Symbolic Logic and “Embedding Language”

Extract

Mr. A. F. Bentley in his Linguistic Analysis of Mathematics has attacked the problem of the “embedding language” of mathematics; “This essay” we read in the Foreword, “deals with the language of mathematics, including not only the mathematical symbols, but also those immediately surrounding forms of expressions and assertions through which the symbols are developed, communicated and interpreted. The writer seeks to establish a firm construction for this embedding language.” Inevitably, in the first instance this embedding language must be, as he puts it, “every-day language”; but this is sadly inadequate: “The every-day language reeks with philosophies—the absolutisms of pointing. It shatters at every touch of advancing knowledge. At its heart is paradox… Mathematicians know this. Yet they feel ever the compulsion to interpret their mathematics in terms of every-day language. So proceeding, their harvest is super-paradox.” Yet the writer recognizes after all that “every-day language is the basal medium of communication between men,” even when we seek to “extend standards of symbolic consistency into the regions of the embedding language.”