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It is not the case that Nominalists like Quine and Nelson Goodman argue that positing abstract unifying objects violates ontological parsimony when functional equivalents exist.
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Reasons For
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Reason for
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1.
Mathematical and logical truths seem to require abstract objects as their truthmakers.
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2.
Nominalist 'functional equivalents' often covertly reintroduce abstract entities through backdoor commitments.
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3.
Parsimony about entities shouldn't override explanatory power and theoretical elegance.
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Reasons Against
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Reason against
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1.
Occam's Razor requires minimizing ontological commitments without explanatory loss.
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2.
Concrete particulars and their relations can replicate all explanatory work abstract objects perform.
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3.
Abstract objects create epistemological puzzles (access, identity) that concrete alternatives avoid.
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