I argue against the Ramseytest connecting indicative conditionals with conditional probability, by means of examples in which conditional probability is high but the conditional is intuitively implausible. At the end of the paper, I connect these issues to patterns of belief revision.
In contemporary discussions of the RamseyTest for conditionals, it is commonly held that (i) supposing the antecedent of a conditional is adopting a potential state of full belief, and (ii) Modus Ponens is a valid rule of inference. I argue on the basis of Thomason Conditionals (such as ' If Sally is deceiving, I do not believe it') and Moore's Paradox that both claims are wrong. I then develop a double-indexed Update Semantics for conditionals which takes these (...) two results into account while doing justice to the key intuitions underlying the RamseyTest. The semantics is extended to cover some further phenomena, including the recent observation that epistemic modal operators give rise to something very like, but also very unlike, Moore's Paradox. (shrink)
Chalmers and Hájek argue that on an epistemic reading of Ramsey’s test for the rational acceptability of conditionals, it is faulty. They claim that applying the test to each of a certain pair of conditionals requires one to think that one is omniscient or infallible, unless one forms irrational Moore-paradoxical beliefs. I show that this claim is false. The epistemic Ramseytest is indeed faulty. Applying it requires that one think of anyone as all-believing and (...) if one is rational, to think of anyone as infallible-if-rational. But this is not because of Moore-paradoxical beliefs. Rather it is because applying the test requires a certain supposition about conscious belief. It is important to understand the nature of this supposition. (shrink)
We present a way of classifying the logically possible ways out of Gärdenfors' inconsistency or triviality result on belief revision with conditionals. For one of these ways—conditionals which are not descriptive but which only have an inferential role as being given by the Ramseytest—we determine which of the assumptions in three different versions of Gärdenfors' theorem turn out to be false. This is done by constructing ranked models in which such Ramsey-test conditionals are evaluated and (...) which are subject to natural postulates on belief revision and acceptability sets for conditionals. Along the way we show that in contrast with what Gärdenfors himself proposed, there is no dichotomy of the form: either the Ramseytest has to be given up or the Preservation condition. Instead, both of them follow from our postulates. (shrink)
The so called Ramseytest is a semantic recipe for determining whether a conditional proposition is acceptable in a given state of belief. Informally, it can be formulated as follows: (RT) Accept a proposition of the form "if A, then C" in a state of belief K, if and only if the minimal change of K needed to accept A also requires accepting C. In Gärdenfors (1986) it was shown that the Ramseytest is, in the (...) context of some other weak conditions, on pain of triviality incompatible with the following principle, which was there called the preservation criterion: (P) If a proposition B is accepted in a given state of belief K and the proposition A is consistent with the beliefs in K, then B is still accepted in the minimal change of K needed to accept A. (RT) provides a necessary and sufficient criterion for when a 'positive' conditional should be included in a belief state, but it does not say anything about when the negation of a conditional sentence should be accepted. A very natural candidate for this purpose is the following negative Ramseytest: (NRT) Accept the negation of a proposition of the form "if A, then C" in a consistent state of belief K, if and only if the minimal change of K needed to accept A does not require accepting C. This note shows that (NRT) leads to triviality results even in the absence of additional conditions like (P). (shrink)
Vann McGee has proposed a counterexample to the RamseyTest. In the counterexample, a seemingly trustworthy source has testified that p and that if not-p, then q. If one subsequently learns not-p, then one has reason to doubt the trustworthiness of the source and so, the argument goes, one has reason to doubt the conditional asserted by the source. Since what one learns is that the antecedent of the conditional holds, these doubts are contrary to the Ramsey (...)Test. We argue that the counterexample fails. It rests on a principle of testimonial dependence that is not applicable when a source hedges his or her claims. (shrink)
In this paper, I analyse a finding by Riggs and colleagues that there is a close connection between people’s ability to reason with counterfactual conditionals and their capacity to attribute false beliefs to others. The result indicates that both processes may be governed by one cognitive mechanism, though false belief attribution seems to be slightly more cognitively demanding. Given that the common denominator for both processes is suggested to be a form of the Ramseytest, I investigate whether (...) Stalnaker’s semantic theory of conditionals, which was inspired by the Ramseytest, may provide the basis for a psychologically plausible model of belief ascription. The analysis I propose will shed some new light on the developmental discrepancy between counterfactual reasoning and false belief ascription. (shrink)
Two of the major problems in AGM-style belief revision, namely the difficulties in accounting for iterated change and for Ramseytest conditionals, have satisfactory solutions in descriptor revision. In descriptor revision, the input is a metalinguistic sentence specifying the success condition of the operation. The choice mechanism selects one of the potential outcomes in which the success condition is satisfied. Iteration of this operation is unproblematic. Ramseytest conditionals can be introduced without giving rise to the (...) paradoxical results that they generate in other systems. In addition to standard Ramseytest conditionals, a more general variant of epistemic conditionals is defined, representing statements of the form ”if the belief state is changed to satisfy condition A then it will satisfy condition B”. An axiomatic characterization of such descriptor conditionals is presented. It is related in intricate ways to the KLM postulates for cumulative reasoning. (shrink)
Haack, S. Is truth flat or bumpy?--Chihara, C. S. Ramsey 's theory of types.--Loar, B. Ramsey 's theory of belief and truth.--Skorupski, J. Ramsey on Belief.--Hookway, C. Inference, partial belief, and psychological laws.--Skyrms, B. Higher order degrees of belief.--Mellor, D. H. Consciousness and degrees of belief.--Blackburn, S. Opinions and chances.--Grandy, R. E. Ramsey, reliability, and knowledge.--Cohen, L. J. The problem of natural laws.--Giedymin, J. Hamilton's method in geometrical optics and Ramsey 's view of theories.
