Part I, Chapter V

OF REASON AND SCIENCE

When a man reasons, he does nothing but conceive a total by adding parts together, or a remainder by subtracting one sum from another. If done with words, this means conceiving the consequence that leads from the names of all the parts to the name of the whole, or from the names of the whole and one part to the name of the other part. And although in some matters, such as numbers, people name operations besides addition and subtraction—multiplication and division—they are the same in kind: multiplication is merely adding equal things together, and division merely subtracting the same thing as many times as possible. These operations concern not only numbers but all things that can be added together and taken from one another. Just as arithmeticians teach addition and subtraction in numbers, geometers teach them in lines, figures both solid and plane, angles, proportions, times, degrees of speed, force, power, and the like. Logicians teach the same in the consequences of words, joining two names to make an assertion, two assertions to make a syllogism, and many syllogisms to make a demonstration; from the sum or conclusion of a syllogism they subtract one proposition to find the other. Writers on politics add agreements together to discover people's duties, and lawyers add laws and facts to determine right and wrong in the actions of private persons. In short, wherever addition and subtraction have a place, reason has a place; where they do not, reason has nothing to do.

From all this we may define—that is, determine—what is meant by reason when we count it among the faculties of the mind. In this sense reason is nothing but reckoning, that is, adding and subtracting the consequences of general names agreed upon to mark and signify our thoughts. I say mark when we reckon by ourselves, and signify when we demonstrate or justify our reckoning to others.

Just as beginners in arithmetic must sometimes make mistakes, and even experts often may add incorrectly, so in any other subject of reasoning the ablest, most attentive, most practiced people can deceive themselves and infer false conclusions. This is not because reason itself is ever anything but right reason, any more than arithmetic ceases to be a certain and infallible art. But no one man's reason, nor the reason of any group of men, establishes certainty; an account is not correctly reckoned merely because many people unanimously approve it. When an account is disputed, the parties must therefore agree to appoint the reason of some arbitrator or judge as right reason and accept his judgment; otherwise, for want of a right reason established by nature, their dispute must either come to blows or remain unsettled. So it is in debates of every kind. When people who think themselves wiser than everyone else clamor for right reason as their judge, while seeking only to have matters decided by no one's reason but their own, their conduct is as intolerable in human society as declaring whatever suit one holds most of to be trumps on every turn after the trump suit has already been drawn. For people do precisely this when they insist that each passion, as it comes to dominate them, be accepted as right reason in their own disputes. Their claim to right reason betrays their lack of it.

The purpose and end of reason is not to find the sum and truth of one or a few consequences far removed from the first definitions and settled meanings of names, but to begin with those definitions and proceed from one consequence to another. No final conclusion can be certain unless all the assertions and negations on which it rests and from which it is inferred are certain. Consider a head of household who totals every bill of expenses into a single sum without examining how the people submitting those bills calculated them, or what he is paying for. He gains no advantage over simply accepting the gross account on trust in each accountant's skill and honesty. Likewise, in reasoning on any subject, a man who takes conclusions on the authority of authors instead of deriving them from the first items in each reckoning—the meanings of names fixed by definitions—wastes his labor. He knows nothing; he merely believes.

When a man reckons without words, as one can in particular cases—for example, when seeing something he conjectures what probably came before it or will probably follow it—if the anticipated consequence does not follow, or the supposed antecedent did not precede it, this is called error, to which even the most prudent are subject. But when we reason in words of general meaning and arrive at a false general inference, though this is commonly called error, it is in fact an absurdity, or senseless speech. Error is simply a mistaken assumption that something has happened or will happen when, though it has not or will not, nothing made it visibly impossible. But if we make a general assertion that is not true, its possibility cannot be conceived. Words of which we conceive nothing but their sound are what we call absurd, meaningless, and nonsense. Thus if a man spoke to me of a round quadrangle, or accidents of bread in cheese, or immaterial substances, or a free subject, a free will, or anything free except free from obstruction by opposition, I would not say he was in error, but that his words had no meaning: they were absurd.

