TO THE RIGHT HONOURABLE, MY NOBLE LORD, WILLIAM, EARL OF DEVONSHIRE.

[i] My most excellent Lord, the Elements of Philosophy will be a monument to my services to you, and to your generosity to me. Section III has already been published; [n.1] and after a long delay, I have finally completed Section I, which I present and dedicate to your Lordship. The book may be short in length, but it is full of content, and big enough if size is judged by the quantity of truth. You will find it clear and easy to understand, at least for a reader, such as yourself, who is attentive and well trained in mathematical demonstrations. It is almost wholly original, but it will cause no-one any offence because of its novelty. [n.2]

I also know that the hypothesis of the daily rotation of the earth [ii] was first thought of by the ancients, but astronomy itself, i.e. celestial physics, which that hypothesis gave birth to, was strangled by the snares of the verbiage of subsequent philosophers. So apart from the observational aspect, I think the beginning of astronomy can be set no earlier than the time of Nicholas Copernicus [n.3] in the last century, when he revived the opinions of Pythagoras, Aristarchus, and Philolaus. [n.4]

Once the motion of the earth was accepted, there then arose the difficult question of the falling of heavy bodies. Wrestling with that difficulty, our contemporary Galileo [n.5] was the first to open for us the first door to general physics, [n.6] namely the nature of motion. So much so, that it seems that the age of physics cannot be dated any earlier.

Finally, the science of the human body, which is the most useful part of physics, was discovered and demonstrated with wonderful cleverness by William Harvey, [n.7] chief physician to Kings James and Charles, in his books on the motion of the blood, and on animal reproduction. As far as I know, he was the only one who managed to overcome the jealousy of others, and see his new doctrine established during his own lifetime.

Before these people, nothing in physics was certain apart from each person’s own experiences of nature, and written records of them (and it is doubtful whether even these should be described as ‘certain’, since they are no more certain than historical writings). [n.8] After them, in a very short space of time, enormous advances have been made in astronomy and general physics by Johann Kepler, [n.9] Pierre Gassendi, [n.10] and Marin Mersenne; [n.11] [iii] and more particularly in the physics of the human body, by the wit and dedication of medics (the only genuine physicists), especially our most learned fellow-countrymen at the London College of Physicians. Physics is therefore a novelty.

But political philosophy is even more of a novelty, since it is no older than my own book De cive (I am provoked into saying this, so that my detractors will know how little they have achieved). But what? Were there no philosophers among the Greeks? No political philosophers any more than natural philosophers? There certainly were people who were called such — witness Lucian, [n.12] who satirised them; and witness the many states which often banished them by public edicts. But this is no evidence that there was any philosophy. Ancient Greece was haunted by a certain phantasm, which bore a passing resemblance to philosophy on account of its outward appearance of seriousness (though within it was full of deceit and vice). Caught off their guard, some people thought it was philosophy, and attached themselves to one or other of its professors (despite the fact that they all disagreed with each other), and handed over their children to them to be taught wisdom for very large fees, only to be taught nothing other than to argue, and to come to their own arbitrary decisions on every question, without any reference to the law.

The first doctors of the Church, who were born after the time of the Apostles, did try to defend the Christian faith against the pagans [iv] through the use of natural reason. But they too began to philosophise, and contaminated the tenets of Holy Scripture with various tenets from the writings of pagan philosophers. At first they brought in various Platonic dogmas, which were relatively harmless. But later they also adopted many silly and false ones from the Physics and Metaphysics of Aristotle, and, so to speak, betrayed the citadel of the Christian faith by letting in the enemy. From that time, instead of the worship of God, we have had so-called scholastic theology, [n.13] walking with one sound foot, which is Holy Scripture, and one gangrenous one, which is the philosophy which the Apostle Paul called ‘vacuous’, and which he could have called ‘pernicious’. For the latter stirred up innumerable controversies about religion throughout Christendom, and out of these controversies arose wars.

It is like Empusa in an Athenian comic writer. [n.14] The Athenians held Empusa to be a demoness who could change her shape, and one of whose feet was of bronze, and the other the foot of a donkey. They believed she was sent by Hecate [n.15] to give the Athenians advance warning of impending disasters. But I believe that no better way of exorcising this Empusa can be thought of than to distinguish between the rules of religion (that is, of honouring and worshipping God), which are enshrined in law, and the rules of philosophy (that is, the dogmas of private citizens). Questions of religion should be settled by Holy Scripture, [v] and questions of philosophy by natural reason.

