M. Lionville reminded his audience that many demonstrations of this celebrated proposition had been attempted, but had not succeeded, because there are limits within which human reason ceases to be accepted by all. M. Lionville even proposed that the question of the postulatum should be classed among those whose examination is interdicted by the Academy, such as the quadrature of the circle, and the trisection of the angle. On this point M. Lionville quoted an anecdote relative to Lagrange. That great mathematician, believing that he had found an absolute solution of the postulatum, went to the Academy to read his demonstration, but on reflection, he changed his mind, and decided that it would be better not to publish it. He put his manuscript in his pocket, and it never came out.
Several geometricians spoke on this occasion, and confirmed the views of M. Lionville; and when the demonstration submitted by the professor was examined, it was found to be false. We must therefore recognize and proclaim that, in geometry, the axioms cannot be demonstrated.
Many people endeavour to derive an argument from that discussion against the certainty of geometry. Among them is M. Bouillaud, a learned physician and member of the Institute, who declared that he could not get over his astonishment at hearing it said that there were several geometries, and that even the bases of that science were doubtful. Reassure yourself, great and good physician, geometry has nothing to lose and nothing to hide, and the certainty of its methods is not imperilled in this question. That which really was at stake was the methodical, classical teaching of geometry. That which was discussed was the best means of instilling the principles of science into the mind. But, as to the truths of geometry, as to the facts themselves, they are secure from all uncertainty, all these disputes upon the truth which must be recognized as axioms, or demonstrated as theorems, are only fancies of the rhetoricians, as vain as they are subtle. No trace of them remains when they are transported into the practice of facts and of mathematical deductions. Ask the astronomers who calculate the orbit of the stars, who fix the moment of an eclipse with unerring precision, ask those who have calculated the parallaxes, whether they trouble themselves by inquiring how it may be demonstrated that the angles of a triangle are equal to two right angles. All the scholastic subtleties are gotten rid of in the course of practical work.
If we may lay aside, without occupying ourselves with them, the mathematicians who amuse themselves by disputing the axioms of geometry, we may do the same with the few sophists who desire to dispute the axioms of philosophy and reason, and especially the principle of the existence of an immortal soul in man. Let us leave them to their disputations, and go on our way.
Second objection:—We have no recollection of having existed prior to our entrance into this world.
This is, we acknowledge the greatest and most serious argument against our system. But we must hasten to add, that if this difficulty did not exist, if the remembrance of a life anterior to our present existence were always before us, the doctrine of plurality of lives would need no reinforcement from the proofs for which we appeal to argument, to the facts of observation, and to logical induction. It would be plain before our eyes, it would be self-evident. All our merit, all our task in this work, is to endeavour to procure admission of the plurality of existences, though we have no remembrance of our past lives.
We have already treated this question incidentally, and we will now summarize all that has been advanced in former chapters to explain the absence of recollection of our past existences.
The soul in its first human incarnation, if it proceeds from a superior animal, could not possess memory, because in animals that faculty has a small range, and brief duration. If a second or third human incarnation is in question, the difficulty is serious, because it implies that the man who has lived and who is born again, has forgotten his previous life.
But, in the first place, this forgetfulness is not absolute. We have remarked before that in the human soul certain results of impressions received prior to the terrestrial life always linger. Natural aptitudes, special faculties, vocations, are the traces of impressions formerly received, of knowledge already acquired, and, being revealed from the cradle, cannot be explained otherwise than by a life gone by. We have lost the remembrance of the facts, but there remains the moral consequence, the resultant, the philosophy, so to speak, and thus the innate ideas indicated by Descartes, which exist in the soul from its birth, and also the principle of causality, which teaches us that every effect has a cause, are explained. This principle can only be derived from facts, because an abstraction can only be based upon concrete facts, upon accomplished events, and this abstraction, or this metaphysical idea, which we have from our birth, implies anterior facts, which must belong to a past life.
We have already said that when the soul gives free course to reverie, it beholds mysterious and undefined spectacles, which seem to belong to worlds which are not quite unknown to us, but in no wise resembling this earth. In this vague contemplation there is something like a confused remembrance of an anterior life. The love which we bear to flowers, plants, and all vegetation, may be as we have already pointed out, a grateful recollection of our first origin.