Find counter arguments by entering NameVs… or …VsName.
The author or concept searched is found in the following 4 entries.
| Disputed term/author/ism | Author |
Entry |
Reference |
|---|---|---|---|
| Consistency | Henkin | Quine IX 224 Henkin: shows the consistency of a ω-contradictory (omega-contradictory) system. (Also Goedel and Tarski). Just interpret "F" as true for all but those objects x that fulfill (7). (7) x ε N, x ≠ 0, x ≠ 1, x ≠ 2... ad infinitum >Sets/Henkin. A theory that is ω-contradictory seems unacceptable even if it is consistent. But according to Henkin, it is easy to see that the term and its definition are misleading. If a system is consistent and yet allows "Ex(x e N u ~Fx)" and "F0", "F1"...all as theorems, and if we guarantee the interpretation of "0" , "1" etc. as names of numbers, then the problem seems to be to interpret "N" as "number" and not more comprehensive. Henkin: shows that "N" can be interpreted as N containing extras even under the most favorable circumstances. (See Sets/Henkin) If the system is ω-contradictory, N must even be interpreted that way. ((s) "Extras": e.g. "...and their successors"). Sometimes it is then possible to limit "N" so that it avoids the extras, and sometimes this is not possible. For example, for every formifiable condition that is verifiably met by 0,1,2... ad infinitum, there is another condition that we can prove is also met by 0,1,2... and yet not by all things that meet the first condition. This is the chronic form of ω-contradictoriness that cannot be cured by an improved version of "N". (Quine: "numerically insegregative"). >Löwenheim. Def Omega-contradictory/(w)/Goedel: (Goedel 1931) is a system when there is a formula "Fx" such that any one of the statements "F0", "F1", "F2",... can be proved ad infinitum in the system, but also "Ex(x ε N and ~Fx)". >Contradictions, >Proofs, >Provability. |
Henkin I Leon Henkin Retracing elementary mathematics New York 1962 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 |
| Quantification | Quine | I 283 Indefinite singular term: quantification disappears in "something is an x such that", "everything is an x ...". I 316 Paraphrases by quantification uncover false existence assumptions. >Existence/Quine VI 41 Quantification/Quine/(s) is a postulation of objects. X 94 Quantification/variable/Quine: in the open sentence after the quantifier "x" stands at a point where a name could be - E.g. also names of numbers - the sentences do not say that names or numbers are walking- "EF" does not say, "is a predicate such and such", but an object that is called by the predicate is so and so" - this object could be a property (pro Frege ) - VsRussell: but not a predicate - mixing up of representation (schema) and quantification (talking about). >Predicates/Quine X 104 Apparent Quantification/Quine: Apparent values of the new quantifiable variables " p", " q ", etc.: truth values - then sentences are exceptionally names of these apparent objects - we can quantify over apparent objects - apparent objects arise from context definition. >Objects/Quine Lauener XI 38 Quantification/Lauener/(s): truth values can only be attributed to quantified sentences. >Truth Value/Quine |
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 Q XI H. Lauener Willard Van Orman Quine München 1982 |
| Symbols | Bigelow | I 176 Symbol/blackening/Bigelow/Pargetter: some authors believe that symbols are mere blackenings on paper (e.g. numbers) or mere noises. >Blackening of the paper, >Numbers, >Formalism. BigelowVsFormalism: Problem: on the one hand there are too many symbols and on the other hand there are not enough. Not enough: for very large numbers there is no corresponding blackening or noise. Too many: for smaller numbers there are too many different ways of representation, more than numbers can be distinguished. Example "4", "four", "IV". >Numerals, >Names of numbers, >Representation, >Presentation. |
Big I J. Bigelow, R. Pargetter Science and Necessity Cambridge 1990 |
| Variables | Frege | II 81 Variable/mathematics/logic/Frege: variables have nothing to do with change. Arithmetic: arithmetic has nothing to do with quantities like e.g. lengths - only with numbers. II 83 f Variable/Frege: a variable is not a name of an "indeterminate" or "variable" number. "X" has no properties (only in context). "Indeterminately": indeterminately is not an adjective but an adverb to the process of the calculation. "Universality": universality is not a meaning but a suggestion. Letters are rarely names of numbers: e.g. π, i and e are not variables but constants. >Indeterminacy. Solution: e.g. "n" is used in the antecedent of a conditional sentence. II 85 Number/Frege: e.g. "a variable takes a value": here, the number must play both roles: as an object it becomes a variable, as a property it is called value. >Numbers. II 87 Variable/designation/description/Frege: "x" designates nothing! X only hints at numbers. Therefore, e.g. "x² + 3x" designates nothing. The whole function only indicates. On the other hand, "sin" (sinus) is a sign that designates. But not a law yet. Law/Frege: e.g. "y = sin x". >Denotation. |
F I G. Frege Die Grundlagen der Arithmetik Stuttgart 1987 F II G. Frege Funktion, Begriff, Bedeutung Göttingen 1994 F IV G. Frege Logische Untersuchungen Göttingen 1993 |
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| Disputed term/author/ism | Author Vs Author |
Entry |
Reference |
|---|---|---|---|
| Frege, G. | Black Vs Frege, G. | II 124 Numbers/BlackVsPlato/BlackVsFrege: false Platonism: imagining them as "extraordinary" or "special", "eternal" objects. II 125 Grammatically, however, the names of numbers (numerals) differ in important aspects from the name of physical objects. E.g. "Two people came in": Here "two" is public. Adverb. This can be transformed into "one and one: "a man came in and then another." This is not possible in the case of "red". (> Paraphrase). BlackVsFrege: These grammatical facts show that numbers are no "special kinds of objects". Frege: the great Frege, however, made no elementary mistake by accepting it anyeay, but he was never really satisfied with it. |
Black I Max Black "Meaning and Intention: An Examination of Grice’s Views", New Literary History 4, (1972-1973), pp. 257-279 In Handlung, Kommunikation, Bedeutung, G. Meggle (Hg) Frankfurt/M 1979 Black II M. Black The Labyrinth of Language, New York/London 1978 German Edition: Sprache. Eine Einführung in die Linguistik München 1973 Black III M. Black The Prevalence of Humbug Ithaca/London 1983 Black IV Max Black "The Semantic Definition of Truth", Analysis 8 (1948) pp. 49-63 In Truth and Meaning, Paul Horwich Aldershot 1994 |
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