The use of the first rule, which concerns particular questions

I have:

• explained the general rule of this method
• showed that:
  • Descartes followed it quite precisely in his system of the world
  • Aristotle and his followers never observed it at all.

What are the particular rules for solving all kinds of questions?

Questions fall into main categories.

Sometimes, we seek:

• the unknown causes of known effects
• unknown effects from their known causes

Fire burns and consumes wood: we look for the cause of this. Fire consists in a very vigorous motion of the wood’s particles; we want to know what effects this motion can produce—whether it can harden mud, melt iron, and so forth.

Sometimes we seek the nature of a thing through its properties; sometimes we seek the properties of a thing whose nature we already know. We know or assume that light travels instantly, yet is reflected and concentrated by means of a concave mirror, so that it disperses or melts even the most solid bodies; and we wish to use these properties to discover its nature.

Conversely, we know or assume that all the spaces extending from the earth to the heavens are filled with tiny spherical bodies in constant motion, always tending to move away from the sun; and we want to know whether the force of these small bodies can be transmitted instantly, and whether, upon being reflected from a concave mirror, they will converge and disperse or melt the hardest substances.

Sometimes we seek all the parts that make up a whole; sometimes we seek a whole from its parts. We look for all the unknown parts of a known whole when, for example, we find all the aliquot parts of a number, all the roots of an equation, or all the right angles contained in a figure.

We look for an unknown whole whose parts are known when we calculate the sum of several numbers, the area of multiple shapes, or the capacity of several vessels; or we seek a whole when one part is known and the others, though unknown, bear some definite relation to what is known—as when we look for a number of which one part is known to be 15, and the other part is half or one‑third of the unknown number; or when we seek an unknown number equal to 15 plus twice its own square root.

Finally, we sometimes ask whether certain things are equal or similar to others, or by how much they differ or are unequal.

We want to know:

• if Saturn is larger than Jupiter, and by how much
• whether the air in Rome is warmer than that in Marseille, and by what degree.

What applies to all questions in general is that we raise them only in order to arrive at some truth; and since all truths are merely relations, we may say generally that in every question we seek only knowledge of certain relations—whether relations between things, between ideas, or between things and their ideas.

Relations are of many kinds: between the natures of things, their sizes, their parts, their attributes, their qualities, their effects, their causes, and so on. But all of them can be reduced to two types: relations of magnitude and relations of quality.

We call relations of magnitude all those that hold between things considered as capable of being greater or smaller; and relations of quality all the rest. Thus we may say that every question aims at uncovering some relation, whether of magnitude or of quality.

The first and most important of all rules is to understand very clearly the nature of the question we set out to solve, and to possess sufficiently distinct ideas of its terms so that we can compare them and thereby identify the unknown relations involved.

First, we must grasp very clearly the unknown relation we are seeking; for it is obvious that if we had no sure way of recognizing this relation while searching for it, or once we had found it, our search would be in vain.

Second, as far as possible, we must form distinct ideas corresponding to the terms of the question, removing any ambiguity in their meaning, and make them clear by considering them with the greatest possible attention. If these ideas are so confused and obscure that we cannot make the comparisons needed to discover the relations we seek, we are not yet in a position to solve the question.

Third, we must examine with the utmost attention any conditions stated in the question, for without doing so we will understand its nature only vaguely. Moreover, conditions usually point the way toward a solution. So once we have clearly grasped the question itself and its conditions, we know both what we are looking for and often even how to go about finding it.

Not all questions have explicit conditions.

But this means they are indeterminate and can be answered in several ways—for instance, if someone asks for a square number, or a triangle, without specifying further details. In other cases, the person posing the question may not know how to solve it, or may deliberately withhold conditions to make it more difficult; for example, asking to find two mean proportionals between two lines without adding “by the intersection of a circle and a parabola, or a circle and an ellipse,” and so on.

It is therefore absolutely necessary that the criterion by which we recognize what we seek be very clear, free of ambiguity, and capable of designating only that which we are looking for; otherwise we cannot be certain we have actually solved the question posed. Similarly, we must take care to remove from the question any conditions that only complicate it and that are not essential to its full meaning; for they unnecessarily distract the mind, and as long as irrelevant conditions remain, we do not truly understand the question distinctly.

