The safety conception of knowledge holds that a belief constitutes knowledge iff relevantly similar beliefs—its epistemic counterparts—are true. It promises an instructive account of why certain general principles of knowledge hold. We focus on two such principles that anyone should endorse: the closure principle that knowledge is downward closed under competent conjunction elimination, and the counter-closure principle that knowledge is upward closed under competent conjunction introduction. We argue that anyone endorsing the former must also endorse the latter on pains of an unacceptable form of bootstrapping. We devise new formal models to identify necessary and sufficient conditions for these principles to hold on conceptions that construe knowledge in terms of true counterparts. These conditions state that counterparts of premise and conclusion beliefs are coordinated in certain ways whenever these beliefs stand in the relevant inferential relations. We show that the safety conception faces insuperable problems vindicating these coordination principles, because its epistemic counterpart relation is symmetric. We conclude that it thus proves unable to account for minimal closure properties of knowledge. More generally, our formal results establish parameters within which any conception must operate that construes knowledge in terms of true counterparts.

知识的安全概念认为，如果相关相似的信念（其认知对应物）为真，则信念构成知识。它承诺对某些一般知识原理为何成立进行富有启发性的说明。我们重点关注任何人都应该认可的两个这样的原则：封闭原则，即在胜任连词消除下知识向下封闭，以及反封闭原则，即在胜任连词引入下知识向上封闭。我们认为，任何支持前者的人也必须支持后者，因为这是一种不可接受的自举形式。我们设计新的形式模型来确定这些原则的必要和充分条件，以坚持根据真实对应物解释知识的概念。这些条件表明，只要这些信念处于相关的推理关系中，前提和结论信念的对应部分就会以某种方式协调。我们表明，安全概念面临着证明这些协调原则的不可克服的问题，因为它的认知对应关系是对称的。我们的结论是，它因此无法解释知识的最小封闭属性。更一般地说，我们的正式结果建立了参数，任何概念都必须在这些参数内运作，以真实对应物来解释知识。