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    Wilhelm Ackermann — Carmelics
    Thinkers/Wilhelm Ackermann
    Wilhelm Ackermann

    Wilhelm Ackermann

    modernMathematical Logic

    1896 – 1962

    Wilhelm Ackermann was a German mathematician and logician, best known for his work in mathematical logic and computability theory. A student of David Hilbert, he made significant contributions to proof theory and is remembered for the Ackermann function, a key example in the theory of computation that demonstrated the existence of computable functions not captured by primitive recursion.

    WWikipedia

    Notable Achievements

    1

    Discovered the Ackermann function, a total computable function that is not primitive recursive

    2

    Co-authored 'Grundzüge der theoretischen Logik' (Principles of Mathematical Logic) with David Hilbert

    3

    Contributed to Hilbert's consistency program and proof theory

    4

    Advanced the study of decidability and the decision problem in formal systems

    Positions & Arguments

    (2)

    Skepticism

    claim

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

    Truth & Knowledge

    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

    2

    Topics

    3

    Era

    modern

    Tradition

    Mathematical Logic

    Topic Influence

    Truth & Knowledge2
    Modality & Possibility1
    Skepticism1

    Related Thinkers

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

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