Gödel's incompleteness theorems showed that any consistent formal system powerful enough to express arithmetic contains true statements it cannot prove. This shattered Hilbert's program to prove mathematics complete and consistent from within. Some interpret this as limiting mechanical computation and supporting human mathematical intuition transcending formal rules. Others caution that the theorems apply to formal systems, not necessarily to human cognition, which may itself be formalizable in ways yet unknown.
The passage suggests that
the implications of mathematical results for understanding human cognition may be genuinely disputed
Hilbert's program was never affected by Gödel's work
human cognition has been proven to be a formal system
all mathematical statements are provable within any system
Correct Answer: A
Choice A is the best answer. Some see cognitive implications; others caution against this reading.
- Context clues: Some interpret Gödel as supporting human intuition transcending rules; others caution the theorems may not apply to cognition.
- Meaning: The cognitive implications are disputed.
- Verify: "Some interpret...Others caution" shows genuine disagreement.
💡 Strategy: When different interpretations of a result's implications exist, infer the implications are disputed.
Choice B is incorrect because Gödel "shattered Hilbert's program." Choice C is incorrect because whether cognition is formalizable remains unknown. Choice D is incorrect because Gödel showed some true statements cannot be proven.