Online research in philosophy

Chow's account of Bayesian inference logic and procedures is replete with fundamental misconceptions, derived from secondary sources and not adequately informed by modern work. The status of subjective probabilities in Bayesian analyses is misrepresented and the cogent reasons for the rejection by many statisticians of the curious inferential hybrid used in psychological research are not presented.

This paper discusses and rejects some objections raised by Chihara to the book Scientific Reasoning: the Bayesian Approach, by Howson and Urbach. Some of Chihara's objections are of independent interest because they reflect widespread misconceptions. One in particular, that the Bayesian theory presupposes logical omniscience, is widely regarded as being fatal to the entire Bayesian enterprise, It is argued here that this is no more true than the parallel charge that the theory of deductive logic is fatally comprised because it presupposes logical omniscience. Neither theory presupposes logical omniscience.

We analyze common reasoning about admissibility in the strategic and extensive form of a game. We define a notion of sequential proper admissibility in the extensive form, and show that, in finite extensive games with perfect recall, the strategies that are consistent with common reasoning about sequential proper admissibility in the extensive form are exactly those that are consistent with common reasoning about admissibility in the strategic form representation of the game. Thus in such games the solution given by common reasoning about admissibility does not depend on how the strategic situation is represented. We further explore the links between iterated admissibility and backward and forward induction.

We analyze common reasoning about admissibility in the strategic and extensive form of a game. We define a notion of sequential proper admissibility in the extensive form, and show that, in finite extensive games with perfect recall, the strategies that are consistent with common reasoning about sequential proper admissibility in the extensive form are exactly those that are consistent with common reasoning about admissibility in the strategic form representation of the game. Thus in such games the solution given by common reasoning about admissibility does not depend on how the strategic situation is represented. We further explore the links between iterated admissibility and backward and forward induction.

This paper offers a short and biased overview of the history of discussion and controversy about the role of different forms of representation in intelligent agents. It repeats and extends some of the criticisms of the `logicist' approach to AI that I first made in 1971, while also defending logic for its power and generality. It identifies some common confusions regarding the role of visual or diagrammatic reasoning including confusions based on the fact that different forms of representation may be used at different levels in an implementation hierarchy. This is contrasted with the way in the use of one form of representation (e.g. pictures) can be {\em controlled} using another (e.g. logic, or programs). Finally some questions are asked about the role of metrical information in biological visual systems.

Chow's book makes a provocative contribution to the debate on the role of statistical significance, but it involves some important misconceptions in the presentation of the Fisher and Neyman/Pearson's theories. Moreover, the author's caricature-like considerations about “Bayesianism” are completely irrelevant for discarding the Bayesian statistical theory. These facts call into question the objectivity of his contribution.

Bayesianism is the position that scientific reasoning is probabilistic and that probabilities are adequately interpreted as an agent's actual subjective degrees of belief, measured by her betting behaviour. Confirmation is one important aspect of scientific reasoning. The thesis of this paper is the following: if scientific reasoning is at all probabilistic, the subjective interpretation has to be given up in order to get right confirmation—and thus scientific reasoning in general. The Bayesian approach to scientific reasoning Bayesian confirmation theory The example The less reliable the source of information, the higher the degree of Bayesian confirmation Measure sensitivity A more general version of the problem of old evidence Conditioning on the entailment relation The counterfactual strategy Generalizing the counterfactual strategy The desired result, and a necessary and sufficient condition for it Actual degrees of belief The common knock-down feature, or ‘anything goes’ The problem of prior probabilities.

In Carruthers’ formulation, cross-domain thinking requires translation of domain specific data into a common format, and linguistic LF thus plays the role of the common medium of exchange. Alternatively, I propose a process-oriented characterization, in which there is no common representation and cross-domain thinking is rather the process of establishing mappings across domains, as in the process of analogical reasoning.