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It is not the case that If disjunctive properties lack ontological status, they cannot ground the real determination relation that determinables require.
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Reasons For
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Reason for
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1.
Disjunctive properties are ontologically respectable if instantiated: 'red or blue' is genuinely instantiated when something is red.
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2.
Determinables can be grounded by multiple distinct determinates; disjunction simply expresses this multi-realizability, which is determinate.
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3.
The claim conflates epistemic indeterminacy about which disjunct holds with metaphysical indeterminacy of the disjunctive property itself.
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Reasons Against
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Reason against
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1.
Real determination requires a determinate ground, but disjunctions (A or B) are indeterminate about which disjunct actually obtains.
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2.
Only properties with intrinsic, unified natures can ground the determinate specifications that determinables demand of their instances.
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3.
Allowing disjunctive grounders would make any determinable groundable by mere logical combinations, undermining determinable-determinate distinction.
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