Suppose someone asks: “Arrange things so that a man, sprinkled with certain liquids and crowned with flowers, cannot remain at rest, even though he sees nothing that could disturb him.”

We must first ask whether the word “man” is being used metaphorically; whether “rest” is ambiguous—referring perhaps to physical movement, or to his emotions, as the phrase “even though he sees nothing that could disturb him” seems to suggest.

We must also determine whether the conditions of being sprinkled with liquid and wearing a crown of flowers are essential. Once the nature of this absurd and indeterminate question is clearly understood, it can easily be answered: simply place the man in a boat, in accordance with the conditions given.

Those who set such questions skillfully add conditions that appear necessary but are not, in order to turn the mind toward matters that do not help in finding the answer. This is like the riddle often told to children: “I saw some hunters—or rather fishermen—who carried away what they did not catch, and threw into the water what they did catch.” Because the mind is already fixed on the idea of fishermen catching fish, it cannot see what is meant.

The whole difficulty of this playful question comes from not understanding it clearly and not considering that hunters and fishermen, like anyone else, sometimes search their clothing for small insects, which they throw away if found and carry away if they do not find them.

Sometimes questions also omit conditions that are necessary for solving them, and this makes them at least as difficult as including irrelevant ones. Consider this example: “Make a man immobile without binding or injuring him; or rather, put the little finger of one hand into his own ear, and through this posture render him so immobile that he cannot leave the spot where he stands until he removes his finger from his ear.”

At first this seems impossible—and indeed it is, for one can easily walk while holding a finger in one’s ear. What is missing is an additional condition, which would remove all difficulty if stated: that the person must embrace a bedpost or similar object, so that the post lies between his arm and his ear. He cannot move away without letting go and taking his finger out of his ear. This further condition is not mentioned, so the mind does not think to look for it, and thus fails to find the solution. Anyone who undertakes to solve such questions must ask all necessary clarifications to understand exactly where the difficulty lies.

These arbitrary questions may seem trivial, and in one sense they are, since nothing new is learned from solving them. Yet they are not as different from questions about nature as one might imagine. Much the same approach is required to answer both. Just as cleverness or trickery can make arbitrary questions confusing and hard to solve, natural phenomena are also by their very nature shrouded in obscurity and uncertainty. We must clear away this darkness through careful attention and through experiments—which are like questions we put to nature—just as we remove ambiguity and irrelevant details from arbitrary questions through focused thought and careful questioning of those who posed them. Let us now explain these points in order, in a more serious and instructive manner.

There are a great many questions that appear extremely difficult simply because they are not properly understood; many of them ought rather to be considered as axioms requiring only some explanation than as genuine questions. For it seems to me that certain statements should not be classified as questions at all once their terms are clearly grasped.

For instance, the question “Is the soul immortal?” is often presented as very difficult, but only because those who ask or try to answer it do not understand its terms distinctly. Since the words “soul” and “immortal” have different meanings, and people are unclear about which sense they intend, they cannot decide whether the soul is immortal—because they do not know precisely what they are asking or what they are looking for.

By “soul” one may mean a substance that thinks, wills, feels, and so on. Or one may take it to mean the motion or circulation of the blood, or the structure of the body’s parts; finally, it may even be understood as the blood itself or the so‑called animal spirits. Similarly, by “immortal” we may mean something that cannot be destroyed by the ordinary forces of nature, or something that cannot change, or something that cannot decay or dissolve like vapor or smoke. So if we take “soul” and “immortal” in any of these senses, even a little reflection will make it clear whether the soul is immortal or not.

First, it is obvious that the soul—understood in the first sense, as a thinking substance—is immortal if “immortal” is also taken in the first sense, meaning something that cannot be destroyed by natural forces. For it is not even conceivable that any substance could simply cease to exist; only an extraordinary act of God’s power could make that possible.

Second, the soul is immortal if “immortal” is taken in the second sense, meaning something that cannot decay or dissolve into vapor or smoke; for it is evident that what cannot be divided into countless parts cannot be destroyed or turned into vapor.

Third, the soul is not immortal if “immortal” is taken in the third sense, meaning something that cannot change; for we have clear proof that our souls do change—sometimes feeling pain, sometimes pleasure; sometimes willing certain things, then ceasing to will them; and while united to the body, it can be separated from it, and so forth.

