Combining Texts

All the ideas for 'Set Theory and related topics (2nd ed)', 'There is No A Priori (and reply)' and 'Review: Meinong 'Uber die Stellung...''

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4 ideas

4. Formal Logic / F. Set Theory ST / 3. Types of Set / e. Equivalence classes

8920	Equivalence relations are reflexive, symmetric and transitive, and classify similar objects [Lipschutz]
	Full Idea: A relation R on a non-empty set S is an equivalence relation if it is reflexive (for each member a, aRa), symmetric (if aRb, then bRa), and transitive (aRb and bRc, so aRc). It tries to classify objects that are in some way 'alike'.
	From: Seymour Lipschutz (Set Theory and related topics (2nd ed) [1998], 3.9)
	A reaction: So this is an attempt to formalise the common sense notion of seeing that two things have something in common. Presumably a 'way' of being alike is going to be a property or a part

9. Objects / A. Existence of Objects / 4. Impossible objects

21547	On Meinong's principles 'the existent round square' has to exist [Russell]
	Full Idea: To my contention that, on his principles, 'the existent round square' exists, Meinong replies that it is existent but does not exist. I must confess that I see no difference between existing and being existent, and I have no more to say on this head.
	From: Bertrand Russell (Review: Meinong 'Uber die Stellung...' [1907], p.93)
	A reaction: Russell is obviously invoking the famously dubious ontological argument for God's existence. Normally impossible objects are rejected because of contradictions, but there might also be category mistakes. 'The slow square'.

12. Knowledge Sources / A. A Priori Knowledge / 4. A Priori as Necessities

19565	How could the mind have a link to the necessary character of reality? [Devitt]
	Full Idea: What non-experiential link to reality could support insights into its necessary character?
	From: Michael Devitt (There is No A Priori (and reply) [2005], 4)
	A reaction: The key to it, I think, is your theory of mind. If you are a substance dualist, then connecting to such deep things looks fine, but if you are a reductive physicalist then it looks absurdly hopeful.

12. Knowledge Sources / A. A Priori Knowledge / 11. Denying the A Priori

19564	Some knowledge must be empirical; naturalism implies that all knowledge is like that [Devitt]
	Full Idea: It is overwhelmingly plausible that some knowledge is empirical. The attractive thesis of naturalism is that all knowledge is; there is only one way of knowing.
	From: Michael Devitt (There is No A Priori (and reply) [2005], 1)
	A reaction: How many ways for us to know seems to depend on what faculties we have. We lump our senses together under a single heading. The arrival of data is not the same as the arrival of knowledge. I'm unconvinced that naturalists like me must accept this.