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    Wittgenstein's rule-following considerations entail that ... — Carmelics
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    Challenges→The notion of a computable set generalizes effective decidability: a relation R is computable just in case there is an algorithm for deciding whether R holds of any tuple of natural numbers that always returns an answer after a finite (though potentially unbounded) number of steps

    Wittgenstein's rule-following considerations entail that no finite symbolic procedure fixes a unique interpretation of 'algorithm,' undermining the determinacy of 'always returns an answer.'

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    Key Terms

    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.
    algorithm(Philosophy of computation and information)
    A fundamental concept in information and computation theory, accepted as a primitive notion alongside data set
    always returns an answer(as the phrase whose meaning is questioned in the statement)
    A phrase meaning that no matter what input you give it, a procedure will definitely produce some result without getting stuck or failing.
    determinacy(Game theory, infinite games)
    The property that for any game property φ, either player i has a strategy to force a set of histories satisfying φ, or player j has a strategy to force ¬φ; formally: {i}φ ∨ {j}¬φ

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    fixes a unique interpretation(describing what a symbolic procedure should do but may fail to do)
    Establishes or pins down one single, definite meaning—prevents multiple different understandings from being valid.
    rule-following considerations(in philosophy of language)
    Wittgenstein's famous puzzle about how we know what rule to follow next: if you learn a rule by seeing examples, how do you know you're applying it correctly to new cases you've never seen before?
    symbolic procedure(as a method for specifying what something means)
    A step-by-step process written out using symbols or formal notation (like mathematical or computer code) that's meant to give exact instructions.

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    Proof of definition segments1 linkedTruth & Knowledge1 linked

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    The notion of a computable set generalizes effective decidability: a relation R ...

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