Abstracts

The nature of simplicity and its relationship to truth are persistent problems in statistics, machine learning, and the philosophy of science. First, we propose an axiomatic theory of empirical simplicity that recovers a unique simplicity order in typical empirical problems, which are assumed to consist of a theory choice question (modeled as a partition over possible worlds) and a specication of possible information states (modeled as a topological basis). Simplicity emerges from topological relations that arise at the boundaries of the theories in the information space, so simplicity essentially involves both the question and the information space. Next, we use the properties of simplicity to show that Ockham's razor is the most deductive of the inductive procedures that answer the question under discussion. Optimal deductiveness involves allowing nature to decide questions she is destined to decide (optimal patience) and retracting prior beliefs as little as possible (optimal monotonicity).

TBA

Hintikka proposed to consider his interrogative logic—which generalizes classical entailment—and their companion ‘interrogative inquiry game’ as a general theory of reasoning. But classical logic, and therefore its extensions,  is a poor  basis for a cognitive theory of reasoning.  On the one hand, mainstream cognitive science has repudiated logic-based models, in the wake of empirical  results about ‘logical reasoning’ tasks (in particular Wason's Selection Task) they could not accommodate.  Bayesian models, who can fit the data, were left as (almost) sole survivors. On the other hand, emerging  cognitive theories of  semantic abilities acknowledge the fruitfulness of formal semantic models. But they view logical reasoning (classical or otherwise) as supervenient  on language interpretation,  itself  exapted by evolution from more general planning abilities, that evolved to meet the needs of cooperation. Yet, recent results show that classical entailment can be captured by epistemic reasoning (aka planning) in algorithmic semantic games, generalizing  Hintikka's interrogative games. Hintikka's proposal can be updated, if strategic planning in these games can yield a general theory of reasoning. I will argue that it does, and that such an account meets possible  objections based on the Selection Task, outperforms the explanatory power of Bayesian models, and reconciles cognitive theories of semantic abilities with some some of their alleged pragmatic' rivals—in particular, relevance theory.