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Completeness  Quine  X 80 Completeness Theorem/deductive/Quantifier Logic/Quine: (B) A scheme fulfilled by each model is provable. Theorem (B) can be proven for many proof methods. If we imagine such a method, then (II) follows from (B). (II) If a scheme is fulfilled by every model, then e is true for all insertions of propositions. X 83 Proof Procedure/Evidence Method/Quine: some complete ones do not necessarily refer to schemata, but can also be applied directly to the sentences X 84 that emerge from the scheme by insertion. Such methods produce true sentences directly from other true sentences. Then we can leave aside schemata and validity and define logical truth as the proposition produced by these proof procedures. 1. VsQuine: this usually triggers a protest: the property "to be provable by a certain method of proof" is uninteresting in itself. It is only interesting because of the completeness theorem, which allows to equate provability with logical truth. 2. VsQuine: if one defines logical truth indirectly by reference to a suitable method of proof, one deprives the completeness theorem of its basis. It becomes empty. QuineVsVs: the danger does not exist at all: the principle of completeness in the formulation (B) does not depend on how we define logical truth, because it is not mentioned at all! Part of its meaning, however, is that it shows that we can define logical truth by merely describing the method of proof, without losing anything of what makes logical truth interesting in the first place. X 100 Fake Theory/quantities/classes/relation/Quine: is masked pure logic. Mathematics: begins when we accept the element relationship "ε" as a real predicate and accept classes as values of the quantified variables. Then we leave the realm of complete proof procedure. Logic: quantifier logic is complete. Mathematics: is incomplete. >Logical Truth/Quine. X 119 Intuitionism/Quine: gained buoyancy through Goedel's incompleteness evidence. XIII 157 Predicate Logic/completeness/Goedel/Quine: Goedel proved its completeness in 1930. 
Quine I W.V.O. Quine Word and Object, Cambridge/MA 1960 German Edition: Wort und Gegenstand Stuttgart 1980 Quine II W.V.O. Quine Theories and Things, Cambridge/MA 1986 German Edition: Theorien und Dinge Frankfurt 1985 Quine III W.V.O. Quine Methods of Logic, 4th edition Cambridge/MA 1982 German Edition: Grundzüge der Logik Frankfurt 1978 Quine V W.V.O. Quine The Roots of Reference, La Salle/Illinois 1974 German Edition: Die Wurzeln der Referenz Frankfurt 1989 Quine VI W.V.O. Quine Pursuit of Truth, Cambridge/MA 1992 German Edition: Unterwegs zur Wahrheit Paderborn 1995 Quine VII W.V.O. Quine From a logical point of view Cambridge, Mass. 1953 Quine VII (a) W. V. A. Quine On what there is In From a Logical Point of View, Cambridge, MA 1953 Quine VII (b) W. V. A. Quine Two dogmas of empiricism In From a Logical Point of View, Cambridge, MA 1953 Quine VII (c) W. V. A. Quine The problem of meaning in linguistics In From a Logical Point of View, Cambridge, MA 1953 Quine VII (d) W. V. A. Quine Identity, ostension and hypostasis In From a Logical Point of View, Cambridge, MA 1953 Quine VII (e) W. V. A. Quine New foundations for mathematical logic In From a Logical Point of View, Cambridge, MA 1953 Quine VII (f) W. V. A. Quine Logic and the reification of universals In From a Logical Point of View, Cambridge, MA 1953 Quine VII (g) W. V. A. Quine Notes on the theory of reference In From a Logical Point of View, Cambridge, MA 1953 Quine VII (h) W. V. A. Quine Reference and modality In From a Logical Point of View, Cambridge, MA 1953 Quine VII (i) W. V. A. Quine Meaning and existential inference In From a Logical Point of View, Cambridge, MA 1953 Quine VIII W.V.O. Quine Designation and Existence, in: The Journal of Philosophy 36 (1939) German Edition: Bezeichnung und Referenz In Zur Philosophie der idealen Sprache, J. Sinnreich (Hg) München 1982 Quine IX W.V.O. Quine Set Theory and its Logic, Cambridge/MA 1963 German Edition: Mengenlehre und ihre Logik Wiesbaden 1967 Quine X W.V.O. Quine The Philosophy of Logic, Cambridge/MA 1970, 1986 German Edition: Philosophie der Logik Bamberg 2005 Quine XII W.V.O. Quine Ontological Relativity and Other Essays, New York 1969 German Edition: Ontologische Relativität Frankfurt 2003 Quine XIII Willard Van Orman Quine Quiddities Cambridge/London 1987 
Definiteness  Ayer  I 288 Determinateness / Ayer: defined by containment: that my shoes are blacc entails that they are not brown, but not vice versa  that I write entails that anybody writes, but not vice versa  Def Determinateness / Ayer: a statement is absolutely specific in L, if no statement can be made that contains this statement, without being included in it  (> mininal / Chisholm)  then hierarchy constructible in L  problem: you may make a statement beconme more specific, by connecting another with it (conjunction,> Goodman: "fake theory" (> slingshot argument)  I 289 > Big fact: expressed by a conjunction of all independent true statements. 