There now remains only Section II, On the Human Being. I completed part of it six years ago, namely eight chapters dealing with optics. I have written the text, and tables of diagrams have been engraved to go with each chapter. With the grace of God, I shall complete the remainder as best I can. [n.16] However, [vi] I know from past experience of the insulting words and shameful slights of many ignorant people, how much less thanks I shall get than I shall deserve, since I am going to talk to human beings about the true nature of humanity. But I shall complete the task I have undertaken, and rather than appeasing those who are jealous of me, I shall get my revenge by increasing their jealousy. For I am content with your favour, which I acknowledge as much as you require, and I shall always return the favour in the only way I can, by praying to Almighty God for your good health.

TO THE READER

[vii] In this book, I embark on the systematic exposition of the elements of philosophy. But, dear reader, do not expect this to be the philosophy which results in philosophers’ stones, or the one which is paraded in the tomes of metaphysicians. Rather, it is natural human reason, painstakingly flying around all things in the created world, and reporting everything that is true about their organisation, causes, and effects. Philosophy is the daughter of your mind and of the whole world, and she is inside you yourself. Perhaps she is not yet fully developed, but is like her father, the world, as it was in the beginning, when it lacked form. [n.17] So what you have to do is what sculptors do when they chisel away superfluous material, and find rather than make an image. Or imitate the process of creation. If you want to take philosophy seriously, your reason must ride high above the confused, bottomless pit of your thoughts and experiences. What is confused must be separated, distinguished, and set in order by marking each thing with its own name.

That is, you need a method which corresponds to the creation of things themselves. The order of creation was light, the distinction between night and day, expanse, [n.18] the heavenly bodies, sensible things, human beings. Later, after the Creation, there was the commandment. Therefore the order of philosophising will be reason, definition, space, the stars, sensible qualities, human beings. And later, once humans have grown up, the citizen. So in Part I of this Section I, which has the title Logic, I kindle the light of reason. In Part II, [viii] which is First Philosophy, I distinguish between the ideas of the most general things by means of precise definitions, in order to eliminate any ambiguity or obscurity. Part III is concerned with the expansion of spaces, [n.19] in other words, geometry. Part IV covers the motion of the stars, and also sensible qualities. God willing, Section II will consider the nature of the human being. Section III deals with the citizen, and it has already been published.

This is the order I have followed; and if you like it, you can use it too. I do not positively recommend my way to you — I merely lay it before you. But whatever approach you are going to take, I would strongly recommend philosophy to you (that is, the study of wisdom), since we have all recently suffered many evils for lack of it. [n.20]

Even those who are only interested in money love wisdom, since the only way they get pleasure out of their wealth is by using it as a mirror in which they can look at themselves, and gloat over their own wisdom. [n.21] Again, those who love being active in public affairs are only interested in having a forum for showing off such wisdom as they have. Indeed, the only reason why people who are obsessed with sex neglect philosophy is because they have no idea how much gratification is to be got from the never-ending and utterly intense intercourse between the supremely beautiful world and the soul. [n.22]

Finally, I commend philosophy to you, if for no other reason than that you can occupy your spare time pleasurably with it. The human mind is as intolerant of empty time as nature is of empty space; so by occupying your time with philosophy, you will avoid annoying people who have better things to do, or harming yourself by letting too much leisure drive you into bad and idle company.

Yours,

THOMAS HOBBES

PART I: CALCULATION OR LOGIC

Chapter 1: Philosophy

1.1. Introduction

[1] It seems to me that among people today, philosophy is in the same state as corn and wine are said to have been in the primitive world of nature. From the very beginning of things, there were vines and cereals here and there in the ground, but they were not deliberately planted. So people lived off acorns, and if anyone dared to try such unknown and dubious fruits, they did so at the risk of their health. Similarly, philosophy, i.e. natural reason, is innate in every human. Everyone can reason about some things to a certain extent; but where a long sequence of reasonings is needed, most people lose track and fall into error, for lack of a correct method — like the failure to plant crops. This is why it happens that those who are content with everyday experience (analogous to those who ate acorns), and either reject or at least do not aspire to philosophy, are commonly considered to have (and do in fact have) saner judgment than those who are filled with opinions which are far from common, but are dubious and casually picked up, [2] and who perpetually argue and squabble as if they were insane. [n.23] I accept that the part of philosophy in which the proportions of magnitudes and figures are calculated has been exceptionally well cultivated. However, I do not see that similar efforts have yet been devoted to the other parts of philosophy. So I intend, as far as I am able, to expound the few primary elements of the whole of philosophy, [n.24] as seeds out of which it seems that pure and genuine philosophy can gradually grow.

