Examples of Errors

Examples of some errors in physics into which one falls, because one supposes that beings which differ in their nature, their qualities, their extension, their duration, and their proportion, are similar in all these things.

We have seen in the preceding chapter that men make a precipitate judgment when they judge that all beings are only of two kinds, minds or bodies. We shall show in those that follow that they not only make precipitate judgments, but that they make very false ones which are the principles of an infinite number of errors, when they judge that beings do not differ in their relations nor in their manners, because they have no idea of these differences.

It is certain that the human mind seeks only the relations of things: first, those that the objects it considers may have with itself, and next, those they have with one another; for the human mind seeks only its own good and truth. To find its good, it carefully considers by reason and by taste or feeling whether objects have a relation of suitability with it. To find truth, it considers whether objects have a relation of equality or resemblance with one another, or what precisely is the magnitude that is equal to their inequality. For just as good is good for the mind only because it is suitable to it, so truth is truth only through the relation of equality or resemblance that is found between two or more things: whether between two or more objects, as between a yardstick and cloth, for it is true that this cloth has a yard, because there is equality between the yardstick and the cloth; or between two or more ideas, as between the two ideas of three and three and that of six; for it is true that three and three make six, because there is equality between the two ideas of three and three and that of six; or finally between ideas and things, when ideas represent what things are; for when I say that there is a sun, my proposition is true, because the ideas I have of existence and of sun represent that the sun exists and that the sun truly exists. All the action and all the attention of the mind to objects is therefore only to try to discover their relations, since one applies oneself to things only to recognize their truth or their goodness.

But, as we have already said in the preceding chapter, attention greatly fatigues the mind. It soon tires of resisting the impression of the senses, which turns it away from its object and carries it toward others that the love it has for its body makes agreeable to it. It is extremely limited, and thus the differences that exist between the subjects it examines being infinite or nearly infinite, it is not capable of distinguishing them. The mind therefore supposes imaginary resemblances where it does not observe positive and real differences; the ideas of resemblance being more present, more familiar, and simpler to it than others. For it is visible that resemblance contains only one relation, and that only one idea is needed to judge that a thousand things are alike; whereas to judge without fear of error that a thousand objects are different from one another, it is absolutely necessary to have a thousand different ideas present to the mind.

Men therefore imagine that things of different nature are of the same nature, and that things of the same species hardly differ from one another at all. They judge that unequal things are equal, that inconstant things are constant, and that things without order and without proportion are very orderly and very proportionate. In a word, they often believe that things different in nature, quality, extension, duration, and proportion are similar in all these things. But this deserves to be explained at greater length by some examples, because it is the cause of an infinite number of errors.

Mind and body, the substance that thinks and that which is extended, are two kinds of beings altogether different and entirely opposed: what is fitting for the one cannot be fitting for the other. However, most men, paying little attention to the properties of thought and being continually affected by bodies, have regarded soul and body as one and the same thing: they have imagined resemblance between two such different things. They have wanted the soul to be material, that is to say, extended throughout the body and figured like the body. They have attributed to the mind what can belong only to the body.

Moreover, men feeling pleasure, pain, odors, tastes, etc., and their body being more present to them than even their own soul—that is, imagining their body easily, and being unable to imagine their soul—they have attributed to it the qualities of sensing, imagining, and sometimes even that of conceiving, which can belong only to the soul. But the following examples will be more striking.

It is certain that all natural bodies, even those called of the same species, differ from one another; that gold is not entirely similar to gold, and that one drop of water differs from another drop of water. It is the same with all bodies of the same species as with faces. All faces have two eyes, a nose, a mouth, etc.; they are all faces and human faces, and yet one can say that there were never two exactly alike. Similarly, a piece of gold has parts very similar to another piece of gold, and a drop of water certainly has much resemblance to another drop of water; nevertheless one can assert that one cannot give two drops, even taken from the same river, that entirely resemble each other. Yet philosophers suppose without reflection essential resemblances between bodies of the same species, or resemblances that consist in the indivisible; for the essences of things consist in an indivisible, according to their false opinion.

