Logical, Semantic and Cultural Paradoxes

The property common to three kinds of paradoxes (logical, semantic, and cultural) is the underlying presence of an exclusive disjunction: even when it is put to a check by the paradox, it is still invoked at the level of implicit discourse. Hence the argumentative strength of paradoxical propositions is derived. Logical paradoxes (insolubilia) always involve two contradictory, mutually exclusive, truths. One truth is always perceived to the detriment of the other, in accordance with a succession which is endlessly repetitive. A check is put on the principle of the excluded middle by the logical paradoxes, because self-reference leads to an endlessly repeating circle, out of which no resolution is conceivable. Logical paradoxes are to be compared with the `objective ambiguity' prevalent in oracles (Gallet, 1990). Semantic paradoxes are contextually-determined occurrences, whose resolution at the metalinguistic level is made possible by the discovery of a middle term. They express a wilful ambiguity, in which the interlocutor is invited to take an active part in the construction of sense, since what must be found is the unexpected sense thanks to which A and not-A can be asserted simultaneously. Cultural paradoxes play about doxa (`common sense') and openly challenge common opinion because of their character as inopinata (`unexpected'). My aim is to show that even cultural paradoxes hide sometimes a flaw of argumentation similar to logical or semantic paradox; they too imply an exclusive disjunction leading to the disappearance of the middle terms. Finally, basing myself on the theory of topoi (Anscombre and Ducrot, 1983), a tentative resolution of the cultural paradoxes will be suggested.     

Quine and Slater on Paraconsistency and Deviance

In a famous and controversial paper, B. H. Slater has argued against the possibility of paraconsistent logics. Our reply is centred on the distinction between two aspects of the meaning of a logical constant ^*c^* in a given logic: its operational meaning, given by the operational rules for ^*c^* in a cut-free sequent calculus for the logic at issue, and its global meaning, specified by the sequents containing ^*c^* which can be proved in the same calculus. Subsequently, we use the same strategy to counter Quine's meaning variance argument against deviant logics. In a nutshell, we claim that genuine rivalry between (similar) logics ^*L^* and ^*L^* is possible whenever each constant in ^*L^* has the same operational meaning as its counterpart in ^*L^* although differences in global meaning arise in at least one case.     

Dummett and Frege on sense and Selbständigkeit

As part of his attack on Frege’s ‘myth’ that senses reside in the third realm, Dummett alleges that Frege’s view that all objects are selbständig (‘self-subsistent’, ‘independent’) is an underlying mistake, since some objects depend upon others. Whatever the merits of Dummett’s other arguments against Frege’s conception of sense, this objection fails. First, Frege’s view that senses are third-realm entities is not traceable to his view that all objects are selbständig. Second, while Frege recognizes that there are objects that are dependent upon other objects, he does not take this to compromise the Selbständigkeit of any objects. Thus, Frege’s doctrine that objects are selbständig does not make the claim of absolute independence that Dummett appears to have taken it to make. Nevertheless, in order to make a good case against Frege based on the dependency of senses, Dummett need only establish his claim that senses depend upon expressions: appeal to an absolute conception of independence is unnecessary. However, Dummett’s arguments for the dependency of senses upon expressions are unsuccessful and they show that Dummett’s conception of what it is to be an expression also differs significantly from Frege’s.