The impossibility of squaring the circle is not really a negative proposition, except in form. It is safer and more convincing when thrown into the positive and definite form that the ratio of area to diameter is incommensurable. That statement is perfectly clear and legitimate; and the illustration may be used as a parable. A positive form should be demanded of every comprehensive denial; and whatever cannot be thrown into positive form, it is wise to mistrust. Its promulgator is probably stepping out of bounds, into the cheap and easy region of negative speculation. He is like a rationalistic microbe denying the existence of a human being.

I have urged that the simple aspect of things is to be considered and not despised; but, for the majority of people, is not the tendency the other way? Are they not too much given to suppose the Universe limited to the simplicity of their first and everyday conception of it? The stockbroker has his idea of the totality of things; the navvy has his. Students of mathematical physics are liable to think of it as a determinate assemblage of atoms and ether, with no room for spiritual entities—no room, as my brilliant teacher, W. K. Clifford, expressed it, no room for ghosts.

Biological students are apt to think of life as a physicochemical process of protoplasmic structure and cell organisation, with consciousness as an epiphenomenon. They watch the lowly stages of animal organisms, and hope to imitate their behaviour by judicious treatment of inorganic materials. By all means let them try; the effort is entirely legitimate, and not unhopeful. That which has come into being in the past may come into being under observation in the present, and the intelligence and co-operation of man may help. Why not? The material vehicle would thus have been provided—in this case, without doubt, purposely and designedly—for some incipient phase of life. But would that in the least explain the nature of life and mind and will, and reduce them to simple atomic mechanism and dynamics? Not a whit. The real nature of these things would remain an unanswered question.

During the past century progress has lain chiefly in the domain of the mechanical and material. The progress has been admirable, and has led to natural rejoicing and legitimate pride. It has also led to a supposition that all possible scientific advance lies in this same direction, or even that all the great fundamental discoveries have now been made! Discovery proceeds by stages, and enthusiasm at the acquisition of a step or a landing-place obscures for a time our perception of the flight of stairs immediately ahead; but it is rational to take a more comprehensive view.

Part of our experience is the connexion of spirit with matter. We are conscious of our own identity, our own mind and purpose and will: we are also conscious of the matter in which it is at present incarnate and manifested. Let us use these experiences and learn from them. Incarnation is a fact; we are not matter, yet we utilise it. Through the mechanism of the brain we can influence the material world; we are in it, but not of it; we transcend it by our consciousness. The body is our machine, our instrument, our vehicle of manifestation; and through it we can achieve results in the material sphere. Why seek to deny either the spiritual or the material? Both are real, both are true. In some higher mind, perhaps, they may be unified: meanwhile we do not possess this higher mind. Scientific progress is made by accepting realities and learning from them; the rest is speculation. It is not likely that we are the only intelligent beings in the Universe. There may be many higher grades, up to the Divine; just as there are lower grades, down to the amœba. Nor need all these grades of intelligence be clothed in matter or inhabit the surface of a planet. That is the kind of existence with which we are now familiar, truly, and anything beyond that is for the most part supersensuous; but our senses are confessedly limited, and if there is any truth in the doctrine of human immortality the existence of myriads of departed individuals must be assumed, on what has been called "the other side."

But how are we to get evidence in favour of such an apparently gratuitous hypothesis? Well, speaking for myself and with full and cautious responsibility, I have to state that as an outcome of my investigation into psychical matters I have at length and quite gradually become convinced, after more than thirty years of study, not only that persistent individual existence is a fact, but that occasional communication across the chasm—with difficulty and under definite conditions—is possible.

This is not a subject on which one comes lightly and easily to a conclusion, nor can the evidence be explained except to those who will give to it time and careful study; but clearly the conclusion is either folly and self-deception, or it is a truth of the utmost importance to humanity—and of importance to us in connexion with our present subject. For it is a conclusion which cannot stand alone. Mistaken or true, it affords a foothold for a whole range of other thoughts, other conclusions, other ideas: false and misleading if the foothold is insecure, worthy of attention if the foothold is sound. Let posterity judge.

Meanwhile it is a subject that attracts cranks and charlatans. Rash opinions are freely expressed on both sides. I call upon the educated of the younger generation to refrain from accepting assertions without severe scrutiny, and, above all, to keep an open mind.

If departed human beings can communicate with us, can advise us and help us, can have any influence on our actions,—then clearly the doors are open to a wealth of spiritual intercourse beyond what we have yet imagined.