Ayer I Alfred J. Ayer "Truth" in: The Concept of a Person and other Essays, London 1963 In Wahrheitstheorien, Gunnar Skirbekk Frankfurt/M. 1977 Ayer II Alfred Jules Ayer Language, Truth and Logic, London 1936 In Philosophie im 20. Jahrhundert, A. Hügli/P. Lübcke Ayer III Alfred Jules Ayer "The Criterion of Truth", Analysis 3 (1935), pp. 2832 In Theories of Truth, Paul Horwich Aldershot 1994 
Slingshot Argument  Ayer  I 288 Assertiveness /Determination/ Ayer:defined by being contained: that my shoes are black, entails that they are not brown, but not vice versa  that I write entails that someone writes, but not vice versa.  ((s) something specific entails something vague.)  Def Assertiveness / Ayer: a statement is absolutely specific in S if no statement can be made that contains this statement, without being contained in it.  ((s) > Def minimal / Chisholm)  then there is a constructible hierarchy in S.  Problem: you can make a statement of specific when connecting another statement with it. (Conjunction, > Goodman: fake theory (> slingshot argument)  I 289 > "Big fact": expressed by a conjunction of all independent true statements . 
Ayer I Alfred J. Ayer "Truth" in: The Concept of a Person and other Essays, London 1963 In Wahrheitstheorien, Gunnar Skirbekk Frankfurt/M. 1977 Ayer II Alfred Jules Ayer Language, Truth and Logic, London 1936 In Philosophie im 20. Jahrhundert, A. Hügli/P. Lübcke Ayer III Alfred Jules Ayer "The Criterion of Truth", Analysis 3 (1935), pp. 2832 In Theories of Truth, Paul Horwich Aldershot 1994 
Theories  Quine  I 34 Theory does not have to be based on intention, it was internalized in the past.  I 56 QuineVsVerification: it is pointless to equate a sentence within the theory with one outside  Intertheoretically no meaning  no additions with "or" (Cf. Goodman, Davidson, "fake theories").  I 57 For the time being, we retain our beliefs in theory creation.  I 74 Theory: Carnap: Terms  Quine: sentences.  I 393 Theory is only predication, universal quantification, truth function (for derived properties)  general term (for primary properties)  (no "because").  I 429 Theory: are isolated systems, mass point, infinitesimal size: behavior in every case more typical, the closer you get to zero, therefore it is acceptable  but not allowed in ontology  unlike geometric object: Position of mass points made no sense  therefore not individuateable  no identity. (> Quine, Word and Object, 1960, §52.)  I 431 Paraphrase (no synonymy): Newton could be reformulated relativistically  like Church: "true in a higher sense"  sometimes acceptable.  I 432 Theory: Structure of meaning, not choice of objects (Ramsey, Russell) Quine: new: even with physical objects they are also theoretical  Reason: sentences are semantically primary.  II 45 Equivalence of theories: is discovered when one discovers the possibility of reinterpretation  both true  but possibly logically incompatible.  VI 134 Theory/Empirically equivalent/logically equivalent/Quine: Two theories can be logically incompatible and yet empirically equivalent. E.g. Riemann/Euclidean geometry  Case 1: even untransformable theories (in the same terminology, where each implies certain sentences that the other one does not imply) are empirically equivalent  no problem  Case 2: additional theoretical terms  Case 3: logically incompatible  Davidson: can be traced back to case 2  because contentious sentences depend on theoretical terms which are not empirical  therefore they are still empirically equivalent  Solution: theoretical term in question in two spellings (according to theory)  that makes them logically compatible.  VI 136 Empirically equivalent/logically incompatible/Theory/Quine: Case 2: (theory for global worlds without context embedding):  solution: eliminate exotic terms (without predictive power)  Important argument: then it is about consistency (otherwise QuineVsConsistency theory)  Elimination: justified by the fact that we have no other access to the truth except our own theory.  VI 139 Empirically equivalent/logically incompatible/Theory/Quine: Variant/Davidson: Both theories are valid, truth predicate: in comprehensive, neutral language  QuineVsDavidson: how much further should the variables reach then?  We need a stop, because we do not want a third theory  "everything different"/Important argument: the two systems definitely describe the same world  purely verbal question.  XII 70 Theory form/Quine: after abstraction of the meanings of the nonlogical vocabulary and the value range of the variables  reinterpretation of the theory form provides models. 
