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.
Let me try and express how in my mind this matter of negative terms has shaped itself. I think of something which I may perhaps best describe as being off the stage or out of court, or as the Void without Implications, or as Nothingness, or as Outer Darkness. This is a sort of hypothetical Beyond to the visible world of human thought, and thither I think all negative terms reach at last, and merge and become nothing. Whatever positive class you make, whatever boundary you draw, straight away from that boundary begins the corresponding negative class and passes into the illimitable horizon of nothingness. You talk of pink things, you ignore, as the arbitrary postulates of Logic direct, the more elusive shades of pink, and draw your line. Beyond is the not-pink, known and knowable, and still in the not-pink region one comes to the Outer Darkness. Not blue, not happy, not iron, all the NOT classes meet in that Outer Darkness. That same Outer Darkness and nothingness is infinite space and infinite time and any being of infinite qualities; and all that region I rule out of court in my philosophy altogether. I will neither affirm nor deny if I can help it about any NOT things. I will not deal with not things at all, except by accident and inadvertence. If I use the word “infinite” I use it as one often uses “countless,” “the countless hosts of the enemy”—or “immeasurable”—“immeasurable cliffs”—that is to say as the limit of measurement, as a convenient equivalent to as many times this cloth yard as you can, and as many again, and so on and so on until you and your numerical system are beaten to a standstill.
Now a great number of apparently positive terms are, or have become, practically negative terms and are under the same ban with me. A considerable number of terms that have played a great part in the world of thought, seem to me to be invalidated by this same defect, to have no content or an undefined content or an unjustifiable content. For example, that word Omniscient, as implying infinite knowledge, impresses me as being a word with a delusive air of being solid and full, when it is really hollow with no content whatever. I am persuaded that knowing is the relation of a conscious being to something not itself, that the thing known is defined as a system of parts and aspects and relationships, that knowledge is comprehension, and so that only finite things can know or be known. When you talk of a being of infinite extension and infinite duration, omniscient and omnipotent and perfect, you seem to me to be talking in negatives of nothing whatever.
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