I said earlier, in the second chapter, that man excels all other animals in this faculty: whatever he conceives, he is inclined to inquire into its consequences and what effects he can produce with it. I now add another degree of the same excellence: he can use words to reduce the consequences he discovers to general rules called theorems or aphorisms. That is, he can reason or reckon not only with numbers but with all other things from which one thing may be added to, or subtracted from, another.

But this privilege is tempered by another: the privilege of absurdity, to which no living creature but man is subject. Among men, those who profess philosophy are most subject to it. What Cicero says of them somewhere is quite true: nothing can be so absurd that it cannot be found in the books of philosophers. The reason is clear. Not one begins his reasoning with definitions or explanations of the names he intends to use, a method practiced only in geometry, whose conclusions have consequently been made indisputable.

The first cause of absurd conclusions I attribute to lack of method: people do not begin their reasoning with definitions, or fixed meanings of their words, as though they could calculate without knowing the value of the number words one, two, and three.

And since all bodies may enter an account under various considerations, which I described in the previous chapter, these considerations bear different names; diverse absurdities arise when their names are confused and improperly joined in assertions. Accordingly:

The second cause of absurd assertions I attribute to giving names of bodies to attributes, or names of attributes to bodies. People do this when they say faith is infused or inspired, though nothing but a body can be poured or breathed into anything; or that extension is body, that phantasms are spirits, and so on.

The third is giving names of the attributes of bodies outside us to the attributes of our own bodies, as when people say that color is in the body or sound is in the air, and so on.

The fourth is giving names of bodies to names or speeches, as when people say that there are universal things, or that a living creature is a genus, a general thing, and so on.

The fifth is giving names of attributes to names and speeches, as when people say that the nature of a thing is in its definition, that a man's command is his will, and the like.

The sixth is using metaphors, figures of speech, and other rhetorical devices in place of proper words. Though in ordinary speech one may say, for instance, the road goes or leads this way or that, or the proverb says this or that—although roads cannot go and proverbs cannot speak—such expressions must not be admitted into reckoning and the pursuit of truth.

The seventh is the use of names that mean nothing but are picked up and learned by rote from the schools, such as hypostatical, transubstantiate, consubstantiate, eternal-now, and similar scholastic jargon.

Anyone who avoids these things is unlikely to fall into absurdity, unless the reckoning is so long that he forgets what came before. For everyone reasons alike and well by nature when equipped with sound principles. Who is so foolish that he would both make a mistake in geometry and persist in it after someone showed him his error?

This shows that reason, unlike sense and memory, is not born with us; nor is it gained merely by experience, as prudence is. It is acquired through effort: first by giving names aptly, and second by finding a sound and orderly method for advancing from the elements, which are names, to assertions formed by joining one name to another, then to syllogisms formed by joining one assertion to another, until we reach knowledge of all the consequences of names that pertain to the subject at hand. This is what people call science. Sense and memory are merely knowledge of fact, of what is past and cannot be undone; science is knowledge of consequences and of the dependence of one fact on another. Through it, knowing what we can do now, we know how to do something else when we choose, or how to do something similar at another time. For when we see how something comes about, through which causes and in what manner, then, when similar causes come under our control, we see how to produce similar effects.

Children therefore possess no reason at all until they acquire speech, though they are called rational creatures because they clearly may come to use reason later. Most people, though able to reason a little way, as in counting to a certain point, find little use for it in ordinary life. There they conduct themselves better or worse according to their differing experience, speed of memory, and inclinations toward different ends, but especially according to good or bad fortune and one another's errors. As for science, or certain rules for their actions, they are so far from possessing it that they do not know what it is. They have taken geometry for magic; and as for other sciences, those who have not learned their beginnings and made some progress in them, so as to see how they are acquired and produced, resemble children who, knowing nothing of reproduction, are persuaded by women that their brothers and sisters were not born but found in the garden.