Quine I W.V.O. Quine Word and Object, Cambridge/MA 1960 German Edition: Wort und Gegenstand Stuttgart 1980 Quine II W.V.O. Quine Theories and Things, Cambridge/MA 1986 German Edition: Theorien und Dinge Frankfurt 1985 Quine III W.V.O. Quine Methods of Logic, 4th edition Cambridge/MA 1982 German Edition: Grundzüge der Logik Frankfurt 1978 Quine V W.V.O. Quine The Roots of Reference, La Salle/Illinois 1974 German Edition: Die Wurzeln der Referenz Frankfurt 1989 Quine VI W.V.O. Quine Pursuit of Truth, Cambridge/MA 1992 German Edition: Unterwegs zur Wahrheit Paderborn 1995 Quine VII W.V.O. Quine From a logical point of view Cambridge, Mass. 1953 Quine VII (a) W. V. A. Quine On what there is In From a Logical Point of View, Cambridge, MA 1953 Quine VII (b) W. V. A. Quine Two dogmas of empiricism In From a Logical Point of View, Cambridge, MA 1953 Quine VII (c) W. V. A. Quine The problem of meaning in linguistics In From a Logical Point of View, Cambridge, MA 1953 Quine VII (d) W. V. A. Quine Identity, ostension and hypostasis In From a Logical Point of View, Cambridge, MA 1953 Quine VII (e) W. V. A. Quine New foundations for mathematical logic In From a Logical Point of View, Cambridge, MA 1953 Quine VII (f) W. V. A. Quine Logic and the reification of universals In From a Logical Point of View, Cambridge, MA 1953 Quine VII (g) W. V. A. Quine Notes on the theory of reference In From a Logical Point of View, Cambridge, MA 1953 Quine VII (h) W. V. A. Quine Reference and modality In From a Logical Point of View, Cambridge, MA 1953 Quine VII (i) W. V. A. Quine Meaning and existential inference In From a Logical Point of View, Cambridge, MA 1953 Quine VIII W.V.O. Quine Designation and Existence, in: The Journal of Philosophy 36 (1939) German Edition: Bezeichnung und Referenz In Zur Philosophie der idealen Sprache, J. Sinnreich (Hg) München 1982 Quine IX W.V.O. Quine Set Theory and its Logic, Cambridge/MA 1963 German Edition: Mengenlehre und ihre Logik Wiesbaden 1967 Quine X W.V.O. Quine The Philosophy of Logic, Cambridge/MA 1970, 1986 German Edition: Philosophie der Logik Bamberg 2005 Quine XII W.V.O. Quine Ontological Relativity and Other Essays, New York 1969 German Edition: Ontologische Relativität Frankfurt 2003 Quine XIII Willard Van Orman Quine Quiddities Cambridge/London 1987 
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Ayer, A. J.  Hempel. Vs Ayer, A. J.  II 112 Demand for Partial Confirmability/(2.3)/Ayer: his criterion is supposed to determine by content that a statement S has an empirical sense if observation statements can be derived from S together with suitable auxiliary hypotheses, which cannot be derived from the auxiliary hypotheses alone. HempelVsAyer: Although this is more similar to the logical structure of the verification, it is much too permeable. ((s) >QuineDuhem Thesis/QDT: allows just any auxiliary hypothesis). Hempel: E.g. "If the absolute is perfect, then this (!) apple is red". This allows the derivation of the observation statements, which obviously does not follow from the auxiliary hypothesis. ((s) But it does not allow to call a green apple red). Stace: "principle of observable species": "The facts that are denied or affirmed, must be of a type or class so that it is logically possible to observe some facts immediately, which are cases of that class or species. If a statement asserts or denies facts about a class, so that it is not logically possible to observe them directly, then the statement is not significant. II 113 HempelVsStace: this is undecided, he does not say how we determine those classes. And that is precisely what the criterion was supposed to do. Moreover, we can always form a class that contains the fact f together with the fact which is expressed by an observation statement at our discretion, which makes f a member of a basically observable class!. Therefore, the first part of the principle, like Ayers original wording, already includes everything. Criterion of Meaning/Ayer: Additionally: a statement has a meaning if it can be derived from observation statements together with an auxiliary hypothesis. HempelVsAyer: too permeable ((s) >"fake theories".) Modification of 2.3/Ayer: limits the auxiliary hypothesis to statements that are either analytical or can be verified independently. Conjunction/HempelVsAyer: this new criterion fulfills the demand for full falsifiability of an arbitrary conjunction S u N and thus has unintended empirical significance for this one. ChurchVsAyer: Suppose there are any three observation statements, none of which implies any of the others alone, then follows for an entirely arbitrary statement S that either itself or its negation has an empirical sense according to Ayers new criterion. 