I am not unaware how difficult it is to free people’s minds from deeply-rooted opinions which have been confirmed by the authority of the most eloquent writers. This is made especially difficult by the fact that genuine (i.e. precise) philosophy deliberately rejects not merely the nuances [n.25] of language, but also virtually all rhetorical embellishments; so the basic foundations of every science are not just unattractive, but seem positively stunted, dry, and almost deformed.

However, there are certainly some people, however few, who take pleasure in truth and sound reasoning for their own sakes, whatever the subject. It is for the benefit of these few that I thought I should go to all this trouble. So I shall now address the task, and start with the very definition of philosophy.

1.2. The definition of philosophy explained.

Philosophy is knowledge of effects or phenomena acquired by correct reasoning from their conceived causes or manner of coming into being; or alternatively, knowledge of possible ways of coming into being from known effects.

In order to understand this definition, it must be noted, firstly, that sensation and memory of things, which humans have in common with all animate beings, are instances of knowledge, but do not constitute philosophy, because they are given immediately by nature, and not acquired by reasoning.

[3] Secondly, since experience is nothing other than memory, and foresight (or prediction of the future) is nothing other than expecting the future to be similar to past experience, foresight should not be considered philosophy either.

By ‘reasoning’ I mean calculation. But to calculate is to unite a number of things added together into a single total, or to know the remainder when one thing is taken away from another. So reasoning is the same as adding and subtracting. I do not mind if you add multiplying and dividing, since multiplication is the same as the addition of equals, and division is the same as the subtraction of equals as many times as is possible. Consequently, all reasoning is reduced to two operations of the mind, namely addition and subtraction.

1.3. Mental reasoning.

However, there is a problem over how we are able to add and subtract by purely mental reasoning, when thinking non-verbally. I shall explain how by means of one or two examples. Suppose someone sees something obscurely from a great distance. Even if no words have yet been imposed on things, they will have the same idea of the thing as the idea by virtue of which they would call it a ‘body’, now that we have imposed names on things. Coming nearer, they will see the same thing somehow changing its position, and they will have a new idea of it, by virtue of which they now call such a thing ‘animated’. Then, standing close up, they would see its shape, hear its voice, and perceive other things which are signs of a rational mind, and would have yet a third idea, even if it had not yet been given a name — that is, the same idea on account of which we say something is ‘rational’. Finally, when they conceive the whole thing as a unity, which is now seen completely and [4] distinctly, this last idea is a compound of the preceding ones. This is how the mind makes compounds of the above ideas, in the same order as the individual names body, animated, and rational are in language compounded into the single name rational-animated-body, or human-being.

In the same way, the concept of a square is compounded from the concepts of having four sides, having equal sides, and having right-angles. For the mind can conceive four-sidedness without the concept of equal-sidedness, and equal-sidedness without the concept of right-angledness, and it can combine these individual concepts into a single concept, namely the unitary concept of a square. So it is obvious how the mind forms compound concepts.

Conversely, if you see a person standing close, you will conceive the whole idea of them; but if they walk away from you, and you follow them only with your eyes, you will lose the ideas of those items which were the signs of rationality, although the idea of something animated will remain in the eyes. So the idea of rational is subtracted from the whole idea of human-being, that is of a rational, animated body, and the remainder is the idea of an animated body. Then a little later, when they are further away, the idea of animated will be lost, and there will remain only the idea of body. And eventually, when nothing more can be perceived because of the distance, the whole idea will disappear from the eyes. So I think that, by means of these examples, I have adequately illustrated the nature of the non-verbal, internal reasoning of the mind.

