"We conceive of each as partaking the quality of infinity."

"Now, let us cut out the diameter of the sun; or rather--since this is what our successors in the school will do,--let us take a line of our earth's longitude which is equally unreal, and measure a degree of this thing which does not exist, and then divide it into equal parts which we will use as a measure or metre. This metre, which is still nothing, as I understand you, is infinitely divisible into points? and the point itself is infinitely small? Therefore we have the finite partaking the nature of the infinite?"

"Undoubtedly!"

"One step more, Mr. Abelard, if I do not weary you! Let me take three of these metres which do not exist, and place them so that the ends of one shall touch the ends of the others. May I ask what is that figure?"

"I presume you mean it to be a triangle."

"Precisely! and what sort of a triangle?"

"An equilateral triangle, the sides of which measure one metre each."

"Now let me take three more of these metres which do not exist, and construct another triangle which does not exist;--are these two triangles or one triangle?"

"They are most certainly one--a single concept of the only possible equilateral triangle measuring one metre on each face."

"You told us a moment ago that a universal could not exist wholly and exclusively in two individuals at once. Does not the universal by definition--THE equilateral triangle measuring one metre on each face--does it not exist wholly, in its integrity of essence, in each of the two triangles we have conceived?"

"It does--as a conception."

"I thank you! Now, although I fear wearying you, perhaps you will consent to let me add matter to mind. I have here on my desk an object not uncommon in nature, which I will ask you to describe."

"It appears to be a crystal."

"May I ask its shape?"

"I should call it a regular octahedron."

"That is, two pyramids, set base to base? making eight plane surfaces, each a perfect equilateral triangle?"

"Concedo triangula (I grant the triangles)."

"Do you know, perchance, what is this material which seems to give substantial existence to these eight triangles?"

"I do not."

"Nor I! nor does it matter, unless you conceive it to be the work of man?"

"I do not claim it as man's work."

"Whose, then?"

"We believe all actual creation of matter, united with form, to be the work of G.o.d."

"Surely not the substance of G.o.d himself? Perhaps you mean that this form--this octahedron--is a divine concept."

"I understand such to be the doctrine of the Church."

"Then it seems that G.o.d uses this concept habitually to create this very common crystal. One question more, and only one, if you will permit me to come to the point. Does the matter--the material--of which this crystal is made affect in any way the form--the nature, the soul--of the universal equilateral triangle as you see it bounding these eight plane surfaces?"

"That I do not know, and do not think essential to decide. As far as these triangles are individual, they are made so by the will of G.o.d, and not by the substance you call triangle. The universal--the abstract right angle, or any other abstract form--is only an idea, a concept, to which reality, individuality, or what we might call energy is wanting. The only true energy, except man's free will, is G.o.d."

"Very good, Mr. Abelard! we can now reach our issue. You affirm that, just as the line does not exist in s.p.a.ce, although the eye sees little else in s.p.a.ce, so the triangle does not exist in this crystal, although the crystal shows eight of them, each perfect. You are aware that on this line which does not exist, and its combination in this triangle which does not exist, rests the whole fabric of mathematics with all its necessary truths. In other words, you know that in this line, though it does not exist, is bound up the truth of the only branch of human knowledge which claims absolute certainty for human processes. You admit that this line and triangle, which are mere figments of our human imagination, not only exist independent of us in the crystal, but are, as we suppose, habitually and invariably used by G.o.d Himself to give form to the matter contained within the planes of the crystal. Yet to this line and triangle you deny reality. To mathematical truth, you deny compulsive force. You hold that an equilateral triangle may, to you and all other human individuals, be a right-angled triangle if you choose to imagine it so. Allow me to say, without a.s.suming any claim to superior knowledge, that to me your logic results in a different conclusion. If you are compelled, at one point or another of the chain of being, to deny existence to a substance, surely it should be to the last and feeblest. I see nothing to hinder you from denying your own existence, which is, in fact, impossible to demonstrate. Certainly you are free, in logic, to argue that Socrates and Plato are mere names--that men and matter are phantoms and dreams. No one ever has proved or ever can prove the contrary, Infallibly, a great philosophical school will some day be founded on that a.s.sumption. I venture even to recommend it to your acute and sceptical mind; but I cannot conceive how, by any process of reasoning, sensual or supersensual, you can reach the conclusion that the single form of truth which instantly and inexorably compels our submission to its laws--is nothing."

Thus far, all was familiar ground; certainly at least as familiar as the Pons Asinorum; and neither of the two champions had need to feel ruffled in temper by the discussion. The real struggle began only at this point; for until this point was reached, both positions were about equally tenable. Abelard had hitherto rested quietly on the defensive, but William's last thrust obliged him to strike in his turn, and he drew himself up for what, five hundred years later, was called the "Coup de Jarnac":--

"I do not deny," he begins; "on the contrary, I affirm that the universal, whether we call it humanity, or equilateral triangle, has a sort of reality as a concept; that it is something; even a substance, if you insist upon it. Undoubtedly the sum of all individual men results in the concept of humanity. What I deny is that the concept results in the individual. You have correctly stated the essence of the point and the line as sources of our concept of the infinite; what I deny is that they are divisions of the infinite. Universals cannot be divided; what is capable of division cannot be a universal. I admit the force of your a.n.a.logy in the case of the crystal; but I am obliged to point out to you that, if you insist on this a.n.a.logy, you will bring yourself and me into flagrant contradiction with the fixed foundations of the Church. If the energy of the triangle gives form to the crystal, and the energy of the line gives reality to the triangle, and the energy of the infinite gives substance to the line, all energy at last becomes identical with the ultimate substance, G.o.d Himself. Socrates becomes G.o.d in small; Judas is identical with both; humanity is of the divine essence, and exists, wholly and undivided, in each of us. The equilateral triangle we call humanity exists, therefore, entire, identical, in you and me, as a subdivision of the infinite line, s.p.a.ce, energy, or substance, which is G.o.d. I need not remind you that this is pantheism, and that if G.o.d is the only energy, human free will merges in G.o.d's free will; the Church ceases to have a reason for existence; man cannot be held responsible for his own acts, either to the Church or to the State; and finally, though very unwillingly, I must, in regard for my own safety, bring the subject to the attention of the Archbishop, which, as you know better than I, will lead to your seclusion, or worse."