If we take “soul” in any other sense, it will be equally easy to see whether it is immortal, provided we keep a fixed and consistent meaning for “immortal.” Thus what makes such questions difficult is not their subject matter, but that we do not understand them clearly and the terms used are ambiguous; they need explanation more than proof.

Admittedly, some people are so dull or so imaginative that they constantly think of the soul only as a certain arrangement of parts in the brain or as the movement of the animal spirits. It is certainly impossible to prove to such people that the soul is immortal and indestructible—for on the contrary, it is obvious that the soul as they understand it is mortal.

Therefore, this is not a question that is hard to solve, but a proposition that is hard to explain to people who do not share our ideas and who deliberately try to avoid understanding them in order to remain in confusion.

Whenever we ask whether the soul is immortal—or any other question—we must first remove ambiguity from the terms and decide in what sense they are being used, so that we clearly grasp the question itself. If those who pose it do not know what they mean, we must question them until they clarify their meaning; and if we find their ideas do not agree with ours, there is no point in answering. For what can we say to someone who claims, for example, that desire is nothing more than the movement of certain animal spirits, that thought is merely a trace or imprint left in the brain by objects or those spirits, and that all human reasoning consists only in the different arrangement of tiny particles shifting in the head? To tell such a person that the soul, in the sense they mean, is immortal would be to mislead them or make ourselves look ridiculous in their eyes; but to say it is mortal would be, in a way, to confirm them in a serious error. It is better not to answer at all, but only to encourage them to reflect within themselves, so that they may receive the same understanding we have, from the One who alone can enlighten them.

Another question that seems difficult is whether animals have souls. Yet once ambiguity is removed, it no longer appears so hard, and most of those who believe they do are, without realizing it, of the same opinion as those who believe they do not.

We may take “soul” to mean something material, spread throughout the body and giving it movement and life; or we may take it to mean something spiritual. Those who say animals have no soul understand the term in the second sense; for no one has ever denied that there is something material in animals that serves as the principle of their life and movement—indeed, no one denies this even of plants. Those who claim animals do have souls, on the other hand, understand it in the first sense; for very few believe animals possess a spiritual and indivisible soul.

Thus, the Aristotelians and Cartesians both agree that animals:

• have a soul in the sense of a material principle of movement
• do not have a soul in the sense of something spiritual and indivisible.

The real difference between the Aristotelians and the so‑called Cartesians is not that the first group claims animals have souls while the second denies it.

Rather:

• the Aristotelians believe animals are capable of feeling pain and pleasure, seeing colors, hearing sounds, and experiencing all the same sensations and emotions we do.
• the Cartesians hold the opposite view

The Cartesians:

• clarify the meaning of terms to avoid ambiguity.
• explain that when we stand too close to fire, its particles strike our hand, shaking the fibers there.

This vibration is transmitted to the brain, which directs the animal spirits contained within it to flow outward in a way that causes the body to pull back.

They agree that all these or similar processes occur in animals because they are purely physical properties.

The Aristotelians also accept this.

But the Cartesians add that in human beings, the disturbance of the brain fibers is accompanied by the feeling of heat, and the flow of animal spirits toward the heart and internal organs gives rise to emotions such as hatred or aversion.

They deny, however, that these feelings and mental states exist in animals.

The Aristotelians, by contrast, maintain that animals feel heat just as we do, have the same aversion to what disturbs them, and in general experience all the sensations and emotions we feel.

The Cartesians do not believe that:

• animals feel pain or pleasure, or love or hate anything, because they accept nothing but matter in animals
• feelings or emotions can be properties of matter, no matter how it is arranged.

Some Aristotelians, however, hold that matter can acquire the capacity for feeling and emotion when it is “refined”.

They claim animals can feel through the action of animal spirits—that is, through an extremely fine and subtle form of matter—and that even the human soul can feel and experience emotion only because it is united to this same kind of matter.

Therefore, to answer whether animals have souls, we must examine carefully our own idea of matter. If we can conceive of matter shaped in some way—square, round, oval, or whatever—as actually being pain, pleasure, heat, color, scent, sound, and so on, then we may say that the soul of animals, however material it may be, is capable of feeling. If we cannot conceive this, we should not claim it, for we ought only to assert what we can clearly understand.

Similarly, if we can imagine matter moving up and down, or in circular, spiral, parabolic, or elliptical paths, and that this motion is love, hatred, joy, or sadness, then we may say animals have the same emotions as we do.

