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    We have good reasons to think that mathematical sentences... — Carmelics
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    Home/Skepticism
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    We have good reasons to think that mathematical sentences are true, and therefore fictionalism about mathematics is false.

    SkepticismTruth & Knowledge
    ?Rate how convincing each reason is below to see the overall strength.
    2 reasons for
    1 reason against

    Reasons For

    2 perspectives
    Reason for 1 of 2
    ?
    • 1.Mathematical truths like '2+2=4' are known a priori with greater certainty than any empirical claim that could be used to doubt them.
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    • 2.Frege's logicism shows that basic arithmetic truths are derivable from logical laws alone, grounding their truth independently of physical applicability.
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    • 3.Any fictionalist 'story' that preserves inferential utility must parasitically rely on the truth of the logical relations it encodes, confirming mathematical realism at the foundational level.
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    Reason for 2 of 2
    ?
    • 1.Putnam's model-theoretic arguments show that truth in mathematics is constrained by structural consistency, not merely by human stipulation or useful fiction.
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    • 2.If mathematical sentences were fictional, the unreasonable effectiveness of mathematics in physics (Wigner 1960) would be a inexplicable cosmic coincidence rather than a natural consequence of mathematical truth.
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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Mathematical sentences form an indispensable part of our empirical theories of the physical world (physics, chemistry, etc.).
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    • 2.We have good reasons for thinking that these empirical theories are true and give accurate pictures of the world.
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    Related

    Any fictionalist 'story' that preserves inferential utility must parasitically r...Frege's logicism shows that basic arithmetic truths are derivable from logical l...If mathematical sentences were fictional, the unreasonable effectiveness of math...Mathematical sentences form an indispensable part of our empirical theories of t...
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    Mathematical truths like '2+2=4' are known a priori with greater certainty than ...Putnam's model-theoretic arguments show that truth in mathematics is constrained...We have good reasons for thinking that these empirical theories are true and giv...

    Similar

    A fictionalist account of mathematics denies that such sentences are l...93%Mathematical theories must be true, and therefore fictionalism about m...91%The most natural explanation of this distinction is that correct mathe...86%Therefore, fictionalists cannot appeal to truth and falsity to explain...85%

    Source

    AI-extracted1/3 agreementValid
    SEP: fictionalism-mathematics
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    By far the most important and widely discussed argument against fictionalism is what’s known as the Quine-Putnam indispensability argument (see, e.g., Quine (1948, 1951), Putnam (1971), Resnik (1997), and Colyvan (2001)). This argument has been formulated in a number of different ways. One very simple version of the argument can be put like this: (i) mathematical sentences form an indispensable part of our empirical theories of the physical world—i.e., our theories of physics, chemistry, and so
    Extraction notes

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

    Details

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