Combining Philosophers

Ideas for Confucius, Paul Bernays and David M. Armstrong

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3 ideas

4. Formal Logic / F. Set Theory ST / 1. Set Theory

18396	The set theory brackets { } assert that the member is a unit [Armstrong]
	Full Idea: The idea is that braces { } attribute to an entity the place-holding, or perhaps determinable, property of unithood.
	From: David M. Armstrong (Truth and Truthmakers [2004], 09.5)
	A reaction: I like this. There is Socrates himself, then there is my concept , and then there is the singleton {Socrates}. Those braces must add something to the concept. You can't add braces to Socrates himself.

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

18393	For 'there is a class with no members' we don't need the null set as truthmaker [Armstrong]
	Full Idea: The null class is useful in formal set theory, but I hope that does not require that there be a thing called the null class which is truthmaker for the strange proposition .
	From: David M. Armstrong (Truth and Truthmakers [2004], 09.1)
	A reaction: It is not quite clear why it doesn't, but then it is not quite clear to philosophers what the status of the null set is, in comparison with sets that have members.

4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory

10304	Very few things in set theory remain valid in intuitionist mathematics [Bernays]
	Full Idea: Very few things in set theory remain valid in intuitionist mathematics.
	From: Paul Bernays (On Platonism in Mathematics [1934])