If we cannot see this, we should not say so unless we wish to speak without knowing what we mean. But I believe it is safe to say that no one who thinks seriously will ever suppose that any movement of matter can be love or joy.

Thus, to settle the question of whether animals feel, we only need to remove ambiguity, as the Cartesians do; in this way the question becomes so simple that even moderate attention is enough to solve it.

Saint Augustine assumed the common belief that animals have souls.

He recognized clearly that it would be contradictory to say a soul or thinking, feeling, desiring substance could be material. Therefore he concluded that the souls of animals must indeed be spiritual and indivisible.

He proved with very clear reasoning that every soul—that is, whatever feels, imagines, fears, desires, and so on—must necessarily be spiritual; but I have not found that he ever gave any reason to assert that animals actually have souls. He did not even bother to prove it, since it seems that in his time no one doubted it.

Today, however, as people try to free themselves entirely from old prejudices and question all opinions not supported by clear and demonstrable reasoning, we have begun to doubt whether animals have souls capable of the same feelings and emotions as ours. Yet there are still many who defend these old beliefs and claim to prove that animals feel, will, think, and even reason much as we do, though in a less perfect way. They point out that dogs recognize their masters, love them, and patiently endure the blows they receive, because they judge it to their advantage not to leave them; while toward strangers they feel such hatred that they will not even allow themselves to be petted. All animals care for their young; and birds that build nests at the very tips of branches clearly show they fear being eaten by other creatures: they judge that those branches are too weak to support their enemies but strong enough to hold themselves, their young, and their nests.

Even spiders and the lowest insects show signs of a guiding intelligence; for we cannot help but admire how an animal, though blind, manages to catch others that have eyes and wings, and dares to attack creatures far larger than itself.

It is true that all the actions of animals suggest intelligence, because anything that follows a regular pattern implies it. Even a clock shows this: chance could never arrange its wheels, and an intelligence must have designed its movements. If you plant a seed upside down, the roots that faced upward will naturally turn downward into the earth, and the sprout that pointed toward the ground will turn upward to emerge—this also indicates intelligence. The plant twists itself as it grows to strengthen its stem; it covers its seeds with a protective coat and surrounds them with thorns for defense—again, this shows intelligence. In short, everything we observe in plants as well as in animals points to an underlying intelligence. All true Cartesians agree with this. But they also make a distinction, removing ambiguity from the terms as much as possible. The movements of animals and plants reveal intelligence, but this intelligence is not part of matter itself; it is distinct from the animals, just as the mind that arranged the gears of a clock is separate from the clock. Ultimately, this intelligence appears infinitely wise and infinitely powerful—the same intelligence that formed us in our mothers’ wombs and causes us to grow, a process we cannot influence at all through our own thoughts or will. Therefore, in animals there is no intelligence or soul in the usual sense of the word. They eat without pleasure, cry out without pain, grow without awareness; they desire nothing, fear nothing, know nothing. And if they act in ways that seem intelligent, it is because God, having created them to survive, designed their bodies so that they automatically avoid danger without feeling fear. Otherwise we would have to say that there is more intelligence in the tiniest insect or even a single seed than in the most spiritual human being; for it is certain that these contain far more different parts and produce far more ordered movements than we can ever comprehend.

But because people are accustomed to confusing things, and imagine that their own soul produces almost all the movements and changes that occur in their bodies, they incorrectly attach to the word “soul” the idea of something that creates and sustains the body. Believing that their soul manages everything necessary for life—even though they do not understand how the body itself is constructed—they assume that animals must also have souls to produce all the movements and changes observed in them, since those movements resemble what happens in our own bodies. Animals reproduce, feed, and grow just as our bodies do; they drink, eat, and sleep as we do. The only difference between us and them, they say, is that we have souls and they do not. Yet our soul does not form our body, does not digest our food, and does not give motion or warmth to our blood. It feels, wills, and reasons; it “animates” the body only in the sense that it has feelings and emotions connected to it. It does not spread through our limbs to transmit feeling and life, because our physical body cannot receive anything from what takes place in our mind.

