The following text is from a philosophy of mathematics article.
Structuralism identifies mathematical objects with positions in structures rather than intrinsic entities. Numbers, for instance, are defined by their relational properties within the number structure, not by some essential nature. This view elegantly handles the indeterminacy of reference between isomorphic structures. Different versions—ante rem (structures exist abstractly) and in re (structures exist only in concrete instantiations)—carry different ontological commitments.
What is the primary purpose of the text?
To provide mathematical proofs of fundamental theorems
To explain structuralism and distinguish versions with different commitments
To argue that numbers do not really exist
To compare mathematical education across different countries
Correct Answer: B
Choice B is the best answer. The text explains structuralism about mathematics and distinguishes ante rem and in re versions with different ontological commitments.
- Evidence: The text explains structuralism: "Structuralism identifies mathematical objects with positions in structures." It distinguishes versions: "ante rem (structures exist abstractly) and in re (structures exist only in concrete instantiations)... carry different ontological commitments."
- Reasoning: The passage introduces a philosophy of math and shows it has flavors with different metaphysical implications.
- Conclusion: The purpose is to explain structuralism and distinguish versions.
💡 Strategy: Summarize: Numbers are positions (Structuralism). Abstract or concrete? (Versions).
Choice A is incorrect because proofs aren't provided. Choice C is incorrect because existence isn't denied. Choice D is incorrect because education isn't compared.