182 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] |
15327 | Kripke's semantic theory has actually inspired promising axiomatic theories [Kripke, by Horsten] |
15343 | Kripke offers a semantic theory of truth (involving models) [Kripke, by Horsten] |
14967 | Certain three-valued languages can contain their own truth predicates [Kripke, by Gupta] |
14966 | The Tarskian move to a metalanguage may not be essential for truth theories [Kripke, by Gupta] |
16328 | Kripke classified fixed points, and illuminated their use for clarifications [Kripke, by Halbach] |
10163 | Propositional modal logic has been proved to be complete [Kripke, by Feferman/Feferman] |
10559 | Kripke's modal semantics presupposes certain facts about possible worlds [Kripke, by Zalta] |
16985 | Possible worlds allowed the application of set-theoretic models to modal logic [Kripke] |
10760 | With possible worlds, S4 and S5 are sound and complete, but S1-S3 are not even sound [Kripke, by Rossberg] |
16189 | The variable domain approach to quantified modal logic invalidates the Barcan Formula [Kripke, by Simchen] |
15132 | The Barcan formulas fail in models with varying domains [Kripke, by Williamson] |
10073 | There cannot be a set theory which is complete [Smith,P] |
10616 | Second-order arithmetic can prove new sentences of first-order [Smith,P] |
10075 | A 'partial function' maps only some elements to another set [Smith,P] |
10074 | A 'total function' maps every element to one element in another set [Smith,P] |
10605 | Two functions are the same if they have the same extension [Smith,P] |
10612 | An argument is a 'fixed point' for a function if it is mapped back to itself [Smith,P] |
10076 | The 'range' of a function is the set of elements in the output set created by the function [Smith,P] |
10615 | The Comprehension Schema says there is a property only had by things satisfying a condition [Smith,P] |
10595 | A 'theorem' of a theory is a sentence derived from the axioms using the proof system [Smith,P] |
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] |
9175 | We may fix the reference of 'Cicero' by a description, but thereafter the name is rigid [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] |
9171 | The function of names is simply to refer [Kripke] |
16982 | A man has two names if the historical chains are different - even if they are the same! [Kripke] |
10792 | The substitutional quantifier is not in competition with the standard interpretation [Kripke, by Marcus (Barcan)] |
10602 | A 'natural deduction system' has no axioms but many rules [Smith,P] |
10613 | No nice theory can define truth for its own language [Smith,P] |
10079 | A 'bijective' function has one-to-one correspondence in both directions [Smith,P] |
10077 | A 'surjective' ('onto') function creates every element of the output set [Smith,P] |
10078 | An 'injective' ('one-to-one') function creates a distinct output element from each original [Smith,P] |
10070 | If everything that a theory proves is true, then it is 'sound' [Smith,P] |
10596 | A theory is 'sound' iff every theorem is true (usually from true axioms and truth-preservation) [Smith,P] |
10086 | Soundness is true axioms and a truth-preserving proof system [Smith,P] |
10069 | A theory is 'negation complete' if one of its sentences or its negation can always be proved [Smith,P] |
10598 | A theory is 'negation complete' if it proves all sentences or their negation [Smith,P] |
10597 | 'Complete' applies both to whole logics, and to theories within them [Smith,P] |
10609 | Two routes to Incompleteness: semantics of sound/expressible, or syntax of consistency/proof [Smith,P] |
10080 | 'Effective' means simple, unintuitive, independent, controlled, dumb, and terminating [Smith,P] |
10087 | A theory is 'decidable' if all of its sentences could be mechanically proved [Smith,P] |
10088 | Any consistent, axiomatized, negation-complete formal theory is decidable [Smith,P] |
10081 | A set is 'enumerable' is all of its elements can result from a natural number function [Smith,P] |
10083 | A set is 'effectively enumerable' if a computer could eventually list every member [Smith,P] |
10084 | A finite set of finitely specifiable objects is always effectively enumerable (e.g. primes) [Smith,P] |
10085 | The set of ordered pairs of natural numbers <i,j> is effectively enumerable [Smith,P] |
10601 | The thorems of a nice arithmetic can be enumerated, but not the truths (so they're diffferent) [Smith,P] |
10600 | Being 'expressible' depends on language; being 'capture/represented' depends on axioms and proof system [Smith,P] |
10599 | For primes we write (x not= 1 ∧ ∀u∀v(u x v = x → (u = 1 ∨ v = 1))) [Smith,P] |
10610 | The reals contain the naturals, but the theory of reals doesn't contain the theory of naturals [Smith,P] |
10619 | The truths of arithmetic are just true equations and their universally quantified versions [Smith,P] |
13007 | Archimedes defined a straight line as the shortest distance between two points [Archimedes, by Leibniz] |
10608 | The number of Fs is the 'successor' of the Gs if there is a single F that isn't G [Smith,P] |
10618 | All numbers are related to zero by the ancestral of the successor relation [Smith,P] |
10849 | Baby arithmetic covers addition and multiplication, but no general facts about numbers [Smith,P] |
10850 | Baby Arithmetic is complete, but not very expressive [Smith,P] |
10852 | Robinson Arithmetic (Q) is not negation complete [Smith,P] |
10851 | Robinson Arithmetic 'Q' has basic axioms, quantifiers and first-order logic [Smith,P] |
10068 | Natural numbers have zero, unique successors, unending, no circling back, and no strays [Smith,P] |
