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It is not the case that Anti-platonists cannot claim that 'that'-clauses refer to sentence types.
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Reasons For
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Reason for 1 of 2
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1.
Sentence types can be construed nominalistically as equivalence classes of physical token inscriptions, requiring no platonic commitment.
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2.
Hartry Field's fictionalism and Geoffrey Hellman's modal structuralism show anti-platonists can accept type-talk via paraphrase strategies.
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3.
If 'that'-clauses refer to sentence types reconceived nominalistically, the anti-platonist incurs no ontological debt to abstract objects.
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Reason for 2 of 2
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1.
The inference from 'sentence types are abstract objects' to 'anti-platonists cannot use sentence types' commits the fallacy of begging the question against nominalist reductions.
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2.
Wilfrid Sellars and later Lynne Rudder Baker argue sentence types can be grounded in linguistic practices and dispositions without positing mind-independent abstracta.
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Reasons Against
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Reason against
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1.
Sentence types are abstract objects
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2.
Anti-platonists reject abstract objects.
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