Combining Texts

Ideas for 'The Problem of Empty Names', 'Logicism and Ontological Commits. of Arithmetic' and 'Metaphysics: a very short introduction'

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 / 7. Second-Order Logic

10015	Higher-order logic may be unintelligible, but it isn't set theory [Hodes]
	Full Idea: Brand higher-order logic as unintelligible if you will, but don't conflate it with set theory.
	From: Harold Hodes (Logicism and Ontological Commits. of Arithmetic [1984], p.131)
	A reaction: [he gives Boolos 1975 as a further reference] This is simply a corrective, because the conflation of second-order logic with set theory is an idea floating around in the literature.

5. Theory of Logic / D. Assumptions for Logic / 4. Identity in Logic

10011	Identity is a level one relation with a second-order definition [Hodes]
	Full Idea: Identity should he considered a logical notion only because it is the tip of a second-order iceberg - a level 1 relation with a pure second-order definition.
	From: Harold Hodes (Logicism and Ontological Commits. of Arithmetic [1984])

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 / I. Semantics of Logic / 1. Semantics of Logic

10016	When an 'interpretation' creates a model based on truth, this doesn't include Fregean 'sense' [Hodes]
	Full Idea: A model is created when a language is 'interpreted', by assigning non-logical terms to objects in a set, according to a 'true-in' relation, but we must bear in mind that this 'interpretation' does not associate anything like Fregean senses with terms.
	From: Harold Hodes (Logicism and Ontological Commits. of Arithmetic [1984], p.131)
	A reaction: This seems like a key point (also made by Hofweber) that formal accounts of numbers, as required by logic, will not give an adequate account of the semantics of number-terms in natural languages.