Yet those who have no science are in a better and nobler condition with their natural prudence than those who, through faulty reasoning or trust in others who reason badly, adopt false and absurd general rules. Ignorance of causes and rules does not lead people so far astray as reliance on false rules, or mistaking for the causes of what they desire things that are not its causes but rather causes of the opposite.

In conclusion, the light of human minds is clear words, their wicks first trimmed by exact definitions and cleansed of ambiguity. Reason is the pace; the growth of science, the way; and the benefit of humankind, the destination. Conversely, metaphors and senseless and ambiguous words are like will-o'-the-wisps; reasoning from them means wandering among innumerable absurdities, ending in contention, sedition, or contempt.

As much experience is prudence, so much science is wisdom. Though we ordinarily call both wisdom, the Latins always distinguished prudentia from sapientia, assigning the former to experience and the latter to science. To make the difference clearer, imagine one man gifted with excellent natural dexterity in handling his weapons, and another who has added to that dexterity an acquired science of where he can strike or be struck by his adversary in every possible posture or guard. The first man's ability would stand to the second's as prudence stands to wisdom. Both are useful, but the latter is infallible. Those who trust only the authority of books and blindly follow the blind are like a man who trusts the false rules of a fencing master and rashly takes on an adversary who kills or humiliates him.

Some signs of science are certain and infallible, others uncertain. They are certain when a person claiming knowledge of something can teach it—that is, clearly demonstrate its truth to another. They are uncertain when only some particular events support his claim, and on many occasions things turn out as he says they must. All signs of prudence are uncertain, because it is impossible to observe from experience and remember every circumstance that might alter the outcome. But in any business where a man has no infallible science to guide him, abandoning his natural judgment for general sayings read in authors, which admit many exceptions, is a sign of folly and is generally mocked as pedantry. Even among those who like to display their reading in politics and history in the councils of the Common-wealth, very few do so in domestic affairs where their own interests are at stake. They have prudence enough for private affairs; in public affairs they prize the reputation of their own cleverness above the success of another's business.

CHAPTER VI. OF THE INNER BEGINNINGS OF VOLUNTARY MOTIONS COMMONLY CALLED THE PASSIONS, AND THE SPEECHES BY WHICH THEY ARE EXPRESSED.

Of Reason and Science

When someone reasons, all he does is conceive a total by adding parts together, or conceive a remainder by subtracting one sum from another. When he does this with words, he conceives how the names of all the parts lead to the name of the whole, or how the names of the whole and one part lead to the name of the other part. With numbers, people also speak of multiplying and dividing, as well as adding and subtracting. But these are the same operations. Multiplication adds equal quantities together; division repeatedly subtracts a quantity as many times as possible. These operations apply not just to numbers but to every kind of thing that can be added together or subtracted from another. Arithmetic teaches addition and subtraction with numbers. Geometry teaches them with lines, figures both solid and flat, angles, proportions, times, degrees of speed, force, power, and the like. Logic does the same with the consequences of words: it joins two names to make a statement, two statements to make a syllogism, and many syllogisms to make a proof. It subtracts one proposition from a syllogism's sum or conclusion to find the other. Writers on politics combine agreements to discover people's duties. Lawyers combine laws and facts to determine right and wrong in the actions of private people. In short, wherever things can be added and subtracted, reason has a place. Where they cannot, reason has nothing to do.

From all this we can define, or settle, what the word reason means when we count it among the mind's abilities. Reason, in this sense, is nothing more than calculating—that is, adding and subtracting—the consequences of general names that people have agreed to use to mark and express their thoughts. I say that we mark our thoughts when we calculate for ourselves. We express them when we show or establish our calculations for others.

