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    A theory containing '∃x x = Obama' is ontologically commi... — Carmelics
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    Home/Modality & Possibility
    HistoryEditSee Inverse

    A theory containing '∃x x = Obama' is ontologically committed to the existence of Obama's head, even though Obama's head need not be assigned as a value to the variable 'x' for the theory to be true.

    Truth & Knowledge
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    1 reason for
    2 reasons against

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.A whole cannot exist without each of its parts existing.
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    • 2.A human cannot exist without his head.
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    • 3.The theory contains '∃x x = Obama', asserting Obama's existence.
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    Reasons Against

    2 perspectives
    Reason against 1 of 2
    ?
    • 1.Ontological commitment is determined solely by what must be within the range of bound variables for a theory's sentences to be true (Quine, 'On What There Is').
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    • 2.Obama's head need not be assigned as a value to any bound variable in '∃x x = Obama' for that sentence to be true.
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    • 3.Therefore, Obama's head falls outside the scope of ontological commitment as Quine defines it, regardless of mereological dependencies.
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    Reason against 2 of 2
    ?
    • 1.P4's principle conflates metaphysical dependence with ontological commitment, treating them as equivalent when they are distinct relations (Fine, 'Ontological Dependence').
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    • 2.A theory may presuppose background conditions for its truth-makers to obtain without thereby being ontologically committed to those conditions in any regimented logical sense.
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    Topics

    Modality & PossibilityTruth & Knowledge

    Key Terms

    Assigned as a value(logic)
    When you give a variable a specific thing it represents. If 'x' is assigned the value Obama, then 'x' now means Obama specifically.
    Existential quantifier (∃x)(formal logic and philosophy of language)
    A symbol in logic that means 'there exists at least one thing' (the ∃ symbol) and 'x' is just a placeholder variable for whatever that thing might be.
    Ontologically committed(describes what a theory must believe exists)
    When a theory claims that certain things actually exist as part of its explanation of the world.
    Ontology/Ontological(in metaphysics)
    The philosophical study of what actually exists or is real, as opposed to what merely seems to exist or what we can know about things.
    Variable (in logic)(logic and formal philosophy)
    A placeholder symbol (like 'x') that can stand in for any object you're talking about, kind of like an empty slot waiting to be filled with a specific thing.

    Connections

    1 topic

    Philosophy of Language1 linked

    Related

    A human cannot exist without his head.A theory may presuppose background conditions for its truth-makers to obtain wit...A whole cannot exist without each of its parts existing.If entity X cannot exist without entity Y existing, then a theory asserting X's ...

    Source

    AI-extracted1/3 agreementValid
    SEP: ontological-commitment
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    The problem of extrinsic properties arises because there are analytic connections between one predicate holding of a thing and another predicate holding of some other thing. Similar problems arise for quantifier criteria if there are metaphysically necessary connections between non-identical things. Thus, if a set cannot exist without its members existing, then it appears that a theory that contains ‘∃x x = {a, b}’ is ontologically committed to the existence of a. But a need not be assigned as
    Extraction notes

    Validity: Extracted via Max plan + API grounding/validity checks

    Details

    +5 moreShow less
    Obama's head need not be assigned as a value to any bound variable in '∃x x = Ob...Ontological commitment is determined solely by what must be within the range of ...P4's principle conflates metaphysical dependence with ontological commitment, tr...The theory contains '∃x x = Obama', asserting Obama's existence.Therefore, Obama's head falls outside the scope of ontological commitment as Qui...

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    Type
    claim
    Perspectives
    3 (1 for, 2 against)
    Edits
    1 edit