As part of the conference commemorating Theoria's 75th anniversary, a round table discussion on philosophy publishing was held in Bergendal, Sollentuna, Sweden, on 1 October 2010. Bengt Hansson was the chair, and the other participants were eight editors-in-chief of philosophy journals: Hans van Ditmarsch (Journal of Philosophical Logic), Pascal Engel (Dialectica), Sven Ove Hansson (Theoria), Vincent Hendricks (Synthese), Søren Holm (Journal of Medical Ethics), Pauline Jacobson (Linguistics and Philosophy), Anthonie Meijers (Philosophical Explorations), Henry S. Richardson (Ethics) and Hans Rott (Erkenntnis).
Bengt Hansson (1983). Epistemology and Evidence. In Peter Gärdenförs, Bengt Hansson, Nils-Eric Sahlin & Sören Halldén (eds.), Evidentiary Value: Philosophical, Judicial, and Psychological Aspects of a Theory: Essays Dedicated to Sören Halldén on His Sixtieth Birthday. C.W.K. Gleerups.
Arrow's theorem is really a theorem about the independence condition. In order to show the very crucial role that this condition plays, the theorem is proved in a refined version, where the use of the Pareto condition is almost avoided.A distinction is made between group preference functions and group decision functions, yielding respectively preference relations and optimal subsets as values. Arrow's theorem is about the first kind, but some ambiguities and mistakes in his book are explained if we assume that (...) he was really thinking of decision functions. The trouble then is that it is not clear how to formulate the independence condition for decision functions. Therefore the next step is to analyse Arrow's argument for accepting the independence condition.The most frequent ambiguity depends on an interpretation of A as the set of all conceivable alternatives, while the variable subset B is the set of all feasible or available alternatives. He then argues that preferences between alternatives that are not feasible shall not influence the choice from the set of available alternatives. But even if this principle is accepted, it only forces us to require independence with respect to some specific set B and not to every B simultaneously. Therefore the independence condition cannot be accepted on these grounds.Another argument is about an election where one of the candidates dies. On one interpretation this argument can be taken to support an independence requirement which leads to a contradiction. On another interpretation it is a condition about connexions between choices from different sets.The so-called problem of binary choice is found to be different from the independence problem and it plays no essential role in Arrow's impossibility result. Other impossibility results by Sen, Batra and Pattanaik and by Schwartz are of a different character.In the last section, several weaker independence conditions are presented. Their relations to Arrow's condition are stated and the arguments supporting them are discussed. (shrink)
The basic theory of preference relations contains a trivial part reflected by axioms A1 and A2, which say that preference relations are preorders. The next step is to find other axims which carry the theory beyond the level of the trivial. This paper is to a great part a critical survey of such suggested axioms. The results are much in the negative — many proposed axioms imply too strange theorems to be acceptable as axioms in a general theory of preference. (...) This does not exclude, of course, that they may well be reasonable axioms for special calculi of preference. I believe that many axioms which are rejected here may be plausible if their range of application is restricted by conditions which are possible to formulate only in a language richer than that of the propositional calculus, e.g. in one containing modal operators or probabilistic concepts. (shrink)