Combining Texts

All the ideas for 'The Ages of the World', 'works' and 'Actualism and Possible Worlds'

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11 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
Von Neumann defines each number as the set of all smaller numbers [Neumann, by Blackburn]
     Full Idea: Von Neumann defines each number as the set of all smaller numbers.
     From: report of John von Neumann (works [1935]) by Simon Blackburn - Oxford Dictionary of Philosophy p.280
4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory
Von Neumann wanted mathematical functions to replace sets [Neumann, by Benardete,JA]
     Full Idea: Von Neumann suggested that functions be pressed into service to replace sets.
     From: report of John von Neumann (works [1935]) by José A. Benardete - Metaphysics: the logical approach Ch.23
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
Von Neumann defined ordinals as the set of all smaller ordinals [Neumann, by Poundstone]
     Full Idea: At age twenty, Von Neumann devised the formal definition of ordinal numbers that is used today: an ordinal number is the set of all smaller ordinal numbers.
     From: report of John von Neumann (works [1935]) by William Poundstone - Prisoner's Dilemma 02 'Sturm'
     A reaction: I take this to be an example of an impredicative definition (not predicating something new), because it uses 'ordinal number' in the definition of ordinal number. I'm guessing the null set gets us started.
7. Existence / A. Nature of Existence / 3. Being / a. Nature of Being
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
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
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
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
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?).
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
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.
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / e. Character
We don't choose our characters, yet we still claim credit for the actions our characters perform [Schelling]
     Full Idea: Nobody has chosen their character; and yet this does not stop anybody attributing the action which follows from his character to themself as a free action.
     From: Friedrich Schelling (The Ages of the World [1810], I.93)
     A reaction: This pinpoints a very nice ambivalence about our attitudes to our own characters. We all have some pride and shame about who we are, without having chosed who we are. At least when we are young. But we make the bed we lie in.