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It is not the case that Frege held that abstract objects like numbers and word meanings are grasped through intellectual intuition, not sensory perception of instances.
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1.
Intellectual intuition lacks clear criteria for verification, making it epistemically inferior to empirical methods grounded in reproducible observation.
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2.
Our understanding of abstract objects may derive from abstraction over sensory experiences of concrete particulars, not requiring separate intellectual faculty.
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3.
Appeals to intellectual intuition risk explaining knowledge through mysterious, non-naturalistic mechanisms incompatible with modern cognitive science.
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Reasons Against
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Reason against
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1.
Numbers cannot be identified with physical objects or sensory properties, so knowledge of them requires a non-sensory cognitive faculty.
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2.
Word meanings are stable and identical across different utterances, suggesting they're abstract entities grasped mentally rather than perceived.
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3.
Mathematical truths hold with necessity across all possible worlds, implying they're grasped through reason rather than empirical observation.
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