Thus it is clear that the reason most questions remain unsolved is that we fail to distinguish—even to think of distinguishing—the different meanings that a single word may have. Not that we never try to make distinctions; but often we do so poorly, and instead of clarifying the meaning of terms, we only make them more confusing. For example, when people ask whether the body is alive, how it lives, how the rational soul gives it life, whether the animal spirits, blood, and other bodily fluids are alive, or whether teeth, hair, and nails are animated, they distinguish between “living” and “being animated” by speaking of life from a rational soul, from a sensitive soul, or from a vegetative soul. But this distinction only complicates the question, for these terms themselves need further explanation; and perhaps the last two—“vegetative soul” and “sensitive soul”—are actually inexplicable and unintelligible in the way they are usually understood.

If, however, we attach clear and distinct ideas to the word “life,” we may say that the life of the soul consists in knowledge of truth and love of goodness—or more simply, that its very thought is its life. The life of the body, on the other hand, consists in the circulation of the blood and the proper balance of bodily fluids—or more precisely, it is the movement of its parts in a way that preserves its existence. Once the ideas associated with “life” are clear, it becomes obvious: first, that the soul cannot communicate its own life to the body, since it cannot make the body think; second, that it cannot give the body the kind of life by which it feeds and grows, since it does not even understand how digestion works; third, that it cannot make the body feel, because matter itself is incapable of sensation. We can then easily answer all other questions raised on this subject, provided the terms used convey clear ideas; but it is impossible to solve them if the ideas behind the words remain confused and obscure. It is not always strictly necessary, however, to have ideas that perfectly represent the things whose relations we wish to examine. Often it is enough to have only partial or incomplete knowledge, because we do not always seek an exact and full understanding of every relation. Let me explain.

Truths and relations fall into two kinds: those that are known exactly, and those known only imperfectly. We know precisely the relation between a given square and a given triangle; but we know only roughly the relation between the sizes of Paris and Orléans. We can say exactly that the square is equal to the triangle, or twice, three times its area, and so on; but we can only say that Paris is larger than Orléans, without knowing by exactly how much. Moreover, there are countless degrees of imperfect knowledge, and such knowledge is considered imperfect only in comparison with more perfect knowledge. For example, we know perfectly well that Paris is larger than the Royal Square; but this knowledge is still imperfect compared to knowing exactly how much larger Paris is than that square.

Thus questions can be divided into four categories:

Those in which we seek a complete and precise understanding of all relations, both of magnitude and quality, that exist between two or more things. Those in which we seek a complete and precise understanding of some particular relation between two or more things. Those in which we seek a reasonably accurate understanding of a relation, even if not perfectly exact. Those in which we only need to recognize a broad, general, or undefined relation.

For questions of the first type—to know perfectly all exact relations between two or more things—we must have distinct ideas that fully represent them, and compare them from every possible angle. For instance, we can fully answer all questions about the exact relations between 2 and 8, because these numbers are clearly defined; we can compare them in every way needed to identify all their relations of magnitude or quality. We know that 8 is four times 2, that both are even numbers, and that neither is a perfect square.

For questions of the second type—to know exactly some particular relation—we only need to understand clearly the specific aspect under which we are comparing them. For example, to determine whether 4 and 16 are even numbers or perfect squares, it is enough to know exactly that they can be divided evenly by two and that each is the product of a number multiplied by itself. We do not need to know their absolute size. To understand relations of quality, we only need a clear idea of their qualities, not their size; and to understand relations of magnitude, we only need their exact measurements, not their nature.

For questions of the third type—to find a reasonably close relation—it is enough to have an approximate understanding of the relevant aspect. For example, I can clearly say that the square root of 8 is greater than 2, because I can estimate its value roughly; but I cannot say exactly how much greater it is, since its precise value cannot be expressed as a whole number or simple fraction.

For questions of the fourth type—to identify only broad or indefinite relations—it is enough to understand the things just well enough to compare them for the purpose at hand. Therefore, it is not always necessary to have extremely distinct ideas of the terms used, or to understand perfectly what they mean. The more exact and numerous the relations we seek, the more precisely we must understand the things involved.

For questions requiring only partial answers, partial knowledge is sufficient; and sometimes we can even answer questions well without having a fully distinct understanding of the terms. When we ask whether fire can melt salt, harden mud, or vaporize lead, for example, we understand the question perfectly and can answer it based on experience, even if we do not fully grasp the true nature of fire, salt, or mud. The questioner only wants to know whether we have observed such effects; so we reply according to what we have learned through our senses, and that is enough.