display all the ideas for this combination of texts
4 ideas
13449 | We could have unrestricted quantification without having an all-inclusive domain [Rayo/Uzquiano] |
Full Idea: The possibility of unrestricted quantification does not immediately presuppose the existence of an all-inclusive domain. One could deny an all-inclusive domain but grant that some quantifications are sometimes unrestricted. | |
From: Rayo,A/Uzquiasno,G (Introduction to 'Absolute Generality' [2006], 1.1) | |
A reaction: Thus you can quantify over anything you like, but only from what is available. Eat what you like (in this restaurant). |
13450 | Absolute generality is impossible, if there are indefinitely extensible concepts like sets and ordinals [Rayo/Uzquiano] |
Full Idea: There are doubts about whether absolute generality is possible, if there are certain concepts which are indefinitely extensible, lacking definite extensions, and yielding an ever more inclusive hierarchy. Sets and ordinals are paradigm cases. | |
From: Rayo,A/Uzquiasno,G (Introduction to 'Absolute Generality' [2006], 1.2.1) |
10009 | Substitutional quantification is just a variant of Tarski's account [Wallace, by Baldwin] |
Full Idea: In a famous paper, Wallace argued that all interpretations of quantifiers (including the substitutional interpretation) are, in the end, variants of that proposed by Tarski (in 1936). | |
From: report of Wallace, J (On the Frame of Reference [1970]) by Thomas Baldwin - Interpretations of Quantifiers | |
A reaction: A significant-looking pointer. We must look elsewhere for Tarski's account, which will presumably subsume the objectual interpretation as well. The ontology of Tarski's account of truth is an enduring controversy. |
13453 | Perhaps second-order quantifications cover concepts of objects, rather than plain objects [Rayo/Uzquiano] |
Full Idea: If one thought of second-order quantification as quantification over first-level Fregean concepts [note: one under which only objects fall], talk of domains might be regimented as talk of first-level concepts, which are not objects. | |
From: Rayo,A/Uzquiasno,G (Introduction to 'Absolute Generality' [2006], 1.2.2) | |
A reaction: That is (I take it), don't quantify over objects, but quantify over concepts, but only those under which known objects fall. One might thus achieve naïve comprehension without paradoxes. Sound like fun. |