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    The formalization ∃x[L(x,j)] ∧ ∃x[L(r,x)] uses 'x' in sco... — Carmelics
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    Challenges→Someone likes Juliet and Romeo likes someone (∃x[L(x,j)] ∧ ∃x[L(r,x)]).

    The formalization ∃x[L(x,j)] ∧ ∃x[L(r,x)] uses 'x' in scopes where it is semantically unrelated, violating the Quinean criterion that canonical notation must eliminate such ambiguity.

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    1 reason for
    1 reason against

    Reasons For

    1 perspective
    Reason for
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    • 1.Quine's canonical notation demands that variables with distinct semantic roles should have distinct notational markers to preserve logical clarity.
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    • 2.Using 'x' in both ∃x[L(x,j)] and ∃x[L(r,x)] obscures that these quantifiers bind semantically independent existential claims.
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    • 3.Ambiguity in notation risks scope confusion and makes logical structure less transparent than using distinct variables like ∃x[L(x,j)] ∧ ∃y[L(r,y)].
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    Reasons Against

    1 perspective
    Reason against
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    • 1.Variable reuse across independent quantifiers is standard practice in first-order logic and causes no actual semantic confusion or formal error.
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    • 2.The Quinean criterion targets material ambiguity in reference, not notational economy; using 'x' twice in separate scopes violates neither principle.
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    • 3.Requiring distinct variables for all independent quantifications would unnecessarily burden notation without improving logical validity or semantic content.
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    Key Terms

    Canonical notation(as used in formal logic)
    A standardized, cleaned-up way of writing logical statements using formal symbols—like translating regular English into a precise logical language that removes ambiguity.
    Formalization(describing what Frege did with existence)
    The process of taking an idea and expressing it precisely using logical symbols and strict rules, like translating messy everyday language into mathematical logic.
    Quinean criterion(philosophy of science and ontology)
    A standard for determining what exists based on the ideas of philosopher Willard Van Orman Quine, particularly his view that we should believe in whatever is necessary for our best scientific theories to work.
    Scope (in logic)(wide vs. narrow scope affects how we interpret whether something is true or false)
    The range or reach of a word's meaning in a sentence; whether a description applies to just part of a sentence or the whole thing.
    Semantically unrelated(as used in philosophy of language)
    Referring to things that have completely different meanings or don't relate to each other in terms of what they're actually talking about.
    ∃x[L(x,j)] ∧ ∃x[L(r,x)](as used in formal logic)
    A symbolic notation meaning 'there exists something that relates to j' AND 'there exists something that r relates to.' The symbols ∃ means 'there exists,' x is a placeholder for 'something,' and L means 'relates to' or 'loves.'

    Connections

    2 topics

    Modality & Possibility1 linkedPhilosophy of Language1 linked

    Related

    Ambiguity in notation risks scope confusion and makes logical structure less tra...Quine's canonical notation demands that variables with distinct semantic roles s...

    Details

    Type
    claim
    Perspectives
    2 (1 for, 1 against)
    Edits
    1 edit
    Requiring distinct variables for all independent quantifications would unnecessa...
    Someone likes Juliet and Romeo likes someone (∃x[L(x,j)] ∧ ∃x[L(r,x)]).
    +3 moreShow less
    The Quinean criterion targets material ambiguity in reference, not notational ec...Using 'x' in both ∃x[L(x,j)] and ∃x[L(r,x)] obscures that these quantifiers bind...Variable reuse across independent quantifiers is standard practice in first-orde...