H. P. Grice, "Crazy Bayesy"

CRAZY BAYESY -- Bayes, Thomas (1702–61) English clergyman and theorist of probability. Bayes established the basis of an account of confirmation, explaining how evidence can support hypotheses by altering the prior probability of the hypotheses being true. Bayesian philosophy of science has flourished in recent decades. His most important work is An Essay towards Solving a Problem in the Doctrine of Chances (1763). Bayes’s theorem Logic, philosophy of science A theorem of the probability calculus, named after the eighteenthcentury English mathematician Thomas Bayes, which compares the degree of support for a hypothesis prior to acquiring new evidence and after obtaining that evidence. As such it provides the basis for a general account of science. The theorem can be formulated as follows: Prob (H/E) = Prob x Prob (E/H)/Prob , where H is the hypothesis whose probability is to be evaluated, and E is new evidence; Prob is the probability of H prior to acquiring the evidence; Prob is the prior probability of acquiring that evidence; Prob (H/E) is the probability of H given the new evidence; and Prob (E/H) is the prior probability of acquiring the evidence given the assumption that H is true. The theory states that the conditional probability of H given E is greater than the unconditional probability of H to the extent that E is improbable in itself, but probable given H. This theorem indicates rational grounds for altering one’s assessment of probability for a hypothesis in the face of new evidence. On the assumption that belief can vary by degrees, evidence that is improbable on other hypotheses but probable on this hypothesis will raise the degree of belief for this hypothesis more than evidence that is similarly probable on this and other hypotheses. “Bayes’ theorem can be used to justify the assignment of a comparatively high . . . posterior probability to a hypothesis provided the latter’s antecedent probability is not too small.” Pap, An Introduction to the Philosophy of Science -- Bayesian epistemology, another expression for Bayesianism -- Bayesianism Epistemology, philosophy of science Also called Bayesian epistemology, a theory of epistemic justification, claiming that a belief P is justified if and only if the probability of P is reasonably high and that the probability for changing epistemic justification through the acquisition of new data can be calculated and predicated according to the probability calculus, including Bayes’s theorem. On a Bayesian view, the assignment of probability to belief is both subjective and rational. Different investigators can subjectively hold hypotheses with different initial degrees of belief. The operation of Bayes’s theorem in rationally altering these subjective assignments in the light of new evidence will tend toward convergence in the beliefs held by the investigators. In using evidence, evidence that is unlikely in itself but likely on a given hypothesis will increase the degree of belief in that hypothesis more than evidence that is likely in itself or equally likely on this and competing hypotheses. Because of its emphasis on the role of new evidence, the theory does not deal so well retrospectively with old evidence, and the prior assignment of likelihood can also be arbitrary. Also the balance between subjectivity and rationality can be questioned, with parallel tracks of investigation rather than convergence being a possible outcome. “Bayesianism is like probabilism in maintaining that: scientists’ (and others’) degrees of belief are measured by probabilities, but unlike probabilism, it sees no significance in very high or low probabilities.” Miller, Critical Rationalism Bayle, Pierre (1647–1706) French skeptic. Bayle argued with wit and scholarship against the presumptions of reason to establish religious and philosophical truth. He examined a wide range of historical thinkers as well as biblical and mythological figures to support his skeptical conclusions. His views were widely influential among eighteenth-century Enlightenment thinkers. His most important work is Historical and Critical Dictionary (1697).