Consequently, it would be wrong to confine calculation (i.e. reasoning) to numbers, as if humans were distinguished from other animate beings only by their ability to count (as Pythagoras is said to have believed). This is because it is also possible to add a magnitude to a magnitude, or to subtract a magnitude from a magnitude, and similarly with bodies, motions, degrees of quality, actions, concepts, proportions, sentences, [5] and names — which cover all branches of philosophy.

But whatever we add or subtract, that is, enter into the accounts, we are said to consider. The Greek for this is logizesthai, and for calculating (i.e. reasoning) itself is syllogizesthai. [n.26]

1.4. What a property is.

Effects and phenomena are the capacities and powers of bodies by which we distinguish one from another — that is, by which we conceive one as being equal or unequal, or similar or dissimilar to another. So, in the above example, after we have got close enough to a body to perceive that it is moving and walking, we distinguish it from a tree, a column, and various other immobile bodies. Consequently, its walking is one of its properties, since it is proper [n.27] to animals, and one of the ways of distinguishing animals from other bodies.

1.5. How the properties of things are derived from how they come into being, and vice versa.

How the knowledge of an effect can be acquired from knowledge of how it came into being will be readily understood from the example of a circle. Confronted with a plane figure of roughly circular shape, we have no way of knowing whether it is really circular or not, simply from our sensation of it. But it is easy if we know how the figure before us was brought into being. Suppose that the figure was created by keeping one end of a body at a fixed point (any body will do), and rotating the other end. We shall then reason as follows. The length of the rotated body always remains the same, and it first coincides with one radius, then with another, then with the third and fourth, and successively with all of them. Consequently, in every direction the same length touches the circumference from the same point — in other words, all the radii are equal. So it is known that this is the sort of way in which there is brought into being a figure which has a single point at the centre, and all its external points are connected to the centre by radii of equal length.

Similarly, given that we know a particular figure, reasoning will lead us [6] to a way of bringing it into being. Even if it is not the way it was actually brought into being, it is at least at least a way it could have been brought into being. Given the above knowledge of the property of a circle, we readily know scientifically that a circle will be brought into being if a body is rotated as we have just described.

1.6. The purpose of philosophy.

The purpose or target of philosophy is for us to be able to use foreseen [n.28] effects to make ourselves more comfortable — in other words, once effects have been conceived in the mind, for people to deliberately produce similar effects by manipulating the interactions of bodies, as far as human strength and the material of things allow, for the advantages of life.

I do not consider it worth the enormous effort philosophy requires, for someone to keep their pleasure to themselves, and silently gloat over having solved an obscure problem, or discovered hidden truths. Nor do I think there is much value in letting someone else know that you know, if you believe that there will be no other benefit to yourself. The purpose of science is power. In geometry, the purpose of a theorem (which is the search for a property) is a problem, or a technique for making a construction. [n.29] In short, the purpose of every speculative enquiry is to enable us to do or make something.

1.7. The usefulness of philosophy.

The best way of realising how useful philosophy is, and especially physics and geometry, is to list the most outstanding benefits of the human race as it is now, and to compare the condition of those who have advantage of them with the condition of those who do not. The greatest benefits of the human race are the arts, namely those of measuring bodies and their motions; of moving heavy weights; of building; of navigation; of making instruments for all sorts of uses; [7] of calculating celestial motions, the aspects of the stars, and moments of time; and of mapping the surface of the earth. It is easier to understand how many benefits humanity has acquired than to put it into words. They are enjoyed by nearly all European peoples, most Asian ones, and some African ones; but the Americans and the people who live near both the poles are completely deprived of them. But why? Are the former cleverer than the latter? Do not all humans have the same kind of soul, and the same capacities of the soul? So what do some have and others lack, apart from philosophy? Therefore the cause of all these useful things is philosophy.

