UNIVERSITATIS APULENSIS No 18 / 2009 ASYMMETRY LEVEL AS A FUZZY MEASURE

Some difficulties with the Counterfactual Theory of David K.Lewis (1941-2001) and its applications to the Causation Analysis have appeared. Among them, the Temporal Asymmetry. Many criticism appeared against the explanation given by Lewis, as in Horwich ́87; Price ́92 & ́96; Hausman ́98. Here, we will analyze the possibility of obtain a new function: the Asymmetry Level, by the intervention of Fuzzy Measures, which will collaborate in the solution of such problem. 2000 Mathematics Subject Classification: 26E50, 28E10, 68T30, 68T01. 1.Introduction Lewis admits that the asymmetry is possibly a contingent characteristic of the actual world, not present in other worlds. So, in a world populated by only one atom such asymmetry on the overdetermination does not hold. For this reason, there exists a possible discontinuity problem in the boundary. Because if we consider a contractive sequence of subworlds, each of them asymmetric, converging to the monoatomic world, denoted W, where asymmetry does hold, we would have a weakness in the theory. Geometrically, the situation (relative to such symmetric character) should be: a contractive set, or decreasing collection, of subworlds, each one totally included in the precedent world, and where each one, but the last, shows asymmetries, whereas in the limit, finally, the symmetry appears. To solve this problem, either we can admit the symmetry as discontinuous function, and so we see that: ASYM → ASYM → ASYM → ...→ ASYM → SYMMETRY