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Let us bear in mind that in aiming at ultimate truths we have no final courts of appeal. Nor are the latter to be assumed even when, in pursuing a theory, we encounter a difficulty, which at first exhibits all the signs of a direct conceptual contradiction. It should rather be realized that a fiction containing an initial but only provisional contradiction serves as a starting-point for just those investigations that are most subtle and that have far-reaching consequences. We should have no Infinitesimal Calculus, no Algebra, no Atomic Theory, no Theory of Gravitation if, to avoid all initial contradictions, we surrender the fiction of differentials, of imaginary quantities, of the atom, of action at a distance. In short, it may, indeed, be said that not only knowledge, but also life, the holding together of people by convention, law, and duty, would become impossible if we did not accept the fiction of free will, which directly contradicts the determinate character of all happening, including actions and motives, which, physically, alone seems recognizable.

Fiction (not to be confused with hypothesis) and anthropomorphism, in spite of their inner inconsistency, are the two poles about which our thoughts and our lives revolve. And no doctrine will ever soar to such heights that it will be able to deny completely its origin from these roots of all thought. The Archimedean thought-centre of the universe, which would enable us to lift the world out of its hinges, is unattainable, because it does not exist at all.

Is this also to apply to the new physics, whose results are to be regarded as the last word in scientific knowledge? Many a hypercritical thinker might be led away by the current of the preceding statement, and feel disposed to answer in the affirmative, were it not that, here too, a contradiction intrudes itself. This is expressed in the fact that not one of the present-day philosophers is in a position to pursue the threads of this theoretical fabric to their hidden ends.

Thus we arrive at a parting of the ways. Whoever aims at becoming thoroughly familiar with Einstein's new world-system finds that the study of the theory claims so much attention that there is scarcely a possibility left of proceeding to an ultimate philosophical analysis. And whoever is absorbed only by the desire of making philosophic investigations soon enough arrives at border-lines of thought, at which his conscience warns him to beware of insufficient scientific knowledge. He will be attacked by doubts as to whether he has properly understood the theory. And he will be confronted with the question whether he is justified in drawing ultimate philosophical conclusions before he has mastered all the mathematical details.

As far as can be judged at present, only one thinker has, so far, had sufficiently wide knowledge to enable him to correlate the physical theory methodically with the theory of knowledge. I mean Professor Moritz Schlick of Rostock, who has set out his ideas systematically in his book Erkenntnislehre, which is extraordinary in itself and in its great scope; it takes us beyond Kant. In Schlick's opinion Einstein's theory furnishes us with the key to new and unexpected chambers of thought; it is a wonderful instrument for opening up new avenues, and would appear more wonderful still if we could use this instrument without having recourse to anthropomorphism. This limitation may lead to a Utopia, or may entail a circulus vitiosus. But we have one philosophy nowadays which applies to what cannot be fulfilled "AS IF" it really is capable of fulfilment. Among the disciples of Vaihinger, the founder of the As-If-doctrine of thought, we, however, notice the tendency to follow anthropomorphic and fictitious paths also in his field of thought.

From numerous utterances of Einstein, I have gathered that he himself does hot give his unqualified approval to all attempts at unravelling the ultimate problems by means of philosophy, that is, by using metaphysics alone. He does not deprecate these endeavours, but even expresses admiration for some of the newer works, as for that of Schlick, yet he sees certain obstacles in the purely philosophical methods, that at least restrain him from taking a systematic interest in them. This reluctant acceptance of, and doubt in, the processes of philosophy, that has never forsaken the exact investigator, this suspicious attitude which scents traces of sophistic and scholastic machinations in all metaphysical arguments, also asserts itself in him in a noticeable form. He feels the absence of rigour and of consistency of direction, which is a guarantee of progress in passing from one result to another, in the method of thought of those who are pure philosophers: and he deplores the spongy and murky appearance of certain expressions of thought, which, it must be admitted, form a poor contrast to the completeness and the crystal clearness of mathematico-physical reasoning. There was an inscription on the portals of the Athenian Academy which stated that entrance was forbidden to all who had had no mathematical training; we may imagine next to it an academy of pure transcendental philosophy, bearing the inscription: No exact research allowed! I believe that this clear-cut distinction would tally with Einstein's view.

