Combining Texts

All the ideas for 'Actualism and Possible Worlds', 'Remarks on axiomatised set theory' and 'On the Jewish Question'

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13 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets

17879	Axiomatising set theory makes it all relative [Skolem]
	Full Idea: Axiomatising set theory leads to a relativity of set-theoretic notions, and this relativity is inseparably bound up with every thoroughgoing axiomatisation.
	From: Thoralf Skolem (Remarks on axiomatised set theory [1922], p.296)

5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems

17878	If a 1st-order proposition is satisfied, it is satisfied in a denumerably infinite domain [Skolem]
	Full Idea: Löwenheim's theorem reads as follows: If a first-order proposition is satisfied in any domain at all, it is already satisfied in a denumerably infinite domain.
	From: Thoralf Skolem (Remarks on axiomatised set theory [1922], p.293)

6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics

17880	Integers and induction are clear as foundations, but set-theory axioms certainly aren't [Skolem]
	Full Idea: The initial foundations should be immediately clear, natural and not open to question. This is satisfied by the notion of integer and by inductive inference, by it is not satisfied by the axioms of Zermelo, or anything else of that kind.
	From: Thoralf Skolem (Remarks on axiomatised set theory [1922], p.299)
	A reaction: This is a plea (endorsed by Almog) that the integers themselves should be taken as primitive and foundational. I would say that the idea of successor is more primitive than the integers.

6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism

17881	Mathematician want performable operations, not propositions about objects [Skolem]
	Full Idea: Most mathematicians want mathematics to deal, ultimately, with performable computing operations, and not to consist of formal propositions about objects called this or that.
	From: Thoralf Skolem (Remarks on axiomatised set theory [1922], p.300)

7. Existence / A. Nature of Existence / 3. Being / a. Nature of Being

14664	Necessary beings (numbers, properties, sets, propositions, states of affairs, God) exist in all possible worlds [Plantinga]
	Full Idea: A 'necessary being' is one that exists in every possible world; and only some objects - numbers, properties, pure sets, propositions, states of affairs, God - have this distinction.
	From: Alvin Plantinga (Actualism and Possible Worlds [1976], 2)
	A reaction: This a very odd list, though it is fairly orthodox among philosophers trained in modern modal logic. At the very least it looks rather parochial to me.

9. Objects / D. Essence of Objects / 1. Essences of Objects

14666	Socrates is a contingent being, but his essence is not; without Socrates, his essence is unexemplified [Plantinga]
	Full Idea: Socrates is a contingent being; his essence, however, is not. Properties, like propositions and possible worlds, are necessary beings. If Socrates had not existed, his essence would have been unexemplified, but not non-existent.
	From: Alvin Plantinga (Actualism and Possible Worlds [1976], 4)
	A reaction: This is a distinctive Plantinga view, of which I can make little sense. I take it that Socrates used to have an essence. Being dead, the essence no longer exists, but when we talk about Socrates it is largely this essence to which we refer. OK?

10. Modality / E. Possible worlds / 1. Possible Worlds / a. Possible worlds

14662	Possible worlds clarify possibility, propositions, properties, sets, counterfacts, time, determinism etc. [Plantinga]
	Full Idea: The idea of possible worlds has delivered insights on logical possibility (de dicto and de re), propositions, properties and sets, counterfactuals, time and temporal relations, causal determinism, the ontological argument, and the problem of evil.
	From: Alvin Plantinga (Actualism and Possible Worlds [1976], Intro)
	A reaction: This date (1976) seems to be the high-water mark for enthusiasm about possible worlds. I suppose if we just stick to 'insights' rather than 'answers' then the big claim might still be acceptable. Which problems are created by possible worlds?

10. Modality / E. Possible worlds / 1. Possible Worlds / d. Possible worlds actualism

16472	Plantinga's actualism is nominal, because he fills actuality with possibilia [Stalnaker on Plantinga]
	Full Idea: Plantinga's critics worry that the metaphysics is actualist in name only, since it is achieved only by populating the actual world with entities whose nature is explained in terms of merely possible things that would exemplify them if anything did.
	From: comment on Alvin Plantinga (Actualism and Possible Worlds [1976]) by Robert C. Stalnaker - Mere Possibilities 4.4
	A reaction: Plantinga seems a long way from the usual motivation for actualism, which is probably sceptical empiricism, and building a system on what is smack in front of you. Possibilities have to be true, though. That's why you need dispositions in actuality.

19. Language / C. Assigning Meanings / 8. Possible Worlds Semantics

16469	Plantinga has domains of sets of essences, variables denoting essences, and predicates as functions [Plantinga, by Stalnaker]
	Full Idea: The domains in Plantinga's interpretation of Kripke's semantics are sets of essences, and the values of variables are essences. The values of predicates have to be functions from possible worlds to essences.
	From: report of Alvin Plantinga (Actualism and Possible Worlds [1976]) by Robert C. Stalnaker - Mere Possibilities 4.4
	A reaction: I begin to think this is quite nice, as long as one doesn't take the commitment to the essences too seriously. For 'essence' read 'minimal identity'? But I take essences to be more than minimal, so use identities (which Kripke does?).

16470	Plantinga's essences have their own properties - so will have essences, giving a hierarchy [Stalnaker on Plantinga]
	Full Idea: For Plantinga, essences are entities in their own right and will have properties different from what instantiates them. Hence he will need individual essences of individual essences, distinct from the essences. I see no way to avoid a hierarchy of them.
	From: comment on Alvin Plantinga (Actualism and Possible Worlds [1976]) by Robert C. Stalnaker - Mere Possibilities 4.4
	A reaction: This sounds devastating for Plantinga, but it is a challenge for traditional Aristotelians. Only a logician suffers from a hierarchy, but a scientist might have to live with an essence, which contains a super-essence.

19. Language / D. Propositions / 1. Propositions

14663	Are propositions and states of affairs two separate things, or only one? I incline to say one [Plantinga]
	Full Idea: Are there two sorts of thing, propositions and states of affairs, or only one? I am inclined to the former view on the ground that propositions have a property, truth or falsehood, not had by states of affairs.
	From: Alvin Plantinga (Actualism and Possible Worlds [1976], 1)
	A reaction: Might a proposition be nothing more than an assertion that a state of affairs obtains? It would then pass his test. The idea that a proposition is a complex of facts in the external world ('Russellian' propositions?) quite baffles me.

24. Political Theory / D. Ideologies / 9. Communism

21989	Man is dominated by money, which is the essence of his alienation [Marx]
	Full Idea: Money is the alienated essence of man's labour and life, and this alien essence dominates him as he worships it.
	From: Karl Marx (On the Jewish Question [1844], p.60), quoted by Peter Singer - Marx 3
	A reaction: Presumably this is inherit in the very nature of money, rather than in the wickedness of capitalists who control it. But money is not inherently alienting for the rich, or for the comfortable bourgeoisie (is it?).

25. Social Practice / C. Rights / 1. Basis of Rights

20519	Marxists say liberal rights are confrontational, and liberal equality is a sham [Marx, by Wolff,J]
	Full Idea: For Marx liberal rights are egoistic rights of separation: they encourage each individual to view others as limitations to his or her freedom. ....Liberals set up a sham community of 'equal' citizens.
	From: report of Karl Marx (On the Jewish Question [1844]) by Jonathan Wolff - An Introduction to Political Philosophy (Rev) 4 'Marxist'
	A reaction: The point is that equality in law does not ensure equal treatment in daily life. I suppose a liberal right can be seen as an opt-out clause for some aspect of society.