8476
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Axiomatization simply picks from among the true sentences a few to play a special role [Orenstein]
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Full Idea:
In axiomatizing, we are merely sorting out among the truths of a science those which will play a special role, namely, serve as axioms from which we derive the others. The sentences are already true in a non-conventional or ordinary sense.
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From:
Alex Orenstein (W.V. Quine [2002], Ch.5)
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A reaction:
If you were starting from scratch, as Euclidean geometers may have felt they were doing, you might want to decide which are the simplest truths. Axiomatizing an established system is a more advanced activity.
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8452
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Traditionally, universal sentences had existential import, but were later treated as conditional claims [Orenstein]
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Full Idea:
In traditional logic from Aristotle to Kant, universal sentences have existential import, but Brentano and Boole construed them as universal conditionals (such as 'for anything, if it is a man, then it is mortal').
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From:
Alex Orenstein (W.V. Quine [2002], Ch.2)
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A reaction:
I am sympathetic to the idea that even the 'existential' quantifier should be treated as conditional, or fictional. Modern Christians may well routinely quantify over angels, without actually being committed to them.
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10529
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If Hume's Principle can define numbers, we needn't worry about its truth [Fine,K]
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Full Idea:
Neo-Fregeans have thought that Hume's Principle, and the like, might be definitive of number and therefore not subject to the usual epistemological worries over its truth.
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From:
Kit Fine (Precis of 'Limits of Abstraction' [2005], p.310)
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A reaction:
This seems to be the underlying dream of logicism - that arithmetic is actually brought into existence by definitions, rather than by truths derived from elsewhere. But we must be able to count physical objects, as well as just counting numbers.
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10530
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Hume's Principle is either adequate for number but fails to define properly, or vice versa [Fine,K]
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Full Idea:
The fundamental difficulty facing the neo-Fregean is to either adopt the predicative reading of Hume's Principle, defining numbers, but inadequate, or the impredicative reading, which is adequate, but not really a definition.
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From:
Kit Fine (Precis of 'Limits of Abstraction' [2005], p.312)
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A reaction:
I'm not sure I understand this, but the general drift is the difficulty of building a system which has been brought into existence just by definition.
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8473
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The logicists held that is-a-member-of is a logical constant, making set theory part of logic [Orenstein]
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Full Idea:
The question to be posed is whether is-a-member-of should be considered a logical constant, that is, does logic include set theory. Frege, Russell and Whitehead held that it did.
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From:
Alex Orenstein (W.V. Quine [2002], Ch.5)
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A reaction:
This is obviously the key element in the logicist programme. The objection seems to be that while first-order logic is consistent and complete, set theory is not at all like that, and so is part of a different world.
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8458
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Just individuals in Nominalism; add sets for Extensionalism; add properties, concepts etc for Intensionalism [Orenstein]
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Full Idea:
Modest ontologies are Nominalism (Goodman), admitting only concrete individuals; and Extensionalism (Quine/Davidson) which admits individuals and sets; but Intensionalists (Frege/Carnap/Church/Marcus/Kripke) may have propositions, properties, concepts.
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From:
Alex Orenstein (W.V. Quine [2002], Ch.3)
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A reaction:
I don't like sets, because of Idea 7035. Even the ontology of individuals could collapse dramatically (see the ideas of Merricks, e.g. 6124). The intensional items may be real enough, but needn't have a place at the ontological high table.
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10527
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An abstraction principle should not 'inflate', producing more abstractions than objects [Fine,K]
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Full Idea:
If an abstraction principle is going to be acceptable, then it should not 'inflate', i.e. it should not result in there being more abstracts than there are objects. By this mark Hume's Principle will be acceptable, but Frege's Law V will not.
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From:
Kit Fine (Precis of 'Limits of Abstraction' [2005], p.307)
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A reaction:
I take this to be motivated by my own intuition that abstract concepts had better be rooted in the world, or they are not worth the paper they are written on. The underlying idea this sort of abstraction is that it is 'shared' between objects.
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8471
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Three ways for 'Socrates is human' to be true are nominalist, platonist, or Montague's way [Orenstein]
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Full Idea:
'Socrates is human' is true if 1) subject referent is identical with a predicate referent (Nominalism), 2) subject reference member of the predicate set, or the subject has that property (Platonism), 3) predicate set a member of the subject set (Montague)
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From:
Alex Orenstein (W.V. Quine [2002], Ch.3)
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A reaction:
Orenstein offers these as alternatives to Quine's 'inscrutability of reference' thesis, which makes the sense unanalysable.
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16745
|
No one even knows the nature and properties of a fly - why it has that colour, or so many feet [Bacon,R]
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Full Idea:
No one is so wise regarding the natural world as to know with certainty all the truths that concern the nature and properties of a single fly, or to know the proper causes of its color and why it has so many feet, neither more nor less.
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From:
Roger Bacon (Opus Maius (major works) [1254], I.10), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 23.6
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A reaction:
Pasnau quotes this in the context of 'occult' qualities. It is scientific essentialism, because Bacon clearly takes it that the explanation of these things would be found within the essence of the fly, if we could only get at it.
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