However, the usefulness of moral and political philosophy is to be judged, not so much by the advantages we enjoy by knowing it, as by the disasters we suffer by being ignorant of it. All the disasters which can be avoided by deliberate human action are the result of war, and especially of civil war, since it is the source of massacres, destitution, and deprivation of everything. These things do not happen because people want them to happen, since one can only want what is good, or at least what appears to be good. Nor is it that they do not know that these things are evil, for who is there who does not feel that death and poverty are evil and harmful to themselves? Therefore the cause is civil war, because they do not know the causes of war and peace; and there are very few people who have learned what their duties are in order to consolidate and preserve peace — that is, the genuine rule of living. Knowledge of this rule is moral philosophy. And why did they not learn it, unless because it has not yet been taught in a clear and correct system? And here is another question. In the old days, Greek, Egyptian, Roman and other teachers were able to persuade masses of uneducated people to believe in innumerable dogmas about the nature of their gods, which even they did not know whether they were true or not, [8] and which were quite obviously false and absurd. So why were they unable to persuade the same mass of people of their duties, if they themselves had known what they were? Again, the few writings of their geometers that have survived had the power to end all controversy about their subject matter. So why did the innumerable and vast tomes of their ethical writers not have the same power, if they contained definite and demonstrated truths? Finally, the writings of the former generate science, and those of the latter merely generate words. [n.30] What cause can be thought of to explain this, except that the former were written by people with scientific knowledge, and the latter by people who were ignorant of their subject matter, and wrote only in order to show off their eloquence or wit? I would not deny that it is sometimes a great pleasure to read such books, since they are very eloquent, and contain many splendid, healthy, and rare sentiments. However, they pronounce them as universally true, even though most of them are not. Consequently, because of changed circumstances of time, place, and social roles, they are as often used to support morally wrong advice, as to enable people to perceive the requirements of their duties. What is most lacking in these writings is a definite criterion for behaviour, which lets us know whether what we are going to do is just or unjust. It is useless to be told (as they tell us) always to do what is right, until a criterion or definite standard for what is right has been established (which no-one has yet succeeded in doing). So since ignorance of duties, i.e. of moral science, leads to civil wars, and hence to the worst of disasters, we shall rightly attribute the opposite advantages to knowledge of moral science. So we see how useful the whole of philosophy is — and this is quite apart from esteem, [9] and other pleasures it gives rise to.

1.8. The subject matter of philosophy.

The subject of philosophy, or the matter which it is about, is every body which can be conceived as coming into being, and which is capable of being compared with other bodies by reference to any aspect of it. This means any body which is susceptible of synthesis and analysis, in other words, every body which can be understood as coming into being, and as having some property or other.

The above can be deduced from the very definition of philosophy, since its task is to track down either the properties of a thing from the way it came into being, or the way it came into being from its properties. It follows that it makes no sense to say that there is any philosophy where there is no coming into being or no property. Consequently, philosophy excludes theology, by which I mean the doctrine of the nature and attributes of eternal, ungenerated, incomprehensible God, in whom it is impossible to undertake any synthesis or analysis, and in whom any coming into being is unintelligible.

It excludes the doctrine of angels, and of all other things which are considered to be neither bodies nor affections of bodies, since they are not amenable to synthesis or analysis, nor is there in them any more or less, and hence no scope for reasoning.

It excludes both natural and civil history, [n.31] even though they are very useful (indeed, indispensable) for philosophy, since such knowledge is either one’s own experience or the testimony of others, and is not reasoning.

It excludes all science which arises from divine inspiration, or revelation, since it is not acquired by reasoning, but by divine grace, and granted as a gift in an instantaneous act (like some sort of supernatural sensation).

It excludes not only any doctrine which is false, [10] but also any which is not well grounded, since anything which is known by right reasoning cannot be either false or doubtful. Consequently it excludes astrology as it parades itself nowadays, and other such doctrines which are guesswork rather than science. Finally, philosophy excludes the doctrine of divine worship, which is to be known by the authority of the Church, and not by natural reason, and hence belongs to faith rather than to science.

1.9. The branches of philosophy.

Philosophy has two main branches. Anyone enquiring into the coming into being and properties of bodies will observe that there are, as it were, two highest genera of bodies, which are as different as could be from each other. One, which is put together by the workings of nature, is called natural body; the other, which is established by the human will through agreements and contracts between people, is called the state. So these give rise to the two primary branches of philosophy, namely natural and civil philosophy. However, in order to know the properties of the state, one must first know the intellectual capacities, the affections, and the customs of human beings. So civil philosophy is usually further subdivided into two branches, of which the one which treats of intellectual capacities and customs is called ethics; and the other, which takes account of the duties of citizens, is called politics, or simply civil philosophy. So, after these prefatory remarks about the nature of philosophy itself, I shall speak in the first place about natural bodies; then in the second place, about the intellectual capacities and customs of human beings and in the third place, about the duties of citizens. [n.32]

1.10. Epilogue.

Finally, there may perhaps be some readers who [n.33] do not like the definition of philosophy I have given above, and who may persist in saying that, since I have allowed the freedom of arbitrary definition, any conclusion can be drawn from anything. [11] In fact I think it can easily be shown that my definition of philosophy is consistent with what everyone means by it. However, so that neither they nor I have any reason to argue about the matter, I shall simply say that, in this work, I shall treat of the elements of the science in which effects are tracked down from knowledge of how a thing came into being, or alternatively, how a thing came into being is tracked down from a known effect. I advise anyone who is in search of a different philosophy to look for it elsewhere.

