15649
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In semantic theories of truth, the predicate is in an object-language, and the definition in a metalanguage [Halbach]
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Full Idea:
In semantic theories of truth (Tarski or Kripke), a truth predicate is defined for an object-language. This definition is carried out in a metalanguage, which is typically taken to include set theory or another strong theory or expressive language.
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From:
Volker Halbach (Axiomatic Theories of Truth (2005 ver) [2005], 1)
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A reaction:
Presumably the metalanguage includes set theory because that connects it with mathematics, and enables it to be formally rigorous. Tarski showed, in his undefinability theorem, that the meta-language must have increased resources.
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15651
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Instead of saying x has a property, we can say a formula is true of x - as long as we have 'true' [Halbach]
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Full Idea:
Quantification over (certain) properties can be mimicked in a language with a truth predicate by quantifying over formulas. Instead of saying that Tom has the property of being a poor philosopher, we can say 'x is a poor philosopher' is true of Tom.
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From:
Volker Halbach (Axiomatic Theories of Truth (2005 ver) [2005], 1.1)
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A reaction:
I love this, and think it is very important. He talks of 'mimicking' properties, but I see it as philosophers mistakenly attributing properties, when actually what they were doing is asserting truths involving certain predicates.
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21598
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Austin revealed many meanings for 'vague': rough, ambiguous, general, incomplete... [Austin,JL, by Williamson]
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Full Idea:
Austin's account brought out the variety of features covered by 'vague' in different contexts: roughness, ambiguity, imprecision, lack of detail, generality, inaccuracy, incompleteness. Even 'vague' is vague.
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From:
report of J.L. Austin (Sense and Sensibilia [1962], p.125-8) by Timothy Williamson - Vagueness 3.1
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A reaction:
Some of these sound the same. Maybe Austin distinguishes them.
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18383
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Plantinga says there is just this world, with possibilities expressed in propositions [Plantinga, by Armstrong]
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Full Idea:
Plantinga rejects other possible worlds, but adds to our world an uncountable multitude of sets of propositions, each set a way that the world might have been, but is in fact not. (Roughly, for each Lewis world, Plantinga has such a set).
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From:
report of Alvin Plantinga (The Nature of Necessity [1974]) by David M. Armstrong - Truth and Truthmakers 07.2
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A reaction:
To me it seems as ontologically extravagant to postulate unexpressed propositions as to postulate concrete possible worlds. I think the best line is that there is just the actual world, with the possibilities implied in its dispositions.
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11891
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Possibilities for an individual can only refer to that individual, in some possible world [Plantinga, by Mackie,P]
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Full Idea:
Plantinga says for an individual to exist with certain properties in some possible world is simply for it to be true that, had that possible world obtained, that individual would have existed with those properties.
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From:
report of Alvin Plantinga (The Nature of Necessity [1974]) by Penelope Mackie - How Things Might Have Been 5.1
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A reaction:
This is intended to dissolve the problem of transworld identity, and is certainly a flat rejection of counterparts. I take the point to be that the individual is the key element in defining the possible world, so can't possibly be different.
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20704
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A possible world contains a being of maximal greatness - which is existence in all worlds [Plantinga, by Davies,B]
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Full Idea:
Plantinga reformulates Malcolm's argument thus: 1) There is a possible world in which there exists a being with maximal greatness, 2) A being has maximal greatness in a world only if it exists in every world.
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From:
report of Alvin Plantinga (The Nature of Necessity [1974], p.213) by Brian Davies - Introduction to the Philosophy of Religion 4 'b Descartes'
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A reaction:
This is only Plantinga's starting point, which says nothing about the nature of God, but only that this 'great' being exists in all worlds. I would like to know why it is a 'being' rather than a 'thing'. Malcolm says if it is possible it is necessary.
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