While first-order modal logic has proven to be quite a powerful tool for philosophical theorizing, it has been observed by a number of philosophers that its expressive power has some inherent limitations. For instance, first-order modal logic cannot express even very basic sentences like “I could have been taller” or “The rich could have all been poor”.  Some amendments to first-order modal logic have been proposed in the literature, but the most successful ones seem to take us all the way to the full expressive power of two-sorted logic, where one can quantify over worlds directly in the object language.  This has led many philosophers to claim that any language with enough expressive power to formalize these kinds of sentences will have at least the expressive power of the two-sorted logic.  In this talk, Kocurek will propose an extension of first-order modal logic based on quantified hybrid logic, which can overcome these expressive limitations, but is provably less expressive than the two-sorted logic.  He will also provide a formal argument to the effect that it is the minimal extension of first-order logic that can overcome these expressive difficulties. 

connect with us


© UC Irvine School of Social Sciences - 3151 Social Sciences Plaza, Irvine, CA 92697-5100 - 949.824.2766