Probability and Conditionals

@article{Stalnaker1970ProbabilityAC,
  title={Probability and Conditionals},
  author={Robert Stalnaker},
  journal={Philosophy of Science},
  year={1970},
  volume={37},
  pages={64 - 80}
}
  • Robert Stalnaker
  • Published 1 March 1970
  • Philosophy, Computer Science
  • Philosophy of Science
The aim of the paper is to draw a connection between a semantical theory of conditional statements and the theory of conditional probability. First, the probability calculus is interpreted as a semantics for truth functional logic. Absolute probabilities are treated as degrees of rational belief. Conditional probabilities are explicitly defined in terms of absolute probabilities in the familiar way. Second, the probability calculus is extended in order to provide an interpretation for… 
Probability for epistemic modalities
This paper develops an information sensitive theory of the semantics and probability of conditionals and statements involving epistemic modals. The theory validates a number of principles linking
Conditionals, Conditional Probabilities, and Conditionalization
TLDR
This paper discusses some of the issues involved and proposes an account of belief update by conditionalization, which is a straightforward integration of this approach in a larger framework of belief representation and dynamics.
Conditionals, Comparative Probability, and Triviality: The Conditional of Conditional Probability Cannot Be Represented in the Object Language
In this paper we examine the thesis that the probability of the conditional is the conditional probability. Previous work by a number of authors has shown that in standard numerical probability
Conditionals Right and Left: Probabilities for the Whole Family
TLDR
This paper examines the source of the problematic predictions and proposes an amendment which corrects them in a principled way and brings intuitions about counterfactual conditionals to bear on the interpretation of indicatives and relies on the notion of causal (in)dependence.
Boolean algebras of conditionals, probability and logic
Deterministic Bayesian Logic
TLDR
It is shown that any unconditioned probability can be extended to the whole logic DBL and at last, it is shown why DBL is compliant with Lewis triviality.
Deterministic modal Bayesian Logic: derive the Bayesian inference within the modal logic T
TLDR
It is shown that any unconditioned probability can be extended to the whole logic DmBL, which is constructed as a deterministic counterpart to the Bayesian conditional.
Epistemic Interpretation of Conditionals
The presence of a connection between conditionals and conditional probabilities has been pointed out by several authors (the first, to my knowledge, was E. W. Adams in his (1965).) The epistemic
The Logic of Subjective Probability
  • B. Ellis
  • Philosophy
    The British Journal for the Philosophy of Science
  • 1973
There is a sense in which our logics of truth and of certainty should coincide. They should satisfy what I call the logical correspondence principle. By a logic of truth I mean a system of logic such
Conditional Deduction Under Uncertainty
TLDR
This paper describes a method for conditional deduction with beliefs which is a generalisation of probabilistic conditional inference and Modus Ponens and allows partial ignorance to be included in the analysis and deduction of statements and hypothesis.
...
...

References

SHOWING 1-10 OF 13 REFERENCES
Probability and the Logic of Conditionals
A Theory of Conditionals
This chapter was the first exposition and defense of an axiom system and model theory for a conditional logic in the possible worlds framework, a theory designed to model counterfactual propositions.
Coherence and the axioms of confirmation
It has been pointed out by Carnap that ‘probability’ is an equivocal term, which is used currently in two senses: (i) the degree to which it is rational to believe a hypothesis h on specified
On requirements for conditional probability functions
  • H. Leblanc
  • Mathematics
    Journal of Symbolic Logic
  • 1960
Let the prepositional calculus (PC) be cast in the following form: (a) The primitive signs of PC are to be a denumerably infinite hst of propositional letters, the two connectives ‘∼’ and ‘&’, and
Fair bets and inductive probabilities
  • J. Kemeny
  • Economics
    Journal of Symbolic Logic
  • 1955
TLDR
It will be shown that the probability axioms are necessary and sufficient conditions to assure that the degrees of confirmation form a set of fair betting quotients, and that one additional, highly controversial, axiom is precisely the condition needed to assures that not only deFinetti's weaker criterion but Shimony's criterion of fairness is also satisfied.
Nomological Necessity and the Paradoxes of Confirmation
Some of the concerns which motivate attempts to provide a philosophical reduction of nomological necessity are briefly introduced in I. In II, Hempel's treatment of the paradoxes is contrasted with a
On confirmation and rational betting
  • R. Lehman
  • Philosophy
    Journal of Symbolic Logic
  • 1955
TLDR
It is the aim to consider rational betting more precisely and attempt to answer some questions about desirable features of a confirmation function and connect the ideas of De Finetti with those of Carnap and Hossiasson-Lindenbaum.
...
...