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It is not the case that Jones must endorse Hamilton's view that predicates are quantified in order to retain the thesis that significant assertion is the assertion of an identity
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Reasons For
2 perspectives
Reason for 1 of 2
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1.
Frege demonstrated in Begriffsschrift that predication is irreducibly asymmetric: the function-argument structure cannot be collapsed into identity without loss of inferential power.
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2.
Jones's identity thesis, if it requires Hamilton's quantified predicates, inherits the circularity Bradley identified: quantifying predicates already presupposes a relational structure that mere identity cannot ground.
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Reason for 2 of 2
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1.
Venn and Jevons showed that Hamilton's quantification of the predicate generates redundant and logically ill-formed propositions that violate the principle of parsimony in formal systems.
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2.
A thesis requiring a flawed logical apparatus as its necessary condition is undermined by the availability of Boole's algebraic logic, which preserves propositional significance without quantifying predicates.
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Reasons Against
1 perspective
Reason against
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1.
Without quantified predicates, 'All humans are mortal' entails the nonsensical 'Mortals are all humans'
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2.
With quantified predicates, the entailed consequence 'Some mortals are all humans' is intelligible as a near-identity statement
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3.
Jones's core thesis requires that significant assertions be interpretable as identity assertions
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