## Rosen Lutskanov

Papers of BAS. Humanities and Social Sciences

Vol. 5, 2018, No. 2

### Is modus ponens a valid inference rule?

**Rosen Lutskanov**

**Abstract. **The present text is organized as follows: (§1) examines briefly the role that modus ponens plays in traditional logic, (§2) discusses four well-known (alleged) counterexamples that cast doubt on its validity, (§3) analyses the interpretation of these counterexamples, as it was proposed by their inventors, (§4) marks the common features of the possible strategies to overcome the criticisms against modus ponens, (§5) considers the conclusions that can be based on the proposed analysis.

**Keywords: **logical consequence, inference, conditionals, modus ponens, logical form

Papers of BAS, Humanities and Social Sciences

Vol. 2, 2015, No. 3-4

*PHILOSOPHY*

**Rational choice and meta-preferences**

**Rosen Lutskanov**

**Abstract: **The theory of rational choice is one of the most important developments of classical microeconomics in the second half of the twentieth century. It was established on a firm basis by three Nobel prize winners Paul Samuelson, Kenneth Arrow and Amartya Sen. Later, it became gradually eclipsed by the rise of behavioral economics, which stresses the well-known fact that the choices which constitute our economic behavior usually are less than fully rational. Putting aside the issue about the descriptive adequacy of rational choice theory, it remains important from a normative point of view. Regrettably, all attempts to incorporate its lessons into a general theory of rational action are hindered by the fact that virtually any axiom of the theory, which functions as a part of the implicit definition of the concept of rational choice, can be juxtaposed with a relatively elementary counterexample. Many such counterexamples were formulated by Sen himself, and the future development of the theory seems possible only if we find a way to sidestep them. The present text proposes a novel solution to some of those counterexamples. It is organized as follows: (§1) introduces the conceptual apparatus of rational choice theory, paying special attention to the notions of feasible set, choice function and revealed preference; (§2) lists some of the popular “axioms” of the theory and sketches their informal meaning; (§3) elaborates on the reasons for Sen’s dissatisfaction with those axioms, linking them with the well-known phenomenon of menu dependence; (§4) introduces a novel approach which employs not one but two relations of preference, the second one being interpreted as a relation of meta-preference since it grades not the alternatives belonging to some feasible set but feasible sets themselves. As we shall see, this allows us to circumvent some of Sen’s criticisms.

**Keywords: **rational choice, choice function, revealed preference