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    Home/Original/inverse
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    Inverse View

    It is not the case that The theory of definite descriptions is essential for justifying the introduction of function symbols into a language with only n-place predicates

    ?Set your confidence on the premises below to see your aggregate.

    Reasons For

    2 perspectives
    Reason for 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 for 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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    Reasons Against

    1 perspective
    Reason against
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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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