Gödel's theorem does not need an introduction. But it is generally not acknowledged that all instances of Gödel's sentence are vacuous (see below). On the contrary Aristotelian logic permits only sentences that are not vacuous. The consequences of these observations are surprising. What does the article title mean? First of all by " Aristotelian logic " we will understand the logic of the tradi...

this paper will examine ibn sina’s theory of the conditional syllogism from a purely logical point of view, and will lay bare the principles he adopted for founding his theory, and the reason why the newly introduced part of his logic remained undeveloped and eventually was removed from the texts of logic in the later islamic tradition. as a preliminary discussion, this paper briefly examines i...

In this paper, we introduce and study AD-logic, i.e., a system of (hybrid) modal logic that can be used to reason about Aristotelian diagrams. The language LAD, is interpreted on kind birelational Kripke frames, which call “AD-frames”. We establish sound strongly complete axiomatization for prove there exists bijection between finite diagrams (up isomorphism) AD-frames isomorphism). then show h...

A new model of vertebrate cognition is introduced: maximization of cogency p(abgdj3). This model is shown to be a direct generalization of Aristotelian logic, and to be rigorously related to a calculable quantity. A key aspect of this model is that in Aristotelian logic information environments it functions logically. However, in non-Aristotelian environments, instead of finding the conclusion ...

The paper deals with Aristotelian logic as the special case of more general epistemology and sociology of both science and common sense. The Aristotelian principles of identity, of noncontradiction, and of excluded middle are to be supplemented by the secondorder cybernetic, or "cybernethic" principles of paradox, of ambivalence, and of control. In this paper we collect some ideas on how to eva...