The reason why they fall into so gross an error is that they do not wish to consider with any care the things upon which they nevertheless compose large volumes. For just as one does not posit a perfect resemblance between faces, because one takes care to look at them closely, and the habit one has acquired of distinguishing them makes one notice their smallest differences; so, if philosophers considered nature with some attention, they would recognize enough causes of diversity in the very things that cause us the same sensations and that we therefore call of the same species, and they would not so easily suppose essential resemblances in them. Blind men would be wrong to suppose an essential resemblance between faces consisting in the indivisible, because they do not sensibly perceive their differences. Philosophers therefore should not suppose such resemblances in bodies of the same species, because they observe no differences in them.

The inclination we have to suppose resemblance in things also leads us to believe that there is a determinate number of differences and forms, and that these forms are not capable of more or less. We think that all bodies differ from one another as by degrees, and that these degrees even maintain certain proportions among themselves. In a word, we judge of material things as of numbers. It is clear that this comes from the fact that the mind loses itself in the relations of incommensurable things, such as the infinite differences found in natural bodies; and that it relieves itself when it imagines some resemblance or proportion among them, because then it represents several things to itself with great ease. For as I have already said, only one idea is needed to judge that several things resemble each other, and several are needed to judge that they differ from one another. For example, if one knows the number of angels, and that for each angel there are ten archangels, and that for each archangel there are ten thrones, and so on, maintaining the same proportion of one to ten up to the last order of intelligences, the mind can know whenever it wishes the number of all these blessed spirits and even judge of it almost at a single glance by paying strong attention to it, which pleases it infinitely. And this is what may have led some persons to judge thus of the number of celestial spirits, as happened to some philosophers who placed a tenfold proportion of weight and lightness between the elements, supposing fire ten times lighter than air, and so on for the others.

When the mind finds itself obliged to admit differences between bodies because of the different sensations it has of them, and also because of some other particular reasons, it always posits as few as possible. It is for this reason that it easily persuades itself that the essences of things consist in the indivisible, and that they are similar to numbers, as we have just said, because then it needs only one idea to represent to itself all the bodies they call of the same species. If, for example, one puts a glass of water into a cask of wine, philosophers want the essence of the wine to remain always the same, and the water to be converted into wine; that just as between three and four there can be no number, since the true unity is indivisible, so it is necessary that the water be converted into the nature and essence of the wine, or that the wine lose its nature; that just as all the numbers of four are entirely similar, so the essence of water is entirely similar in all waters; that as the number three differs essentially from the number two, and cannot have the same properties as it, so two bodies of different species differ essentially, and in such a way that they never have the same properties that come from essence, and other such notions. However, if men considered the true ideas of things with some attention, they would soon discover that all bodies being extended, their nature or essence has nothing similar to numbers, and that it cannot consist in the indivisible.

Men do not only suppose identity of resemblance or of proportion in nature, in number, and in the essential differences of substances; they suppose it in everything they perceive. Almost all men judge that all the fixed stars are attached to the sky as to a vault at an equal distance from the earth. Astronomers for a long time claimed that the planets moved in perfect circles, and they invented a very great number of them—such as concentrics, eccentrics, epicycles, deferents, and equants—to explain the phenomena that contradicted their prejudice.

It is true that in recent centuries the most able have corrected the error of the ancients, and they believe that the planets describe certain ellipses by their movement. But if they claim that these ellipses are regular, as one is inclined to believe, because the mind supposes regularity where it sees no irregularity, they fall into an error all the more difficult to correct in that the observations that can be made on the course of the planets cannot be exact or precise enough to show the irregularity of their movements. Only physics can correct this error, for it is much less noticeable than that found in the system of perfect circles.

But a rather peculiar thing has happened concerning the distance and movement of the planets; for astronomers, not having been able to find any arithmetical or geometrical proportion in them, this manifestly contradicting observations, some have imagined that they maintain a kind of proportion called harmonic in their distances and in their movements. Hence an astronomer of this century, in his new Almagest, begins the section entitled De systemate mundi harmonico with these words: “There is no astronomer, however little versed in what pertains to astronomy, who does not recognize a kind of harmony in the movement and intervals of the planets, if he attentively considers the order found in the heavens.” It is not that this author is of this opinion; for the observations that have been made have sufficiently shown him the extravagance of this imaginary harmony, which has nevertheless been the admiration of several ancient and modern authors, whose opinions Father Riccioli reports and refutes. Pythagoras and his followers are even said to have believed that the heavens, by their regulated movements, produced a marvelous concert that men do not hear because they are accustomed to it, just as, he said, those who live near the falls of the Nile do not hear its noise. But I bring up this particular opinion of the harmonic proportion of the distances and movements of the planets only to show that the mind delights in proportions, and that it often imagines them where they are not.

