物理学和数学的一致理论
Towards a Coherent Theory of Physics and Mathematics
摘要：
作为一种方法的一切理论的框架，发展一个连贯的理论，数学和物理学一起描述。这种理论的主要特征是：理论必须是有效的和足够强的，它必须最大限度地描述自己的有效性和足够强。有效性的数学逻辑定义被使用，足够的强度被认为是一个必要和有用的概念。最大描述自身有效性和足够强度的要求可能有助于拒绝描述小于最大描述的候选相干理论。其他方面的一个连贯的理论讨论包括普遍适用性，人择原理的关系，和可能的唯一性。它表明，物理和数学宇宙的基本属性是包容和出现一个连贯的理论。对这一点的支持包括与中等大小的附近系统相比，非常小或非常大的遥远系统的属性的间接现实状态。语言的必要物理性质的讨论包括语言的物理模型和证明任何可公理化理论的表达式的意义内容似乎独立于理论的算法复杂性。哥德尔映射对于一个连贯的理论似乎不如对于纯粹的数学理论有用，因为任何语言的所有符号和单词都必须有已经在连贯理论领域中的物理系统状态的表示。
英文摘要：
As an approach to a Theory of Everything a framework for developing a coherent theory of mathematics and physics together is described. The main characteristic of such a theory is discussed: the theory must be valid and and sufficiently strong, and it must maximally describe its own validity and sufficient strength. The mathematical logical definition of validity is used, and sufficient strength is seen to be a necessary and useful concept. The requirement of maximal description of its own validity and sufficient strength may be useful to reject candidate coherent theories for which the description is less than maximal. Other aspects of a coherent theory discussed include universal applicability, the relation to the anthropic principle, and possible uniqueness. It is suggested that the basic properties of the physical and mathematical universes are entwined with and emerge with a coherent theory. Support for this includes the indirect reality status of properties of very small or very large far away systems compared to moderate sized nearby systems. Discussion of the necessary physical nature of language includes physical models of language and a proof that the meaning content of expressions of any axiomatizable theory seems to be independent of the algorithmic complexity of the theory. Gödel maps seem to be less useful for a coherent theory than for purely mathematical theories because all symbols and words of any language musthave representations as states of physical systems already in the domain of a coherent theory.
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