强决定论与可计算性
Strong Determinism vs. Computability
摘要：
思想是否受物理定律的支配？物理定律是可计算的吗？有意识的思维过程是可计算的吗？目前，对于这些问题的正确答案是什么，几乎没有达成一致意见。彭罗斯更进一步，断言：{ \it确实需要一个激进的新理论，而且我还建议，当这个理论被发现时，它将具有本质上的非计算性质。}本文的目的有三个：1）检查强决定论和可计算性假设之间的不相容性，2）给出不可计算的物理定律的新例子，3）讨论哥德尔不完全性定理在反驳算法理论（如强人工智能）可以提供足够的心理理论的说法中的相关性。最后，我们质疑计算理论是否足以讨论物理定律和思维过程。
英文摘要：
Are minds subject to laws of physics? Are the laws of physics computable? Are conscious thought processes computable? Currently there is little agreement as to what are the right answers to these questions. Penrose goes one step further and asserts that: {\it a radical new theory is indeed needed, and I am suggesting, moreover, that this theory, when it is found, will be of an essentially non-computational character.} The aim of this paper is three fold: 1) to examine the incompatibility between the hypothesis of strong determinism and computability, 2) to give new examples of uncomputable physical laws, and 3) to discuss the relevance of Gödel's Incompleteness Theorem in refuting the claim that an algorithmic theory---like strong AI---can provide an adequate theory of mind. Finally, we question the adequacy of the theory of computation to discuss physical laws and thought processes.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