According to the RamseyTest hypothesis the conditional claim that if A then B is credible just in case it is credible that B, on the supposition that A. If true the hypothesis helps explain the way in which we evaluate and use ordinary language conditionals. But impossibility results for the RamseyTest hypothesis in its various forms suggest that it is untenable. In this paper, I argue that these results do not in fact have this (...) implication, on the grounds that similar results can be proved without recourse to the Ramseytest hypothesis. Instead they show that a number of well entrenched principles of rational belief and belief revision do not apply to conditionals. (shrink)
Epistemic conditionals have often been thought to satisfy the Ramseytest : If A, then B is acceptable in a belief state G if and only if B should be accepted upon revising G with A. But as Peter Gärdenfors has shown, RT conflicts with the intuitively plausible condition of Preservation on belief revision. We investigate what happens if RT is retained while Preservation is weakened, or vice versa. We also generalize Gärdenfors' approach by treating belief revision as (...) a relation rather than as a function.In our semantic approach, the same relation is used to model belief revision and to give truth-conditions for conditionals. The approach validates a weak version of the RamseyTest — essentially, a restriction of RT to maximally consistent belief states. (shrink)
The purpose of this note is to formulate some weaker versions of the so called Ramseytest that do not entail the following unacceptable consequenceIf A and C are already accepted in K, then if A, then C is also accepted in K. and to show that these versions still lead to the same triviality result when combined with a preservation criterion.
In ‘A Defence of the RamseyTest’, Richard Bradley makes a case for not concluding from the famous impossibility results regarding the RamseyTest — the thesis that a rational agent believes a conditional if he would believe the consequent upon learning the antecedent — that the thesis is false. He lays the blame instead on one of the other premisses in these results, namely the Preservation condition. In this paper, we explore how this condition can (...) be weakened by strengthening the notion of consistency which appears in it. After considering the effects of such weakenings for Bradley's argument, we propose a refinement of the Preservation condition which does not fall prey to Bradley's argument nor to Gärdenfors's impossibility theorem. We briefly compare it to Bradley's suggested restriction of Preservation. (shrink)
Richard Bradley has initiated a new debate, with Brian Hill and Jake Chandler as further participants, about the implications of a number of so-called triviality results surrounding the Ramseytest for conditionals. I comment on this debate and argue that ‘Inclusion’ and ‘Preservation’, which were originally introduced as postulates for the rational revision of factual beliefs, have little to recommend them in the first place when extended to languages containing conditionals. I question the philosophical method of postulation that (...) was applied in the new debate, and instead base my arguments on explicit representations of belief states and canonical constructions of belief state revisions. (shrink)
Abstract I analyse the relationship between the RamseyTest (RT) for the acceptance of indicative conditionals and the so-called problem of decision-instability. In particular, I argue that the situations which allegedly bring about this problem are troublesome just in case the relevant conditionals are evaluated by non-suppositional versions, e.g. causal/evidential, of the test. In contrast, a suppositional RT, by highlighting the metacognitive nature of the evaluation of indicative conditionals, allows an agent to run a simulation of such (...) evaluation, without yet committing her to the acceptance of such conditionals. I conclude that a suppositional interpretation of RT is superior to its nonsuppositional counterparts and by briefly showing that a suppositional RT is compatible with a deliberational decision theory. (shrink)
Peter G¨ ardenfors proved a theorem purporting to show that it is impossible to adjoin to the AGM -postulates for belief-revision a principle of monotonicity for revisions. The principle of monotonicity in question is implied by the Ramseytest for conditionals. So G¨.
There is an important class of conditionals whose assertibility conditions are not given by the Ramseytest but by an inductive extension of that test. Such inductive Ramsey conditionals fail to satisfy some of the core properties of plain conditionals. Associated principles of nonmonotonic inference should not be assumed to hold generally if interpretations in terms of induction or appeals to total evidence are not to be ruled out.
