The reliability challenge (Hartry Field, 1989) stands independent of causal theories: any epistemology must explain why mathematicians' beliefs systematically correlate with abstract truths.

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Abstract truths(as what mathematicians' beliefs are said to correspond with): True statements about things that don't physically exist, like numbers, geometric shapes, or logical principles.
Causal theories(as the type of theory Field's challenge works independently of): Explanations based on cause-and-effect relationships—the idea that one thing directly causes another to happen (like how touching a hot stove causes pain).
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.
Systematically correlate(as describing the relationship between mathematicians' beliefs and mathematical truths): When two things tend to line up or match with each other reliably and repeatedly, following a consistent pattern.

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