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    If any class closed under isomorphism is definable in sor... — Carmelics
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    Challenges→Sort logic is an alternative way of looking at mathematics where definition rather than construction is the focus

    If any class closed under isomorphism is definable in sort logic, then sort logic inherits the same structural abstraction that set-theoretic construction already provides, making the contrast with set theory superficial.

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    Key Terms

    Definable(in logic)
    Able to be described or specified using a particular set of rules or language—for example, you could 'define' all even numbers using mathematical notation.
    closed under isomorphism(as used in logic and mathematics)
    A group of mathematical objects that stay in the same group whenever you can transform them into each other while keeping their essential structure intact.
    contrast with set theory superficial(as used in comparative logic)
    The differences between sort logic and set theory appear to be surface-level or unimportant, rather than representing a deep fundamental difference.
    set-theoretic construction(as used in mathematical logic and foundations)
    A method of building mathematical objects and systems using set theory, which is based on the idea that everything can be represented as collections of things.

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    sort logic(Extension of many-sorted first-order logic; Väänänen 2014)
    A many-sorted second-order logic that allows quantification over new sorts via a new logical symbol ∃̃, enabling formulas to look outside the structure where the formula is being interpreted
    structural abstraction(as used in logic and mathematics)
    The process of focusing on the underlying patterns and relationships that matter in a system, while ignoring the specific details that don't affect how it works.

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    Truth & Knowledge1 linkedPhilosophy of Language1 linked

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    Sort logic is an alternative way of looking at mathematics where definition rath...

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