10603 | The logic of arithmetic must quantify over properties of numbers to handle induction [Smith,P] |
10604 | Incompleteness results in arithmetic from combining addition and successor with multiplication [Smith,P] |
10848 | Multiplication only generates incompleteness if combined with addition and successor [Smith,P] |
14896 | Kripke's metaphysics (essences, kinds, rigidity) blocks the slide into sociology [Kripke, by Ladyman/Ross] |
10617 | The 'ancestral' of a relation is a new relation which creates a long chain of the original relation [Smith,P] |
17000 | We might fix identities for small particulars, but it is utopian to hope for such things [Kripke] |
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] |
11868 | A different piece of wood could have been used for that table; constitution isn't identity [Wiggins on 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] |
16981 | With the necessity of self-identity plus Leibniz's Law, identity has to be an 'internal' relation [Kripke] |
17044 | A relation can clearly be reflexive, and identity is the smallest reflexive relation [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] |
4942 | The indiscernibility of identicals is as self-evident as the law of contradiction [Kripke] |
16999 | A vague identity may seem intransitive, and we might want to talk of 'counterparts' [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] |
17058 | What many people consider merely physically necessary I consider completely necessary [Kripke] |
4970 | What is often held to be mere physical necessity is actually metaphysical necessity [Kripke] |
17059 | Unicorns are vague, so no actual or possible creature could count as a unicorn [Kripke] |
16984 | I don't think possible worlds reductively reveal the natures of modal operators etc. [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] |
9385 | The very act of designating of an object with properties gives knowledge of a contingent truth [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] |
9174 | It is necessary that this table is not made of ice, but we don't know it a priori [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] |
4943 | Instead of talking about possible worlds, we can always say "It is possible that.." [Kripke] |
4950 | Possible worlds are useful in set theory, but can be very misleading elsewhere [Kripke] |
16992 | Possible worlds aren't puzzling places to learn about, but places we ourselves describe [Kripke] |
16983 | Probability with dice uses possible worlds, abstractions which fictionally simplify things [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] |
9172 | A 'rigid designator' designates the same object in all possible worlds [Kripke] |
17003 | Kaplan's 'Dthat' is a useful operator for transforming a description into a rigid designation [Kripke] |
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] |
9173 | We cannot say that Nixon might have been a different man from the one he actually was [Kripke] |
9176 | Modal statements about this table never refer to counterparts; that confuses epistemology and metaphysics [Kripke] |
9221 | The best known objection to counterparts is Kripke's, that Humphrey doesn't care if his counterpart wins [Kripke, by Sider] |
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] |
17052 | The a priori analytic truths involving fixing of reference are contingent [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] |
4969 | I regard the mind-body problem as wide open, and extremely confusing [Kripke] |
4967 | It seems logically possible to have the pain brain state without the actual pain [Kripke] |
9177 | Identity theorists must deny that pains can be imagined without brain states [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] |
9178 | Pain, unlike heat, is picked out by an essential property [Kripke] |
19269 | 'Quus' means the same as 'plus' if the ingredients are less than 57; otherwise it just produces 5 [Kripke] |
19271 | No rule can be fully explained [Kripke] |
16383 | Puzzled Pierre has two mental files about the same object [Recanati on Kripke] |
7305 | Kripke's Wittgenstein says meaning 'vanishes into thin air' [Kripke, by Miller,A] |
19270 | If you ask what is in your mind for following the addition rule, meaning just seems to vanish [Kripke] |
17874 | Kripke has a definitional account of kinds, but not of naming [Almog on Kripke] |
16394 | Kripke derives accounts of reference and proper names from assumptions about worlds and essences [Stalnaker 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] |
4956 | A description may fix a reference even when it is not true of its object [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] |
17032 | Even if Gödel didn't produce his theorems, he's still called 'Gödel' [Kripke] |
11076 | Community implies assertability-conditions rather than truth-conditions semantics [Kripke, by Hanna] |
14893 | Rigid designation creates a puzzle - why do some necessary truths appear to be contingent? [Kripke, by Maciŕ/Garcia-Carpentiro] |
11075 | The sceptical rule-following paradox is the basis of the private language argument [Kripke, by Hanna] |
17056 | Terms for natural kinds are very close to proper names [Kripke] |
4963 | The properties that fix reference are contingent, the properties involving meaning are necessary [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] |
17050 | Tigers may lack all the properties we originally used to identify them [Kripke] |
17051 | The original concept of 'cat' comes from paradigmatic instances [Kripke] |
17049 | 'Tiger' designates a species, and merely looking like the species is not enough [Kripke] |