Language and Logic

Abstract

It has been claimed by many of today’s logicians that logical-epistemological investigations can reach clear and precise results only if the object of study is a linguistic system constructed according to precise rules. Due to the vagueness pervading it, ordinary language is unable to satisfy this condition. According to this view, it must therefore be replaced by a formalized language or a series of formalized languages to be constructed on the basis of certain explicitly formulated rules. When one speaks of the vagueness of ordinary language what comes immediately to mind is so-called equivocation, i.e., the multiple meanings an expression may take; e.g. the expression ‘bark’ may mean respectively (1) the outer covering of trees, (2) the kind of sound omitted by dogs, or (3) a type of sailing ship. Such ambiguities, however, are trivial, for one can without difficulty gather from the respective context exactly which of the several meanings of that word is intended. Hence it would be absurd to justify the demand for a more precise logical language by pointing to ambiguous expressions such as ‘bark’. But, there are still other reasons for using a symbolic language to pursue logical studies, the main one being the possibility of achieving greater perspicuity and economy of expression. Just as mathematics would have made but little progress without resorting to the appropriate mathematics symbols, so logic cannot be expected to arrive at significant results if denied the use of symbolic language. Were we not permitted to resort to algebraic symbols, even a simple math statement like: ‘(a+b)2=a2+2ab2+b2’ would commit us to the rather complicated expression: the square of the sum of any two numbers is the same as the sum of the square of the first, plus the product of the first and second times two, plus the square of the second’. In an analogous way, statements of an even more complicated structure would, as a whole, require such a complicated formulation in ordinary language that a logical analysis would become troublesome and time-consuming unless this formulation be replaced by a more transparent one allowing free recourse to symbols.