Topic: PARACONSISTENCY
Dialetheism, logical consequence and hierarchy
By Bruno Whittle
Dialetheism is defined by Graham Priest to be the view that there are true contradictions. It is supposed to offer treatments of the semantic paradoxes that avoid the problems faced by more orthodox resolutions. The advantage of these treatments is supposed to be that they avoid the sort of appeal to a hierarchy of languages or concepts that more orthodox resolutions seem invariably to have to make. For since a dialetheist can simply accept as sound the derivations of contradictions involved in the paradoxes, there is no need for him to invoke a hierarchy to block these derivations.
In this article I argue that dialetheists have a problem with the concept of logical consequence. The upshot of this problem is that dialetheists must appeal to a hierarchy of concepts of logical consequence. Since this hierarchy is akin to those invoked by more orthodox resolutions of the semantic paradoxes, its emergence would appear to seriously undermine the dialetheic treatments of these paradoxes. And since these are central to the case for dialetheism, this would represent a significant blow to the position itself.
In ?1 I explain why and how a dialetheist needs to be able to talk about logical consequence. In ?2 I argue that there are in fact severe restrictions upon how exactly a dialetheist can talk about logical consequence. These restrictions stem from a version of Curry's paradox. I then argue in ?3 that a dialetheist must appeal to a hierarchy of concepts of logical consequence, and, further, that each of these concepts is dialetheically unobjectionable. The justification of this latter claim involves proving that the addition of these concepts together with natural rules for them conservatively extends dialetheic logic. This is proved in the appendix.
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Posted by Tony Marmo
at 00:01 BST
Updated: Wednesday, 20 October 2004 04:23 BST
