Eleanor F. Jourdain

“ The general result of the inquiry has been, as far as we can judge, that metaphysics has exercised an inspiring force on mathematics, and mathematics has defined and strengthened the conceptions of metaphysics at every critical stage in the history of philosophy. But where metaphysics has been treated as the proof of science, where it has been laid down as the foundation for exact knowledge, the results have not corresponded with the truth of experience, and the quality of thought has become degenerate. ”

“ The Pragmatist denies scientific law and also logic, and makes his appeal to facts. No conclusion can be drawn from that denial except by the use of logic itself. If he consistently denied logic, his position would be unassailable by logic, but he uses the method he denies, and is thus open to attack. On the subject of the Laws of Science the Pragmatist points out truly that there is no actual continuity between a fact and a law. But laws are concepts, the result of mental activities; they are themselves subject to the laws of logic. ”

“ A cinematograph would not explain the reappearance of the old wood in all its denseness; nor the rapid disappearance of the cart and horse in an open field; nor the music, which, six years later, was found to be a piecing together of eighteenth century operas.
No amount of masqueraders explains to us the ease with which we dismissed from sight and hearing the usual August crowds in the middle of a fine afternoon, and the impossibility of harmonising our recollections of the scenery with anything but the old maps and records. ”

“ But it has only lately been realised that fourth and other dimensions may be actual fact in the world round us. Of course, from the point of view of a point there are only three dimensions to be known, but to a line in the same space there are five, to the surface probably six. Our intelligence at present does not go beyond the point; but if we could think of space from the point of view of a solid, worlds upon worlds would rise before our view. ”

“ Even in happy times some natural impatience in the Queen’s nature made it imperative to her to run away and be alone sometimes. It was at the Petit Trianon that she had found relief from tiresome restrictions, importunities of etiquette, and obsequious crowds. ”

“ If the Finite and the Infinite can in turn be deduced from one another, neither conception can be truly called an axiom. The real axiom is existence, which includes both, and which is defined by mathematicians as that which is not self-contradictory.
Now the problem of Infinity includes also that of continuity; in other words, the problem of number includes that of cardinal and ordinal number. It is time to get to the mathematical definition of number, which we have found as a conception can be attached both to the Finite and to the Infinite. What is number in mathematics? ”

“ The Pragmatist, however, opposes to law what he calls a new fact—​what should rather be called a hypothesis. He asserts that in every event, action, experiment, there is a margin unseen and unrecognised by us; that at every moment, therefore, the unknown, the unexpected, may take shape and voice and denounce all our careful and reasoned conclusions. “Why should the sun rise to-morrow because he has risen to-day and yesterday?” asks the Pragmatist. “We are making an enormous assumption,” he says, “in claiming the uniformity of Nature and the principle of causality.” ”

“ It did not seem to be the place where we had met the garden officials.
We spent a long time looking for the old paths. Not only was there no trace of them, but the distances were contracted, and all was on a smaller scale than I recollected. The kiosk was gone; so was the ravine and the little cascade which had fallen from a height above our heads, and the little bridge over the ravine was, of course, gone too. The large bridge with the rocher over it, crossing one side of the lake at the foot of the Belvédère, had no resemblance to it. ”

“ The methods by which the problems are attacked and the adequacy of the solutions they receive vary, from age to age, in close correspondence with the general development of science. Every great metaphysical conception has exercised its influence on the general history of science, and in return every important movement in science has affected the development of metaphysics. The metaphysician could not if he would, and would not if he could, escape the duty of estimating the bearing of the great scientific theories of his time upon our ultimate conceptions of the nature of the world as a whole. ”

“ VISITS TO THE PETIT TRIANON Miss Morison’s Account of the First Visit to the Petit Trianon
August, 1901 After some days of sight-seeing in Paris, to which we were almost strangers, on an August afternoon, 1901, Miss Lamont and I went to Versailles. We had very hazy ideas as to where it was or what there was to be seen. Both of us thought it might prove to be a dull expedition. We went by train, and walked through the rooms and galleries of the Palace with interest, though we constantly regretted our inability through ignorance to feel properly the charm of the place. ”

“ An overpowering sense of mystery, joined to a premature desire for definition without scientific analysis, sapped the vigour of mediæval thought.
Throughout the middle ages, then, we see the conditions of the Greek period reversed: philosophy during the second period is not, as in the first, engaged in giving a stimulus to the efforts of pure reason; rather the intuitions of philosophy are treated as axiomatic, and a false superstructure of knowledge, alien to experience and reality, is erected upon these foundations. ”

“ It is a science of relations rather than of mere number. Founded, then, on the laws of symbolic logic, it is a valuable aid and illustration to philosophy; philosophy, on the other hand, can imagine lines for the exercise of the constructive power involved in mathematics. It is the object of this paper to show that the close though apparently accidental union of philosophy and mathematics throughout the history of thought can now be explained, and that the problems with which pure mathematics is now concerned are those which lie at the core of philosophic thought and speculation. ”

“ Well-known bars of Monsigny’s music mingled with reminiscences of Sacchini’s and Grétry’s operas. Was it not on an August day, twelve years ago, that she first acted herself in the charming little newly-built theatre? [103] It was in a play of Sedaine (Le Roi et le Fermier) for which Monsigny had written music, especially for the Trianon; and with pain it was remembered that the plot of the play was the favourite one at Trianon, viz. the superiority of the farmer’s condition over that of the King. Vaudreuil had acted the part of the farmer lover to her Jenny. ”

“ He concludes, therefore, that by analogy there is no Absolute, since what we perceive always implies something against which we perceive it; thus that there is no goal by which and at which the spirit of man can find rest. On his theory we could never claim to reach the conception of an Absolute, though he admits the progressive character of human thought, and the increasing reach, lucidity, and depth of the human mind. The true answer to this argument is that it proves exactly what it sets out to disprove. ”

“ When we were first asked whether the man from the side building was real or not, we laughed at the idea of any unreality; all was so quietly natural that we are still uncertain whether the tall gardener belonged to another century or not. ”

“ Are we then looking out upon a third dimensional world, and realising it as such because we are mentally capable of conceiving dimensions beyond it? Our world sensibly contains one dimensional and two dimensional facts—​the first such as a time series, for which one number is sufficient to fix a point, and the second such as a plane where position can be fixed by two numbers. Does our world contain facts of other dimensions? ”

“ We walked on, crossing a small bridge that went across a green bank, high on our right hand and shelving down below as to a very small overshadowed pool of water glimmering some way off. A tiny stream descended from above us, so small as to seem to lose itself before reaching the little pool. We then followed a narrow path till almost immediately we 20came upon the English garden front of the Petit Trianon. The place was deserted; but as we approached the terrace I remember drawing my skirt away with a feeling as though someone were near and I had to make room, and then wondering why I did it. ”