Skip to content
Carmelics
TopicsThinkersChangesContributorsLoading account…

    Carmelics

    A reasoning platform. Break down any belief into clear reasons, explore both sides, and weigh the evidence honestly.

    Navigate

    • Topics
    • Search
    • Recent Changes
    • Contribute
    • How It Works
    • Glossary
    • Thinkers
    • Contributors
    • About
    • Statistics
    • Terms
    • Privacy

    Database

    Statements
    —
    Perspectives
    —
    Topics
    —

    Press ? for keyboard shortcuts

    LoyalLoyalJusticeJustice
    Made withinDC&Austin
    Statements
    321,452
    Perspectives
    108,905
    Topics
    42
    Proof identity in the correspondence presupposes that syn... — Carmelics
    Home
    HistoryEditSee Inverse

    Part of a larger discussion

    Challenges→The Curry-Howard correspondence holds not only between provable formulae and type ascriptions, but also between proof terms and proofs of corresponding formulae

    Proof identity in the correspondence presupposes that syntactically distinct proofs of the same formula are genuinely different, but proof-irrelevance principles in some type theories collapse this distinction.

    ?Rate how convincing each reason is below to see the overall strength.

    No one has weighed in yet. Be the first to share reasons for or against this statement.

    Sign in or register to share your perspective on this statement.

    Key Terms

    Correspondence(in philosophy of logic)
    The idea that something (like a proof) has a specific meaning or identity that matches up with something else in a precise way.
    Proof identity(in logic and mathematics)
    The question of when two different mathematical or logical proofs count as the 'same' proof or 'different' proofs, even if they reach the same conclusion.
    Proof-irrelevance principles(in type theory and logic)
    Rules in certain logical systems that say it doesn't matter *how* you prove something is true—only that it is true; the method of proof is irrelevant.
    Syntactically distinct(describing representations that are written/structured differently)
    Having different grammatical structure or written form—basically, looking or sounding different as sentences or expressions.

    Next step

    Based on where you are in your exploration

    Explore a random proposition
    Start fresh with something unrelated.
    Type theories(in mathematical logic and computer science)
    Formal logical systems used in mathematics and computer science that classify things into different 'types' to avoid contradictions and organize reasoning.
    formula(in logic)
    A statement written out using symbols and rules, like a recipe that follows strict steps to combine things in a valid way.

    Connections

    2 topics

    Truth & Knowledge1 linkedPhilosophy of Language1 linked

    Related

    The Curry-Howard correspondence holds not only between provable formulae and typ...

    Details

    Type
    claim
    Perspectives
    0 (0 for, 0 against)
    Edits
    1 edit

    Open for perspectives

    This idea is waiting for its first supporting or challenging perspective.

    Share the first perspective