Combining Philosophers

Ideas for Hermarchus, Timon and David M. Armstrong

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3 ideas

4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / g. System S4

15544	If what is actual might have been impossible, we need S4 modal logic [Armstrong, by Lewis]
	Full Idea: Armstrong says what is actual (namely a certain roster of universals) might have been impossible. Hence his modal logic is S4, without the 'Brouwersche Axiom'.
	From: report of David M. Armstrong (A Theory of Universals [1978]) by David Lewis - Armstrong on combinatorial possibility 'The demand'
	A reaction: So p would imply possibly-not-possibly-p.

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.