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    Carmelics

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    Home/Original/inverse
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    Inverse View

    It is not the case that The claim that a potentially infinite array of expressions can be 'passed to' concrete sensory-motor and conceptual-intentional systems is problematic, because passing each one would require a potentially infinite amount of time.

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

    Reasons For

    1 perspective
    Reason for
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    • 1.Sensory-motor and conceptual-intentional systems are concrete physical parts of the organism (muscles, nerves, articulatory organs, perceptual channels, neuronal activity).
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    • 2.Passing each expression from a potentially infinite array to such concrete systems would take a finite amount of time per expression.
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    • 3.Passing all expressions from a potentially infinite array would therefore require a potentially infinite amount of time.
      ?

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    Reasons Against

    2 perspectives
    Reason against 1 of 2
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    • 1.Chomsky's I-language is an internal computational system whose generative capacity is logically distinct from any physical performance system's temporal constraints.
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    • 2.The interface between I-language and sensory-motor systems is a mapping relation, not a sequential queuing process, so infinite generative capacity does not entail infinite processing time.
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    • 3.Marr's tri-level hypothesis establishes that computational-level descriptions (what is computed) are explanatorily independent of implementational-level facts (how long physical execution takes).
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    Reason against 2 of 2
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    • 1.Potential infinity, as distinguished by Aristotle and formalized in constructivist mathematics, denotes an unbounded but never-completed totality, requiring no actual infinite process to be instantiated.
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    • 2.A system with potential infinity of outputs commits only to the absence of a finite upper bound, not to the simultaneous or sequential actualization of all outputs, so no infinite time is entailed.
      ?

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