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 flames, though there are good reasons for concluding that he made mistakes in them.
It is an old prejudice in philosophy that all statements must be either "empirical statements" or else be “known a priori", that is, independent of experience. This dichotomy goes back to Hume, and was further fixed in the minds of philosophers by Kant. But it is totally false and misleading, like so many other hard and fast antitheses. Thus mathematical principles are not established empirically like the generalisations of the empirical sciences, but they are certainly derived from experience and not known independently of experience. And this is true also of the principles concerning "categories" which are of primary interest to philosophy.
The systematic or methodical investigation of categories has to do with the word‑function of abstraction. Formal logic deals with abstraction only in the way of calculating the logical operations involved in abstracting a conclusion from premises. For instance, from information "All A's that are B are C”, plus information that "This A is C”, can be abstracted the conclusion "This A is C”. This is the sort of abstraction a computer can be programmed to perform. And of course, when very complicated information is fed into it, it can abstract conclusions, as required, which human brains would make very heavy work of abstracting.
But there are procedures of abstraction depending not on the logical form but on the meaning. For instance, from information "This rose is red" may be abstracted "This rose is not white"; and that abstraction does not depend on the logical form of propositions but on meaning. Suppose a rose grower had a computer to tell him how many roses of different colours he had sold, so that for each sale it registered the colour of the rose. It would not work unless in programming it he had been guided by the principle: "These are the colours of roses . . . and a rose of one colour is not of any other colour". But that is not a proposition of formal logic, and is not demonstrable 