Marxism and the Linguistic Philosophy
The Laws of Thought
1. FORMAL LOGIC
IN discussing the linguistic philosophers' investigations of the actual use of language I came to the conclusion that what distinguishes language as a means of communication is its expression of propositions. Language has the unique functions of negating, abstracting and generalising. These, by the way, should not be conceived of as separable or co‑exclusive functionslike walking, running and jumping as achieved by moving the legs. For purposes of logical exposition we can, of course, speak about or represent symbolically negation as distinct from generalisation, or generalisation as distinct from abstraction. But all propositions combine negating, abstracting and generalising functions. Every significant sentence negates, abstracts and generalises.
Operations involved in making propositions can be considered purely formally. That is to say, we can investigate the proposition‑making operations performed in sentences in abstraction from their meaning. For a formal investigation is one which abstracts from meaning. For example, consider such sentences in English as "This rose is red", "This pig has wings", "This triangle is equilateral", and equivalent sentences in English expressed in other idioms (such as "The rose I am calling your attention to has the colour denoted by the word 'red’”), and equivalent sentences in other languages, and then abstract the logical operations exemplified by all those sentences by disregarding the differences of both meaning and verbal construction. To do that is to start a formal investigation of logical operations. This is what is done in formal logic, and to do it the specialised symbolic techniques of formal logic have been worked out (starting from the rather crude and inadequate techniques of Aristotle's Analytics, his genius having consisted in inventing a technique but not in perfecting it).
The special business of formal logic is to work out the symbolic techniques of representing logical operations (of key importance was the recent invention of quantification technique); and to construct a logical calculus, with techniques for testing it and demonstrating consistency and completeness. This is a specialised science, allied to mathematics. What it does is to demonstrate how to conduct with consistency logical operations of any degree of complexity.
Those responsible for the great recent advances in formal logic were perhaps motivated mainly by personal interest and curiosity: they wanted to make these demonstrations because they can be made, much as mountaineers wanted to climb Everest "because it is there" (though some, like Russell, were apparently inspired also by a notion that they would achieve a revelation of the ultimate structure of the universe). Certainly, the science that has been achieved is far removed from the paltry practical aim sometimes claimed for formal logicof being an aid to the art of disputation or catching other people out in logical fallacies. But the fact remains that formal logic, like various branches of mathematics, was not developed until advances of empirical sciences and of technology provided a stimulus and a demand; and though it is not of very much use to human beings as a compendium of instructions on how to think consistently (it is far easier to think consistently than to master such a complicated science as formal logic), it is of the greatest use, and indeed indispensable, for the purpose of programming computers. Machines do not think for themselves, and so a calculus of logical operations has to be available before we can make them think for us.
Formal logic, then, has become a formal science in its own right, with a status like that of mathematics. It is no part of philosophy, but, something philosophy has to take into account. In the past, its development was hampered by being treated as a part of philosophyas a result of which quite different sorts of questions were continually mixed up together and the quite different procedures required for dealing with them were 