Online research in philosophy

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.

THE PAPER EXAMINES WHAT IS MEANT BY ’EVIDENCE’ WHEN IT IS SAID THAT A THEORY IS PROBABLE ON CERTAIN EVIDENCE. IT CONSIDERS WHAT IS THE RELATION BETWEEN A THEORY BEING PROBABLE ON CERTAIN EVIDENCE, A THEORY BEING BELIEVED, AND A THEORY BEING CREDIBLE. IT DISTINGUISHES VARIOUS SENSES OF ’ACCEPT’ IN WHICH SCIENTISTS ARE SAID TO ACCEPT THEORIES, ONLY ONE OF WHICH IS THE SENSE OF ’ACCEPT’ IN WHICH IT IS EQUATED WITH ’BELIEVE’. IT ANALYSES THE LOGICAL RELATIONS BETWEEN A THEORY BEING PROBABLE ON THE EVIDENCE, AND A THEORY BEING ACCEPTED, AND A THEORY BEING ACCEPTABLE, IN THE DIFFERENT SENSES OF ’ACCEPT’.

In contemporary discussions of the Ramsey Test 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 Ramsey Test. 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.

We present a semantic analysis of the Ramsey test, 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 Ramsey test; 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.

I formulate a counterfactual version of the notorious ‘Ramsey Test’. Whereas the Ramsey Test for indicative conditionals links credence in indicatives to conditional credences, the counterfactual version links credence in counterfactuals to expected conditional chance. I outline two forms: a Ramsey Identity on which the probability of the conditional should be identical to the corresponding conditional probability/expectation of chance; and a Ramsey Bound on which credence in the conditional should never exceed the latter. Even in the weaker, bound, form, the counterfactual Ramsey Test makes counterfactuals subject to the very argument that Lewis used to argue against the indicative version of the Ramsey Test. I compare the assumptions needed to run each, pointing to assumptions about the time-evolution of chances that can replace the appeal to Bayesian assumptions about credence update in motivating the assumptions of the argument. I finish by outlining two reactions to the discussion: to indicativize the debate on counterfactuals; or to counterfactualize the debate on indicatives.

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 Ramsey test 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.

How to accept a conditional? F. P. Ramsey proposed the following test in (Ramsey 1990).(RT) If A, then B must be accepted with respect to the current epistemic state iff the minimal hypothetical change of it needed to accept A also requires accepting B.

The so called Ramsey test 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 Ramsey test 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 Ramsey test: (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).

Frank Ramsey writes: If two people are arguing ‘if p will q?’ and both are in doubt as to p, they are adding p hypothetically to their stock of knowledge and arguing on that basis about q. We can say that they are fixing their degrees of belief in q given p. (1931) Chalmers and Hájek write: Let us take the first sentence [of Ramsey] the way it is often taken, as proposing the following test for the acceptability of an indicative conditional: ‘if p then q’ is acceptable to a subject S iff, were S to accept p and consider q, S would accept q.

Alvin Plantinga titles the closing chapter of his book Warrant and Proper Function "Is Naturalism Irrational?" He answers that it is. More precisely, he claims that anyone who is aware of the epistemological argument that he presents in this chapter has an unavoidable reason to doubt the combination of naturalism (according to which there is no God as conceived of in traditional theism) and evolutionary theory (according to which our cognitive capabilities are the products of blind processes operating on genetic variations). But then, he says, anyone who still accepts these propositions is irrational because it is irrational to accept a belief for which one knows there are unavoidable reasons to doubt.