It will perhaps give a clearer idea of what I am seeking to convey if I suggest a concrete image for the whole world of a man’s thought and knowledge. Imagine a large clear jelly, in which at all angles and in all states of simplicity or contortion his ideas are imbedded. They are all valid and possible ideas as they lie, none incompatible with any. If you imagine the direction of up or down in this clear jelly being as it were the direction in which one moves by analysis or synthesis, if you go down for example from matter to atoms and centres of force and up to men and states and countries--if you will imagine the ideas lying in that manner--you will get the beginnings of my intention. But our instrument, our process of thinking, like a drawing before the discovery of perspective, appears to have difficulties with the third dimension, appears capable only of dealing with or reasoning about ideas by projecting them upon the same plane. It will be obvious that a great multitude of things may very well exist together in a solid jelly, which would be overlapping and incompatible and mutually destructive when projected together upon one plane. Through the bias in our instrument to do this, through reasoning between terms not in the same plane, an enormous amount of confusion, perplexity, and mental deadlocking occurs. The old theological deadlock between predestination and free will serves admirably as an example of the sort of deadlock I mean. Take life at the level of common sensation and common experience and there is no more indisputable fact than man’s freedom of will, unless it is his complete moral responsibility. But make only the least penetrating of scientific analyses and you perceive a world of inevitable consequences, a rigid succession of cause and effect. Insist upon a flat agreement between the two, and there you are! The instrument fails. So far as this particular opposition is concerned, I shall point out later the reasonableness and convenience of regarding the common-sense belief in free will as truer for one’s personal life than determinism. 1.10. PRACTICAL CONCLUSIONS FROM THESE CONSIDERATIONS. Now what is the practical outcome of all these criticisms of the human mind? Does it follow that thought is futile and discussion vain? By no means. Rather these considerations lead us toward mutual understanding. They clear up the deadlocks that come from the hard and fast use of terms, they establish mutual charity as an intellectual necessity. The common way of speech and thought which the old system of logic has simply systematized, is too glib and too presumptuous of certainty. We must needs use language, but we must use it always with the thought in our minds of its unreal exactness, its actual habitual deflection from fact. All propositions are approximations to an elusive truth, and we employ them as the mathematician studies the circle by supposing it to be a polygon of a very great number of sides.