Find counter arguments by entering NameVs… or …VsName.
The author or concept searched is found in the following 1 entries.
| Disputed term/author/ism | Author |
Entry |
Reference |
|---|---|---|---|
| Paradoxes | Grelling | Berka I 382 Heterology/Grelling/Nelson/Berka: Let j (M) be the word that refers to the concept defined by M. M is an element of the subset M* of the set of all sets M. j refers to the allocation, by which the elements of F (a set equivalent to M*) are allocated to the elements of M*. This word is either element of M or not. Def autological is the word when it is element of M. I.e. the word has the concept that it refers to, as a feature. heterological is the word, if it is not member of the set M. Antinomy/Grelling - the word "heterological" is in turn either autological or heterological. a) Assume that it is autological, then it is member of the class defined by the notion that refers to itself, it is therefore heterological, contrary to the assumption. b) Assume it is autological, then it is not member of the set, which refers to itself, it is therefore not heterological, again contrary to the assumption.(1) 1. K. Grelling/L. Nelson, Bemerkungen zu den Paradoxien von Rzussell und Burali-Forti, Abh. Fries. Sch, N. F. II, H. 3 (1908), 301-324; Abgedruckt in: Nelson, L , Beiträge zur Philosophie der Logik und Mathematik, Frankfurt/M. 1959, 59-86 |
Grelling I Kurt Grelling Leonard Nelson K. Grelling/L. Nelson, Bemerkungen zu den Paradoxien von Rzussell und Burali-Forti, Abh. Fries. Sch, N. F. II, H. 3 (1908), 301-324; Abgedruckt in: Nelson, L , Beiträge zur Philosophie der Logik und Mathematik, Frankfurt/M. 1959, 59-86 In Logik Texte, K. Berka/L. Kreiser Berlin 1986 Berka I Karel Berka Lothar Kreiser Logik Texte Berlin 1983 |
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| Disputed term/author/ism | Author Vs Author |
Entry |
Reference |
|---|---|---|---|
| substit. Quantific. | Quine Vs substit. Quantific. | V 158 VsSubstitutional Quantification/SQ/Quine: the SQ has been deemed unusable for the classic ML for a false reason: because of uncountability. The SQ does not accept nameless classes as values of variables. ((s) E.g. irrational numbers, real numbers, etc. do not have names, i.e. they cannot be Gödel numbered). I.e. SQ allows only a countable number of classes. Problem: Even the class of natural numbers has uncountably many sub-classes. And at some point we need numbers! KripkeVs: in reality there is no clear contradiction between SQ and hyper-countability! No function f lists all classes of natural numbers. Cantor shows this based on the class {n:~ (n e f(n))} which is not covered by the enumeration f. refQ: demands it in contrast to a function f enumerating all classes of natural numbers? It seems so at first glance: it seems you could indicate f by numbering all abstract terms for classes lexicographically. Vs: but the function that numbers the expressions is not quite the desired f. It is another function g. Its values are abstract terms, while the f, which would contradict the Cantor theorem, would have classes as values... V 159 Insertion character: does ultimately not mean that the classes are abstract terms! ((s) I.e. does not make the assumption of classes necessary). The cases of insertion are not names of abstract terms, but the abstract terms themselves! I.e. the alleged or simulated class names. Function f: that would contradict Cantor's theorem is rather the function with the property that f(n) is the class which is denoted by the n-th abstract term g(n). Problem: we cannot specify this function in the notation of the system. Otherwise we end up with Grelling's antinomy or that of Richard. That's just the feared conflict with Cantor's theorem. This can be refute more easily: by the finding that there is a class that is not denoted by any abstract term: namely the class (1) {x.x is an abstract term and is not a member of the class it denotes}. That leaves numbers and uncountability aside and relates directly to expressions and classes of expressions. (1) is obviously an abstract expression itself. The antinomy is trivial, because it clearly relies on the name relation. ((s) x is "a member of the class of abstract expressions and not a member of this class"). V 191 Substitutional Quantification/SQ/Nominalism/Quine: the nominalist might reply: alright, let us admit that the SQ does not clean the air ontologically, but still we win something with it: E.g. SQ about numbers is explained based on expressions and their insertion instead of abstract objects and reference. QuineVsSubstitutional Quantification: the expressions to be inserted are just as abstract entities as the numbers themselves. V 192 NominalismVsVs: the ontology of real numbers or set theory could be reduced to that of elementary number theory by establishing truth conditions for the sQ based on Gödel numbers. QuineVs: this is not nominalistic, but Pythagorean. This is not about the extrapolation of the concrete and abhorrence of the abstract, but about the acceptance of natural numbers and the refutal of the most transcendent nnumbers. As Kronecker says: "The natural numbers were created by God, the others are the work of man." QuineVs: but even that does not work, we have seen above that the SQ about classes is, as a matter of principle, incompatible with the object quantification over objects. V 193 VsVs: the quantification over objects could be seen like that as well. QuineVs: that was not possible because there are not enough names. Zar could be taught RZ coordination, but that does not explain language learning. Ontology: but now that we are doing ontology, could the coordinates help us? QuineVs: the motivation is, however, to re-interpret the SQ about objects to eliminate the obstacle of SQ about classes. And why do we want to have classes? The reason was quasi nominalistic, in the sense of relative empiricism. Problem: if the relative empiricism SQ talks about classes, it also speaks for refQ about objects. This is because both views are closest to the genetic origins. Coordinates: this trick will be a poor basis for SQ about objects, just like (see above) SQ about numbers. Substitutional/Referential Quantification/Charles Parsons/Quine: Parsons has proposed a compromise between the two: according to this, for the truth of an existential quantification it is no longer necessary to have a true insertion, there only needs to be an insertion that contains free object variables and is fulfilled by any values of the same. Universal quantification: Does accordingly no longer require only the truth of all insertions that do not contain free variables. V 194 It further requires that all insertions that contain free object variables are fulfilled by all values. This restores the law of the single sub-classes and the interchangeability of quantifiers. Problem: this still suffers from impredicative abstract terms. Pro: But it has the nominalistic aura that the refQ completely lacks, and will satisfy the needs of set theory. XI 48 SQ/Ontology/Quine/Lauener: the SQ does not make any ontological commitment in so far as the inserted names do not need to designate anything. I.e. we are not forced to assume values of the variables. XI 49 QuineVsSubstitutional Quantification: we precisely obscure the ontology by that fact that we cannot get out of the linguistic. XI 51 SQ/Abstract Entities/Quine/Lauener: precisely because the exchange of quantifiers is prohibited if one of the quantifiers referential, but the other one is substitutional, we end up with refQ and just with that we have to admit the assumption of abstract entities. XI 130 Existence/Ontology/Quine/Lauener: with the saying "to be means to be the value of a bound variable" no language dependency of existence is presumed. The criterion of canonical notation does not suppose an arbitrary restriction, because differing languages - e.g. Schönfinkel's combinator logic containing no variables - are translatable into them. Ontological Relativity/Lauener: then has to do with the indeterminacy of translation. VsSubstitutional Quantification/Quine/Lauener: with it we remain on a purely linguistic level, and thus repeal the ontological dimension. But for the variables not singular terms are used, but the object designated by the singular term. ((s) referential quantification). Singular Term/Quine/Lauener: even after eliminating the singular terms the objects remain as the values of variables. XI 140 QuineVsSubstitutional Quantification: is ontologically disingenuous. |
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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