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    Sharing a variable 'x' across two existential quantifiers... — Carmelics
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    Challenges→Someone likes Juliet and Romeo likes someone (∃x[L(x,j)] ∧ ∃x[L(r,x)]).

    Sharing a variable 'x' across two existential quantifiers in separate conjuncts creates a misleading syntactic appearance of a linked ranging, which Prior warned distorts logical form.

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    1 reason for
    1 reason against

    Reasons For

    1 perspective
    Reason for
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    • 1.Prior demonstrated that ∃x(P(x)) ∧ ∃x(Q(x)) syntactically suggests a single domain of x, misleading readers about actual logical independence.
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    • 2.Formal semantics requires separate variable instantiations across conjuncts; shared notation obscures this by implying coordinated quantification.
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    • 3.Pedagogically, students routinely misinterpret such formulas as expressing constraints between the two existential domains, requiring explicit clarification.
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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Standard logical notation uses variable renaming conventions that trivially resolve ambiguity; the issue is notational carelessness, not logical distortion.
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    • 2.Experienced logicians automatically parse ∃x(P(x)) ∧ ∃x(Q(x)) correctly as independent; the 'distortion' exists only for novices lacking competence.
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    • 3.Prior's warning conflates cognitive psychology with logical form; syntax perfectly captures the truth conditions regardless of how readers interpret appearance.
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    Key Terms

    Conjuncts(the three separate conditions being listed in this analysis)
    Individual parts or conditions that are joined together; think of them as separate claims connected by 'and'.
    Linked ranging(in formal logic)
    A situation where a variable appears to connect multiple parts of a statement, making them seem more related than they actually are logically.
    Prior, Arthur N.(in modern logic and philosophy)
    A 20th-century philosopher and logician known for studying how the way statements are written can hide or reveal their true logical meaning.
    Syntactic appearance(in logic and linguistics)
    How something looks or is written on the surface, as opposed to what it actually means underneath.
    Variable(as used in logic and causation)
    Something that can change or have different values—like temperature, height, or whether a light is on or off.
    existential quantifier(Philosophy of logic; debate over ontological commitment in first-order logic)
    The logical symbol '∃x', traditionally called the existential quantifier, but argued here to be better termed the 'particular quantifier' because it does not inherently carry existential commitment.
    logical form(Used to characterize logical consequence)
    The way that a sentence is built up from the logical particles.

    Connections

    2 topics

    Modality & Possibility1 linkedPhilosophy of Language1 linked

    Related

    Experienced logicians automatically parse ∃x(P(x)) ∧ ∃x(Q(x)) correctly as indep...Formal semantics requires separate variable instantiations across conjuncts; sha...

    Details

    Type
    claim
    Perspectives
    2 (1 for, 1 against)
    Edits
    1 edit
    Pedagogically, students routinely misinterpret such formulas as expressing const...
    Prior demonstrated that ∃x(P(x)) ∧ ∃x(Q(x)) syntactically suggests a single doma...
    +3 moreShow less
    Prior's warning conflates cognitive psychology with logical form; syntax perfect...Someone likes Juliet and Romeo likes someone (∃x[L(x,j)] ∧ ∃x[L(r,x)]).Standard logical notation uses variable renaming conventions that trivially reso...