ABSTRACT

A standard approach to indeterminacy treats ‘determinately’ and ‘indeterminately’ as modal operators. Determinacy behaves like necessity; indeterminacy like contingency. This raises two questions. What is the appropriate modal system for these operators? And how should we interpret that system? Ken Akiba has developed an account of ontic indeterminacy that interprets possible worlds as worldly precisifications. He argues that this account vindicates S4 as the logic of indeterminacy. In this paper I explore one significant and surprising consequence of this view. I do this in two stages. First, I prove a technical result, which I call the Infinite Indeterminacy Theorem. Roughly put, this theorem states that, at any given precisification w, either every instance of indeterminacy admits of never-ending higher-order indeterminacy, or else there's indeterminacy in an infinite amount of distinct atomic formulas. In slogan form: either all indeterminacy is infinitely ascending or else there's infinitely wide indeterminacy. Second, I unpack the metaphysical consequences of this technical result (under its intended interpretation) and assess their plausibility. I conclude that these consequences commit Akiba's theory to highly contentious – and arguably untenable – views about the metaphysics of indeterminacy and related matters.

摘要

不确定性的标准方法将“确定地”和“不确定地”视为模态运算符。决定性的行为就像必然性；不确定性如偶然性。这就提出了两个问题。对于这些操作员来说，合适的模态系统是什么？我们应该如何解释这个系统？Ken Akiba 开发了一种关于本体不确定性的解释，将可能的世界解释为世俗的精确性。他争辩说，这个解释证明了 S4 是不确定性的逻辑。在本文中，我探讨了这一观点的一个重要且令人惊讶的结果。我分两个阶段进行。首先，我证明了一个技术结果，我称之为无限不确定性定理。粗略地说，这个定理指出，在任何给定的精度w，要么每个不确定性实例都承认永无止境的高阶不确定性，要么在无限数量的不同原子公式中存在不确定性。以口号的形式：要么所有的不确定性都是无限上升的，要么就是无限宽的不确定性。其次，我解开这个技术结果的形而上学后果（在其预期解释下）并评估它们的合理性。我的结论是，这些后果使 Akiba 的理论对不确定性和相关问题的形而上学产生了极具争议的——而且可以说是站不住脚的——观点。