35. Chaos

Some time ago, a highly peculiar book was published that shares the fate of receiving far too little attention with similar literary phenomena of its genre in the present day: "Chaos in Cosmic Selection" by Paul Mongré. But it deserves a different fate. Anyone who goes through the book without being blinded by contemporary prejudices will find that there is little today that is so stimulating, indeed, for those who are intensely interested in the highest questions of existence, even exciting. The author confesses to being a dilettante in philosophical matters. He does not have a thorough knowledge of philosophical literature. That is why he does not approach his task with the same bias as many of our philosophically trained contemporaries. This gives the book something philosophically naive. Paul Mongré admits that it is not his personality that has driven him to the problem, but that the problem has, so to speak, overwhelmed him, that it has approached him and has not let go until he has gained a position, a relationship to it. There is something much more natural about this than when someone comes to such a task through a philosophical education. If we start from philosophy as such, we all too often have to ask ourselves: would this man have come to his questions at all if he had happened to become a physician or chemist rather than a philosopher? And when we read the writings of such a personality, we are reminded of this question again and again by all sorts of things. This is not the case with Paul Mongré. Rather, we are constantly reminded of how powerfully the questions raised weigh on the human soul, how they torment us no matter what else we do in life, and how the relationship we develop with them is infinitely influential for our happiness in life.

The author comes from mathematics. This is evident in every sentence. His whole way of thinking is mathematical. Now this way of thinking has just as many advantages as disadvantages. The conclusions of mathematics have an exemplary reliability. Anyone who is trained in mathematics will also strive for the same reliability when thinking about other things as he is used to from his science. But mathematical thinking has its pitfalls. As such, it has nothing directly to do with reality. It rests on assumptions that are purely ideal. If a point in a plane moves in such a way that its distance from a fixed point always remains the same, then a circle is formed. And all the laws that we get to know through mathematics apply to the circle. All these laws would also be correct if there were no circle anywhere in reality. In any case, the reasons why we consider these laws to be correct are quite different from those on the basis of which we assert the correctness of any real process. In a way, mathematics is a great poem. If I want to prove the Pythagorean theorem, I do not measure the two sides of a right-angled triangle and then the hypotenuse to prove that the square over the latter is equal to the sum of the two over the former. I prove this by mathematical means using a purely ideal structure. Nevertheless, on a real right-angled triangle, what I have established purely intellectually must be justified. In mathematics, I decide on relationships in reality without asking them first. And it always proves me right with regard to all conclusions if it fulfills my assumptions. If there is a right-angled triangle or a circle somewhere, then they fulfill the laws that I have established about them without first asking reality. This seems so self-evident to most people. But if you go deeper, a big question is revealed here. Everyone is convinced that the mathematical laws he has devised here with his earthly mind also apply on Mars. But he did not even ask about the conditions on Mars. We invent mathematical laws, and reality is always good enough to fulfill them for us.

I don't want to talk about what it is that actually distinguishes mathematical judgments from those about real things. Nor do I want to talk about whether there is anything else in our lives that carries the same or similar certainty as mathematics. But I wanted to talk about the subjective habits of thought that distinguish the mathematician from those who work in another branch of knowledge.

The mathematician is accustomed to asking only himself, only his own mental necessities, when he makes decisions. And he is also used to finding his truths absolutely valid in reality. With such feelings, he basically enters every sphere into which life leads him.

And with such feelings, Paul Mongr& steps onto the ground of the great question of existence. That is his danger. It is doubtless that his conclusions will be decisive for these highest questions of existence, just as the Pythagorean theorem is decisive for reality, if the presuppositions of reality are just as true for those conclusions as they are for the Pythagorean theorem. Yes, if it weren't for this "if"!!! Construct mathematical relationships. There are two possibilities for you. Either in reality there are somewhere such presuppositions as you make, then you can also spin the conclusions that reality draws from these presuppositions into your mathematical web. If, however, reality does not fulfill your presuppositions, then your mathematical inventions will float in the void. But neither the one nor the other does any harm to the truth of your assertions. The Pythagorean theorem would remain true even if it were not fulfilled in any reality. The truth of the mathematical is therefore not at all dependent on reality in this respect. The mathematician is therefore only dealing with himself.

In no other case than the right-angled triangle towards the mathematician is the human being towards the mathematical thinker. A mathematical thinker is too inclined to overlook this. He easily believes that he can talk about the world problem as if it were a mathematical problem. Paul Mongré falls into this error. An example. He puts forward the following idea, which has already been asserted elsewhere: "Because of the relativity of our measurement, the absolute dimensions of the spatial formations do not fall into our consciousness - we would not notice anything if the universe suddenly increased or decreased its real dimensions a hundredfold, since both the objects to be measured and our scales participate in this overall change. Does this mean that the universe is really, in the transcendentally realistic sense, a rubber ball that swells or shrinks at will? No, but only that beyond our relative perception of size, the concept of spatial size becomes irrelevant." That is mathematical thinking. But suppose someone were to go further and draw the conclusion from this undoubtedly true thought: if everything outside our consciousness loses its validity in the same way as the determinations of size seem to do, then it could also be correct that within our consciousness we rightly regard ourselves as descended from lower organisms; outside, however, a demon could be at work that apes human formations. For mathematical thinking there is no objection to drawing such a conclusion. If it were valid, then I would only ever be dealing with conclusions, with truths that apply to me - within my consciousness; outside of it would lie endless possibility - for me chaos, about which I know nothing, about which I am not even allowed to talk without having to make it clear to myself that I am going beyond what I am allowed to assert. Two things would then be certain. I would have truths; these would apply to me. But they apply to nothing but me. I seek the laws according to which the things that are spread out before my senses work; I seek the laws of my own working. But apart from me, none of this could be as it appears to me. Instead of the laws of light, there could be a demon at work, instead of my psychological and physiological laws, according to which I direct my foot to move forward, there could be a demon pushing it forward. That is one thing. The other is: I know the limits to which my truths extend. I build a lawful world for myself within these limits. And yet I say: this far and no further. The mathematician says: I measure things. They have this certain size in relation to my scale. If everything and therefore my scale grows, then I am at the end. I can't go any further. And for me, we are at a crucial point. Is there any point in talking about size if we can't measure it? What does it mean to say that the universe is getting bigger if nothing retains its former size? Has the universe really become larger if nothing has retained its original size? Does a size exist at all without being compared with another? But if it makes no sense to talk of increasing size where there is no measurement, does it not also make sense to allow measurement to apply unconditionally where there is measurement? Or, from a broader perspective: if it makes no sense to speak of an animal descent of man outside our world, is it not also correct to say that it makes absolute sense within this world and cannot be otherwise?

