Structural Reflexivity and the Semantic Paradoxes

17 September 2015

GAP.9, Osnabrück

That one can deal with the semantic paradoxes by restricting or rejecting structural rules is now relatively well known. In particular, solutions which reject the structural rule of cut and contraction are currently en vogue. What has not been seriously considered are the prospects of dealing with the paradoxes by rejecting the ur-structural rule of reflexivity—for all formulas $A$: $A \vdash A$. Here we will show that the non-reflexive approach to the semantic paradoxes bears further investigation. In particular we will show that a fully non-reflexive approach can capture much of what is desirable about classical reasoning.

  • More details are available at the GAP.9 Website here
  • Here is the Handout
  • Here are the Slides