On Hume’s Theory Of Probability

The problems of induction and causality are core subjects of philosophical study. Hume gave much attention to both of them and his thoughts have been widely discussed in academic circles at home and abroad. However Hume’s study of a third very closely related subject, the subject of probability, still remains largely overlooked. This paper discusses the meaning of probability in Hume’s philosophy, as well as the relationship between Hume’s conception of probability, chances, and causes, and probability in modern inductive logic.This paper begins with Hume’s division of knowledge. Through systematically dissecting how Hume proposed probability and the whole process of argumentation in A Treatise of Human Nature, this paper tries to reveal that probability has three kinds of roles in Hume’s argumentation, namely, non-constant conjunction, probable argument, and prior probability. It is clarified that Hume’s conception of probability plays different roles in different stages of his argument and has three different meanings. On this basis, this paper investigates the relationship between Hume’s concept of probability and the concept of probability in modern inductive logic. It i s shown that Hume’s probability not only takes the form of classical probability, it is an initial definition of classical probability. Probability of chances and causal probability are the main body of this paper. Hume’s analysis of chances paves the way for causal probability. Hume discussed the nature of chances in his books A Treatise of Human Nature and An Enquiry Concerning Human Understanding. Hume thought a chance was the negation of a cause, a chance was perfectly indifferent, and that there was a mixture of causes among chances. Chapter Two reconstructs Hume’s arguments of equal probability events, his argument of the influence of majority chances on human mind and belief, and his calculation of the probability of chances. Thereby, this paper will try to reveal that Hume gave us a subjective interpretation of probability from the principle of the conjunction of superior chances.Chapter Three is about Hume’s three conceptions of the probability of causes, which are derived from imperfect experience, contrary causes, or analogy. The four species of the probability of causes, which are aroused from the weakening of evidence, the lack of freshness in the memory, a long chain of consequences, or general rules, were seen by Hume as unphilosophical probability. By talking about these seven species of probability, Hume clarified probability as the low-level stage of a perfect argument, and as a probable argument which is weaker than a demonstration in terms of reliability.Through analyzing probability and chances, and probabi lity and causes, we can see that Hume had developed an essentially reasonable inductive logic system of probability, even though this system was informal. Hume’s system is a forerunner of Carnap’s work. The principles and rules founded in Hume’s system such as semiregularity, symmetry, predictive irrelevance and positive instantiation relevance are innovative. These principles logically imply the straight rule. Through the reflection about Hume’s conception of probability, it states clearly that Hume’s conception is innovative not only in terms of theory creativity, but also in terms of form itself. But whether it presents the characteristics of Bayes’ theorem still deserves a further discussion.This paper is a monographic study of Hume’s conception of probability. Based on Hume’s classical texts, following his own analytical style and methods, it discusses probability from three dimensions, and thereby defines probability uniquely and systematically. Following, it dissects the different levels of the probability of chances and the probability of causes, discussing principles refined from Hume’s thoughts. In conclusion, it comments on the value and influence of Hume’s conception of probability.