Aspects of Aristotle's Logic of Modalities by J. van Rijen

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By J. van Rijen

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Diese allgemeine Dialogregel, die dem Proponenten bei jedem Zug gestattet, eine beliebige vorhergehende Aussage des Op­ ponenten anzugreifen, sei die effektive Dialogregel genannt. Es wird sich herausstellen, dass die effektiven Dialoge genau zur intuitionistischen Logik führen - ich vermeide den Ausdruck "intuitionistisch" nur deshalb, weil ich zur Begründung dieser Dialog­ regel nicht auf die Gründe zurückgreife, die Brouwer und Heyting für die intuitionistische Logik benutzt haben. In effektiven Dialogen ist eine Subjunktion folgendermassen zu behandeln.

Sie darf benutzt werden, als ob sie eine Kal­ külregel wäre, sie gehört aber nicht zur Definition des Sequenzen- P. LORENZEN 28 kalküls. Durch Beth ist es dann üblich geworden, diese Sequenzenkal­ küle zunächst upside-down zu lesen. Statt eine Ableitung zu suchen die oben von Axiomen ausgeht, und durch Deduktionsschritte nach unten schliesslich zu einer vorgegebenen Sequenz gelangt, geht man oben von der Sequenz aus und "entwickelt" nach unten bis man in allen Zweigen schliesslich zu Axiomen gelangt.

The approach is different from, but of course not incompat­ ible with those largely inspired by formal logic, such as that of Paul Lorenzen. An example of an argumentation rule of his approach: If a person says p & q, it is sufficient to refute p orq in order to refute him, but if he says p v q, one then has to refute both p and q. Empirical studies do not start with prop­ ositions, but with u t t e r a n c e s in concrete situations. The func­ tions of the utterances are normally complex, having relevant per­ formative aspects, but careful analysis may result in 'destining' p's and q's appropriate for formal treatment.

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