A General Non-Probabilistic Theory of Inductive Reasoning
David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
In R. D. Shachter, T. S. Levitt, J. Lemmer & L. N. Kanal (eds.), Uncertainty in Artificial Intelligence 4. Elsevier (1990)
Probability theory, epistemically interpreted, provides an excellent, if not the best available account of inductive reasoning. This is so because there are general and definite rules for the change of subjective probabilities through information or experience; induction and belief change are one and same topic, after all. The most basic of these rules is simply to conditionalize with respect to the information received; and there are similar and more general rules. 1 Hence, a fundamental reason for the epistemological success of probability theory is that there at all exists a well-behaved concept of conditional probability. Still, people have, and have reasons for, various concerns over probability theory. One of these is my starting point: Intuitively, we have the notion of plain belief; we believe propositions2 to be true (or to be false or neither). Probability theory, however, offers no formal counterpart to this notion. Believing A is not the same as having probability 1 for A, because probability 1 is incorrigible3; but plain belief is clearly corrigible. And believing A is not the same as giving A a probability larger than some 1 - c, because believing A and believing B is usually taken to be equivalent to believing A & B.4 Thus, it seems that the formal representation of plain belief has to take a non-probabilistic route. Indeed, representing plain belief seems easy enough: simply represent an epistemic state by the set of all propositions believed true in it or, since I make the common assumption that plain belief is deductively closed, by the conjunction of all propositions believed true in it. But this does not yet provide a theory of induction, i.e. an answer to the question how epistemic states so represented are changed tbrough information or experience. There is a convincing partial answer: if the new information is compatible with the old epistemic state, then the new epistemic state is simply represented by the conjunction of the new information and the old beliefs. This answer is partial because it does not cover the quite common case where the new information is incompatible with the old beliefs. It is, however, important to complete the answer and to cover this case, too; otherwise, we would not represent plain belief as conigible. The crucial problem is that there is no good completion. When epistemic states are represented simply by the conjunction of all propositions believed true in it, the answer cannot be completed; and though there is a lot of fruitful work, no other representation of epistemic states has been proposed, as far as I know, which provides a complete solution to this problem. In this paper, I want to suggest such a solution. In , I have more fully argued that this is the only solution, if certain plausible desiderata are to be satisfied. Here, in section 2, I will be content with formally defining and intuitively explaining my proposal. I will compare my proposal with probability theory in section 3. It will turn out that the theory I am proposing is structurally homomorphic to probability theory in important respects and that it is thus equally easily implementable, but moreover computationally simpler. Section 4 contains a very brief comparison with various kinds of logics, in particular conditional logic, with Shackle's functions of potential surprise and related theories, and with the Dempster - Shafer theory of belief functions.
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
Branden Fitelson (2007). Likelihoodism, Bayesianism, and Relational Confirmation. Synthese 156 (3):473 - 489.
Franz Huber (2008). Assessing Theories, Bayes Style. Synthese 161 (1):89 - 118.
Emil Weydert (2012). Conditional Ranking Revision. Journal of Philosophical Logic 41 (1):237-271.
Similar books and articles
John L. Pollock (1983). Epistemology and Probability. Noûs 17 (1):65-67.
Patrick Maher (2006). The Concept of Inductive Probability. Erkenntnis 65 (2):185 - 206.
Robert C. Stalnaker (1970). Probability and Conditionals. Philosophy of Science 37 (1):64-80.
Wolfgang Spohn (1993). Causal Laws Are Objectifications of Inductive Schemes. In J. Dubucs (ed.), Philosophy of Probability. Kluwer, Dordrecht. 223-252.
Bas C. Van Fraassen (1980). Rational Belief and Probability Kinematics. Philosophy of Science 47 (2):165 - 187.
Prakash P. Shenoy (1991). On Spohn's Theory of Epistemic Beliefs. In B. Bouchon-Meunier, R. R. Yager & L. A. Zadeh (eds.), Uncertainty in Knowledge Bases. Springer. 1--13.
Prakash P. Shenoy (1991). On Spohn's Rule for Revision of Beliefs. International Journal of Approximate Reasoning 5 (2):149-181.
Wolfgang Spohn (1988). Ordinal Conditional Functions. A Dynamic Theory of Epistemic States. In W. L. Harper & B. Skyrms (eds.), Causation in Decision, Belief Change, and Statistics, vol. II. Kluwer.
Sorry, there are not enough data points to plot this chart.
Added to index2009-07-31
Recent downloads (6 months)0
How can I increase my downloads?