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Inverse View
It is not the case that Mathematical structures like complex numbers and Hilbert spaces ground physical conceptions without any direct sensory correlate.
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Reasons For
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Reason for
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1.
All mathematical structures ultimately arise from cognitive patterns built on sensory abstraction, making the distinction illusory.
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2.
Success of mathematics in physics may reflect our choice of useful description rather than discovery of mind-independent grounding structures.
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3.
Instrumentalism explains physics predictively without claiming abstract structures ground physical reality independently of human interpretation.
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Reasons Against
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Reason against
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1.
Quantum mechanics makes identical empirical predictions using Hilbert spaces yet fails without them, suggesting they capture real structure.
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2.
Mathematical structures often predict phenomena before observation (like antimatter), indicating they access reality beyond sensory access.
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3.
No sensory experience directly accesses electromagnetic fields or spacetime curvature, yet these require abstract mathematics to describe.
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