Combining Texts

Ideas for 'The Problem of Empty Names', 'Russell's Mathematical Logic' and 'Logical Necessity: Some Issues'

unexpand these ideas     |    start again     |     choose another area for these texts

display all the ideas for this combination of texts

4 ideas

5. Theory of Logic / A. Overview of Logic / 8. Logic of Mathematics
10035 Mathematical Logic is a non-numerical branch of mathematics, and the supreme science [Gödel]
     Full Idea: 'Mathematical Logic' is a precise and complete formulation of formal logic, and is both a section of mathematics covering classes, relations, symbols etc, and also a science prior to all others, with ideas and principles underlying all sciences.
     From: Kurt Gödel (Russell's Mathematical Logic [1944], p.447)
     A reaction: He cites Leibniz as the ancestor. In this database it is referred to as 'theory of logic', as 'mathematical' seems to be simply misleading. The principles of the subject are standardly applied to mathematical themes.
5. Theory of Logic / F. Referring in Logic / 1. Naming / e. Empty names
18946 Unreflectively, we all assume there are nonexistents, and we can refer to them [Reimer]
     Full Idea: As speakers of the language, we unreflectively assume that there are nonexistents, and that reference to them is possible.
     From: Marga Reimer (The Problem of Empty Names [2001], p.499), quoted by Sarah Sawyer - Empty Names 4
     A reaction: Sarah Swoyer quotes this as a good solution to the problem of empty names, and I like it. It introduces a two-tier picture of our understanding of the world, as 'unreflective' and 'reflective', but that seems good. We accept numbers 'unreflectively'.
5. Theory of Logic / G. Quantification / 2. Domain of Quantification
10042 Reference to a totality need not refer to a conjunction of all its elements [Gödel]
     Full Idea: One may, on good grounds, deny that reference to a totality necessarily implies reference to all single elements of it or, in other words, that 'all' means the same as an infinite logical conjunction.
     From: Kurt Gödel (Russell's Mathematical Logic [1944], p.455)
5. Theory of Logic / K. Features of Logics / 8. Enumerability
10038 A logical system needs a syntactical survey of all possible expressions [Gödel]
     Full Idea: In order to be sure that new expression can be translated into expressions not containing them, it is necessary to have a survey of all possible expressions, and this can be furnished only by syntactical considerations.
     From: Kurt Gödel (Russell's Mathematical Logic [1944], p.448)
     A reaction: [compressed]