 Logical entailments involving moral judgments are explained as follows: A constellation of attitudes which includes the attitudes expressed by the conditional and by the seemingly assertive premises but not those expressed by the conclusion is irrational, because it goes against the purposes of moral discourse. Somewhat more sophisticated ways of developing this strategy can be worked out but the basic idea is well exemplified in this proposal. The logic of attitudes strategy has met with much resistance on the part of cognitivists. One line of thought is that these proposals conflate genuine inconsistency with mere pragmatic incoherence (Hale 1986; Schueler 1988; Brighouse 1990; Zangwill 1992; van Roojen 1996). And non-cognitivists have responded with increasingly more sophisticated proposals about the logic of attitudes, including several proposals that do not employ higher order attitudes (Baker &amp; Woods 2015; Blackburn 1988b; Gibbard 1990, 2003; Horgan and Timmons 2006b; Schroeder 2008a, 2008b, 2008c). These are discussed in more detail in the supplementary document Embedding Problem Response Strategies.