DeRose on the conditionals of deliberation

I take issue with two claims of DeRose: Conditionals of deliberation must not depend on backtracking grounds. ‘Were’ed-up conditionals coincide with future-directed indicative conditionals; the only difference in their meaning is that they must not depend on backtracking grounds. I use Egan’s counterexamples to causal decision theory to contest the first and an example of backtracking reasoning by David Lewis to contest the second claim. I tentatively outline a rivaling account of ‘were’ed-up conditionals which combines features of the standard analysis of counterfactuals with the contextual relevance of the corresponding indicative conditionals

Desire, belief, and conditional belief

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Linguistics and Philosophy, 2008.Includes bibliographical references (leaves 127-132).This dissertation studies the logics of value and conditionals, and the question of whether they should be given cognitivist analyses. Emotivist theories treat value judgments as expressions of desire, rather than beliefs about goodness. Inference ticket theories of conditionals treat them as expressions of conditional beliefs, rather than propositions. The two issues intersect in decision theory, where judgments of expected goodness are expressible by means of decision-making conditionals. In the first chapter, I argue that decision theory cannot be given a Humean foundation by means of money pump arguments, which purport to show that the transitivity of preference and indifference is a requirement of instrumental reason. Instead, I argue that Humeans should treat the constraints of decision theory as constitutive of the nature of preferences. Additionally, I argue that transitivity of preference is a stricter requirement than transitivity of indifference. In the second chapter, I investigate whether David Lewis has shown that decision theory is incompatible with anti-Humean theories of desire. His triviality proof against "desire as belief' seems to show that desires can be at best conditional beliefs about goodness. I argue that within causal decision theory we can articulate the cognitivist position where desires align with beliefs about goodness, articulated by the decision making conditional. In the third chapter, I turn to conditionals in their own right, and especially iterated conditionals.(cont.) I defend the position that indicative conditionals obey the import-export equivalence rather than modus ponens (except for simple conditionals), while counterfactual subjunctive conditionals do obey modus ponens. The logic of indicative conditionals is often thought to be determined by conditional beliefs via the Ramsey Test. I argue that iterated conditionals show that the conditional beliefs involved in indicative supposition diverge from the conditional beliefs involved in learning, and that half of the Ramsey Test is untenable for iterated conditionals.by David Jeffrey Etlin.Ph.D

Bayesian Decision Theory and Stochastic Independence

Stochastic independence has a complex status in probability theory. It is not part of the definition of a probability measure, but it is nonetheless an essential property for the mathematical development of this theory. Bayesian decision theorists such as Savage can be criticized for being silent about stochastic independence. From their current preference axioms, they can derive no more than the definitional properties of a probability measure. In a new framework of twofold uncertainty, we introduce preference axioms that entail not only these definitional properties, but also the stochastic independence of the two sources of uncertainty. This goes some way towards filling a curious lacuna in Bayesian decision theory

Distinguishing Cause and Effect via Second Order Exponential Models

We propose a method to infer causal structures containing both discrete and continuous variables. The idea is to select causal hypotheses for which the conditional density of every variable, given its causes, becomes smooth. We define a family of smooth densities and conditional densities by second order exponential models, i.e., by maximizing conditional entropy subject to first and second statistical moments. If some of the variables take only values in proper subsets of R^n, these conditionals can induce different families of joint distributions even for Markov-equivalent graphs. We consider the case of one binary and one real-valued variable where the method can distinguish between cause and effect. Using this example, we describe that sometimes a causal hypothesis must be rejected because P(effect|cause) and P(cause) share algorithmic information (which is untypical if they are chosen independently). This way, our method is in the same spirit as faithfulness-based causal inference because it also rejects non-generic mutual adjustments among DAG-parameters.Comment: 36 pages, 8 figure

Bayesian Decision Theory and Stochastic Independence

As stochastic independence is essential to the mathematical development of probability theory, it seems that any foundational work on probability should be able to account for this property. Bayesian decision theory appears to be wanting in this respect. Savage’s postulates on preferences under uncertainty entail a subjective expected utility representation, and this asserts only the existence and uniqueness of a subjective probability measure, regardless of its properties. What is missing is a preference condition corresponding to stochastic independence. To fill this significant gap, the article axiomatizes Bayesian decision theory afresh and proves several representation theorems in this novel framework

"If Oswald had not killed Kennedy" – Spohn on Counterfactuals

Wolfgang Spohn's theory of ranking functions is an elegant and powerful theory of the structure and dynamics of doxastic states. In two recent papers, Spohn has applied it to the analysis of conditionals, claiming to have presented a unified account of indicative and subjunctive (counterfactual) conditionals. I argue that his analysis fails to account for counterfactuals that refer to indirect causes. The strategy of taking the transitive closure that Spohn employs in the theory of causation is not available for counterfactuals. I have a close look at Spohn's treatment of the famous Oswald-Kennedy case in order to illustrate my points. I sketch an alternative view that seems to avoid the problems