Text 1: Philosopher Dr. Anna Black defends mathematical platonism. "Numbers exist independently of minds," Black argues. "Mathematicians discover truths about abstract objects. Mathematical facts hold regardless of human beliefs."
Text 2: Mathematician Dr. David Wells advocates constructivism. "Mathematics is human creation," Wells contends. "We invent rather than discover mathematical structures. Different axiom choices yield different mathematics. Nothing exists independently awaiting discovery."
What ontological question divides Black and Wells?
Whether mathematicians are people
Whether mathematical objects have mind-independent existence
Whether axioms are used in mathematics
Whether proofs can be verified
Correct Answer: B
Choice B is the correct answer. Black says numbers exist independently—discovered. Wells says mathematics is created—invented. The dispute is about mathematical ontology: platonism vs. constructivism.
- Evidence: Black: numbers exist "independently of minds"; Wells: "human creation."
- Reasoning: Discovered vs. invented requires different ontological commitments.
- Conclusion: Mind-independent existence is the central dispute.
Choice A is incorrect because both accept mathematicians exist. Choice C is incorrect because Wells uses axiom choices as evidence for constructivism. Choice D is incorrect because proof verification isn't disputed.