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    ∀x is equivalent to ¬∃¬ — Carmelics
    Home/Philosophy of Language
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    Supports→∀x[P(x) → D(x)] is equivalent to ¬∃x[P(x) ∧ ¬D(x)]

    ∀x is equivalent to ¬∃¬

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    By de Morgan's Laws, ¬∃x¬[¬P(x) ∨ D(x)] iff ¬∃x[P(x) ∧ ¬D(x)]P(x) → D(x) is equivalent to ¬P(x) ∨ D(x) by Frege's definitions∀x[P(x) → D(x)] is equivalent to ¬∃x[P(x) ∧ ¬D(x)]

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    Related propositions within the same area of thought.
    R is equivalent to V.98%Logical equivalents can sometimes explain each other.83%P equals coP83%PSPACE equals NPSPACE83%

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    With regard to the proposition that some politician is deceitful, traditional grammar suggests the division ‘Some politician / is deceitful’, with the noun ‘politician’ combining with the quantificational word to form a complex subject. But on a Fregean view, grammar masks the logical division between the existential quantifier and the rest: \(\exists x [P(x) \land D(x)]\). With regard to the proposition that every politician is deceitful, Frege also stresses the logical division between the qua

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