Abstract

Being a pragmatic and not a referential approach to semantics, dialogi-cal logic does not understand semantics as mapping names, propositions and relationships into the real world to obtain an abstract counterpart of it, but as dealing (handeln) with them in a particular way. This allows a very simple formulation of free logic the core of which can be expressed in a nutshell, namely: in an argumentation, it sometimes makes sense to restrict the introduction of singular terms in the context of quantification to a formal use o f them. That is, the proponent is allowed to use a constant if f this constant has been explicitly conceded by the opponent. More technically, we show a new, dialogical way to build free logic systems fo r first-order logic with classical and intuitionistic features and present their corresponding tableaux. I. In tro d u ctio n I I. F r e e logics ON DIALOGUES A ND ONTOLOGY THE DIAL OGICAL APPROACH TO FREE LOGIC The proposition "God does not exist" contains a paradox sometimes referred to as Plato's beard: if God does not exist and the proposition should be true, standard referential semantics fo r quantified logic fails to give meaning to the name "God". But, given compositionality, since the meaning of a sentence is combined from the meanings o f its parts,-G o d d o e s not exist" does not evaluate. It is easy to see that related difficulties appear in every formula that contains singular terms. In standard logic, it is impossible to state that God is either good or evil without presupposing his existence, or that the round * My work on this article has been supported by the Fritz-Thyssen-Stiftung which I wish to thank expressly.