In arithmetic, beginners necessarily make mistakes, and even experts may often calculate incorrectly. Likewise, even the most able, attentive, and practiced people can deceive themselves and draw false conclusions in any other field of reasoning. This does not mean reason itself is ever anything but correct reason, any more than arithmetic ceases to be a sure and reliable art. But no single person's reason, or that of any group, guarantees certainty. An account is not correct merely because many people have unanimously approved it. When people dispute an account, they must agree to accept an arbitrator or judge whose reasoning will count as correct and whose decision both sides will abide by. Otherwise they must either fight or leave their dispute unsettled, since nature has not appointed a standard of correct reason. The same holds in every kind of debate. Some people consider themselves wiser than everybody else and loudly demand correct reason as their judge, but want everything decided by their own reasoning alone. This is as intolerable in human society as letting a card player, after the trump suit has been set, declare whichever suit he holds most of to be trump whenever he pleases. People who demand that each of their Passions, as it takes control of them, count as correct reason in their own disputes are doing exactly this. Their claim itself reveals their lack of correct reason.

The use and aim of reason is not to find the sum and truth of one or a few consequences far removed from the first definitions and established meanings of names. It is to start with these and proceed from consequence to consequence. We cannot be certain of the final conclusion unless we are certain of every statement and denial on which it rests. Consider a head of a household checking the accounts. Suppose he totals all the expense bills but does not check how the people who submitted them totaled each bill, or even what he is paying for. He gains no more than he would by accepting the whole account at once on trust in the skill and honesty of each accountant. The same is true of reasoning about anything else. Someone who accepts authors' conclusions on trust instead of tracing them back to the first items in every calculation—the meanings of names fixed by definitions—wastes his effort. He knows nothing; he merely believes.

Someone can calculate without words when dealing with particular things. Seeing something, for instance, we can guess what probably came before it or what will probably follow. If the expected event does not follow, or the supposed earlier event did not occur, that is called error. Even the most prudent people make such mistakes. But when we reason in general words and reach a false general conclusion, that is not really an error, though it is commonly called one. It is an absurdity, or meaningless speech. An error is a mistaken expectation about the past or future when the supposed event, though it did not or will not occur, was not recognizably impossible. But when we make a general claim that is untrue, we cannot even conceive its possibility. Words from which we conceive nothing beyond their sound are what we call absurd, meaningless, or nonsense. So if someone talked to me about a round quadrangle, the attributes of bread in cheese, immaterial substances, a free subject, a free will, or anything free in a sense other than unhindered by opposition, I would not call him mistaken. I would say his words have no meaning: they are absurd.

I said earlier, in the second chapter, that human beings surpass other animals in this ability: whenever a person conceives anything, he tends to ask what will follow from it and what effects he can produce with it. I now add another degree of that same advantage. Through words, he can turn the consequences he discovers into general rules called theorems or aphorisms. In other words, he can reason, or calculate, not just with numbers but with anything whose parts can be added to or subtracted from one another.

But this privilege comes with another: the privilege of absurdity, which no living creature other than a human being possesses. Among human beings, those who claim to be philosophers are most prone to it. Cicero was quite right to say somewhere that nothing is too absurd to be found in philosophers' books. The reason is clear. Not one of them begins reasoning with definitions or explanations of the names he will use. This method has been used only in geometry, which is why its conclusions cannot be disputed.

I attribute the first cause of absurd conclusions to a lack of method. People fail to begin their reasoning with definitions—that is, with fixed meanings for their words—as though they could calculate without knowing the value of the number words one, two, and three.

As I mentioned in the preceding chapter, bodies can be counted under several different aspects. When people give these aspects different names and then confuse the names or join them badly in statements, various absurdities result. Therefore:

I attribute the second cause of absurd statements to giving names for bodies to their attributes, or names for attributes to bodies. People do this when they say faith is poured in or breathed in, though only a body can be poured or breathed into anything. They do it when they say extension is a body, or images are spirits, and so on.

The third cause is giving the names of attributes of bodies outside us to attributes of our own bodies. Examples include saying that color is in the body and sound is in the air.

The fourth cause is giving names for bodies to names or forms of speech. Examples include saying that there are universal things, or that a living creature is a genus, or a general thing.

The fifth cause is giving names for attributes to names and forms of speech. People do this when they say the nature of a thing is in its definition or a person's command is his will.

