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Inductive influence
 British Journal for the Philosophy of Science
"... Objective Bayesianism has been criticised for not allowing learning from experience: it is claimed that an agent must give degree of belief 1 to the next raven being black, however many other black ravens have 2 been observed. I argue that this objection can be overcome by appealing to objective Bay ..."
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Cited by 9 (7 self)
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Objective Bayesianism has been criticised for not allowing learning from experience: it is claimed that an agent must give degree of belief 1 to the next raven being black, however many other black ravens have 2 been observed. I argue that this objection can be overcome by appealing to objective Bayesian nets, a formalism for representing objective Bayesian degrees of belief. Under this account, previous observations exert an inductive influence on the next observation. I show how this approach can be used to capture the JohnsonCarnap continuum of inductive methods, as well as the NixParis continuum, and show how inductive influence can
Objective Bayesianism with predicate languages. Synthese
, 2008
"... Objective Bayesian probability is often defined over rather simple domains, e.g., finite event spaces or propositional languages. This paper investigates the extension of objective Bayesianism to firstorder logical languages. It is argued that the objective Bayesian should choose a probability func ..."
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Cited by 5 (5 self)
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Objective Bayesian probability is often defined over rather simple domains, e.g., finite event spaces or propositional languages. This paper investigates the extension of objective Bayesianism to firstorder logical languages. It is argued that the objective Bayesian should choose a probability function, from all those that satisfy constraints imposed by background knowledge, that is closest to a particular frequencyinduced probability function which generalises the λ = 0 function of Carnap’s continuum of inductive methods.
Binary induction and Carnap’s continuum
 In Proceedings of the 7th Workshop on Uncertainty Processing (WUPES
, 2006
"... We consider the problem of induction over languages with binary predicates and show that a natural generalization of Johnson’s Sufficientness Postulate eliminates all but two solutions. We discuss the historical context and connections to the unary case. 1 ..."
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Cited by 2 (0 self)
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We consider the problem of induction over languages with binary predicates and show that a natural generalization of Johnson’s Sufficientness Postulate eliminates all but two solutions. We discuss the historical context and connections to the unary case. 1
PROBABILISTIC RELATIONSHIPS, RELEVANCE AND IRRELEVANCE WITHIN THE FIELD OF UNCERTAIN REASONING
, 2007
"... ..."
A Characterization of the Language Invariant Families satisfying Spectrum Exchangeability in Polyadic Inductive Logic
, 2008
"... A necessary and sufficient condition in terms of a de Finetti style representation is given for a probability function in Polyadic Inductive Logic to satisfy being part of a Language Invariant family satisfying Spectrum Exchangeability. This theorem is then considered in relation to the unary Carnap ..."
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Cited by 1 (1 self)
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A necessary and sufficient condition in terms of a de Finetti style representation is given for a probability function in Polyadic Inductive Logic to satisfy being part of a Language Invariant family satisfying Spectrum Exchangeability. This theorem is then considered in relation to the unary Carnap and NixParis Continua.
Pure Inductive Logic
"... Before a football match can begin the tradition is that the referee tosses a coin and one of the captains calls, heads or tails, whilst the coin is in the air. If the captain gets it right s/he picks which end to start playing at, or alternatively to have the kick off. There never seems to be an iss ..."
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Before a football match can begin the tradition is that the referee tosses a coin and one of the captains calls, heads or tails, whilst the coin is in the air. If the captain gets it right s/he picks which end to start playing at, or alternatively to have the kick off. There never seems to be an issue of which captain actually
DOI 10.1007/s112290079298y Objective Bayesianism with predicate languages
"... Abstract Objective Bayesian probability is often defined over rather simple domains, e.g., finite event spaces or propositional languages. This paper investigates the extension of objective Bayesianism to firstorder logical languages. It is argued that the objective Bayesian should choose a probabi ..."
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Abstract Objective Bayesian probability is often defined over rather simple domains, e.g., finite event spaces or propositional languages. This paper investigates the extension of objective Bayesianism to firstorder logical languages. It is argued that the objective Bayesian should choose a probability function, from all those that satisfy constraints imposed by background knowledge, that is closest to a particular frequencyinduced probability function which generalises the λ = 0 function of Carnap’s continuum of inductive methods.