Psychological research on people’s understanding of natural language connectives has traditionally used truth table tasks, in which participants evaluate the truth or falsity of a compound sentence given the truth or falsity of its components in the framework of propositional logic. One perplexing result concerned the indicative conditional if A then C which was often evaluated as true when A and C are true, false when A is true and C is false but irrelevant“ (devoid of value) when A is (...) false (whatever the value of C). This was called the “psychological defective table of the conditional.” Here we show that far from being anomalous the “defective” table pattern reveals a coherent semantics for the basic connectives of natural language in a trivalent framework. This was done by establishing participants’ truth tables for negation, conjunction, disjunction, conditional, and biconditional, when they were presented with statements that could be certainly true, certainly false, or neither. We review systems of three-valued tables from logic, linguistics, foundations of quantum mechanics, philosophical logic, and artificial intelligence, to see whether one of these systems adequately describes people’s interpretations of natural language connectives. We find that de Finetti’s (1936/1995) three-valued system is the best approximation to participants’ truth tables. (shrink)

A conception of probability as an irreducible feature of the physical world is outlined. Propensity analyses of probability are examined and rejected as both formally and conceptually inadequate. It is argued that probability is a non-dispositional property of trial-types; probabilities are attributed to outcomes as event-types. Brier's Rule in an objectivist guise is used to forge a connection between physical and subjective probabilities. In the light of this connection there are grounds for supposing physical probability to obey some standard set (...) of axioms. However, there is no a priori reason why this should be the case. (shrink)

This paper uses Popper's treatment of probability and an epistemic constraint on probability assignments to conditionals to extend the Bayesian representation of rational belief so that revision of previously accepted evidence is allowed for. Results of this extension include an epistemic semantics for Lewis' theory of counterfactual conditionals and a representation for one kind of conceptual change.

A starting point for this paper is that there is at least one concept of probability, call it epistemic probability, which can be identified with belief or some sort of idealised belief. If this identification is to be of any significance, then it needs to be shown that epistemic probability is a ‘true’ probability concept and is subject to those restrictions and requirements which relate and govern probabilities, which we call the probability calculus.The most rehearsed argument to establish the probability (...) calculus for epistemic probabilities is the Dutch Book Argument. There are two intuitions behind the DBA. The first is that if we can find some fine-grained behavioural measure of epistemic probability, then we may be able to show that epistemic probabilities obey the probability calculus by showing that the behaviour is of a kind which is, as a matter of necessity, subject to certain limitations and restrictions. (shrink)

There is a new Bayesian, or probabilistic, paradigm in the psychology of reasoning, with new psychological accounts of the indicative conditional of natural language. In psychological experiments in this new paradigm, people judge that the probability of the indicative conditional, P(if A then C), is the conditional probability of C given A, P(C | A). In other experiments, participants respond with what has been called the 'de- fective' truth table: they judge that if A then C is true when A (...) holds and C holds, is false when A holds and C does not, and is neither true nor false when A does not hold. We argue that these responses are not 'defective' in any negative sense, as many psychologists have implied. We point out that a number of normative researchers, including de Finetti, have proposed such a table for various coherent interpretations of the third value. We review the relevant general tables in the normative literature, in which there is a third value for A and C and the logically compound forms of the natural language conditional, negation, conjunction, disjunction, and the material conditional. We describe the results of an experiment on which of these tables best describes ordinary people's judgements when the third value is interpreted as indicating uncertainty. (shrink)

This paper explores the ways in which truth is better than falsehood, and suggests that, among other things, it depends on the kinds of proposition to which these values are attached. Ordinary singular propositions like “It is raining” seem to fit best the bivalent “scheme” of classical logic, the general proposition “It is always raining” is more appropriately rated according to how often it rains, and a “practically vague” proposition like “The lecture will start at 1” is appropriately rated according (...) to its nearness to exactness. Implications for logic of this “rating system” are commented on. (shrink)