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    If the domain of singleton functions is indeterminate or ... — Carmelics
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    Challenges→The translation from singular reference to 'the' singleton function into universal quantification over singleton functions introduces no inconsistency into mathematics.

    If the domain of singleton functions is indeterminate or subject to paradox (e.g., via Cantorian diagonalization on function spaces), the quantification inherits that indeterminacy.

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    Key Terms

    Cantorian diagonalization(in mathematics and logic; named after mathematician Georg Cantor)
    A mathematical proof technique invented by Georg Cantor to show that infinite sets of different sizes exist—by constructing something that differs from every item in a list.
    Indeterminate(Reichenbach's three-valued quantum logic)
    The value of propositions that quantum theory implies cannot be assessed to be either true or false
    Quantification(logic)
    The part of a statement that specifies how many things you're talking about—words like 'all,' 'some,' or 'none'.
    domain(Both f1 and f2 have the reals as their domain)
    The set of input values over which a function is defined.
    function spaces(advanced mathematics)

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    Abstract mathematical collections where the individual items are themselves functions rather than numbers or objects.
    paradox(R. M. Sainsbury's definition, presented as a target of criticism)
    An apparently unacceptable conclusion derived by apparently acceptable reasoning from apparently acceptable premises
    singleton functions(mathematical logic and set theory)
    Functions that map multiple inputs to a single output, or more technically, functions with a domain containing only one element.

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    Modality & Possibility1 linkedPhilosophy of Language1 linked

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    The translation from singular reference to 'the' singleton function into univers...

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