Volume 23, Issue 1

The following article consists of a few short remarks on the inevitable incomprehensibility of science on the one hand and, in order to overcome this incomprehensibility, on common structures between science and the life-world on the other

This article deals with algebraic logic. In particular, it discusses the theory of consequence operations and the general concept of logical independency. The advantage of this general view is its gr- eat applicability: The stated properties of consequence operations hold for almost every logical system. The notion of independency is well known and important in logic, philosophy of science and mathematics. Roughly speaking, a set is independent with respect to a consequence operation, if none of its elements is a consequence of the other elements. The property of being an independent set guarantees therefore that none of its elements is superfluous. In particular, I'm going to show fundamental results for every consequence operation, and hence for every logic: no infinite independent set is finite axiomatizable, and every finite axiomatizable set has relative to a finitary consequence operation an independent axiom system. The main result is that in sentential logic every set of formulas has an independend axiom system.

In this article we prove step by step the main theorem of Smullyan sets. This main theorem says that each element of a Smullyan set is simultaneously satisfiable in a semantic system of model sets and therefore also, for example, in a semantic system of truth sets as well as in a semantic system according to Henkin. After that, we prove the semantical compactness of a propositional logic system as an example of a utilisation of Smullyan sets and its main theorem.

I believe that a radically fine-grained property-exemplification theory is the right approach to the metaphysics of events. In this paper I will not be arguing for this detail but will be more concerned with issues over the internal consistency of the property-exemplification theory; in particular, I want to resolve issues about the individuation of property-tokens.

The conditional analysis interprets power/capability as disposition and gives it a counterfactual analysis. The phenomenon of finkishness poses a problem for this account. I argue that the conditional analysis has to be modified in order to solve these problems. The new analysis, I claim, is well suited to deal with Frankfurt-style scenarios as well, which conditional analyses are frequently thought to be incapable of.

In his Critique of Pure Reason Immanuel Kant presents four anti- nomies. In his attempt to solve the first of these antinomies he examines and analyzes"thesis" and "antithesis" more thoroughly and employs the terms `part', `whole' and `boundary' in his argumentation for their validity. According to Kant, the whole problem surrounding the antinomy was caused by applying the concept of the world to nature and then using both terms interchangeably. While interesting, this solution is still not that much more than a well thought out idea if it does not also include an adequate formal explication. Since the aforementioned terms all have counterparts in modern mereotopology, a discipline that has seen significant progress in recent times, we will apply these concepts to Kant's analysis in an attempt to evaluate Kant's solution in light of modern analytic philosophy.