conditional probability, and posterior probability). The bias–variance tradeoff is a framework that incorporates the Occam's razor principle in its balance between overfitting (associated with lower bias but higher variance) and underfitting (associated with lower variance but higher bias). Other philosophers Karl Popper Karl Popper argues that a preference for simple theories need not appeal to practical or aesthetic considerations. Our preference for simplicity may be justified by its falsifiability criterion: we prefer simpler theories to more complex ones "because their empirical content is greater; and because they are better testable". The idea here is that a simple theory applies to more cases than a more complex one, and is thus more easily falsifiable. This is again comparing a simple theory to a more complex theory where both explain the data equally well. Elliott Sober The philosopher of science Elliott Sober once argued along the same lines as Popper, tying simplicity with "informativeness": The simplest theory is the more informative, in the sense that it requires less information to a question. He has since rejected this account of simplicity, purportedly because it fails to provide an epistemic justification for simplicity. He now believes that simplicity considerations (and considerations of parsimony in particular) do not count unless they reflect something more fundamental. Philosophers, he suggests, may have made the error of hypostatizing simplicity (i.e., endowed it with a sui generis existence), when it has meaning only when embedded in a specific context (Sober 1992). If we fail to justify simplicity considerations on the basis of the context in which we use them, we may have no non-circular justification: "Just as the question 'why be rational?' may have no non-circular answer, the same may be true of the question 'why should simplicity be considered in evaluating the plausibility of hypotheses?'" Richard Swinburne Richard Swinburne argues for simplicity on logical grounds: According to Swinburne, since our choice of theory cannot be determined by data (see Underdetermination and Duhem–Quine thesis), we must rely on some criterion to determine which theory to use. Since it is absurd to have no logical method for settling on one hypothesis amongst an infinite number of equally data-compliant hypotheses, we should choose the simplest theory: "Either science is irrational [in the way it judges theories and predictions probable] or the principle of simplicity is a fundamental synthetic a priori truth.". Ludwig Wittgenstein From the Tractatus Logico-Philosophicus: 3.328 "If a sign