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    Carmelics

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    LoyalLoyalJusticeJustice
    Made withinDC&Austin
    Statements
    321,452
    Perspectives
    108,905
    Topics
    42
    Home/Original/inverse
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    Inverse View

    It is not the case that We have good reasons to think that mathematical sentences are true, and therefore fictionalism about mathematics is false.

    ?Set your confidence on the premises below to see your aggregate.

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.Mathematical sentences form an indispensable part of our empirical theories of the physical world (physics, chemistry, etc.).
      ?

      Think about whether this reason is strong or weak

    • 2.We have good reasons for thinking that these empirical theories are true and give accurate pictures of the world.
      ?

      Think about whether this reason is strong or weak

    Reasons Against

    2 perspectives
    Reason against 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.
      ?

      Think about whether this reason is strong or weak

    • 2.Frege's logicism shows that basic arithmetic truths are derivable from logical laws alone, grounding their truth independently of physical applicability.
      ?

      Think about whether this reason is strong or weak

    • 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.
      ?

      Think about whether this reason is strong or weak

    Reason against 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.
      ?

      Think about whether this reason is strong or weak

    • 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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    Strongest counterpoint
    Explore the most compelling reason on the other side.