Newcomb's problem and backward causality - Formalization of Weber's protestant ethic

Newcomb's Problem is a paradoxical decision making problem invented by William Newcomb. This problem has been widely debated primarily among philosophers and logicians, but not among social scientists. It involves a certain being called the Predictor. The problem requires a different approach depending on the capacity of the Predictor. In this paper, we focus on the so-called perfect Predictor, and analyze the problem from two perspectives. The first perspective is the one from mathematical logic, particularly the consistency of axiomatic system. We will show that Newcomb's Problem is not logically decidable as a decision making proposition. Furthermore, the essence of this problem is the selection between two types of causality, namely forward causality and backward causality. The second perspective is sociological. We will apply this formulation to a concrete social phenomenon. In particular, we will associate our formulation with a formalization of Max Weber's Protestant Ethic. The predestination concept of Calvinism provides us with the setting equivalent to Newcomb's Problem where God corresponds to the perfect Predictor.