Proponents of the projection strategy take an epistemic rule for the evaluation of English conditionals, the Ramseytest, as clue to the truth-conditional semantics of conditionals. They also construe English conditionals as stronger than the material conditional. Given plausible assumptions, however, the Ramseytest induces the semantics of the material conditional. The alleged link between Ramseytest and truth conditions stronger than those of the material conditional can be saved by construing conditionals as ternary, (...) rather than binary, propositional functions with a hidden contextual parameter. But such a ternary construal raises problems of its own. (shrink)
We introduce two new belief revision axioms: partial monotonicity and consequence correctness. We show that partial monotonicity is consistent with but independent of the full set of axioms for a Gärdenfors belief revision sytem. In contrast to the Gärdenfors inconsistency results for certain monotonicity principles, we use partial monotonicity to inform a consistent formalization of the Ramseytest within a belief revision system extended by a conditional operator. We take this to be a technical dissolution of the well-known (...) Gärdenfors dilemma.In addition, we present the consequential correctness axiom as a new measure of minimal revision in terms of the deductive core of a proposition whose support we wish to excise. We survey several syntactic and semantic belief revision systems and evaluate them according to both the Gärdenfors axioms and our new axioms. Furthermore, our algebraic characterization of semantic revision systems provides a useful technical device for analysis and comparison, which we illustrate with several new proofs. (shrink)
I am not so insular and I hope not so presumptuous as to suppose that there is no contemporary philosophy apart from that empiricism which dominates very much of Great Britain, North America and Scandinavia. So let us notice that contemporary philosophy embraces broadly three points of view, though it will be part of my argument that they largely combine in the lessons they have to teach us, and in many of their implications for theology.
This book by one of the world's foremost philosophers in the fields of epistemology and logic offers an account of suppositional reasoning relevant to practical deliberation, explanation, prediction and hypothesis testing. Suppositions made 'for the sake of argument' sometimes conflict with our beliefs, and when they do, some beliefs are rejected and others retained. Thanks to such belief contravention, adding content to a supposition can undermine conclusions reached without it. Subversion can also arise because suppositional reasoning is ampliative. These two (...) types of nonmonotonic logic are the focus of this book. A detailed comparison of nonmonotonicity appropriate to both belief contravening and ampliative suppositional reasoning reveals important differences that have been overlooked. (shrink)
Test for the rational acceptance of conditionals and it still incites much of the interest in conditional reasoning. For instance, the test has been considered as a good starting point for several formal semantics for conditionals. Furthermore, its ramifications have important implications for several disciplines, from logic and artificial intelligence to decision theory and psychology. This volume presents a small but fine sample of the state of the art of such multifarious area of research.
Peter Gärdenfors has proved (Philosophical Review, 1986) that the Ramsey rule and the methodologically conservative Preservation principle are incompatible given innocuous-looking background assumptions about belief revision. Gärdenfors gives up the Ramsey rule; I argue for preserving the Ramsey rule and interpret Gärdenfors's theorem as showing that no rational belief-reviser can avoid reasoning nonmonotonically. I argue against the Preservation principle and show that counterexamples to it always involve nonmonotonic reasoning. I then construct a new formal model of belief (...) revision that does accommodate nonmonotonic reasoning. (shrink)
We present a semantic analysis of the Ramseytest, pointing out its deep underlying flaw: the tension between the “static” nature of AGM revision (which was originally tailored for revision of only purely ontic beliefs, and can be applied to higher-order beliefs only if given a “backwards-looking” interpretation) and the fact that, semantically speaking, any Ramsey conditional must be a modal operator (more precisely, a dynamic-epistemic one). Thus, a belief about a Ramsey conditional is in fact (...) a higher-order belief, hence the AGM revision postulates are not applicable to it, except in their “backwards-looking” interpretation. But that interpretation is consistent only with a restricted (weak) version of Ramsey’s test (in-applicable to already revised theories). The solution out of the conundrum is twofold: either accept only the weak Ramseytest; or replace the AGM revision operator ∗ by a truly “dynamic” revision operator ⊗, which will not satisfy the AGM axioms, but will do something better: it will “keep up with reality”, correctly describing revision with higher-order beliefs. (shrink)
Consider the frame S believes that—. Fill it with a conditional, say If you eat an Apple, you'll drink a Coke. what makes the result true? More generally, what facts are marked by instances of S believes ? In a sense the answer is obious: beliefs are so marked. Yet that bromide leads directly to competing schools of thought. And the reason is simple. Common-sense thinks of belief two ways. Sometimes it sees it as a three-part affair. When so viewed (...) either you believe, disbelieve, or suspend judgment. This take on belief is coarse-grained . It says belief has three flavours: acceptance, rejection, neither. But it's not the only way common-sense thinks of belief. Sometimes it's more subtle: ‘How strong is your faith?’ can be apposite between believers. That signals an important fact. Ordinary practice also treats belief as a fine-grained affair. It speaks of levels of confidence. It admits degrees of belief . It contains a fine-grained take as well. There are two ways belief is seen in everyday life. One is coarse-grained. The other is fine-grained. (shrink)