Prolepsis y justicia en el epicureísmo
The influential 19th century philosophical historiography did not recognize in Epicureanism a political philosophy worthy of study. Based on an analysis of the Principal Doctrines and texts of Hermarchus, Polystratus and Lucretius, this paper aims to show that Epicureans developed a relevant political theory that connected two traditions: the Ionian naturalism and the Socratic reformulation of philosophy as the only true politics. In the establishment of justice through covenants and its continuity in the language through the prolepsis of what is just, they saw a finding that offered man the required security to satisfy his necessary natural desires and his survival.
Prolepsis and Ennoia in the Early Stoa
This book offers a reconstruction of the early Stoic doctrine of prolepsis, revealing it to be much closer to Platonic recollection in certain respects than previously thought. The standard interpretation of prolepsis as preconceptions is inconsistent with their status as criteria of truth. Rather, prolepsis is a form of tacit knowledge that requires articulation and systematization. This reconstruction is supported by a comprehensive collection of texts relating to prolepsis from Epicurus to Alexander of Aphrodisias.
Decidability of some intuitionistic predicate theories
Suppose T is a first order intuitionistic theory (more precisely, a theory of Heyting's predicate calculus, e.g., abelian groups, one unary function, dense linear order, etc.) presented to us by a set of axioms (denoted also by) T. Question. Is T decidable? One knows that if the classical counterpart of T (i.e., take the same axioms but with the classical predicate calculus as the underlying logic) is not decidable, then T cannot be decidable. The problem remains for theories whose classical counterpart is decidable. In [8], sufficient conditions for undecidability were given, and several intuitionistic theories such as abelian groups and unary functions (both with decidable equality) were shown to be undecidable. In this note we show decidability results (see Theorems 1 and 2 below), and compare these results with the undecidability results previously obtained. The method we use is the reduction-method, described fully in [12] and widely applied in [3], which is applied here roughly as follows: Let T be a given theory of Heyting's predicate calculus. We know that Heyting's predicate calculus is complete for the Kripke-model type of semantics. We choose a class M of Kripke models for which T is complete, i.e., all axioms of T are valid in any model of the class and whenever φ is not a theorem of T, φ is false in some model of M.