论文标题
变质学的物理化及其对数学基础的影响
The Physicalization of Metamathematics and Its Implications for the Foundations of Mathematics
论文作者
论文摘要
从观察者中，唯一的Ruliad结构与所有可能的计算的纠缠极限相对应的独特的RuliAD结构的样本中都认为，变质学和物理学都可以从采样中出现。人类可以访问的高级数学的可能性被认为是对物理观察者对物理空间感知的数学观察者的模拟。对数学基础的传统公理方法的大量极限进行了物理化分析，以及一些形式化数学示例的明确经验性的过度的。讨论了数学的一般物理定律，这些定律与诸如MetAmagical运动，不可避免的二元性，证明拓扑结构和Metamathematimation的概念有关。有人认为，目前所实践的数学可以被视为以直接的柏拉图时尚的形式衍生出的，类似于我们对物理世界的经验，而公理的表述通常很方便，但并没有捕捉数学的最终特征。在这种观点的含义中，只有某些公理收集可能与人类数学观察者的不可避免的特征一致。讨论的历史和哲学联系以及对数学未来的基本影响。
Both metamathematics and physics are posited to emerge from samplings by observers of the unique ruliad structure that corresponds to the entangled limit of all possible computations. The possibility of higher-level mathematics accessible to humans is posited to be the analog for mathematical observers of the perception of physical space for physical observers. A physicalized analysis is given of the bulk limit of traditional axiomatic approaches to the foundations of mathematics, together with explicit empirical metamathematics of some examples of formalized mathematics. General physicalized laws of mathematics are discussed, associated with concepts such as metamathematical motion, inevitable dualities, proof topology and metamathematical singularities. It is argued that mathematics as currently practiced can be viewed as derived from the ruliad in a direct Platonic fashion analogous to our experience of the physical world, and that axiomatic formulation, while often convenient, does not capture the ultimate character of mathematics. Among the implications of this view is that only certain collections of axioms may be consistent with inevitable features of human mathematical observers. A discussion is included of historical and philosophical connections, as well as of foundational implications for the future of mathematics.
