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Disputed term/author/ism | Author |
Entry |
Reference |
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Syntax | Geach | I 116
Syntax: replacing salva congruitate: the word chain remains correct when it is replaced.
QuineVs: Replacing changes syntax: e.g. Copernicus was a complete idiot, if and only if the earth is adisk. - different ranges: a) Copernicus with predicate + sentence b) complex predicate. Then there is no ambiguous word chain, but different analyzes are possible. Ambiguity: "An astronomer is a great idiot iff the earth is flat" can be seen as an operator (like negation). Different brackets are possible. Syntax/Quine/Geach: Quine's 1st Syntactic insight: spurious names: these are a problem of range - for real names the problem does not exist. >Names/Quine, >Range/Quine, >Improper names. GeachVsQuine: he, himself blurs the distinction by regarding names as abbreviations of certain descriptions. >Descriptions/Quine. I 120
3rd Syntactic insight of Quine: E.g. "lx (2x² + 3x³)".
This function of a number: twice its square plus three times its third power - such complex descriptions can be eliminated by usage definition. (Russell):> Relative-clause.I 126
4th Syntactic insight of Quine: Introducing a predicate by a schema letter F.
>Schematic letters/Quine.Problem: E.g.: "Every sentence or its opposite is true" must not become "(Every sentence is true) or (Every sentence is not true)". Solution: "F() is then -__ or __s opposite is true". Geach: sub-clauses (relative-clauses) and pronouns are not mere substitutes. - This is even a mistake in modern logic books. >Clauses, >Substitution, >Proxy. |
Gea I P.T. Geach Logic Matters Oxford 1972 |

Disputed term/author/ism | Author Vs Author |
Entry |
Reference |
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Pythagoras | Quine Vs Pythagoras | XII 75
Löwenheim/Skolem/Strong Form/Axiom of Choice/Ontology/Reduction/Ontological Relativity/Quine: (early form): Thesis: if a theory is true and has a hyper-countable object range, then everything except for a countable section is superfluous, in the sense that it can be eliminated from the range of the variables, without any sentence becoming false.
I.e. all acceptable theories can be reduced to countable ontologies. And these, in turn, to a specific ontology of natural numbers. For that you take the list, as far as it is explicitly known, as SF. And even if the list is not known, it exists. Accordingly, we can interpret all our objects as natural numbers, even though the list number ((s) the name) is not always known.Ontology: could we not establish a Pythagorean multi-purpose ontology once and for all? Pythagorean Ontology/Terminology/Quine: consists either only of numbers or only of bodies, or of sets, etc. Problem: Suppose we had such an ontology and somebody offered us something that would have appeared as an ontological reduction prior to our decision for the Pythagorean ontology, namely a method by which all things of a certain type A are superfluous in future theories, while the remaining portion would still be infinite. XII 76
In the new Pythagorean framework his discovery would still retain its essential content, even though it could no longer be called a reduction; it would be only a maneuver in which some numbers - we do not even know which - would lose a number property corresponding to A.
VsPythagoreism: it shows that an all-engulfing Pythagoreanism is not attractive, because it only offers new and more obscure versions of old methods and problems.Solution: Ontological relativity, relativistic theory. It's simply pointless to speak of the ontology of a theory in absolute terms. ((s) i.e. in this case to assert that everything is a number.) (>inside/outside). The relevant predicates, e.g. "number", "set", "body" or whatever, would be distinguishable in the frame theory, however, by the roles they play in the laws of this theory. Quine: an ontological reduction is only interesting if we can specify an SF. If we have the axiom of choice and even a sign for a general selection operator, can we then specify an SF that concretizes the Löwenheim theorem? 1) We divide the object range into a countable number of equivalence classes, each with indistinguishable objects. (Indistinguishability Classes). We can dispense with all members of every equivalence class, except one. 2) Then we'll make use of the axiom of choice to pick out a survivor from each equivalence class. XII 77
Quine: if this were possible, we could write down a representative function with Hilbert's selection operator.
Löwenheim/Quine: but the proof of the theorem has a different structure: it does not seem to justify the assumption that a representative function could be formulated in any theory that maps a hyper-countable range in a countable one.At first glance, such an SF is of course impossible: it would have to be reversibly unique to provide different real numbers with different function values. And this contradicts the mapping of a hyper-countable into a countable range, because it cannot be reversibly unambiguous. ((s) Because it has to assign the same value to two arguments somehow.) Framework Theory/Stronger/Weaker/Theory/Ontology/Quine: there are three strength levels of requirements regarding what is said about the ontology of the object theory within the framework theory. 1) weakest requirement to the framework theory: is sufficient if we do not want any reduction, but only explain about what things the theory is. I.e. we translate the object theory into the framework theory. I.e. we make translation proposals, with which, however, the inscrutability of reference still is to be taken into account. The two theories may even be identical, e.g. if some terms are explained by definitions by other terms of the same language. XII 78
2) stronger: in case of reduction by an SF, here the frame theory must assume the non-reduced range. (see above, analogy to raa, reductio ad absurdum).
3) strongest requirements: in case of reductions according to Löwenheim: i.e. from a hyper-countable to a countable range: here, the SF must be from a truly stronger frame theory. I.e. we can no longer accept it in the spirit of the raa.Conclusion: this thwarts an argument from the Löwenheim theorem in favor of Pythagoreanism. Ontological Relativity/Finite Range/Quine: in a finite range, ontological relativity is trivial. Since instead of quantification you can assume finite conjunctions or disjunctions, the variables and thus also the question of their value range also disappear. Even the distinction between names and other signs is eliminated. Therefore, an ontology for a finite theory about named objects is pointless. That we have just talked about it is because we were moving in a broader context. Names/Quine: are distinguished by the fact that they may be used for variables. |
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 InFrom a Logical Point of View, Cambridge, MA 1953 Quine VII (b) W. V. A. Quine Two dogmas of empiricism InFrom a Logical Point of View, Cambridge, MA 1953 Quine VII (c) W. V. A. Quine The problem of meaning in linguistics InFrom a Logical Point of View, Cambridge, MA 1953 Quine VII (d) W. V. A. Quine Identity, ostension and hypostasis InFrom a Logical Point of View, Cambridge, MA 1953 Quine VII (e) W. V. A. Quine New foundations for mathematical logic InFrom a Logical Point of View, Cambridge, MA 1953 Quine VII (f) W. V. A. Quine Logic and the reification of universals InFrom a Logical Point of View, Cambridge, MA 1953 Quine VII (g) W. V. A. Quine Notes on the theory of reference InFrom a Logical Point of View, Cambridge, MA 1953 Quine VII (h) W. V. A. Quine Reference and modality InFrom a Logical Point of View, Cambridge, MA 1953 Quine VII (i) W. V. A. Quine Meaning and existential inference InFrom 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 InZur 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 |