PLACING PROBABILITIES OF CONDITIONALS IN CONTEXT

2014 ◽  
Vol 7 (3) ◽  
pp. 415-438
Author(s):  
RONNIE HERMENS
Keyword(s):  
Conditional Probability ◽  
Modus Ponens ◽  
Bayes Rule ◽  
Context Sensitive ◽  
Intuitive Rules ◽  
Triviality Results

AbstractIn this paper I defend the tenability of the Thesis that the probability of a conditional equals the conditional probability of the consequent given the antecedent. This is done by adopting the view that the interpretation of a conditional may differ from context to context. Several triviality results are (re-)evaluated in this view as providing natural constraints on probabilities for conditionals and admissible changes in the interpretation. The context-sensitive approach is also used to re-interpret some of the intuitive rules for conditionals and probabilities such as Bayes’ rule,Import-Export, and Modus Ponens. I will show that, contrary to consensus, the Thesis is in fact compatible with these re-interpreted rules.

Probability

2017 ◽  
Author(s):  
Andrew Gelman ◽  
Deborah Nolan
Keyword(s):  
Conditional Probability ◽  
Bayes Rule ◽  
Probability Models ◽  
Classroom Activities ◽  
Basic Probability

This chapter contains many classroom activities and demonstrations to help students understand basic probability calculations, including conditional probability and Bayes rule. Many of the activities alert students to misconceptions about randomness. They create dramatic settings where the instructor discerns real coin flips from fake ones, students modify dice and coins in order to load them, students “accused” of lying based on the outcome of an inaccurate simulated lie detector face their classmates. Additionally, probability models of real outcomes offer good value: first we can do the probability calculations, and then can go back and discuss the potential flaws of the model.

Two Interpretations of the Ramsey Test

2017 ◽  
Author(s):  
R.A. Briggs
Keyword(s):  
Conditional Probability ◽  
Ramsey Test ◽  
Triviality Results

According to Adams’ thesis the probability of a conditional is the conditional probability of the consequent given the antecedent. According to Stalnaker semantics, a conditional is true at a world just in case its consequent is true at all closest antecedent worlds to the original world. The chapter argues that Adams’ thesis and Stalnaker semantics are ways of cashing out the same ‘Ramsey test’ idea. Unfortunately, a well-known class of triviality theorems shows that Adams’ thesis and Stalnaker semantics are incompatible. Stefan Kaufmann has proposed (for reasons largely independent of the triviality theorems) a revised version of Adams’ thesis, which the chapter calls Kaufmann’s thesis. The chapter proves that combining Kaufmann’s thesis with Stalnaker semantics leads to ‘local triviality’ results, which seem just as absurd as the original triviality results for Adams’ thesis.

Indicative conditionals

2018 ◽  
Author(s):  
Sarah Moss
Keyword(s):  
Conditional Probability ◽  
Inference Rules ◽  
Indicative Conditionals ◽  
Valid Inference ◽  
Logical Operators ◽  
Context Sensitive ◽  
Probabilistic Semantics ◽  
Truth Conditional ◽  
Conditional Credence

This chapter defends a probabilistic semantics for indicative conditionals and other logical operators. This semantics is motivated in part by the observation that indicative conditionals are context sensitive, and that there are contexts in which the probability of a conditional does not match the conditional probability of its consequent given its antecedent. For example, there are contexts in which you believe the content of ‘it is probable that if Jill jumps from this building, she will die’ without having high conditional credence that Jill will die if she jumps. This observation is at odds with many existing non-truth-conditional semantic theories of conditionals, whereas it is explained by the semantics for conditionals defended in this chapter. The chapter concludes by diagnosing several apparent counterexamples to classically valid inference rules embedding epistemic vocabulary.

scholarly journals Preservation, Commutativity and Modus Ponens: Two Recent Triviality Results

Mind ◽  
2016 ◽  
Vol 126 (502) ◽  
pp. 579-602 ◽  
Author(s):  
Jake Chandler
Keyword(s):  
Modus Ponens ◽  
Triviality Results

Conditional Probability, Bayes’ Rule and Bayesian Estimation

2020 ◽  
pp. 45-52
Author(s):  
Armando Barreto ◽  
Malek Adjouadi ◽  
Francisco R. Ortega ◽  
Nonnarit O-larnnithipong
Keyword(s):  
Bayesian Estimation ◽  
Conditional Probability ◽  
Bayes Rule

scholarly journals A Bridge from Monty Hall to the Hot Hand: Restricted Choice, Selection Bias, and Empirical Practice

2018 ◽  
Author(s):  
Joshua Benjamin Miller ◽  
Adam Sanjurjo
Keyword(s):  
Conditional Probability ◽  
Selection Bias ◽  
Experimental Subject ◽  
Bayes Rule ◽  
Card Game ◽  
Hot Hand ◽  
Monty Hall ◽  
Monty Hall Problem ◽  
Available Information ◽  
Inferential Rule

We show how classic conditional probability puzzles, such as the Monty Hall problem, are intimately related to the hot hand selection bias. We explain the connection by way of the principle of restricted choice, an intuitive inferential rule from the card game bridge, which we show is naturally quantified as the updating factor in the odds form of Bayes Rule. We illustrate how, just as the experimental subject fails to use available information to update correctly when choosing a door in the Monty Hall problem, researchers may neglect analogous information when designing experiments, analyzing data, and interpreting results.

scholarly journals Dutch Book against Lewis

Synthese ◽  
2021 ◽  
Author(s):  
Anna Wójtowicz ◽  
Krzysztof Wójtowicz
Keyword(s):  
Present Article ◽  
Conditional Probability ◽  
Crucial Role ◽  
Probability Space ◽  
Dutch Book ◽  
Natural Way ◽  
Triviality Results

AbstractAccording to the PCCP thesis, the probability of a conditional A → C is the conditional probability P(C|A). This claim is undermined by Lewis’ triviality results, which purport to show that apart from trivial cases, PCCP is not true. In the present article we show that the only rational, “Dutch Book-resistant” extension of the agent’s beliefs concerning non-conditional sentences A and C to the conditional A → C is by assuming that P(A → C) = P(C|A) (i.e., in accord with PCCP). In other cases a diachronic Dutch Book against the agent can be constructed. There is a tension between our findings and Lewis’ results, which needs to be explained. Therefore, we present a probability space which corresponds in a natural way to the diachronic Dutch Book—and which allows the conditional A → C to be interpreted as an event in a mathematically sound way. It also allows to formalize the notion of conditionalizing A → C on ¬C which plays a crucial role in Lewis’ proof. Our conclusion is that Lewis’ proof is circular, so it cannot be considered to be a sound argument against PCCP.

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