When beliefs are quantified as credences, they are related to each other in terms of closeness and accuracy. The “accuracy first” approach in formal epistemology wants to establish a normative account for credences (probabilism, Bayesian conditioning, principle of indifference, and so on) based entirely on the alethic properties of the credence: how close it is to the truth. To pull off this project, there is a need for a scoring rule. There is widespread agreement about some constraints on this scoring rule (for example propriety), but not whether a unique scoring rule stands above the rest. The Brier score equips credences with a structure similar to metric space and induces a “geometry of reason.” It enjoys great popularity in the current debate. I point out many of its weaknesses in this article. An alternative approach is to reject the geometry of reason and accept information theory in its stead. Information theory comes fully equipped with an axiomatic approach which covers probabilism, standard conditioning, and Jeffrey conditioning. It is not based on an underlying topology of a metric space, but uses a non-commutative divergence instead of a symmetric distance measure. I show that information theory, despite initial promise, also fails to accommodate basic epistemic intuitions; and speculate on its remediation.

当信念被量化为可信度时，它们在接近度和准确性方面相互关联。形式认识论中的“准确性第一”方法希望完全基于信任的道德属性：它与真相的接近程度，为信任（概率论、贝叶斯条件反射、无差异原则等）建立规范性解释。为了完成这个项目，需要一个评分规则。关于此评分规则的一些限制（例如适当性），人们普遍同意，但不同意独特的评分规则是否高于其他规则。Brier 分数为信任配备了类似于度量空间的结构，并引发了“理性几何”。它在当前的辩论中非常受欢迎。我在这篇文章中指出了它的许多弱点。另一种方法是拒绝理性的几何学而接受信息论。信息论完全配备了公理化方法，涵盖概率论、标准条件反射和杰弗里条件反射。它不是基于度量空间的底层拓扑，而是使用非交换散度而不是对称距离度量。我表明，尽管最初的承诺，信息理论也不能适应基本的认知直觉；并推测其修复方法。但使用非交换散度而不是对称距离度量。我表明，尽管最初的承诺，信息理论也不能适应基本的认知直觉；并推测其修复方法。但使用非交换散度而不是对称距离度量。我表明，尽管最初的承诺，信息理论也不能适应基本的认知直觉；并推测其修复方法。