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    Wittgenstein argued in 'Remarks on the Foundations of Mat... — Carmelics
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    Challenges→The consistency statement Cons(F) cannot be provable in F

    Wittgenstein argued in 'Remarks on the Foundations of Mathematics' that the diagonal construction conflates object-language provability with metatheoretic truth in a way that begs the question.

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    Key Terms

    Provability(as the standard by which large cardinal hypotheses are being compared)
    The ability to prove something is true using logical rules and established facts—whether a statement can be demonstrated with certainty.
    Remarks on the Foundations of Mathematics(the specific work being referenced)
    A book by Wittgenstein where he questions basic assumptions about what mathematics is and how it works, rather than accepting math as simply describing truths about numbers.
    Wittgenstein
    Ludwig Wittgenstein was an Austrian-British philosopher who fundamentally changed how people think about language and meaning in the 20th century. He argued that many philosophical problems arise from misunderstanding how words actually work in everyday life, rather than from deep metaphysical mysteries. His ideas influenced not just philosophy but also mathematics, logic, and even how people approach psychology and artificial intelligence today.
    begs the question(Informal fallacy in epistemic justification)

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    A circular argument in which warrant for the premises already presupposes the truth of the conclusion
    diagonal construction(as used in formal logic and mathematics)
    A technical method in logic where you create a new statement by combining or manipulating existing statements in a specific systematic way.
    metatheoretic(Used to characterize the role of logical semantics)
    Providing a framework for theorizing about the relationship between symbols (used externally in language and internally in thought) and the world, rather than positing cognitive entities for computational manipulation
    object-language(Davidsonian theory of meaning)
    The language to which a theory of meaning applies

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    The consistency statement Cons(F) cannot be provable in F

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