   On first sight it seems natural to say that one can believe to ‘know’ something, even when in fact one does not actually know it. So believing to know something is philosophically conceived to be different from claiming true knowledge. Yet, under the assumption that what is known is also believed, this specific interplay between modalities for knowledge and belief can lead us into trouble if we identify belief with a KD45-modality B, and knowledge with a S5-modality for K. For suppose \(BK\varphi \land \lnot K\varphi\) is assumed. Then, by negative introspection of the second conjunct, we derive \(K\lnot K\varphi\). But as knowledge implies belief, we derive \(B\lnot K\varphi\). This together with the first conjunct \(BK\varphi\) will give us, by additivity of belief, \(B(K\varphi \land \lnot K\varphi)\). Hence we derive the belief in a contradiction, which is not compatible with the assumption of consistency of beliefs (axiom D) in KD45. This problem is known as the paradox of the perfect believer (and also as the Voorbraak paradox), as it was originally (but equivalently) described (Voorbraak 1993) as the derivability of the bridge principle \(BK\varphi \rightarrow K\varphi\), which states that a belief in knowing a given \(\varphi\) is enough to know \(\varphi\). (The derivation of \(BK\varphi \rightarrow K\varphi\) also relies on the negative introspection of knowledge, the normality and consistency of beliefs, and the bridge principle stating that knowledge implies belief; Gochet &amp; Gribomont 2006: 114.)