## Philosophy Lexicon of Arguments | |||

Substitutional Quantification: the substitutional quantification is concerned with the determination of whether linguistic expressions can be formed for a situation. E.g. "There is a true sentence that ...". In contrast, the referential quantification - the form of quantification normally used in predicate logic - tells us something about objects. E.g. "There is at least one object x with the property ..." or "For all objects x applies ...". The decisive difference between the two types of quantification is that, in the case of the possible replacement of a linguistic expression by another expression, a so-called substitution class must be assumed which cannot exist in the case of objects since the everyday subject area is not classified into classes is. E.g. you can replace a table by some box, but you cannot replace the word table by any available word. See also referential quantification, quantification, substitution, inference, implication, stronger/weaker, logic, systems, semantic rise._____________ Annotation: The above characterizations of concepts are neither definitions nor exhausting presentations of problems related to them. Instead, they are intended to give a short introduction to the contributions below. – Lexicon of Arguments. | |||

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Books on Amazon |
V 140 Substitutional quantification/Quine: is open for other grammatical categories than just singular term but has other truth function. - Referential quantification/Referential Quantification: here, the objects do not even need to be specifiable by name. --- V 141 Language learning: first substitution quantification: from relative pronouns. - Later: referential quantification: because of categorical sentences. - Substitution quantification: would be absurd: that every inserted name that verifies Fx also verifies Gx - absurd: that each apple or rabbit would have to have a name or a singular description. - Most objects do not have names. --- V 140 Substitutional Quantification/Referential Quantification/Truth Function/Quine: referential universal quantification: can be falsified by one single object, even though this is not specifiable by a name. - The same substitutional universal quantification: in contrast, remains true. - Existential quantification: referential: may be true due to a non-assignable value. - The same in substitutional sense: does not apply for lack of an assignable example. --- V 146f Substitutional Quantification/Quine: Problem: Blind spot: substitutional universal quantification: E.g. none of the substitution cases should be rejected, but some require abstention. - Existential quantification: E.g. none of the cases is to be approved, but some abstention is in order.- then neither agree nor abstain. (Equivalent to the alternation). --- Ad V 170 Substitutional Quantification/(s): related to the quantification over apparent classes in Quine’s meta language? --- V 175 Numbers/Classes/Quantification/Ontology/Substitutional quantification/Quine: first substitutional quantification through numbers and classes. - Problem: Numbers and classes can then not be eliminated. - Can also be used as an object quantification (referential quantification) if one allows every number to have a successor. - ((s) with substitution quantification each would have to have a name. Class quantifier becomes object quantifier if one allows the exchange of the quantifiers (AQU/AQU/ - EQu/EQu) - so the law of the partial classes of one was introduced. --- X 124 Substitutional quantification/Quine: requires name for the values of the variables. - referential quantification/(s) speaks of objects at most. - Definition truth/Substitutional Quantification/Barcan/Quine: applying-Quantification - is true iff at least one of its cases, which is obtained by omitting the quantifier and inserting a name for the variable, is true. - Problem: almost never enough names for the objects in a not overly limited world. - E.g. no Goedel numbers for irrational numbers. - Then substitution quantification can be wrong, because there is no name for the object, but the referential quantification can be true at the same time - i.e. both are not extensionally equal. --- X 124 Names/logic/Substitutional Quantification/Quine: Problem: never enough names for all objects in the world: e.g. if a set is not determined by an open sentence, it also has no name - otherwise E.g. Name a, Determination: x e a - E.g. irrational numbers cannot be attributed to integers. - (s) > substitution class. --- XII 79f Substitutional Quantification/Quine: Here the variables are placeholders for words of any syntactic category (except names) - Important argument: then there is no way to distinguish names from the rest of the vocabulary and real referential variables. --- XII 80 From others (indistinguishability). - ((s) Does that mean that one cannot distinguish fragments like object and greater than, and that structures like "there is a greater than" would be possible?). --- XII 80 Substitutional Quantification/Quine: Problem: Assuming an infinite range of named objects. - Then it is possible to show for each substitution result of a name the truth of a formula and simultaneously to refute the universal quantification of the formula. - (everyone/all). - Then we have shown that the range has at least one unnamed object. - ((s) (> not enough names) -. Therefore QuineVsSubstitutional Quantification. E.g. assuming the range contained the real name - Then not all could be named, but the unnamed cannot be separated. - The theory can always be strengthened to name a certain number, but not all - referential quantification: attributes nameless objects to itself - trick: (see above) every substitution result with a name is true, but makes universal quantification false ((s) thus an infinite number of objects secured) - A theory of real names must be based on referential quantification. _____________ Explanation of symbols: Roman numerals indicate the source, arabic numerals indicate the page number. The corresponding books are indicated on the right hand side. ((s)…): Comment by the sender of the contribution. |
Q I W.V.O. Quine Wort und Gegenstand Stuttgart 1980 Q II W.V.O. Quine Theorien und Dinge Frankfurt 1985 Q III W.V.O. Quine Grundzüge der Logik Frankfurt 1978 Q IX W.V.O. Quine Mengenlehre und ihre Logik Wiesbaden 1967 Q V W.V.O. Quine Die Wurzeln der Referenz Frankfurt 1989 Q VI W.V.O. Quine Unterwegs zur Wahrheit Paderborn 1995 Q VII W.V.O. Quine From a logical point of view Cambridge, Mass. 1953 Q VIII W.V.O. Quine Bezeichnung und Referenz InZur Philosophie der idealen Sprache, J. Sinnreich (Hg), München 1982 Q X W.V.O. Quine Philosophie der Logik Bamberg 2005 Q XII W.V.O. Quine Ontologische Relativität Frankfurt 2003 |

> Counter arguments against **Quine**

> Counter arguments in relation to **Substitutional Quantification**

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Ed. Martin Schulz, access date 2017-06-26