If I wanted to discuss all the mathematically conceived details that Paul Mongré presents, I would have to write a book myself, at least as comprehensive as his. But I only want to characterize his way of thinking. To do this, it will suffice to deal with as simple a matter as possible in the sense that dominates his entire way of looking at things. In the world of experience in which we live, we see the son following the father, the son following the grandson. This succession occurs in the course of time. If we now look at this time sequence, no other sequence is conceivable in it than this: Father - son - grandson? Another is also conceivable. We can imagine that there is some observer of the world who does not see forwards as we do, but backwards, that is: grandson - son - father. We could think of another observer who sees the following sequence: son - grandson - father, another one: grandson - father - son. Thus, what we see is only a special case of other possible, abstractly conceivable cases. If we now extend this observation in the most manifold way to the whole world of experience before us, we can imagine that all the regularity which we perceive as a cosmic connection is only a special individual case of an infinite number of conceivable worlds. All laws, all concepts that we apply to our world are only special cases. Where do we end up if we imagine all cosmic lawfulness in this way as a special case? We come to the conclusion that in the vast number of general worlds none of the laws that apply in ours apply, that none of our concepts apply in them. We come to the conclusion that when we leave our world and enter another, we enter into lawlessness and lawlessness, into chaos. And finally we go even further. Nothing compels the various possibilities that exist apart from us (in our example: son - grandson - father; grandson - father - son and so on) to take on the particular form of existence given to us (in our example: to become father - son - grandson). Indeed, none of the conceivable possibilities need exist at all. And since for thinking ours has no preference over the other conceivable ones, ours does not necessarily have to exist either. Our entire world, which we perceive, therefore does not need to exist before a higher instance (in the transcendental sense, as Paul Mongré's terminology puts it). "Why shy away from the name? Our idealism here, if the last consequence applies, runs out into the sharp and dangerous point of a transcendental nihilism" (p. 188).

Paul Mongré's mathematical thinking has now led him to such extravagances of the concept. The mathematician separates time and space from the other content of the world in his thoughts and then deals with them as abstract entities. He can speak of the passage of time that exists alongside the sequence: father - son - grandson. But in reality, this passage of time does not exist as such at all. It is not separate from the content of the sequence: father - son - grandson. The son is only possible as a consequence of the father and the grandson only as a consequence of the son. They give themselves the time sequence. And the latter has no meaning at all without them, is an empty abstraction. Another observer of the world may, for my sake, see the grandson first, then the son, then the father. This does not change the fact that the order which he does not give to the three members, but which they give to themselves, remains the same. Paul Mongré first separates his many conceivable worlds from our real one through abstraction. They are conceivable. But that does nothing. They are only conceivable as abstractions from the real one. They are nothing without it. No matter how boldly we speculate, we cannot leave our world. We remain within it. We cannot be dealing with a majority of worlds, but only with the one, with our cosmos. And because this is the case, this cosmos is also necessary, it has its lawfulness in itself through itself. It is not a single case out of an immeasurable number; it is the unity, the direction and cause, which also has the reason for its existence in itself. Paul Mongré's conclusion can also be illustrated by the following comparison. A ruler governs his people according to certain laws, which have grown out of the feelings, habits and so on of the people. They only endure because of the latter. Now someone comes along and says: Let us detach the ruler from the laws. These can now also be others. We can think of countless possibilities; how he governs his people is just one case of countless possible ones. Here everyone immediately sees the inadmissibility of the conclusion. We can indeed think of infinite possibilities for the ruler, but such thinking takes place in a complete void. How this ruler rules is only possible in one way due to the peculiarity of the people. Paul Mongré's entire conclusion is inadmissible. It must not be drawn at all.

As you can see from my "Philosophy of Freedom" published several years ago, I agree with Mongré to the extent that I, too, restrict all observation of the world to the world of experience given to us, as I, too, reject any thinking about another (transcendent) world. But for me, our world is also the only one we are entitled to talk about. Paul Mongré rejects metaphysics because its content is chaos; I reject it because nothing leads out of our world and one does not talk about what there is no reason to talk about. But I also do not arrive at nihilism because I do not say to myself: since none of the conceivable worlds has anything ahead of another, ours must not exist either, and can therefore stand out from the chaos of nothing as an appearance and dream image, but I say to myself: because there is none conceivable to us apart from ours, ours is necessary, must be as it is through itself, not through selection from an infinite number of worlds.