Mathematical Platonism holds that mathematical objects (numbers, sets) exist independently of minds—we discover rather than invent them. This explains mathematics' objectivity and applicability to physics. But it faces an epistemological puzzle: if mathematical objects are abstract and causally inert, how do we know about them? Physical perception won't work. Anti-Platonists propose that mathematics is a useful fiction or formal game, but then must explain its apparent objectivity and indispensability to science.
Based on the passage, it can be inferred that
Platonism has no virtues as a philosophy of mathematics
anti-Platonists face no explanatory challenges
major positions in philosophy of mathematics may each explain some features while struggling with others
mathematical knowledge is obtained through ordinary perception
Correct Answer: C
Choice C is the best answer. Platonism explains objectivity but struggles with knowledge; anti-Platonism vice versa.
- Context clues: Platonism explains objectivity but faces epistemological puzzle; anti-Platonism avoids that but must explain objectivity.
- Meaning: Each position trades strengths for weaknesses.
- Verify: The reciprocal challenges show both partially succeed and partially fail.
💡 Strategy: When competing theories each face the challenges the other avoids, infer partial success for both.
Choice A is incorrect because Platonism "explains mathematics' objectivity and applicability." Choice B is incorrect because anti-Platonists "must explain" objectivity and indispensability. Choice D is incorrect because physical perception "won't work" for abstract objects.