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- Richard Bradley (2002). Indicative Conditionals. Erkenntnis 56 (3):345-378.Adams Thesis has much evidence in its favour, but David Lewis famously showed that it cannot be true, in all but the most trivial of cases, if conditionals are proprositions and their probabilities are classical probabilities of truth. In this paper I show thatsimilar results can be constructed for a much wider class of conditionals. The fact that these results presuppose that the logic of conditionals is Boolean motivates a search for a non-Boolean alternative. It is argued that the exact proposition expressed by a conditional depends on the context in which it is uttered. Consequentlyits probability of truth will depend not only on the probabilities of the various propositions it might express, but also on the probabilities of the contexts determining which proposition it does in fact express.The semantic theory developed from this is then shown to explain why agents degrees of belief satisfyAdams Thesis. Finally the theory is compared with proposals for a three-valued logic of conditionals.Reading list | Discuss | Edit | Categorize |My bibliography
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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.
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| | Other links: philosophie.rwth-aachen.de | Scholar | More options ... This paper presents a new theory of the truth conditions for indicative conditionals. The theory allows us to give a fairly unified account of the semantics for indicative and subjunctive conditionals, though there remains a distinction between the two classes. Put simply, the idea behind the theory is that the distinction between the indicative and the subjunctive parallels the distinction between the necessary and the a priori. Since that distinction is best understood formally using the resources of two-dimensional modal logic, those resources will be brought to bear on the logic of conditionals.
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| | Other links: blackwell-synergy.com jstor.org phonline.org dx.doi.org | Scholar | At my library | More options ... This is a 'state of the art' collection of essays on the relation between probabilities, especially conditional probabilities, and conditionals. It provides new negative results which sharply limit the ways conditionals can be related to conditional probabilities. There are also positive ideas and results which will open up new areas of research. The collection is intended to honour Ernest W. Adams, whose seminal work is largely responsible for creating this area of inquiry. As well as describing, evaluating, and applying Adams' work the contributions extend his ideas in directions he may or may not have anticipated, but that he certainly inspired. In addition to a wide range of philosophers of science, the volume should interest computer scientists and linguists.
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| | Scholar | At my library | More options ... This collection introduces the reader to some of the most interesting current work on conditionals. Particular attention is paid to possible world semantics for conditionals, the role of conditional probability in helping us to understand conditionals, implicature and the material conditional, and subjunctive versus indicative conditionals. Contributors include V.H. Dudman, Dorothy Edgington, Nelson Goodman, H.P. Grice, David Lewis, and Robert Stalnaker.
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| | Scholar | At my library | More options ... This paper uses the framework of Popper and Miller''s work on axiom systems for conditional probabilities to explore Adams'' thesis concerning the probabilities of conditionals. It is shown that even very weak axiom systems have only a very restricted set of models satisfying a natural generalisation of Adams'' thesis, thereby casting severe doubt on the possibility of developing a non-Boolean semantics for conditionals consistent with it.
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| Discuss | Edit | Categorize | My bibliography | Export citation | Other links: eprints.lse.ac.uk springer.com springerlink.com dx.doi.org jstor.org | Scholar | At my library | More options ...
| | Other links: eprints.lse.ac.uk springer.com springerlink.com dx.doi.org jstor.org | Scholar | At my library | More options ... We will look at several theories of indicative conditionals grouped into three categories: those that base its semantics on its logical counterpart (the material conditional); intensional analyses, which bring in alternative possible worlds; and a third subgroup which denies that indicative conditionals express propositions at all. We will also look at some problems for each kind of approach.
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| | Scholar | More options ... Adams' famous thesis that the probabilities of conditionals are conditional probabilities is incompatible with standard probability theory. Indeed it is incompatible with any system of monotonic conditional probability satisfying the usual multiplication rule for conditional probabilities. This paper explores the possibility of accommodating Adams' thesis in systems of non-monotonic probability of varying strength. It shows that such systems impose many familiar lattice theoretic properties on their models as well as yielding interesting logics of conditionals, but that a standard complementation operation cannot be defined within them, on pain of collapsing probability into bivalence.
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| | Other links: eprints.lse.ac.uk springerlink.com | Scholar | At my library | More options ... We show that the implicational fragment of intuitionism is the weakest logic with a non-trivial probabilistic semantics which satisfies the thesis that the probabilities of conditionals are conditional probabilities. We also show that several logics between intuitionism and classical logic also admit non-trivial probability functions which satisfy that thesis. On the other hand, we also prove that very weak assumptions concerning negation added to the core probability conditions with the restriction that probabilities of conditionals are conditional probabilities are sufficient to trivialize the semantics.
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| | Other links: jstor.org | Scholar | At my library | More options ... Discusses how to capture the link between the probability of indicative conditionals and conditional probability using a classical semantics for conditionals.
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| | Other links: onlinelibrary.wiley.com dx.doi.org doi.wiley.com | Scholar | At my library | More options ... This paper explores the possibility of supplementing the suppositional view of indicative conditionals with a corresponding view of epistemic modals. The most striking feature of the suppositional view consists in its claim that indicative conditionals are to be evaluated by conditional probabilities. On the basis of a natural link between indicative conditionals and epistemic modals, a corresponding thesis about the probabilities of statements governed by epistemic modals can be derived. The paper proceeds by deriving further consequences of this thesis, in particular, the logic of epistemic modals and their logical interaction with indicative conditionals are studied.
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| | Scholar | At my library | More options ... Discussion of Richard Bradley, Indicative conditionals
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