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    Quine's thesis that intensional contexts are eliminable i... — Carmelics
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    Challenges→The second incompleteness theorem is an intensional result, not merely an extensional one.

    Quine's thesis that intensional contexts are eliminable in favor of extensional paraphrase applies here: Con(F) is a purely syntactic, recursively defined sentence whose meaning just is its extension over arithmetic.

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    Key Terms

    Arithmetic
    Arithmetic is the branch of mathematics dealing with basic number operations—addition, subtraction, multiplication, and division. It's the foundation of math that you use in everyday life, like calculating change at a store, splitting a bill, or figuring out measurements. Essentially, it's the practical math skill everyone learns early in school to work with numbers in simple, straightforward ways.
    Con(F)(The consistency claim formalized within F for the second incompleteness theorem.)
    A formal sentence intended to express the consistency of a formal system F — that F does not prove a contradiction.
    Extensional paraphrase(what Quine proposed as a replacement for intensional language)
    Rewording a sentence so it only cares about *what* things are, not *how* we describe them—basically, translating something into simpler logical language that focuses only on what actually exists.
    Intensional contexts(technical expansion of sense and reference)
    Situations in language where you can't simply swap two expressions that refer to the same thing without changing the meaning—like how 'I want to marry the morning star' doesn't mean the same as 'I want to marry the evening star,' even though both refer to Venus.

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    Quine(as a proper name referring to the philosopher whose theory is being discussed)
    Willard Van Orman Quine was a 20th-century American philosopher who wrote about how we know things and how language works. In this statement, we're discussing one of his specific ideas about observation.
    Recursively defined(how the sentence Con(F) is constructed in logic)
    Built up step-by-step using a rule that applies to itself repeatedly, like how you can build bigger numbers by always adding 1 to the previous number.
    Syntactic(as used in linguistics)
    Related to the rules and structure of how words are arranged in language, rather than their meaning.
    extension(Semantics and philosophy of language)
    Another term for reference, i.e., the object or set of objects a term picks out

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    Truth & Knowledge1 linkedPhilosophy of Language1 linked

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    The second incompleteness theorem is an intensional result, not merely an extens...

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