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18084
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When successive variable values approach a fixed value, that is its 'limit' [Cauchy]
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Full Idea:
When the values successively attributed to the same variable approach indefinitely a fixed value, eventually differing from it by as little as one could wish, that fixed value is called the 'limit' of all the others.
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From:
Augustin-Louis Cauchy (Cours d'Analyse [1821], p.19), quoted by Philip Kitcher - The Nature of Mathematical Knowledge 10.4
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A reaction:
This seems to be a highly significan proposal, because you can now treat that limit as a number, and adds things to it. It opens the door to Cantor's infinities. Is the 'limit' just a fiction?
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14664
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Necessary beings (numbers, properties, sets, propositions, states of affairs, God) exist in all possible worlds [Plantinga]
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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.
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From:
Alvin Plantinga (Actualism and Possible Worlds [1976], 2)
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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.
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14666
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Socrates is a contingent being, but his essence is not; without Socrates, his essence is unexemplified [Plantinga]
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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.
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From:
Alvin Plantinga (Actualism and Possible Worlds [1976], 4)
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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?
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14662
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Possible worlds clarify possibility, propositions, properties, sets, counterfacts, time, determinism etc. [Plantinga]
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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.
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From:
Alvin Plantinga (Actualism and Possible Worlds [1976], Intro)
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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?
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16472
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Plantinga's actualism is nominal, because he fills actuality with possibilia [Stalnaker on Plantinga]
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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.
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From:
comment on Alvin Plantinga (Actualism and Possible Worlds [1976]) by Robert C. Stalnaker - Mere Possibilities 4.4
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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.
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16469
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Plantinga has domains of sets of essences, variables denoting essences, and predicates as functions [Plantinga, by Stalnaker]
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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.
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From:
report of Alvin Plantinga (Actualism and Possible Worlds [1976]) by Robert C. Stalnaker - Mere Possibilities 4.4
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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?).
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16470
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Plantinga's essences have their own properties - so will have essences, giving a hierarchy [Stalnaker on Plantinga]
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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.
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From:
comment on Alvin Plantinga (Actualism and Possible Worlds [1976]) by Robert C. Stalnaker - Mere Possibilities 4.4
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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.
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14663
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Are propositions and states of affairs two separate things, or only one? I incline to say one [Plantinga]
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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.
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From:
Alvin Plantinga (Actualism and Possible Worlds [1976], 1)
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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.
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