CAN THERE BE REASONS FOR PUTTING LIMITATIONS ON CLASSICAL LOGIC
The question in the title is answered with a yes, albeit with a special proviso. In the first place the answer agrees with Pat Suppes' words "there are a number of reasons for moving very slowly to the adoption of a new logic." Secondly, the strategy proposed is not to move to a new logic but to put limitations or filters on Classical Logic when needed. This is based on the conviction that those questions where the application of classical logic leads to difficulties - like that of probability assignments to conjunctions, redundant elements of the consequence class, non-invariance of results against language frames - are beyond questions of validity (of semantics in the narrow sense) and therefore cannot be solved by changing classical validity. A more appropriate way seems therefore to leave classical logic (and validity) unchanged and distinguish it from new properties which are obtained by putting special limitations (filters) on it. The procedure is as follows: after classifying certain difficulties in Section 2 problems are given in detail in Section 3 which are special examples for these difficulties. In Section 4 limitative criteria for classical logic are offered which give solutions to the problems of Section 3. Moreover, special formal properties of these limitative criteria are discussed and some theorems about them are proved.