 Principle E4 (Data Priority) reveals that Thagard’s theory is not a pure coherence theory, as it gives some epistemic priority to observational beliefs, making it rather a form of weak foundationalism, i.e., the view that some propositions have some initial epistemic support apart from coherence. Moreover, Thagard’s theory is based on binary coherence/incoherence relations, i.e., relations holding between two propositions. His basic theory does not handle incompatibilities that involve, in an essential way, more than two propositions. But incompatibilities of that sort may very well arise, as exemplified by the three propositions “Jane is taller than Martha”, “Martha is taller than Karen” and “Karen is taller than Jane”. Nevertheless, Thagard reports the existence of computational methods for converting constraint satisfaction problems whose constraints involve more than two elements into problems that involve only binary constraints, concluding that his characterization of coherence “suffices in principle for dealing with more complex coherence problems with nonbinary constraints” (Thagard 2000, 19). Thagard (2009) argues that there is a connection between explanatory coherence and (approximate) truth, where explaining consists in describing causal mechanisms. Several other authors have advocated coherence theories that emphasize the importance of explanatory relations. See, for example, Lycan (1988, 2012) and, for a book-length defense of explanatory coherentism, Poston (2014). Also related to Thagard’s work is Susan Haack’s so-called foundherentist theory, which draws on a proposed analogy between coherence justification (with foundationalist ingredients) and crossword puzzle-solving (Haack, 2009).