Combining Philosophers

Ideas for Confucius, Paul Bernays and David M. Armstrong

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4 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.
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])