Logics and Metalogics

The focus of the workshop lies in emphasizing the fact that in the study of logics, there always takes place an interplay between items belonging to object level, meta-level and metameta-level. Making a clear distinction of levels is crucial in logics, particularly in those systems where non-classical views are incorporated in the object language by denying bi-valence and/or denying some classical laws of reasoning. Many-valued logics, fuzzy logics , theory of graded consequence, Similarity based reasoning are a few to name. We shall base greatly on the prescription proposed by Alonzo Church in his book Introduction to Mathematical Logic, vol.1. Princeton University Press, N.J., 1956.

One of our attempts would be to draw attention to the fact that logic-studies do not usually pay due attention in distinguishing levels, due to which there do arise misconceptions, and even mistakes. Carnap's remark after Tarski's lecture at Vienna Circle meeting in the year 1930 may be recalled: "Of special interest to me was his emphasis that certain concepts used in logical investigations e.g., consistency of axioms, the provability of theorems in a deductive system, and the like are to be expressed not in the language of the axioms (later called the object language), but in metamathematical language (later called meta-language)."

However, in recent times this issue is being raised by some researchers, and in some cases, though it has not been explicitly mentioned, researchers introduced different languages for different levels of a logic discourse.