Similarly, Carnap (1952) would maintain that both scientists might be rational because rationality is relative to an inductive method or confirmation function, and the two scientists might be employing different inductive methods or confirmation functions.
It is a closely reasoned, deductively argued defense of the rationality of inductive inference, well meriting continued attention.
As the foregoing discussion indicates, the dynamical study of equilibrium selection is a diverse, fast-growing area of research.[7] Moreover, it raises difficult questions on the boundary between economics and philosophy, such as how to analyze inductive reasoning, how much rationality to attribute to social agents, and so on.
According to McTaggart, we need an argument for the rationality of induction, and such an argument will not be an inductive argument.
At that time, statistics and probability theory took on a methodological role as an analysis of inductive inference, and attempts to ground the rationality of induction in the axioms of probability theory have continued throughout the 20th century and in to the present.
One solution to the problem, associated with Peter Strawson (1952), is that "adopting the inductive practices and principles that we do is constitutive of our concept of rationality".
Many epistemologists have proposed various categorical imperatives for inductive inquiry, for example in the form of an "inductive logic" or norms of "epistemic rationality".
These principles include deductive and inductive logic, probability, parsimony and hypothesis testing, as well as science's presuppositions, limitations, ethics and bold claims of rationality and truth.
Those two features are: (1) the introduction of a formal apparatus for inductive logic; (2) the introduction of a pragmatic self-defeat test (as illustrated by Dutch Book Arguments) for epistemic rationality as a way of extending the justification of the laws of deductive logic to include a justification for the laws of inductive logic.
Other attempts to establish the foundations of inductive inference were undertaken by Ajdukiewicz (via statistics, decision theory and game theory (he mainly investigated the problem of the rationality of modes of fallible inference), Czeżowski (via probability logic in the sense of Reichenbach) and Zawirski (via a combination of many-valued logic and probability theory).