In the case of the great Ernst Mach, for whom Einstein has intense admiration, we observe a similar attitude, or we may say that, in the language of allegory, he sang openly the same refrain in another key. He never ceased reiterating that he was properly "no philosopher at all, but only an investigator of Nature." At the beginning of the introduction to one of his works we read his confession: "Without in the slightest degree being a philosopher, or even wishing to be one ..."; and some lines further on he calls himself sarcastically "a mere amateur sportsman" in philosophical regions. Yet, Mach's initial remark is followed by a remarkable result, for the book in question, Knowledge and Error (Erkenntnis und Irrtum), is to be reckoned among the most important works in philosophical literature; and he himself, the amateur sportsman, who did not even desire to be called a philosopher, accepted in 1895 the post of Professor of Philosophy at Vienna University. It was merely his timidity in the face of the philosophical fraternity that had made him emphasize repeatedly the distinction between his own work and that of the philosophers, whereas in his heart he had nourished a passion for Philosophy, the first mother of Science. And in my opinion such a moment may arrive for even the most rigorous investigator when he succumbs to the siren strains from the shores of philosophy.

As far as Einstein himself is concerned, I cannot venture on a prognostication. Even though he belongs to the category and rank of Descartes, Pascal, d'Alembert, and Leibniz, in whom Mathematics and speculative Philosophy are intermingled, he is yet characterized by such a pronounced individuality, that it is quite inadmissible to draw conclusions about him from others. He has no need to experience a day of Damascus, for he carries the gospel of salvation in himself, and it radiates from him. One thing seems possible, in my opinion, namely, that Einstein will occasionally roam into the neighbouring realm merely from æsthetic motives. Although the means of philosophy are nebulous and more indefinite than those of exact science, which are almost glaringly distinct, philosophy itself for this reason is the more closely related to Art. And a theory that applies to the whole universe must assuredly contain many germs that may come to life if subjected to the methods of Art. The connecting link between Kant and Schiller shows in what sense this is to be understood. Even at present there are indications in Art which tend to show that it is ready to establish points of contact with Knowledge. In France symphonic poems were written on the measure relations of the circle, and on logarithms: these are at present only curiosities, but may in future become models. At a much later date, perhaps, the four-dimensional universe may become ripe for treatment by such methods of Art. On the way to this goal there is the treatment with the symbolic, non-rigorous, and semi-poetic means of expression used by Philosophy. Many will use their efforts to achieve this, and perhaps they will come within closer range of success, if Einstein himself lends a helping hand. It will not be possible to arrive at new physical truths by following this path, but those that are actually known will be traced more readily to the great mainstream of philosophy. To fathom the secrets of the world is the work of a recluse, but to make it comprehensible to a wide circle, a preacher is necessary, who uses the beautiful methods of philosophical rhetoric. Cosmos denotes the World and its Ornamentation; its creator, Demiurge, is a master who fashions his forms along the lines of Art.

Thus we have learned what Einstein regards as the sole purpose of Science, namely, the search after Truth. For him, the latter is something absolute in itself, and the possibility of getting nearer to it is as great as the impossibility of deriving results of scientific use from, say, ethical discoveries. For ethics is a field which is haunted by the conceptual ghosts, and the manner of treatment, ordine geometrico, that Spinoza wished to apply to it, is reserved for physics. Einstein leaves the inverse philosophical query: "Is not Truth in itself only something that we have constructed in imagination?" to those who find pleasure in sauntering along paths of thought that are totally unconnected, whereas he himself advances in a straight line with the consciousness that even if the goal is unattainable, he will at least not lose the right direction!