psillos] |
| 17037 | Physical necessity may be necessity in the highest degree [Kripke] |
| 4728 | Kripke separates necessary and a priori, proposing necessary a posteriori and contingent a priori examples [Kripke, by O'Grady] |
| 16990 | A priori = Necessary because we imagine all worlds, and we know without looking at actuality? [Kripke] |
| 9386 | The meter is defined necessarily, but the stick being one meter long is contingent a priori [Kripke] |
| 2408 | Kripke has demonstrated that some necessary truths are only knowable a posteriori [Kripke, by Chalmers] |
| 4960 | "'Hesperus' is 'Phosphorus'" is necessarily true, if it is true, but not known a priori [Kripke] |
| 4966 | Theoretical identities are between rigid designators, and so are necessary a posteriori [Kripke] |
| 13967 | Kripke's essentialist necessary a posteriori opened the gap between conceivable and really possible [Soames on Kripke] |
| 13970 | Kripke gets to the necessary a posteriori by only allowing conceivability when combined with actuality [Kripke, by Soames] |
| 16992 | Possible worlds aren't puzzling places to learn about, but places we ourselves describe [Kripke] |
| 16993 | If we discuss what might have happened to Nixon, we stipulate that it is about Nixon [Kripke] |
| 16998 | Transworld identification is unproblematic, because we stipulate that we rigidly refer to something [Kripke] |
| 17001 | A table in some possible world should not even be identified by its essential properties [Kripke] |
| 4952 | Identification across possible worlds does not need properties, even essential ones [Kripke] |
| 7761 | Test for rigidity by inserting into the sentence 'N might not have been N' [Kripke, by Lycan] |
| 7693 | Kripke avoids difficulties of transworld identity by saying it is a decision, not a discovery [Kripke, by Jacquette] |
| 5821 | Saying that natural kinds are 'rigid designators' is the same as saying they are 'indexical' [Kripke, by Putnam] |
| 14068 | If Kripke names must still denote a thing in a non-actual situation, the statue isn't its clay [Gibbard on Kripke] |
| 10436 | A rigid expression may refer at a world to an object not existing in that world [Kripke, by Sainsbury] |
| 4953 | We do not begin with possible worlds and place objects in them; we begin with objects in the real world [Kripke] |
| 4961 | It is a necessary truth that Elizabeth II was the child of two particular parents [Kripke] |
| 16986 | That there might have been unicorns is false; we don't know the circumstances for unicorns [Kripke] |
| 8259 | Kripke has breathed new life into the a priori/a posteriori distinction [Kripke, by Lowe] |
| 16989 | Rather than 'a priori truth', it is best to stick to whether some person knows it on a priori evidence [Kripke] |
| 4947 | A priori truths can be known independently of experience - but they don't have to be [Kripke] |
| 13975 | Kripke was more successful in illuminating necessity than a priority (and their relations to analyticity) [Kripke, by Soames] |
| 17048 | Analytic judgements are a priori, even when their content is empirical [Kripke] |
| 4948 | Intuition is the strongest possible evidence one can have about anything [Kripke] |
| 4958 | Identities like 'heat is molecule motion' are necessary (in the highest degree), not contingent [Kripke] |
| 4967 | It seems logically possible to have the pain brain state without the actual pain [Kripke] |
| 7430 | Kripke assumes that mind-brain identity designates rigidly, which it doesn't [Armstrong on Kripke] |
| 7867 | If consciousness could separate from brain, then it cannot be identical with brain [Kripke, by Papineau] |
| 3228 | Kripke says pain is necessarily pain, but a brain state isn't necessarily painful [Kripke, by Rey] |
| 5832 | Identity must be necessary, but pain isn't necessarily a brain state, so they aren't identical [Kripke, by Schwartz,SP] |
| 4968 | Identity theorists seem committed to no-brain-event-no-pain, and vice versa, which seems wrong [Kripke] |
| 8715 | Infinities expand the bounds of the conceivable; we explore concepts to explore conceivability [Cantor, by Friend] |
| 13454 | Cantor says (vaguely) that we abstract numbers from equal sized sets [Hart,WD on Cantor] |
| 16394 | Kripke derives accounts of reference and proper names from assumptions about worlds and essences [Stalnaker on Kripke] |
| 17874 | Kripke has a definitional account of kinds, but not of naming [Almog on Kripke] |
| 5822 | The important cause is not between dubbing and current use, but between the item and the speaker's information [Evans on Kripke] |
| 17033 | We may refer through a causal chain, but still change what is referred to [Kripke] |
| 4689 | Kripke makes reference a largely social matter, external to the mind of the speaker [Kripke, by McGinn] |
| 17504 | Kripke's theory is important because it gives a collective account of reference [Kripke, by Putnam] |
| 17035 | We refer through the community, going back to the original referent [Kripke] |
| 16988 | Descriptive reference shows how to refer, how to identify two things, and how to challenge existence [Kripke, by PG] |
| 17029 | It can't be necessary that Aristotle had the properties commonly attributed to him [Kripke] |
| 14893 | Rigid designation creates a puzzle - why do some necessary truths appear to be contingent? [Kripke, by Macià/Garcia-Carpentiro] |
| 8119 | Art aims only at beauty, of form, of idea, and (above all) of expression [Winckelmann, by Tolstoy] |
| 4963 | The properties that fix reference are contingent, the properties involving meaning are necessary [Kripke] |
| 17056 | Terms for natural kinds are very close to proper names [Kripke] |
| 17053 | Gold's atomic number might not be 79, but if it is, could non-79 stuff be gold? [Kripke] |
| 4964 | 'Cats are animals' has turned out to be a necessary truth [Kripke] |
| 6765 | Nominal essence may well be neither necessary nor sufficient for a natural kind [Kripke, by Bird] |
| 9387 | The scientific discovery (if correct) that gold has atomic number 79 is a necessary truth [Kripke] |
| 17054 | Scientific discoveries about gold are necessary truths [Kripke] |
| 17057 | Once we've found that heat is molecular motion, then that's what it is, in all possible worlds [Kripke] |
| 4965 | Science searches basic structures in search of essences [Kripke] |
| 10863 | Cantor proved that three dimensions have the same number of points as one dimension [Cantor, by Clegg] |
| 17050 | Tigers may lack all the properties we originally used to identify them [Kripke] |
| 17049 | 'Tiger' designates a species, and merely looking like the species is not enough [Kripke] |
| 17051 | The original concept of 'cat' comes from paradigmatic instances [Kripke] |
| 13465 | Only God is absolutely infinite [Cantor, by Hart,WD] |