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    Mathematical singular terms occur in canonical scientific... — Carmelics
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    Challenges→The singular term argument for propositions is more powerful than the singular term argument for mathematical objects

    Mathematical singular terms occur in canonical scientific theories whose indispensability is argued by Quine-Putnam, giving them stronger ontological pressure than propositional terms.

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    Reasons For

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    • 1.Quine-Putnam indispensability argument shows mathematical objects are necessary for our best scientific theories to function.
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    • 2.Scientific theories quantify over numbers/sets with no plausible paraphrasing away these commitments without loss of explanatory power.
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    • 3.Propositional entities lack the same systematic indispensability; we can often rephrase propositions without harming scientific content.
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    Reasons Against

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    • 1.Mathematical terms may be instrumentally indispensable without being ontologically committed—they could be useful fictions or notational conveniences.
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    • 2.The indispensability argument conflates pragmatic utility in theory with genuine ontological commitment to the entities those theories mention.
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    • 3.Propositional terms also appear indispensably in semantic, logical, and epistemic theories foundational to all science, matching mathematics' status.
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    Key Terms

    Canonical scientific theories(in philosophy of science)
    The established, widely-accepted scientific theories that we currently rely on to describe how the world works.
    Indispensability(describing what makes something essential to philosophical theorizing)
    Something that is absolutely necessary and cannot be done without. If something is indispensable to a theory, that theory cannot work or make sense without it.
    Mathematical singular terms(in philosophy of mathematics)
    Specific names or references to mathematical objects, like 'the number 5' or 'pi'—as opposed to general statements about math.
    Ontological pressure(in metaphysics and philosophy of mathematics)
    The degree to which something pushes us to believe it actually exists in reality, rather than being just a useful tool or concept.
    Propositional terms(in logic and philosophy of language)
    Words or phrases that represent claims or statements that can be true or false, as opposed to names of things.
    Quine-Putnam (argument/indispensability argument)(in philosophy of mathematics)
    An argument by philosophers Willard Quine and Hilary Putnam that if mathematics is necessary for our best scientific theories to work, then mathematical objects must actually exist.

    Connections

    2 topics

    Truth & Knowledge1 linkedPhilosophy of Language1 linked

    Related

    Mathematical terms may be instrumentally indispensable without being ontological...Propositional entities lack the same systematic indispensability; we can often r...

    Details

    Type
    claim
    Perspectives
    2 (1 for, 1 against)
    Edits
    1 edit
    Propositional terms also appear indispensably in semantic, logical, and epistemi...
    Quine-Putnam indispensability argument shows mathematical objects are necessary ...
    +3 moreShow less
    Scientific theories quantify over numbers/sets with no plausible paraphrasing aw...The indispensability argument conflates pragmatic utility in theory with genuine...The singular term argument for propositions is more powerful than the singular t...