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    Supports→The notion of explanatory power of mathematics in science has no ontological import and cannot be used in the enhanced indispensability argument.

    If mathematical entities were ontologically implicated by explanatory power, replacing one mathematical framework with an equivalent one would alter the ontology of science, which is absurd (Field 1980).

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    Key Terms

    Field (1980)(as a cited source in philosophy of mathematics)
    A reference to philosopher Hartry Field, who argued in 1980 that we shouldn't assume mathematical objects (like numbers) actually exist just because math is useful in science.
    Mathematical framework(as used in philosophy of mathematics)
    A system of mathematical tools and rules used to describe and solve problems—like how physicists use different types of math to model the same physical phenomena.
    Ontologically implicated(as used in the statement about mathematical entities)
    If something is ontologically implicated, it means you're committed to saying that thing actually exists as part of reality.
    Ontology(Carnap argues this enterprise is based on a mistake)
    The philosophical discipline that tries to answer hard questions about what there really is.

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    equivalent(Snowdon's proposed reading of 'equivalent' in the context of Hinton's argument about Neutral Experience Reports and Perception-Illusion disjunctions.)
    'P' is equivalent to 'Q' if and only if it is a priori that necessarily (P if and only if Q).
    explanatory power(Socratic definition)
    The capacity of a defining feature to explain why instances of the thing defined have that property (e.g., why reverent people or actions are reverent).

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    Truth & Knowledge1 linkedModality & Possibility1 linked

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    The notion of explanatory power of mathematics in science has no ontological imp...

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    If mathematical entities were ontologically implicated by... — Carmelics