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It is not the case that The theory of computing occupies common ground among competing mathematical philosophies (Formalism, Platonism, Intuitionism)
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Reasons For
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Reason for 1 of 2
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1.
Platonists hold that Turing machines and recursive functions are discovered abstract objects, while formalists treat them as meaningless symbol systems.
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2.
This ontological disagreement about what computation *is* persists even when practitioners converge on the same formal results.
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3.
Shared extensional output does not constitute 'common ground' when the intensional philosophical commitments remain irreconcilably distinct.
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Reason for 2 of 2
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1.
Intuitionists like Brouwer reject classical logic's law of excluded middle, which underlies key computability proofs (e.g., halting problem via reductio).
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2.
Agreement on finite computational procedures does not entail agreement on the logical foundations that justify or delimit those procedures.
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Reasons Against
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Reason against
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1.
Computing theory is finitistic and constructivist in nature
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2.
Formalist, Platonic, and intuitionistic views of mathematics each overlap on finitistic, constructivist ground
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3.
Adherents of any of these mathematical philosophies can agree on what effective computation is
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