to me, had taken a common innate error of the mind and had emphasised it in order to develop a system of reasoning that should be exact in its processes. I turned my attention to the examination of that. For in common with the general run of men I had supposed that logic professed to supply a trustworthy science and method for the investigation and expression of reality.
A mind nourished on anatomical study is of course permeated with the suggestion of the vagueness and instability of biological species. A biological species is quite obviously a great number of unique individuals which is separable from other biological species only by the fact that an enormous number of other linking individuals are inaccessible in time — are in other words dead and gone — and each new individual in that species does, in the distinction of its own individuality, break away in however infinitesimal degree from the previous average properties of the species. There is no property of any species, even the properties that constitute the specific definition, that is not a matter of more or less.
If, for example, as species be distinguished by a single large red spot on the back, you will find if you go over a great number of specimens that red spot shrinking here to nothing, expanding there to a more general redness, weakening to pink, deepening to russet and brown, shading into crimson, and so on and so on. And this is true not only of biological species. It is true of the mineral specimens constituting a mineral species, and I remember as a constant refrain in the lectures of Professor Judd upon rock classification, the words, “they pass into one another by insensible gradations.” It is true, I hold, of all things.
You will think perhaps of atoms of the elements as instances of identically similar things, but these are things not of experience but of theory, and there is not a phenomenon in chemistry that is not equally well explained on the supposition that it is merely the immense quantities of atoms necessarily taken in any experiment that masks by the operation of the law of averages the fact that each atom also has its unique quality, its special individual difference.
This ideal of uniqueness in all individuals is not only true of the classifications of material science; it is true and still more evidently true of the species of common thought; it is true of common terms. Take the word “Chair.” When one says chair, one thinks vaguely of an average chair. But collect individual instances; think of armchairs and reading-chairs and dining-room chairs, and kitchen chairs, chairs that pass into benches, chairs that cross the boundary and become settees, dentist’s chairs, thrones, opera stalls, seats of all sorts, those miraculous fungoid growths that cumber the floor of the Arts and Crafts exhibition, and you will perceive what a lax bundle in fact is this simple straightforward term. In co-operation with an intelligent joiner I would undertake to defeat any definition of chair or chairishness that you gave me. Chairs just as much as individual organisms, just as much as mineral and rock specimens, are unique things — if you know them well enough you will find an individual difference even in a set of machine-made chairs — and it is only because we do not possess minds of unlimited capacity, because our brain has only a limited number of pigeon-holes for our correspondence with an unlimited universe of objective uniques, that we have to delude ourselves into the belief that there is a chairishness in this species common to and distinctive of all chairs.
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
