|Quantifiers: in the predicate logic, quantifiers are the symbol combinations (Ex) and (x) for the set of objects to which one or more properties are attributed to. A) Existence quantification (Ex)(Fx) ("At least one x"). B) Universal quantification (x)(Fx) ("Everything is F"). For other objects e.g. y, z,… are chosen. E.g. (x) (Ey) (Fx > Gy). See also quantification, generalized quantifiers._____________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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|Hintikka I 15 ff
Language as a universal medium/LUM/Hintikka: the thesis of language as a universal medium (LUM) does not include the impossibility of semantics at all. It is just not possible to articulate. For example Frege has the opinion that the meaning of quantifiers cannot be appropriatly expressed linguistically.
I 57 ff
Object/property/relation/Wittgenstein/Tractatus/Hintikka: additional proof that Wittgenstein ascribes relations and properties to the objects should be the treatment of names. According to the opinion criticized by Hintikka they must stand on the same level.
If there were no categorical distinction between Wittgenstein's objects all quantifiers would necessarily have the same area and any fixing would be impossible.
Here, as so often, it is revealing what a philosopher does not know what he says: Quine has said that it shows which entities the philosopher lets apply, once he expresses his willingness to quantification. So Wittgenstein says:
"One can describe the world completely by completely generalized sentences, i.e. without assigning any name from the outset to a certain object. To then arrive at the customary way of expression one simply has to after an expression: "There is one and only one x, which..." And this x is a.
... Precisely because of this timelessness of simple objects their substantiality is not affected by the instability or even the rise and fall of the temporal objects, these changes do not affect the range of Wittgenstein's quantifiers.
Logic 2 level/Frege/Wittgenstein/Hintikka: quantifiers of higher level are accepted by both without any hesitation.
Quantifiers/logic/Tractatus/Wittgenstein/Hintikka: since existence in the Tractatus is inexpressible, it is something a priori. - ((s) then there are no quantifiers.) - E.g. Wittgenstein: if there are Schmitz and Meier in the room, they are necessarily there. - In contrast, Russell: with him the classes of objects are determined by our lexicon, our grammar. - ((s) about it is quantified.) - Wittgenstein: instead: disjunction._____________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.
Vorlesungen 1930-35 Frankfurt 1989
Das Blaue Buch - Eine Philosophische Betrachtung Frankfurt 1984
Tractatus Logico Philosophicus Frankfurt/M 1960
Jaakko and Merrill B. Hintikka
The Logic of Epistemology and the Epistemology of Logic Dordrecht 1989
J. Hintikka/M. B. Hintikka
Untersuchungen zu Wittgenstein Frankfurt 1996