Online research in philosophy

If we receive information from multiple independent and partially reliable information sources, then whether we are justified to believe these information items is affected by how reliable the sources are, by how well the information coheres with our background beliefs and by how internally coherent the information is. We consider the following question. Is coherence a separable determinant of our degree of belief, i.e. is it the case that the more coherent the new information is, the more justified we are in believing the new information, ceteris paribus? We show that if we consider sets of information items of any size (Holism), and if we assume that there exists a coherence Ordering over such sets and that coherence is a function of the probability distribution over the propositions in such sets (Probabilism), then Separability fails to hold.

Abstract In his seminal book, "Against Coherence", Erik Olsson hinges his case against the coherence theory of justification on an ingenious impossibility theorem that appears to show that there is no informative relationship between probabilistic measures of coherence and higher likelihood of truth. Although Olsson's important results offer insight into Bayesian coherentism, in this essay I argue that what those results tell us about the prospects for a formal theory of coherence is much more limited in scope than is generally believed. A key issue is the role of conditional independence assumptions within standard Bayesian models for witness testimony, which includes Olsson's model of Lewis witness scenarios. Olsson believes that the independence assumptions built into these models are both charitable to (probabilistic) coherence theories and suitable ceteris paribus conditions. In this essay I argue that neither claim is true, and I point to recent positive results which outline a rich framework for developing a formal theory of coherence after all.

A measure of coherence is said to be truth conducive if and only if a higher degree of coherence (as measured) results in a higher likelihood of truth. Recent impossibility results strongly indicate that there are no (non-trivial) probabilistic coherence measures that are truth conducive. Indeed, this holds even if truth conduciveness is understood in a weak ceteris paribus sense (Bovens & Hartmann, 2003, Bayesian epistemology. New York, Oxford: Oxford University Press; Olsson, 2005, Against coherence: Truth probability and justification. Oxford: Oxford University Press). This raises the problem of how coherence could nonetheless be an epistemically important property. Our proposal is that coherence may be linked in a certain way to reliability. We define a measure of coherence to be reliability conducive if and only if a higher degree of coherence (as measured) results in a higher probability that the information sources are reliable. Restricting ourselves to the most basic case, we investigate which coherence measures in the literature are reliability conducive. It turns out that, while a number of measures fail to be reliability conducive, except possibly in a trivial and uninteresting sense, Shogenji’s measure and several measures generated by Douven and Meijs’s recipe are notable exceptions to this rule.

A coherent story is a story that fits together well. This notion plays a central role in the coherence theory of justification and has been proposed as a criterion for scientific theory choice. Many attempts have been made to give a probabilistic account of this notion. A proper account of coherence must not start from some partial intuitions, but should pay attention to the role that this notion is supposed to play within a particular context. Coherence is a property of an information set that boosts our confidence that its content is true ceteris paribus when we receive information from independent and partially reliable sources. We construct a measure cr that relies on hypothetical sources with certain idealized characteristics. A maximally coherent information set, i.e. a set with equivalent propositions, affords a maximal confidence boost. cr is the ratio of the actual confidence boost over the confidence boost that we would have received, had the information been presented in the form of maximally coherent information, ceteris paribus. This measure is functionally dependent on the degree of reliability r of the sources. We use cr to construct a coherence quasi-ordering over information sets S and S’: S is no less coherent than S’ just in case c_r(S) is not smaller than c_r(S’) for any value of the reliability parameter. We show that, on our account, the coherence of the story about the world gives us a reason to believe that the story is true and that the coherence of a scientific theory, construed as a set of models, is a proper criterion for theory choice.

