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    The existential quantifier in 'would entail the existence... — Carmelics
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    Challenges→A polynomial time algorithm for any single NP-complete problem would entail the existence of polynomial time algorithms for all problems in NP.

    The existential quantifier in 'would entail the existence of' conflates constructive and non-constructive existence, a distinction central to intuitionist mathematics.

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    Reasons For

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    Reason for
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    • 1.Intuitionist mathematics fundamentally requires constructive proof; asserting existence without construction violates this core principle.
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    • 2.Classical logic's existential quantifier presupposes the law of excluded middle, which intuitionists reject as non-constructive.
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    • 3.Conflating these existences obscures whether a claimed entity can actually be exhibited or only theoretically follows from axioms.
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    Reasons Against

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    • 1.The phrase 'would entail existence' is itself a modal/counterfactual claim, not a direct assertion of existence requiring constructivism.
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    • 2.Different logical frameworks can coexist without 'conflation' if the context or metalanguage clarifies which notion of existence applies.
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    • 3.Many philosophers and mathematicians use classical and intuitionistic logic in different domains without confusing their distinct standards.
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    Proof of definition segments1 linkedModality & Possibility1 linked

    Related

    A polynomial time algorithm for any single NP-complete problem would entail the ...Classical logic's existential quantifier presupposes the law of excluded middle,...Conflating these existences obscures whether a claimed entity can actually be ex...Different logical frameworks can coexist without 'conflation' if the context or ...
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    Intuitionist mathematics fundamentally requires constructive proof; asserting ex...Many philosophers and mathematicians use classical and intuitionistic logic in d...The phrase 'would entail existence' is itself a modal/counterfactual claim, not ...

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    2 (1 for, 1 against)
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