What special problems, if any, arise for The Correspondence Theory Of Truth with regard to negative claims (for example "There is no cat on SK's matt"). Can The Correspondence Theory of Truth over come the problems associated with this type of claim?
A negative claim denotes the absence of something. Unlike positive claims such as "The cat is on the matt" which refers to something positive, some state of affairs or some fact. To say "The cat is not on the matt" refers to something that is not there, an absence of a certain state of affairs. This, you may well think, is obvious enough and brings no real problems to our ideas of truth. However if we are to maintain the correspondence theory of truth we have to address such negative claims. Correspondence theorists claim that the words we use correspond to something in reality or some state of affairs, but a negative claim does not follow this rule, it does not have a truthmaker. A negative claim does not refer to anything in reality, instead it refers to realities lack of something. In a sense a negative claim is that of an abstract one, not relating to anything physical but instead to an abstract thought, an absence. A negative claim does not have a truth maker as you cannot point to the non existing cat that isn't on the matt or at least we must try to find a truthmaker for these negative facts that is compatible with the correspondence theory of truth.
George Molnar Talks in his paper "Truthmakers for Negative Truths" about the idea of exclusion as suggested by Grossman and Raphael Demos. Exclusion being the idea of negative truths having positive Truthmakers. More precisely, negative truths finding their Truthmakers in "Logical Incompatibility". This means that a negative facts ...