Combining Texts

All the ideas for 'Elucidation of some points in E.Schröder', 'Frege on Apriority' and 'works'

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4 ideas

4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set

14238	A class is an aggregate of objects; if you destroy them, you destroy the class; there is no empty class [Frege]
	Full Idea: A class consists of objects; it is an aggregate, a collective unity, of them; if so, it must vanish when these objects vanish. If we burn down all the trees of a wood, we thereby burn down the wood. Thus there can be no empty class.
	From: Gottlob Frege (Elucidation of some points in E.Schröder [1895], p.212), quoted by Oliver,A/Smiley,T - What are Sets and What are they For?
	A reaction: This rests on Cantor's view of a set as a collection, rather than on Dedekind, which allows null and singleton sets.

6. Mathematics / A. Nature of Mathematics / 2. Geometry

9159	You can't simply convert geometry into algebra, as some spatial content is lost [Burge]
	Full Idea: Although one can translate geometrical propositions into algebraic ones and produce equivalent models, the meaning of geometrical propositions seems to me to be thereby lost. Pure geometry involves spatial content, even if abstracted from physical space.
	From: Tyler Burge (Frege on Apriority [2000], IV)
	A reaction: This supports Frege's view (against Quine) that geometry won't easily fit into the programme of logicism. I agree with Burge. You would be focusing on the syntax of geometry, and leaving out the semantics.

9. Objects / D. Essence of Objects / 5. Essence as Kind

13074	Only natural kinds and their members have real essences [Suárez, by Cover/O'Leary-Hawthorne]
	Full Idea: On Suarez's account, only natural kinds and their members have real essences.
	From: report of Francisco Suárez (works [1588]) by Cover,J/O'Leary-Hawthorne,J - Substance and Individuation in Leibniz 1.3.1 n21
	A reaction: Interesting. Rather than say that everything is a member of some kind, we leave quirky individuals out, with no essence at all. What is the status of the very first exemplar of a given kind?

26. Natural Theory / C. Causation / 4. Naturalised causation

7563	The old 'influx' view of causation says it is a flow of accidental properties from A to B [Suárez, by Jolley]
	Full Idea: The 'influx' model of causation says that causes involve a process of contagion, as it were; when the kettle boils, the gas infects the water inside the kettle with its own 'individual accident' of heat, which literally flows from one to the other.
	From: report of Francisco Suárez (works [1588]) by Nicholas Jolley - Leibniz Ch.2
	A reaction: This nicely captures the scholastic target of Hume's sceptical thinking on the subject. However, see Idea 2542, where the idea of influx has had a revival. It is hard to see how the water could change if it didn't 'catch' something from the gas.