{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,9]],"date-time":"2025-12-09T15:38:07Z","timestamp":1765294687985,"version":"3.40.5"},"reference-count":57,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2015,1,5]],"date-time":"2015-01-05T00:00:00Z","timestamp":1420416000000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Rev. symb. logic"],"published-print":{"date-parts":[[2015,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Robert Aumann presents his<jats:italic>Agreement Theorem<\/jats:italic>as the<jats:italic>key conditional<\/jats:italic>: \u201cif two people have the same priors and their posteriors for an event<jats:italic>A<\/jats:italic>are common knowledge, then these posteriors are equal\u201d (Aumann, 1976, p. 1236). This paper focuses on four assumptions which are used in Aumann\u2019s proof but are not explicit in the key conditional: (1) that agents commonly know, of some prior<jats:italic>\u03bc<\/jats:italic>, that it is the common prior; (2) that agents commonly know that each of them updates on the prior by conditionalization; (3) that agents commonly know that if an agent knows a proposition, she knows that she knows that proposition (the \u201c<jats:italic>KK<\/jats:italic>\u201d principle); (4) that agents commonly know that they each update only on true propositions. It is shown that natural weakenings of any one of these strong assumptions can lead to countermodels to Aumann\u2019s key conditional. Examples are given in which agents who have a common prior and commonly know what probability they each assign to a proposition nevertheless assign that proposition unequal probabilities. To alter Aumann\u2019s famous slogan: people<jats:italic>can<\/jats:italic>\u201cagree to disagree\u201d, even if they share a common prior. The epistemological significance of these examples is presented in terms of their role in a defense of the<jats:italic>Uniqueness Thesis<\/jats:italic>: If an agent whose total evidence is<jats:italic>E<\/jats:italic>is fully rational in taking doxastic attitude<jats:italic>D<\/jats:italic>to<jats:italic>P<\/jats:italic>, then necessarily, any subject with total evidence<jats:italic>E<\/jats:italic>who takes a different attitude to<jats:italic>P<\/jats:italic>is less than fully rational.<\/jats:p>","DOI":"10.1017\/s1755020314000380","type":"journal-article","created":{"date-parts":[[2015,1,5]],"date-time":"2015-01-05T09:42:41Z","timestamp":1420450961000},"page":"11-45","source":"Crossref","is-referenced-by-count":16,"title":["PEOPLE WITH COMMON PRIORS CAN AGREE TO DISAGREE"],"prefix":"10.1017","volume":"8","author":[{"given":"HARVEY","family":"LEDERMAN","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2015,1,5]]},"reference":[{"key":"S1755020314000380_ref9","doi-asserted-by":"publisher","DOI":"10.1016\/j.geb.2009.02.003"},{"key":"S1755020314000380_ref26","doi-asserted-by":"publisher","DOI":"10.5840\/jphil2014111411"},{"key":"S1755020314000380_ref40","doi-asserted-by":"publisher","DOI":"10.1017\/S0266267100003382"},{"key":"S1755020314000380_ref18","doi-asserted-by":"publisher","DOI":"10.1215\/00318108-2366479"},{"key":"S1755020314000380_ref45","unstructured":"Sadzik T . 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