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  1. Causal Models and the Logic of Counterfactuals.Jonathan Vandenburgh - manuscript
    Causal models provide a framework for making counterfactual predictions, making them useful for evaluating the truth conditions of counterfactual sentences. However, current causal models for counterfactual semantics face limitations compared to the alternative similarity-based approach: they only apply to a limited subset of counterfactuals and the connection to counterfactual logic is not straightforward. This paper argues that these limitations arise from the theory of interventions where intervening on variables requires changing structural equations rather than the values of variables. Using an (...)
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    Conditional Learning Through Causal Models.Jonathan Vandenburgh - 2020 - Synthese (1-2):2415-2437.
    Conditional learning, where agents learn a conditional sentence ‘If A, then B,’ is difficult to incorporate into existing Bayesian models of learning. This is because conditional learning is not uniform: in some cases, learning a conditional requires decreasing the probability of the antecedent, while in other cases, the antecedent probability stays constant or increases. I argue that how one learns a conditional depends on the causal structure relating the antecedent and the consequent, leading to a causal model of conditional learning. (...)
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  3. A Causal Safety Criterion for Knowledge.Jonathan Vandenburgh - manuscript
    Safety purports to explain why cases of accidentally true belief are not knowledge, addressing Gettier cases and cases of belief based on statistical evidence. However, numerous examples suggest that safety fails as a condition on knowledge: a belief can be safe even when one's evidence is clearly insufficient for knowledge and knowledge is compatible with the nearby possibility of error, a situation ruled out by the safety condition. In this paper, I argue for a new modal condition designed to capture (...)
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  4. Learning as Hypothesis Testing: Learning Conditional and Probabilistic Information.Jonathan Vandenburgh - manuscript
    Complex constraints like conditionals ('If A, then B') and probabilistic constraints ('The probability that A is p') pose problems for Bayesian theories of learning. Since these propositions do not express constraints on outcomes, agents cannot simply conditionalize on the new information. Furthermore, a natural extension of conditionalization, relative information minimization, leads to many counterintuitive predictions, evidenced by the sundowners problem and the Judy Benjamin problem. Building on the notion of a `paradigm shift' and empirical research in psychology and economics, I (...)
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  5. Triviality Results, Conditional Probability, and Restrictor Conditionals.Jonathan Vandenburgh - manuscript
    Conditional probability is often used to represent the probability of the conditional. However, triviality results suggest that the thesis that the probability of the conditional always equals conditional probability leads to untenable conclusions. In this paper, I offer an interpretation of this thesis in a possible worlds framework, arguing that the triviality results make assumptions at odds with the use of conditional probability. I argue that these assumptions come from a theory called the operator theory and that the rival restrictor (...)
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