, Assume C is consistent, hence a subset of a rational constitution C 2 T. We show that CjS C

, It su¢ ces to specify a constitution C such that CjS violates R. Simply let C be any constitution such that F C. Since F C and C CjS, we have F CjS. So the revised constitution CjS violates R. = ?, it su¢ ces to prove Theorem 4. Consider any theory T. (a) By de?nition, each conditional-completeness requirement of T is conditional on some set P of states, and has at least one U-state. For each such requirement, ?x an arbitrary member m U of U , and de?ne the rule r U = (P; m U ). Let S be any reasoning system containing one such rule for each conditional-completeness requirement. Clearly, S achieves all conditional-completeness requirements of T. (b) Consider any conditional-completeness requirement of T , de?ned by some P and U (where U 6 = ?). Suppose some consistency-preserving reasoning system S achieves this requirement. Since the requirement is achieved, there must be some m 0 2 U such that m 0 2 P jS. To complete the proof, it su¢ ces to show that m 0 is not falsi?able given P. To that end, we consider a consistent C 0 P , and must show consistency of C 0, The ?rst is that C is closed under S, because it is rational and hence in particular satis?es all closedness requirements of T

, For any constitution C 6 2 T , T makes the requirement not to have that constitution, i.e., the 'unique-exclusion'requirement R C = fC 0 : C 0 6 = Cg: The theory is expressible as the conjunction (intersection) of its unique-exclusion requirements: T = \ CM :C6 2T R C. Each R C is a uni?ed requirement, as it equivalently demands that possession of all states in C implies possession of at least one state not in C, formally R C = fC 0 : C C 0 ) C 0 \ (M \ C) 6 = ?g. C References Boghossian, Rationality, reasoning and rules: re ?ections on Broome's rationality through reasoning, vol.173, pp.3385-3397, 2016.

J. Broome, Wide or narrow scope? Mind, vol.116, pp.360-370, 2007.

J. Broome, Synchronic requirements and diachronic permissions, Canadian Journal of Philosophy, vol.45, pp.630-646, 2013.

R. Cubitt and R. Sugden, On money pumps, Games and Economic Behavior, vol.37, pp.121-160, 2001.

R. Cubitt and R. Sugden, Common knowledge, salience and convention: a reconstruction of David Lewis's game theory, Economics and Philosophy, vol.19, p.20, 2003.

, Documents de travail du Centre d'Economie de la Sorbonne-2018, vol.30, pp.175-210

G. Cullity, Describing rationality, Philosophical Studies, vol.173, pp.3399-3411, 2016.

F. Dietrich and C. List, Mentalism versus behaviourism in economics: a philosophyof-science perspective, Economics and Philosophy, vol.32, issue.3, pp.249-281, 2016.
DOI : 10.1017/s0266267115000462

URL : http://eprints.lse.ac.uk/62444/1/List_Mentalism%20vs%20behaviourism_2016.pdf

F. Dietrich and C. List, Reason-based choice and context-dependence: an explanatory framework, Economics and Philosophy, vol.32, issue.3, pp.175-229, 2016.
DOI : 10.1017/s0266267115000474

URL : https://hal.archives-ouvertes.fr/halshs-01249514

F. Dietrich and C. List, What matters and how it matters: a choice-theoretic representation of moral theories, Philosophical Review, vol.126, pp.421-479, 2017.
URL : https://hal.archives-ouvertes.fr/halshs-01744079

F. Dietrich, A. Staras, and R. Sugden, Psychology analysed logically: when are our attitudes consistent, complete, and deductively closed?, The Philosophy of Economics: An Anthology, 2007.

D. Hausman, . Preference, C. Value, ;. G. Welfare, G. Lecouteux et al., Preference puri?cation and the inner rational agent: a critique of the conventional wisdom of behavioural welfare economics, Journal of Economic Methodology, vol.23, pp.1-25, 2012.

N. Kolodny, Why be rational? Mind, vol.114, pp.509-563, 2005.

N. Kolodny, State or process requirements? Mind, vol.116, pp.371-385, 2007.

D. Lewis, Convention: A Philosophical Study, 1969.

P. Manzini and M. Mariotti, Categorize then choose: Boundedly rational choice and welfare, Journal of the European Economic Association, vol.10, pp.939-1213, 2012.
DOI : 10.1111/j.1542-4774.2012.01078.x

S. Okasha, On the interpretation of decision theory, Economics and Philosophy, vol.32, issue.3, pp.409-433, 2016.

D. ;. Par?tt and J. Broome, Reasons and Motivation, Proceedings of the Aristotelian Society, vol.1, pp.99-146, 1997.

P. Pettit, Broome on reasoning and rule-following, Philosophical Studies, vol.173, pp.3373-3384, 2016.
DOI : 10.1007/s11098-016-0718-z

L. J. Savage, The foundations of statistics, Philosophical Studies, vol.173, pp.3413-3430, 1954.

J. Sta¤el, Can there be reasoning with degrees of belief?, Synthese, vol.190, issue.16, pp.3535-3551, 2013.

A. ;. Tarski, C. ;. Sunstein, S. Lindsey, and T. Y. Schooler, Nudge: Improving Decisions About Health, Wealth, and Happiness, On Fundamental Concepts of Metamathematics Thaler, vol.107, pp.101-126, 1930.

C. Wright, Comment on Paul Boghossian, Philosophical Studies, vol.169, pp.27-37, 2014.