Combining Texts

All the ideas for 'The Problem of Empty Names', 'External and Internal Relations' and 'Intros to Russell's 'Essays in Analysis''

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4 ideas

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 / L. Paradox / 5. Paradoxes in Set Theory / b. Cantor's paradox

21554	Sets always exceed terms, so all the sets must exceed all the sets [Lackey]
	Full Idea: Cantor proved that the number of sets in a collection of terms is larger than the number of terms. Hence Cantor's Paradox says the number of sets in the collection of all sets must be larger than the number of sets in the collection of all sets.
	From: Douglas Lackey (Intros to Russell's 'Essays in Analysis' [1973], p.127)
	A reaction: The sets must count as terms in the next iteration, but that is a normal application of the Power Set axiom.

5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / c. Burali-Forti's paradox

21553	It seems that the ordinal number of all the ordinals must be bigger than itself [Lackey]
	Full Idea: The ordinal series is well-ordered and thus has an ordinal number, and a series of ordinals to a given ordinal exceeds that ordinal by 1. So the series of all ordinals has an ordinal number that exceeds its own ordinal number by 1.
	From: Douglas Lackey (Intros to Russell's 'Essays in Analysis' [1973], p.127)
	A reaction: Formulated by Burali-Forti in 1897.

8. Modes of Existence / A. Relations / 2. Internal Relations

21342	A relation is internal if two things possessing the relation could not fail to be related [Moore,GE, by Heil]
	Full Idea: Moore characterises internal relations modally, as those essential to their relata. If a and b are related R-wise, and R is an internal relation, a and b could not fail to be so related; otherwise R is external.
	From: report of G.E. Moore (External and Internal Relations [1919]) by John Heil - Relations 'Internal'
	A reaction: I don't think of Moore as an essentialist, but this fits the essentialist picture nicely, and is probably best paraphrased in terms of powers. Integers are the standard example of internal relations.