Blackwell Reference Online

Extract

Scientists often appeal to a criterion of simplicity as a consideration that helps them decide which hypotheses are most plausible. Some such principle seems to be essential; the data, all by themselves, apparently cannot single out as best one hypothesis among the set of competitors. A standard setting in which considerations of simplicity are brought to bear is the curve-fitting problem , depicted in figure 64.1 . Suppose a scientist wishes to discover what general relationship obtains between two quantitative characteristics - for example, the temperature of the gas in a closed chamber and the pressure that the gas exerts on the sides of the chamber. The scientist might gather data on this question by observing a system that displays some value of the independent variable, x, and seeing what value of the dependent variable, y, the system exhibits. By making several observations of this sort, the scientist accumulates a set of <x, y> values, each of which may be represented as a point in the coordinate system depicted in the figure. What role might these data points play in the task of evaluating different competing hypotheses, each of which corresponds to some curve drawn in the x–y plane? If one could assume that the observations were entirely free from error, one could conclude that any curve that fails to pass exactly through the data points must be false. However, ... log in or subscribe to read full text