The notion of epistemic peerhood is central to the debate about peer disagreement. This paper argues that 'peerhood' is ambiguous, and pernisciously so. Taking Elga's equal-likelihood notion as a starting point, peerhood holds when two agents are equally likely to be right. One one reading, two agents are peers when they are in fact equally likely to be right. On another, they are peers when they are equally likely to be right in expectation, allowing for some random variation in their actual likelihood of being right. I show that this ambiguity affects other existing accounts of peerhood, including Gelfert's requirement of equal reflective ignorance. While the ambiguity has previously been noted (Weber 2017), its normative implications have not been properly understood. I examine these implications via a probabilistic truth-approximation model. In this model, peerhood-in-fact entails a unimodal posterior over the true value, supporting conciliation. By contrast, peerhood-in-expectation entails a bimodal posterior, warranting steadfast responses. Whether conciliation or steadfastness is warranted depends, in part, on whether two agents are peers-in-fact, or peers-in-expectation.

It has recently been argued that understanding requires compression (Wilkenfeld 2019; Carbonell 2023; Queloz Beckmann 2025). On these views, understanding a domain requires appropriately compressed mental representations that support abilities characteristic of understanding, such as the ability to produce relevant explanations, predictions, and counterfactual judgments. Yet, these proposals remain programmatic. Drawing on a notion of compression from computer science, they leave open what compression could amount to in human minds. This paper closes that gap, by offering accounts of mental compression within two influential models of human cognition: the Language of Thought and graph-like cognitive maps. I argue for these accounts on both conceptual and empirical grounds. Within a LoT framework, mental compression can be understood in terms of representational economy measured by the number of syntactic primitives required to encode some proposition. Conceptually, I address worries about the opaqueness of LoT implementation by appealing to the Language Invariance Theorem, which constrains the extent to which compression depends on the choice of coding scheme. Empirically, I draw on computational modeling work (e.g., Sabl´e-Meyer et al., 2022) showing that human learners prefer objects with descriptions with fewer syntactic primitives. Within a graph-based framework, I argue that compression occurs at at least two levels. First, graphs compress information about many possible states of the world by encoding systematic dependency relations among nodes. Second, hierarchical graphical representations compress lower-level detail into higher-level abstractions. Empirically, response-time patterns in studies of hierarchical graph learning (e.g., Xia et al., 2023) suggest that humans represent graphical structure at multiple levels of abstraction. The resulting notion of mental compression explains central features of understanding: grasping of dependency relations, the ability to generalize to novel cases, and the intuitive contrast between genuine understanding and brute memorization.

We sometimes receive non-lopsided higher-order defeat: evidence that leaves our first-order credences intact, while casting doubt that our credences are the right credences to have. The resilience revision view (Steglich-Petersen, 2019) maintains that agents facing such defeat ought to lower their credences' resilience. This paper argues that this view faces a problem of normative over-determination: a situation in which standard Bayesian norms and the resilience revision view issue conflicting verdicts about how agents ought to update. To resolve this conflict, I argue for weighted conditionalization: an updating rule on which an agent's posterior is a weighted average of the credence supported by her prior evidence and the credence supported by incoming evidence, with the weight determined by rational higher-order attitudes. I derive this rule via two independent routes: first, from an independently supported bridge principle linking higher-order confidence to a normalized notion of resilience, and second, from a Bayesian signal aggregation model treating an agent's credences as noisy signals of a rationally optimal credence. The convergence of these independent derivations provides strong support for weighted conditionalization as the natural updating rule in contexts of higher-order uncertainty. Doubting oneself well, it turns out, is not just a matter of lowering one's higher-order confidence, but of updating in proportion to that doubt.