Section 1.) Introduction-Keynes’s axiom of Non -additivity
Consider the following assessment made by Keynes in the A Treatise on Probability in chapter 26 concerning the use of mathematics in the social sciences and liberal arts (Keynes’s terms these moral sciences) :
“The hope, which sustained many investigators in the course of the
Nineteenth century, of gradually bringing the moral sciences under the sway of mathematical reasoning, steadily recedes—if we mean, as they meant, by mathematics the introduction of precise numerical methods. The old assumptions, that all quantity is numerical and that all quantitative characteristics are additive, can be no longer sustained. Mathematical reasoning now appears as an aid in its symbolic rather …show more content…
The axiom used by the neoclassical schools of economics follows Jeremy Bentham’s emphasis on additivity and quantification. Thus, Keynes’s reference to Euclidean, non-Euclidean, and the axiom of parallels (Keynes, GT; 1936, p.16) is actually a contrast between additivity and non-additivity. Keynes’s axiom of non additivity can be contrasted with the neoclassical axiom of additivity. All of the neoclassical results, such as neutrality of money and gross substitutes, follow from the assumptions of additivity and …show more content…
The concept of interval valued probability in then developed and applied in chapters 15,16,17,20, 22, and 26 of the TP by Keynes. Interval –valued probabilities are non additive and non linear, since the inequality constraints used can involve powers greater than one. See Brady, 1993;Brady,2002;Brady,2004A; Brady 2004B, and Brady and Arthmar,2012 for a technical discussion of Keynes’s application of his non additive, nonlinear approach to decision making. See Brady,2012, for a general overview of Keynes’s non additive
Consider the following assessment made by Keynes in the A Treatise on Probability in chapter 26 concerning the use of mathematics in the social sciences and liberal arts (Keynes’s terms these moral sciences) :
“The hope, which sustained many investigators in the course of the
Nineteenth century, of gradually bringing the moral sciences under the sway of mathematical reasoning, steadily recedes—if we mean, as they meant, by mathematics the introduction of precise numerical methods. The old assumptions, that all quantity is numerical and that all quantitative characteristics are additive, can be no longer sustained. Mathematical reasoning now appears as an aid in its symbolic rather …show more content…
The axiom used by the neoclassical schools of economics follows Jeremy Bentham’s emphasis on additivity and quantification. Thus, Keynes’s reference to Euclidean, non-Euclidean, and the axiom of parallels (Keynes, GT; 1936, p.16) is actually a contrast between additivity and non-additivity. Keynes’s axiom of non additivity can be contrasted with the neoclassical axiom of additivity. All of the neoclassical results, such as neutrality of money and gross substitutes, follow from the assumptions of additivity and …show more content…
The concept of interval valued probability in then developed and applied in chapters 15,16,17,20, 22, and 26 of the TP by Keynes. Interval –valued probabilities are non additive and non linear, since the inequality constraints used can involve powers greater than one. See Brady, 1993;Brady,2002;Brady,2004A; Brady 2004B, and Brady and Arthmar,2012 for a technical discussion of Keynes’s application of his non additive, nonlinear approach to decision making. See Brady,2012, for a general overview of Keynes’s non additive