Whether Abelard used these precise words is nothing to the point.

The words he left on record were equivalent to these. As translated by M. de Remusat from a ma.n.u.script ent.i.tled: "Glossulae magistri Petri Baelardi super Porphyrium," the phrase runs: "A grave heresy is at the end of this doctrine; for, according to it, the divine substance which is recognized as admitting of no form, is necessarily identical with every substance in particular and with all substance in general." Even had he not stated the heresy so bluntly, his objection necessarily pushed William in face of it.

Realism, when pressed, always led to pantheism. William of Champeaux and Bishop or Archbishop Hildebert were personal friends, and Hildebert's divine substance left no more room for human free will than Abelard saw in the geometric a.n.a.logy imagined for William.

Throughout the history of the Church for fifteen hundred years, whenever this theological point has been pressed against churchmen it has reduced them to evasion or to apology. Admittedly, the weak point of realism was its fatally pantheistic term.

Of course, William consulted his friends in the Church, probably Archbishop Hildebert among the rest, before deciding whether to maintain or to abandon his ground, and the result showed that he was guided by their advice. Realism was the Roman arch--the only possible foundation for any Church; because it a.s.sumed unity, and any other scheme was compelled to prove it, for a starting-point.

Let us see, for a moment, what became of the dialogue, when pushed into theology, in order to reach some of the reasons which reduced William to tacit abandonment of a doctrine he could never have surrendered unless under compulsion. That he was angry is sure, for Abelard, by thus thrusting theology into dialectics, had struck him a full blow; and William knew Abelard well:--

"Ah!" he would have rejoined; "you are quick, M. du Pallet, to turn what I offered as an a.n.a.logy, into an argument of heresy against my person. You are at liberty to take that course if you choose, though I give you fair warning that it will lead you far. But now I must ask you still another question. This concept that you talk about-- this image in the mind of man, of G.o.d, of matter; for I know not where to seek it--whether is it a reality or not?"

"I hold it as, in a manner, real."

"I want a categorical answer--Yes or No!"

"Distinguo! (I must qualify.)"

"I will have no qualifications. A substance either is, or not.

Choose!"

To this challenge Abelard had the choice of answering Yes, or of answering no, or of refusing to answer at all. He seems to have done the last; but we suppose him to have accepted the wager of battle, and to answer:--

"Yes, then!"

"Good!" William rejoins; "now let us see how your pantheism differs from mine. My triangle exists as a reality, or what science will call an energy, outside my mind, in G.o.d, and is impressed on my mind as it is on a mirror, like the triangle on the crystal, its energy giving form. Your triangle you say is also an energy, but an essence of my mind itself; you thrust it into the mind as an integral part of the mirror; identically the same concept, energy, or necessary truth which is inherent in G.o.d. Whatever subterfuge you may resort to, sooner or later you have got to agree that your mind is identical with G.o.d's nature as far as that concept is concerned.

Your pantheism goes further than mine. As a doctrine of the Real Presence peculiar to yourself, I can commend it to the Archbishop together with your delation of me."

Supposing that Abelard took the opposite course, and answered:--

"No! my concept is a mere sign."

"A sign of what, in G.o.d's name!"

"A sound! a word! a symbol! an echo only of my ignorance."

"Nothing, then! So truth and virtue and charity do not exist at all.

You suppose yourself to exist, but you have no means of knowing G.o.d; therefore, to you G.o.d does not exist except as an echo of your ignorance; and, what concerns you most, the Church does not exist except as your concept of certain individuals, whom you cannot regard as a unity, and who suppose themselves to believe in a Trinity which exists only as a sound, or a symbol. I will not repeat your words, M. du Pallet, outside this cloister, because the consequences to you would certainly be fatal; but it is only too clear that you are a materialist, and as such your fate must be decided by a Church Council, unless you prefer the stake by judgment of a secular court."

In truth, pure nominalism--if, indeed, any one ever maintained it-- afforded no cover whatever. Nor did Abelard's concept help the matter, although for want of a better refuge, the Church was often driven into it. Conceptualism was a device, like the false wooden roof, to cover and conceal an inherent weakness of construction.

Unity either is, or is not. If soldiers, no matter in what number, can never make an army, and worshippers, though in millions, do not make a Church, and all humanity united would not necessarily const.i.tute a State, equally little can their concepts, individual or united, const.i.tute the one or the other. Army, Church, and State, each is an organic whole, complex beyond all possible addition of units, and not a concept at all, but rather an animal that thinks, creates, devours, and destroys. The attempt to bridge the chasm between multiplicity and unity is the oldest problem of philosophy, religion, and science, but the flimsiest bridge of all is the human concept, unless somewhere, within or beyond it, an energy not individual is hidden; and in that case the old question instantly reappears: What is that energy?