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## A Survey of Ranking Theory

### Degrees of Belief (2009-01-01) 342: 185-228 , January 01, 2009

## Chance and Necessity

### The Place of Probability in Science (2010-01-01) 284: 101-131 , January 01, 2010

Probability abounds in the natural and social sciences. Yet, science strives for objectivity. Scientists are not pleased when told that probability is just opinion and there is no more sense to it. They are prone to believe in objective probabilities or chances. This is an essay about how to understand them.

## Laws, Ceteris Paribus Conditions, and the Dynamics of Belief

### Ceterus Paribus Laws (2002-01-01): 97-118 , January 01, 2002

The characteristic difference between laws and accidental generalizations lies in our epistemic or inductive attitude towards them. This idea has taken various forms and dominated the discussion about lawlikeness in the last decades. Likewise, the issue about *ceteris paribus* conditions is essentially about how we epistemically deal with exceptions. Hence, ranking theory with its resources of defeasible reasoning seems ideally suited to explicate these points in a formal way. This is what the paper attempts to do. Thus it will turn out that a law is simply the deterministic analogue of a sequence of independent, identically distributed random variables. This entails that de Finetti’s representation theorems can be directly transformed into an account of confirmation of laws thus conceived.

## Analogy and inductive logic: A note on Niiniluoto

### Erkenntnis (1981-03-01) 16: 35-52 , March 01, 1981

## A Brief Comparison Of Pollock's Defeasible Reasoning And Ranking Functions

### Synthese (2002-04-01) 131: 39-56 , April 01, 2002

In this paper two theories of defeasible reasoning, Pollock's account and my theory of ranking functions, are compared, on a strategic level, since a strictly formal comparison would have been unfeasible. A brief summary of the accounts shows their basic difference: Pollock's is a strictly computational one, whereas ranking functions provide a regulative theory. Consequently, I argue that Pollock's theory is normatively defective, unable to provide a theoretical justification for its basic inference rules and thus an independent notion of admissible rules. Conversely, I explain how quite a number of achievements of Pollock's account can be adequately duplicated within ranking theory. The main purpose of the paper, though, is not to settle a dispute with formal epistemology, but rather to emphasize the importance of formal methods to the whole of epistemology.

## A Rationalization of Cooperation in the Iterated Prisoner’s Dilemma

### Rationality, Rules, and Structure (2000-01-01) 28: 67-84 , January 01, 2000

According to the standard account, strategies respond to various possible circumstances. I conceive them rather as responding to various possible future decision situations (including all internal factors). This is far more general since changing decision situations may arise in a foreseeable way not only due to information, as in the standard account, but also due to forgetfulness, endogeneous changes of preferences etc.

The main problem, then, is to state an optimality criterion for such strategies. This is a problem since maximization of expected utility then becomes either unreasonable or even meaningless (maximization of which utility?). The problem is serious, as the widely disagreeing literature on the issue displays. I propose a general solution by essentially referring, in a specific way, to a relation of superiority/ inferiority between possible decision situations (which is part of the agent’s view). This is the first part of the paper.

The second part suggests how this framework provides new theoretical means for dealing with the iterated prisoner’s dilemma thus allowing for a full rationalization of cooperation. The ideas extend to Newcomb’s problem and related cases and are hence relevant to the debate between causal and evidential decision theory.