The sixth cause is using metaphors, other figures, and rhetorical language in place of precise words. In everyday speech it is fine to say, for instance, “The road goes or leads here or there,” or “The proverb says this or that.” Roads cannot go anywhere and proverbs cannot speak, however. Such expressions should not be admitted when calculating and seeking the truth.

The seventh cause is the use of names that mean nothing but are learned by rote from the schools: hypostatical, transubstantiate, consubstantiate, eternal-now, and similar scholarly jargon.

Someone who avoids these things is unlikely to fall into absurdity, unless a calculation is so long that he forgets an earlier step. Everyone by nature reasons equally and reasons well from sound principles. Who could make a mistake in geometry and then persist in it when someone else points it out?

This shows that reason is not something we are born with, like sensation and memory. Nor do we get it from experience alone, as we do prudence. We acquire it through work: first by assigning names properly, and second by developing a good, orderly method. We proceed from the elements, which are names, to statements made by joining one name with another, then to syllogisms made by joining one statement with another. Finally we gain knowledge of all the consequences of the names relevant to the subject. People call this science. Sensation and memory give us knowledge only of facts, which are past and cannot be changed. Science gives us knowledge of consequences and of how one fact depends on another. It lets us use what we can do now to learn how to do something else whenever we want, or how to do the same thing on another occasion. Once we see how something happens, from which causes and by what process, we can produce the same effects when similar causes are in our power.

Children have no reason at all until they learn to speak. We call them rational creatures because they clearly may be able to reason later. Most adults can reason a little, as in counting up to a point, but find little use for it in ordinary life. They manage their lives more or less well according to differences in experience, speed of memory, and the ends they seek, and especially according to good or bad fortune and one another's errors. They have so little science, or certain rules for their actions, that they do not even know what it is. They have thought geometry was magic. As for other sciences, people who have not been taught their starting points and enough of their development to see how they arise and are acquired resemble children who know nothing about reproduction and believe women who tell them their brothers and sisters were found in the garden rather than born.

Yet people with no science are in a better and more honorable condition when they use their natural prudence than people who reason badly, or trust bad reasoners, and arrive at false and absurd general rules. Ignorance of causes and rules does not lead people as far astray as reliance on false rules and the mistaken belief that things opposed to their aims are causes that advance those aims.

To conclude, clear words are the light of human minds, once exact definitions have trimmed the wick and removed ambiguity. Reason sets the pace; growing scientific knowledge is the road; and the benefit of humanity is the destination. Metaphors and senseless or ambiguous words, by contrast, are like deceptive marsh lights. To reason with them is to wander among countless absurdities. The result is conflict, rebellion, or contempt.

Just as extensive experience is prudence, extensive science is wisdom. Though we usually use the single word wisdom for both, the Romans always distinguished prudentia from sapientia, applying the first to experience and the second to science. To see the distinction more clearly, imagine one person naturally very skilled at handling his weapons. Imagine another who has that same skill and has also learned the science of where he can strike an opponent, or be struck by him, in every possible stance or guard. The first person's skill stands to the second's as prudence stands to scientific wisdom. Both are useful, but the second is reliable. People who rely solely on the authority of books and blindly follow blind guides are like someone who trusts the false rules of a fencing master and rashly faces an opponent who kills or humiliates him.

Some signs of science are certain and reliable; others are uncertain. A certain sign is that someone claiming knowledge can teach it—that is, can clearly demonstrate its truth to someone else. An uncertain sign is that some particular events turn out as he predicted, even if many do. All signs of prudence are uncertain, for no one can observe through experience and remember every circumstance that could change the result. When someone lacks certain science to guide him in a matter, it is foolish to abandon his own natural judgment for general sayings from authors that admit many exceptions. People commonly mock this as pedantry. Even among people who like to show off their reading of politics and history in councils of the Common-wealth, very few do so in household matters where their own interests are at stake. They have enough prudence for their private concerns. In public matters, though, they care more about their reputation for cleverness than about success in someone else's business.

Chapter VI. Of the Internal Beginnings of Voluntary Motions Commonly Called the Passions, and the Speech That Expresses Them.