论文标题
拥抱不可证实的性：认知需求和理论评估
Embracing undecidability: Cognitive needs and theory evaluation
论文作者
论文摘要
我们不知道有很多方法。即使在我们创建自己的系统中，例如，数学逻辑中的系统，Goëdel和Tarski的定理也对我们知道的知识施加了限制。当我们尝试谈论现实世界时，事情变得越来越困难。我们希望将数学理论的结果与观察进行比较，这意味着使用归纳方法。虽然我们可以证明理想的概率诱导应如何工作，但这种方法的要求包括一些无限。此外，即使能够计算这些方法并获得预测还不够。在某些情况下，不确定的情况可能是不可避免的，例如量子力学的解释或弦理论的当前状态。尽管如此，科学家仍然表现得好像他们能够知道真相。很明显，这种行为会导致严重的认知错误，因此需要接受我们的限制，我们的自然人类限制和我们创造的工具的局限性，都变得显而易见。本文将讨论我们必须如何接受知识几乎仅限于形式系统。而且，即使在这些中，总会有不可决定的命题。我们还将看到这些问题如何影响对物理学当前理论的评估。
There are many ways we can not know. Even in systems that we created ourselves, as, for example, systems in mathematical logic, Goëdel and Tarski's theorems impose limits on what we can know. As we try to speak of the real world, things get even harder. We want to compare the results of our mathematical theories to observations, and that means the use of inductive methods. While we can demonstrate how an ideal probabilistic induction should work, the requirements of such a method include a few infinities. Furthermore, it would not be even enough to be able to compute those methods and obtain predictions. There are cases where underdeterminacy might be unavoidable, such as the interpretation of quantum mechanics or the current status of string theory. Despite that, scientists still behave as if they were able to know the truth. As it becomes clear that such behavior can cause severe cognitive mistakes, the need to accept our limits, both our natural human limits and the limits of the tools we have created, become apparent. This essay will discuss how we must accept that knowledge is almost only limited to formal systems. Moreover, even in those, there will always be undecidable propositions. We will also see how those questions influence the evaluation of current theories in physics.