A coherent story is a story that fits together well. This notion plays a central role in the coherence theory of justification and has been proposed as a criterion for scientific theory choice. Many attempts have been made to give a probabilistic account of this notion. A proper account of coherence must not start from some partial intuitions, but should pay attention to the role that this notion is supposed to play within a particular context. Coherence is a property of an information set that boosts our confidence that its content is true ceteris paribus when we receive information from independent and partially reliable sources. We construct a measure cr that relies on hypothetical sources with certain idealized characteristics. A maximally coherent information set, i.e. a set with equivalent propositions, affords a maximal confidence boost. cr is the ratio of the actual confidence boost over the confidence boost that we would have received, had the information been presented in the form of maximally coherent information, ceteris paribus. This measure is functionally dependent on the degree of reliability r of the sources. We use cr to construct a coherence quasi-ordering over information sets S and S’: S is no less coherent than S’ just in case c_r(S) is not smaller than c_r(S’) for any value of the reliability parameter. We show that, on our account, the coherence of the story about the world gives us a reason to believe that the story is true and that the coherence of a scientific theory, construed as a set of models, is a proper criterion for theory choice.

A coherent story is a story that fits together well. This notion plays a central role in the coherence theory of justification and has been proposed as a criterion for scientific theory choice. Many attempts have been made to give a probabilistic account of this notion. A proper account of coherence must not start from some partial intuitions, but should pay attention to the role that this notion is supposed to play within a particular context. Coherence is a property of an information set that boosts our confidence that its content is true ceteris paribus when we receive information from independent and partially reliable sources. We construct a measure cr that relies on hypothetical sources with certain idealized characteristics. A maximally coherent information set, that is, a set with equivalent propositions, affords a maximal confidence boost. cr is the ratio of the actual confidence boost over the confidence boost that we would have received, had the information been presented in the form of maximally coherent information, ceteris paribus. This measure is functionally dependent on the degree of reliability r of the sources. We use cr to construct a coherence quasi-ordering over information sets S and S : S is no less coherent than S just in case cr(S) is not smaller than cr(S ) for any value of the reliability parameter. We show that, on our account, the coherence of the story about the world gives us a reason to believe that the story is true and that the coherence of a scientific theory, construed as a set of models, is a proper criterion for theory choice.

We construct a probabilistic coherence measure for information sets which determines a partial coherence ordering. This measure is applied in constructing a criterion for expanding our beliefs in the face of new information. A number of idealizations are being made which can be relaxed by an appeal to Bayesian Networks.

Bayesian Coherence Theory of Justification or, for short, Bayesian Coherentism, is characterized by two theses, viz. (i) that our degree of confidence in the content of a set of propositions is positively affected by the coherence of the set, and (ii) that coherence can be characterized in probabilistic terms. There has been a longstanding question of how to construct a measure of coherence. We will show that Bayesian Coherentism cannot rest on a single measure of coherence, but requires a vector whose components exhaustively characterize the coherence properties of the set. Our degree of confidence in the content of the information set is a function of the reliability of the sources and the components of the coherence vector. The components of this coherence vector are weakly but not strongly separable, which blocks the construction of a single coherence measure.

Bayesian Coherence Theory of Justification or, for short, Bayesian Coherentism, is characterized by two theses, viz. (i) that our degree of confidence in the content of a set of propositions is positively affected by the coherence of the set, and (ii) that coherence can be characterized in probabilistic terms. There has been a longstanding question of how to construct a measure of coherence. We will show that Bayesian Coherentism cannot rest on a single measure of coherence, but requires a vector whose components exhaustively characterize the coherence properties of the set. Our degree of confidence in the content of the information set is a function of the reliability of the sources and the components of the coherence vector. The components of this coherence vector are weakly but not strongly separable, which blocks the construction of a single coherence measure.

Bayesian Coherence Theory of Justification or, for short, Bayesian Coherentism, is characterized by two theses, viz. (i) that our degree of confidence in the content of a set of propositions is positively affected by the coherence of the set, and (ii) that coherence can be characterized in probabilistic terms. There has been a longstanding question of how to construct a measure of coherence. We will show that Bayesian Coherentism cannot rest on a single measure of coherence, but requires a vector whose components exhaustively characterize the coherence properties of the set. Our degree of confidence in the content of the information set is a function of the reliability of the sources and the components of the coherence vector. The components of this coherence vector are weakly but not strongly separable, which blocks the construction of a single coherence measure.