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    The theory of definite descriptions is essential for just... — Carmelics
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    The theory of definite descriptions is essential for justifying the introduction of function symbols into a language with only n-place predicates

    Philosophy of LanguageProof of definition segments
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    1 reason for
    2 reasons against

    Reasons For

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    Reason for
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    • 1.In contemporary logic, the notion of a 'functional relation' can be used to justify the introduction of function symbols into a language with only n-place predicates
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    • 2.The theory of definite descriptions is required to make this argument work
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    Reasons Against

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    Reason against 1 of 2
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    • 1.Church and Henkin showed that function symbols can be introduced into typed lambda calculus through lambda abstraction, with no appeal to definite descriptions.
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    • 2.The theory of definite descriptions is a device for eliminating singular terms, whereas function symbols require only stipulation of input-output mappings over a domain.
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    • 3.Because the logical work of grounding functions is done by lambda abstraction or primitive stipulation, the theory of definite descriptions is at most a dispensable convenience, not an essential justification.
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    Reason against 2 of 2
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    • 1.Frege's Grundgesetze introduces function symbols via value-ranges and extensions without requiring any theory of definite descriptions.
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    • 2.If function symbols can be grounded in Fregean extensions independently of descriptive operators, then definite descriptions are not essential to their justification.
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    Philosophy of LanguageProof of definition segments

    Related

    Because the logical work of grounding functions is done by lambda abstraction or...Church and Henkin showed that function symbols can be introduced into typed lamb...Frege's Grundgesetze introduces function symbols via value-ranges and extensions...If function symbols can be grounded in Fregean extensions independently of descr...
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    In contemporary logic, the notion of a 'functional relation' can be used to just...The theory of definite descriptions is a device for eliminating singular terms, ...The theory of definite descriptions is required to make this argument work

    Similar

    The theory of definite descriptions is required to make this argument ...83%In contemporary logic, the notion of a 'functional relation' can be us...79%Names have the same meanings as definite descriptions79%The relation between a definite description and its denotation is logi...75%

    Source

    AI-extracted1/3 agreementValid
    SEP: principia-mathematica
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    Russell presented his theory of definite descriptions in “On Denoting” (1905) and it has probably been the most widely discussed application of the logic of PM. The role of the theory of definite desciptions in PM, however, is exhausted by its use in ∗30 to define what are called “Descriptive functions”. In contemporary logic it is routine to show how the notion of a “functional relation” can be used to justify the introduction of function symbols into a language with only n-place predicates. Th
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    Details

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    claim
    Perspectives
    3 (1 for, 2 against)
    Edits
    1 edit