Fictionalists like Hartry Field accept the same compositional semantics for mathematical sentences as platonists, making the semantic agreement a substantive theoretical commitment, not a trivial consequence.

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Reasons For

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Reason for

1.Field's fictionalism rejects abstract objects while accepting compositional semantics, revealing a genuine theoretical divergence from platonism.
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2.The shared compositional semantics requires explanation—it cannot be merely coincidental that fictionalists and platonists assign identical truth conditions.
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3.This semantic agreement despite ontological disagreement demonstrates that fictionalism is a substantive position about mathematical reference, not trivial.
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Reasons Against

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Reason against

1.If fictionalists and platonists assign identical truth conditions, the semantics are determined by those conditions—making agreement logically inevitable, not substantive.
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2.Compositional semantics for mathematical language (recursive rules from basic terms) is a minimal, conventional framework any adequate theory must adopt.
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3.The real theoretical difference lies in ontology and truth-conditions, not semantics—semantic agreement is thus a consequence of shared linguistic meaning, not commitment.
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Key Terms

Fictionalists(as the main subject of the statement): Philosophers who believe that certain things we talk about (like abstract objects) don't actually exist in reality, even though it's useful to talk about them as if they do—similar to how we talk about characters in novels.
Hartry Field(the author of the nominalist program discussed): A contemporary philosopher who developed a theory showing that we might not actually need to believe in abstract objects (like numbers) even though they seem useful in science and math.
Mathematical sentences(what the statement is about): Statements written in mathematical language, like 'two plus two equals four' or more complex equations and theorems.
Platonists(as the group of philosophers defending this position): Philosophers who believe in Platonism—that abstract objects like numbers and mathematical truths exist independently of our minds.
Substantive theoretical commitment(philosophy of mathematics): A real, important assumption or belief that an idea depends on, rather than something obvious or trivial.
Trivial consequence(describing whether the results should be expected as an automatic outcome): A result that follows automatically or obviously from the starting point, without needing anything extra or surprising.
compositional semantics(Contrasted with holistic semantics in debates about meaning holism): A semantics in which the meanings of complex expressions can be determined solely from the meanings of their component parts

Connections

2 topics

Modality & Possibility1 linked Philosophy of Language1 linked

Compositional semantics for mathematical language (recursive rules from basic te...Field's fictionalism rejects abstract objects while accepting compositional sema...

Details

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