Classification and number, which in truth ignore the fine differences of objective realities, have in the past of human thought been imposed upon things...
Greek thought impresses me as being over much obsessed by an objective treatment of certain necessary preliminary conditions of human thought—number and definition and class and abstract form! But these things,—number, definition, class and abstract form,—I hold, are merely unavoidable conditions of mental activity—regrettable conditions rather than essential facts. THE FORCEPS OF OUR MINDS ARE CLUMSY FORCEPS AND CRUSH THE TRUTH A LITTLE IN TAKING HOLD OF IT...
Let me give you a rough figure of what I am trying to convey in this first attack upon the philosophical validity of general terms. You have seen the result of those various methods of black and white reproduction that involve the use of a rectangular net. You know the sort of process picture I mean—it used to be employed very frequently in reproducing photographs. At a little distance you really seem to have a faithful reproduction of the original picture, but when you peer closely you find not the unique form and masses of the original, but a multitude of little rectangles, uniform in shape and size. The more earnestly you go into the thing, the closelier you look, the more the picture is lost in reticulations. I submit, the world of reasoned inquiry has a very similar relation to the world of fact. For the rough purposes of every day the network picture will do, but the finer your purpose the less it will serve, and for an ideally fine purpose, for absolute and general knowledge that will be as true for a man at a distance with a telescope as for a man with a microscope, it will not serve at all.
It is true you can make your net of logical interpretation finer and finer, you can fine your classification more and more—up to a certain limit. But essentially you are working in limits, and as you come closer, as you look at finer and subtler things, as you leave the practical purpose for which the method exists, the element of error increases. Every species is vague, every term goes cloudy at its edges; and so in my way of thinking, relentless logic is only another name for a stupidity—for a sort of intellectual pigheadedness. If you push a philosophical or metaphysical inquiry through a series of valid syllogisms—never committing any generally recognised fallacy—you nevertheless leave behind you at each step a certain rubbing and marginal loss of objective truth, and you get deflections that are difficult to trace at each phase in the process. Every species waggles about in its definition, every tool is a little loose in its handle, every scale has its individual error. So long as you are reasoning for practical purposes about finite things of experience you can every now and then check your process and correct your adjustments. But not when you make what are called philosophical and theological inquiries, when you turn your implement towards the final absolute truth of things.
This real vagueness of class terms is equally true whether we consider those terms used extensively or intensively, that is to say whether in relation to all the members of the species or in relation to an imaginary typical specimen. The logician begins by declaring that S is either P or not P. In the world of fact it is the rarest thing to encounter this absolute alternative; S1 is pink, but S2 is pinker, S3 is scarcely pink at all, and one is in doubt whether S4 is not properly to be called scarlet. The finest type specimen you can find simply has the characteristic quality a little more rather than a little less. The neat little circles the logician uses to convey his idea of P or not P to the student are just pictures of boundaries in his mind, exaggerations of a natural mental tendency. They are required for the purposes of his science, but they are departures from the nature of fact.
1.6.
EMPTY TERMS.
Classes in logic are not only represented by circles with a hard firm outline, whereas in fact they have no such definite limits, but also there is a constant disposition to think of all names as if they represented positive classes. With words just as with numbers and abstract forms there have been definite phases of human development. There was with regard to number, the phase when man could barely count at all, or counted in perfect good faith and sanity upon his fingers. Then there was the phase when he struggled with the development of number, when he began to elaborate all sorts of ideas about numbers, until at last he developed complex superstitions about perfect numbers and imperfect numbers, about threes and sevens and the like. The same was the case with abstract forms; and even to-day we are scarcely more than heads out of the vast subtle muddle of thinking about spheres and ideally perfect forms and so on, that was the price of this little necessary step to clear thinking. How large a part numerical and geometrical magic, numerical and geometrical philosophy have played in the history of the mind! And the whole apparatus of language and mental communication is beset with like dangers. The language of the savage is I suppose purely positive; the thing has a name, the name has a thing. This indeed is the tradition of language, and even to-day, we, when we hear a name are predisposed—and sometimes it is a very vicious disposition—to imagine forthwith something answering to the name. WE ARE DISPOSED, AS AN INCURABLE MENTAL VICE, TO ACCUMULATE INTENSION IN TERMS. If I say to you Wodget or Crump, you find yourself passing over the fact that these are nothings, these are, so to speak mere blankety blanks, and trying to think what sort of thing a Wodget or a Crump may be. You find yourself led insensibly by subtle associations of sound and ideas to giving these blank terms attributes.
Now this is true not only of quite empty terms but of terms that carry a meaning. It is a mental necessity that we should make classes and use general terms, and as soon as we do that we fall into immediate danger of unjustifiably increasing the intension of these terms. You will find a large proportion of human prejudice and misunderstanding arises from this universal proclivity.
1.7.
NEGATIVE TERMS.
There is a particular sort of empty terms that has been and is conspicuously dangerous to the thinker, the class of negative terms. The negative term is in plain fact just nothing; "Not-A" is the absence of any trace of the quality that constitutes A, it is the rest of everything for ever. But there seems to be a real bias in the mind towards regarding "Not-A" as a thing mysteriously in the nature of A, as though "Not-A" and A were species of the same genus. When one speaks of Not-pink one is apt to think of green things and yellow things and to ignore anger or abstract nouns or the sound of thunder. And logicians, following the normal bias of the mind, do actually present A and not-A in this sort of diagram:—
(the letter A inside a circular boundary, together with the words Not A, all inside a bigger circular boundary.)
ignoring altogether the difficult case of the space in which these words are printed. Obviously the diagram that comes nearer experienced fact is:—
(the word Not, followed by the letter A inside a circular boundary, followed by the letter A)
with no outer boundary. But the logician finds it necessary for his processes to present that outer Not-A as bounded (Vide e.g. Kayne's "Formal Logic" re Euler's diagrams and Immediate Inferences.), and to speak of the total area of A and Not-A as the Universe of Discourse; and the metaphysician and the commonsense thinker alike fall far too readily into the belief that this convention of method is an adequate representation of fact.