感知公理与欧几里德几何学是不可调和的
Semir Zeki1, Zachary F Hale1, Ahmad Beyh1
1Laboratory of Neurobiology, University College London, London, UK.
The European journal of neuroscience
|May 28, 2024
概括
这项研究揭示了视觉感知和数学逻辑之间存在着根本的断开. 光学错觉的感知公理不能与欧几里德几何相协调,这表明不同的大脑现实.
科学领域:
- 神经科学是一个神经科学.
- 认知科学 认知科学
- 数学的哲学数学的哲学
背景情况:
- 公理是逻辑和数学中的基本真理,但戈德尔的不完整性定理证明了公理系统固有的局限性.
- 之前关于公理系统的研究没有解释大脑产生和调解逻辑的机制.
- 光学错觉为研究感知与形式系统之间的关系提供了一个独特的机会.
研究的目的:
- 调查视觉感知公理与数学描述 (特别是欧几里德几何) 之间的潜在不兼容性.
- 探索是否可以调整感知公理以符合认知 (数学) 系统.
- 为视觉感知和数学认知的独特和独立性提供证据.
主要方法:
- 参与者被呈现了光学错觉,在视觉感知和欧几里德几何描述之间产生了差异.
- 参与者试图调整他们的感知几何公理,以匹配欧几里德的描述.
- 测量了感知和数学描述之间的不匹配程度.
主要成果:
- 在视觉感知和欧几里德几何描述光学错觉之间观察到一个显著和不可调和的差异.
- 参与者无法使他们的感知公理完全符合欧几里德的描述,即使意识到差异.
- 不匹配的程度因个人而异,表明个性化的感知公理.
结论:
- 感知公理,代表感知真实陈述,不能被准确地描述的数学系统,如欧几里德几何学.
- 视觉感知系统的逻辑基本上与认知 (数学) 系统是不可调和的.
- 这种不可调和性表明,不同的大脑现实存在,不一定会被认知知识更新,挑战单一客观大脑现实的概念.
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