From a textbook by Arial Caticha, Entropic Inference and the Foundations of Physics (HERE).
The framework for inference will be constructed by a process of eliminative induction. The objective is to design the appropriate tools, which in our case, means designing the theory of probability and entropy. The different ways in which probabilities and entropies are defined and handled will lead to different inference schemes and one can imagine a vast variety of possibilities. To select one we must first have a clear idea of the function that those tools are supposed to perform, that is, we must specify design criteria or design specifications that the desired inference framework must obey. Finally, in the eliminative part of the process one proceeds to systematically rule out all those inference schemes that fail to comply with the design criteria — that is, that fail to perform as
There is no implication that an inference framework designed in this way is in any way “true”, or that it succeeds because it achieves some special intimate agreement with reality. Instead, the claim is pragmatic: the method succeeds to the extent that the inference framework works as designed and its performance will be deemed satisfactory as long as it leads to scientific models that are empirically adequate. Whatever design criteria are chosen, they are meant to be only provisional — just like everything else in science, there is no reason to consider them immune from further change and improvement.
The pros and cons of eliminative induction have been the subject of considerable philosophical research. On the negative side, eliminative induction, like any other form of induction, is not guaranteed to work. On the positive side, eliminative induction adds an interesting twist to Popper’s scientific methodology. According to Popper scientific theories can never be proved right, they can only be proved false; a theory is corroborated only to the extent that all attempts at falsifying it have failed. Eliminative induction is fully compatible with Popper’s notions but the point of view is just the opposite. Instead of focusing on failure to falsify one focuses on success: it is the successful falsification of all rival theories that corroborates the surviving one. The advantage is that one acquires a more explicit understanding of why competing theories are eliminated.