The mind also supposes uniformity in the duration of things, and imagines that they are not subject to change and instability when it is not as if forced by the reports of the senses to judge otherwise.

All material things, being extended, are capable of division and consequently of corruption. When one reflects a little on the nature of bodies, one visibly recognizes that they are corruptible. Nevertheless, there have been a very great number of philosophers who persuaded themselves that the heavens, although material, were incorruptible.

The heavens are too far from us for us to be able to discover the changes that occur there, and it is rare that changes happen there great enough to be seen from down here. This has sufficed for an infinite number of persons to believe that they were in fact incorruptible. What further confirmed them in their opinion is that they attribute to the contrariety of qualities the corruption that occurs in sublunary bodies. For since they have never been in the heavens to see what goes on there, they have had no experience that this contrariety of qualities is found there; which led them to believe that indeed it is not found there. Thus they concluded that the heavens were exempt from corruption, for this reason that what corrupts, according to their view, all bodies here below is not found up there.

It is visible that this reasoning has no solidity at all, for one does not see why there could not be some other cause of corruption than this contrariety of qualities they imagine, nor upon what foundation they can assert that there is neither heat, nor cold, nor dryness, nor humidity in the heavens, that the sun is not hot and that Saturn is not cold.

There is some appearance of reason in saying that very hard stones, glass, and other bodies of this nature do not corrupt, since one sees them subsist for a long time in the same state and one is close enough to them to see the changes that might happen to them. But being as far from the heavens as we are, it is altogether contrary to reason to conclude that they do not corrupt, because one does not feel contrary qualities there and one does not see them corrupt. However, it is not only said that they do not corrupt; it is said absolutely that they are unalterable and incorruptible, and some Peripatetics almost say that celestial bodies are so many divinities, as Aristotle their master believed.

The beauty of the universe does not consist in the incorruptibility of its parts, but in the variety found there; and this great work of the world would not be so admirable without that vicissitude of things that one observes in it. A matter infinitely extended, without movement, and consequently without form and without corruption, would indeed make known the infinite power of its author, but it would give no idea of his wisdom. It is for this reason that all corporeal things are corruptible, and that there is no body to which some change does not occur that alters and corrupts it with time. Stones and even glass serve as food for some insects. These bodies, although very hard and very dry, nevertheless become corrupted with time. The air and the sun, to which they are exposed, change some of their parts, and worms are found that feed on them, as experience shows.

There is no other difference between these very hard and very dry bodies and the others, except that they are composed of very coarse and very solid parts, and consequently less capable of being agitated and separated from one another by the movement of those that strike against them, which is why they are regarded as incorruptible. Nevertheless, they are not so by their nature, as time, experience, and reason sufficiently show.

But as for the heavens, they are composed of the most fluid and most subtle matter, and principally the sun; and so far from being without heat and incorruptible, as the followers of Aristotle say, it is on the contrary of all bodies the hottest and most subject to change. It is even this which heats, agitates, and changes all things; for it is this which produces by its action, which is nothing other than its heat or the movement of its parts, all that we see new in the changes of the seasons. Reason demonstrates these things: but if one can resist reason, one cannot resist experience; for since spots as large as the whole earth have been discovered in the sun, by means of telescopes or large lenses, which formed there and dissipated in a short time, one can no more deny that it is much more subject to change than the earth we inhabit.

All bodies are therefore in a continual movement and change, and principally those that are most fluid, such as fire, air, and water; then the parts of living bodies, such as flesh and even bones; and finally the hardest: and the mind should not suppose a kind of immutability in things, for this reason that it sees no corruption or change in them. For it is not a proof that a thing is always like itself because one recognizes no difference in it, nor that things do not exist because one has no idea or knowledge of them.