This is the seventh of eleven Letters of Euler I will rewrite and post on the subject of infinitesimals (the infinitely small), an idea that is fundamental to a good understanding of calculus. Click here to read the previous letter.
Principle of the satisfying Reason, the strongest Support of the Monadists.
You must be perfectly sensible that one of the two systems, which have undergone such ample discussion, is necessarily true, and the other false, seeing they are contradictory. It is admitted on both sides, that bodies are divisible: the only question is, “Whether this divisibility is limited?”, or “Whether it may always be carried further, without the possibility of ever arriving at indivisible particles?”
The system of monads is established in the former case, since after having divided a body into indivisible particles, these very particles are monads, and there would be reason for saying that all bodies are composed of them, and each of a certain determinate number. Whoever denies the system of monads, must likewise, then, deny that the divisibility of bodies is limited. he is under the necessity of maintaining, that it is always possible to carry this divisibility further, without ever being obliged to stop; and this is the case of divisibility in infinitum, on which system we absolutely deny the existence of ultimate particles: consequently the difficulties resulting from their infinite number fall to the ground themselves. In denying monads, it is impossible to talk any longer of ultimate particles, and still less of the number of them which enters into the composition of each body.
You must have remarked, that what I have hitherto produced in support of the system of monads is destitute of solidity. I now proceed to inform you that its supporters rest their cause chiefly on the great principle of the sufficient reason, which they know how to employ so dexterously, that by means of it they are in a condition to demonstrate whatever suits their purpose, and to demolish whatever makes against them. The blessed discovery made, then, is this, “That nothing can be without a sufficient reason;” and to modern philosophers we stand indebted for it.
In order to give you an idea of this principle, you have only to consider, that in every thing presented to you, it may always be asked, “Why it is such?” And the answer is what they call the sufficient reason, supporting it really to correspond with the question proposed. Wherever the “why” can take place, the possibility of a satisfactory answer is taken for granted, which shall, of course, contain the sufficient reason of the thing.
This is very far, however, from being a mystery of modern discovery. Men in every age have asked “why;” an incontestable proof of their conviction that every thing must have a satisfying reason of its existence. This principle, that nothing is without a cause, was very well known to ancient philosophers; but unhappily this cause is for the most part concealed from us. To little purpose do we ask “why:” no one is qualified to assign the reason. It is not a matter of doubt, that every thing has its cause; but a progress thus far hardly deserves the name; and so long as it remains concealed, we have not advanced a single step in real knowledge.
You may perhaps imagine, that modern philosophers, who make such a boast of the principle of a satisfying reason, have actually discovered that of all things, and are in a condition to answer every why that can be proposed to them; which would undoubtedly be their very summit of human knowledge; but, in this respect, they are just as ignorant as their neighbors: their whole merit amounts to no more than pretension to have demonstrated, that wherever it is possible to ask the question “why,” there must be a satisfying answer to it, though concealed from us.
They readily admit, that the ancients had a knowledge of this principle, but a knowledge very obscure; whereas they pretend to have placed it in its clearest light, and to have demonstrated the truth of it: and therefore it is that they know how to turn it most to their account, and that this principle puts them in a condition to prove, that bodies are composed of monads.
Bodies, they say, must have their sufficient reason somewhere, but if they were divisible to infinity, such reason could not take place: and hence they conclude, with an air altogether philosophic, “that, as every thing must have its sufficient reason, it is absolutely necessary that all bodies should be composed of monads:” which was to be demonstrated. This, I must admit, is a demonstration to be resisted.
It were greatly to be wished that a reasoning so slight could elucidate to us questions of this importance; but I frankly confess, I comprehend nothing of the matter. They talk of the sufficient reason of bodies, by which they mean to reply to a certain “wherefore,” which remains unexplained. But it would be proper, undoubtedly, clearly to understand, and carefully to examine a question, before a reply is attempted; in the present case, the answer is given before the question is formed.
Is it asked, “Why do bodies exist?” It would be ridiculous, in my opinion, to reply, “Because they are composed of monads;” as if they contained the cause of that existence. Monads have not created bodies: and when I ask, “Why such a being exists?” I see no other reason that can be given but this, “Because the Creator has given it existence;” and as to the manner in which creation is performed, philosophers, I think, would do well honestly to acknowledge their ignorance.
But they maintain, that God could not have produced bodies, without having created monads, which were necessary to form the composition of them. This manifestly supposes, that bodies are composed of monads, the point which they meant to prove by this reasoning. And you are abundantly sensible, that it is not fair reasoning to take for granted the truth of a proposition which you are bound to prove by reasoning. It is a sophism known in logic by the name of a petitio principii, or, begging the question.
16th May, 1761.
Studying His Word and His Works 
