Posted: May 17, 2012 8:39 pm
I hope you can understand why classical logic can not help with shrunks argument as he is using a term "square circle" which is an empty set.
http://plato.stanford.edu/entries/logic-free/
Classical logic requires each singular term to denote an object in the domain of quantification—an “existing” object. Free logic does not. Free logic is therefore useful for analyzing discourse containing singular terms that either are empty (have no referent or refer to objects that do not exist) or might be.
http://plato.stanford.edu/entries/logic-free/