Mental probability logic

Abstract

We discuss Oaksford & Chater's (O&C's) probabilistic approach from a probability logical point of view. Specifically, we comment on subjective probability, the indispensability of logic, the Ramsey test, the consequence relation, human nonmonotonic reasoning, intervals, generalized quantifiers, and rational analysis.

New paradigm psychology of reasoning

“…But as just pointed out above, that would be a mistaken impression. O&C agree with Pfeifer and Kleiter (2009) that inductive or probability logic, the logic of partial belief and uncertainty, is a generalisation of truth functional and extensional logic (Oaksford & Chater, 2009b, p. 107). In the old, binary paradigm, participants are asked to assume the premises of an inference are true and to state only what necessarily follows from those assumptions.…”

“…Sometimes O&C use ''standard'' or ''conventional'' for the ''logic'' they are rejecting in the ''logicist'' paradigm, which might suggest to the careful reader of their book that they follow Ramsey and de Finetti in thinking of Bayesian rationality as including a ''non-standard'' logic of uncertainty: probability logic. Indeed, they happily accept in their reply to Pfeifer and Kleiter (2009) that they can be seen ''. .…”

Imprecise probabilities in engineering analyses

“…In these contexts, when logical inferences are made about propositions characterized by interval probabilities rather than simple binary truth values [160], there can be subtleties in the denition, use, and interpretation of these characterizations [146]. For instance, the probability of A given B is entirely dierent from the probability of the implication B → A [161], even though they might seem to represent the same thing.…”

Dynamic inference and everyday conditional reasoning in the new paradigm

“…While there is a broad consensus within the new paradigm about the need for a probabilistic account of human inference, most of this work proceeds at the computational level (Douven & Verbrugge, 2013;Gilio & Over, 2012;Pfeifer & Kleiter, 2010;Over et al, 2010) or at the level of cognitive architecture Stanovich, 2011). The representations and processes that implement the probabilistic approach receive much less attention (although see Evans & Over, 2004;Oaksford & Chater, 2010c).…”

“…This is not to say that researchers in the new paradigm are neutral on this issue. For example, Pfeifer and Kleiter (2010) explicitly present their model as a mental probability logic. That is, the formalism they provide is explicitly regarded as a probabilistic 7 As we remarked in footnote 1, if probability conditionals cannot be regarded as propositions, then this notation can only be interpreted as a pseudo-probability (see Douven & Verbrugge, 2013).…”