f 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 not observed. While Boole, Frege and others were turning formal logic into a science, a whole crop of rival and incompatible philosophical "logics" emerged, ranging from J. S. Mill's to F. H. Bradley's. These can now be written off. But as with other sciences, including mathematics, questions remain about what formal logic does and how it does it, and about its connections with other sciences; and these can properly be regarded as coming within the sphere of philosophical investigation.
Professor Ryle distinguished what he called the logical investigation of categories from formal logic. While his account of both is open to criticism (and was duly criticised above), the distinction is of profound and far‑reaching philosophical importance.
To start investigating categories is to become concerned with meaning, and to depart from purely formal inquiry. For this reason there is not and cannot be anything like a calculus of categories, nor are symbolic techniques like those of formal logic and mathematics applicable. At the same time, while not a formal inquiry, an inquiry about categories is not an empirical inquiry either—for its findings are not subject to empirical test. As Ryle has said, a "category proposition" is a generalisation to contradict which leads to absurdity; and so it is certainly not empirically falsifiable, like an empirical generalisation.
Hume proclaimed that whatever was neither formally certified nor empirically verified should be committed to the flames. But the very fact that he said so showed that he could not have meant what he said, for such a principle is self‑destructive. The conclusions he himself arrived at were neither formally certified nor empirically verified, nor could such conclusions be. Hume was, in fact (in a rather unmethodical way, but he deserves perpetual respect as a pioneer), undertaking an investigation of categoriesespecially in his famous discussions about material objects, minds and causality. There are no good reasons for committing his philosophical writings to the