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    Stephen Cole Kleene — Carmelics
    Thinkers/Stephen Cole Kleene
    Stephen Cole Kleene

    Stephen Cole Kleene

    modernMathematical Logic

    1909 – 1994

    Stephen Cole Kleene was an American mathematician and logician who made foundational contributions to recursion theory, intuitionistic logic, and the theory of computation. A student of Alonzo Church at Princeton, he helped establish the mathematical foundations of computer science and is considered one of the founders of theoretical computer science.

    WWikipedia

    Notable Achievements

    1

    Founded recursion theory and introduced the Kleene hierarchy of arithmetical and analytical sets

    2

    Invented regular expressions and the Kleene star operator

    3

    Proved the recursion theorem (Kleene's fixed-point theorem)

    4

    Developed realizability interpretation for intuitionistic logic

    5

    Co-formulated the Church-Turing thesis and proved key results on computable functions

    Positions & Arguments

    (3)

    Skepticism

    claim

    Turing's thesis is not susceptible to mathematical proof

    claim

    There is a fundamental tension between treating logical knowledge as a priori and the computational intractability of deciding logical validity.

    Truth & Knowledge

    claim

    Turing's thesis is not susceptible to mathematical proof

    claim

    There is a fundamental tension between treating logical knowledge as a priori and the computational intractability of deciding logical validity.

    claim

    The universal function u_1(i,x) = g_i(x) for unary primitive recursive functions cannot itself be primitive recursive

    Modality & Possibility

    claim

    The universal function u_1(i,x) = g_i(x) for unary primitive recursive functions cannot itself be primitive recursive

    At a Glance

    Ideas

    3

    Topics

    3

    Era

    modern

    Tradition

    Mathematical Logic

    Topic Influence

    Truth & Knowledge3
    Skepticism2
    Modality & Possibility1

    Related Thinkers

    David Lewis3 sharedImmanuel Kant3 sharedBrian Skyrms3 sharedAristotle3 sharedBertrand Russell3 sharedDavid Hume3 sharedPlato3 sharedStathis Psillos3 shared

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