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    Free logic, not an enriched first-order predicate, is the... — Carmelics
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    Challenges→The correct first-order translation of 'dragons exist' is '∃x (Exists(x) ∧ Dragon(x))', not '∃x Dragon(x)'.

    Free logic, not an enriched first-order predicate, is the proper formal tool for handling non-referring terms like 'dragon', preserving a neutral domain without inflating the predicate inventory.

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    Key Terms

    Enriched(describing a version of first-order predicate logic that free logic avoids being)
    In this context, made more complicated or expanded by adding extra elements or assumptions beyond what's minimally necessary.
    First-order predicate logic(contrasted with free logic as a formal tool)
    A system of formal logic that uses symbols and rules to talk about objects and their properties; it's the standard mathematical language philosophers use to represent arguments precisely.
    Non-referring terms(examples given: 'dragon')
    Words or phrases that seem to name something but don't actually point to anything that exists in reality, like 'unicorn' or 'the king of France'.
    Predicate inventory(what the speaker wants to avoid inflating)
    The complete set of properties or qualities (like 'is red' or 'is tall') that your logical system allows you to use and work with.

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    domain(Both f1 and f2 have the reals as their domain)
    The set of input values over which a function is defined.
    free logic(Contrasted with standard first-order predicate logic)
    A logical system in which the existential generalization '∃x φ(x)' cannot in general be derived from 'φ(t)' for a singular term 't', meaning singular terms do not automatically carry existential import

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    The correct first-order translation of 'dragons exist' is '∃x (Exists(x) ∧ Drago...

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