2.1. The necessity for memory of sensible records or notes. Definition of ‘note’.

Everyone knows from their absolutely certain personal experience how transitory and fleeting people’s thoughts are, and how much a matter of chance it is whether we can recall them. No-one can remember quantities without the presence of sensible standards of measurement, or colours without the presence of perceptible samples, or [12] numbers without the names of numerals set in order and learned by heart. So without some such aid, whatever someone may have gathered by reasoning in their own mind will immediately be lost, and can only be regained by repeating the laborious process. From this it follows that the acquisition of philosophy requires certain sensible records, so that past thoughts can be both recalled and, so to speak, filed in their proper order. Records of this sort are what we call notes, which I define as sensible things arbitrarily chosen, so that when we sense them, they can recall to our minds thoughts similar to the thoughts they were used for.

2.2. The necessity of notes for signifying concepts of the mind.

2.3. Names fulfil both these functions.

Human words connected in such a way as to be signs of thoughts are called language, and its individual parts are called names. But since, as I have said, philosophy requires both notes and signs (notes so that we can remember, and signs so that we can communicate our thoughts), names fulfil both functions. But their function as notes is prior to their function as signs. For someone could use them for remembering, even if they were the only person in the world; but they could be of no use for communication, unless there were someone else to communicate them to. Besides, individual names by themselves are notes, since they recall the objects of thought even in isolation; but they are signs only in so far as they are arranged in a sentence and are parts of it. e.g. the word ‘man’ conjures up in the hearer the idea of a man; but (unless someone adds ‘is an animal,’ or something equivalent) it does not signify that any particular idea was in the mind of the speaker. All it shows is that they wanted to say something, which could indeed have begun with the word ‘man’, but could equally well have begun with the word ‘manifest’. [n.34] So the nature of a name consists primarily in its being a note used for the purpose of remembering; but it also has the accidental function of signifying and communicating the things [14] we hold in memory.

Therefore let us define name as follows:

2.4. The definition of ‘name’.

A name is a human word used arbitrarily by humans as a note by which a thought similar to a past thought can be excited in the mind, and which, arranged in speech and uttered to others, is a sign for them of what thought has or has not previously occurred to the communicator. For the sake of brevity, I think we can accept as virtually indubitable my assumption that names originate in arbitrary human choices. No-one could imagine that the names of things are derived from the natures of the things themselves, after seeing how new words are born and old ones die every day, how different ones are used by different peoples, and how there is not the slightest similarity between things and words, and that they cannot even be brought in to comparison with each other. For although God taught Adam and Eve certain names of animals, [n.35] and of other things they used, he had himself chosen those names arbitrarily; and later, both at the Tower of Babel, and also with the passage of time, they indiscriminately fell into disuse and oblivion, and their places were taken by other words arbitrarily invented and accepted by humans.

2.5. Names are signs of thoughts, not things.

2.6. What things names are names of.

It is not necessary for every name to be the name of some thing. Just as the words ‘human’, ‘tree’, and ‘stone’ are the names of the things themselves, it is equally the case that the images of a person, a tree, and a stone which appear to people in their dreams, have their own names, even though they are not things, but only figments and phantasms of things. Given that we retain memories of these things, we must note and signify them with names no less than the things themselves. The word ‘future’ is also a name, but no future thing yet exists, nor do we know that what we call ‘future’ will ever exist; [n.36] nevertheless, because we are used to connecting past things with present things in thought, we signify a similar connection by the name ‘future’. [n.37] Again, even that which neither is, nor was, nor will be, nor can be will have a name — just that, in fact: ‘what neither is, nor was, etc.’, or, more succinctly, ‘impossible’. Again, the word ‘nothing’ is a name, even though it cannot be the name of a thing. For example, if we subtract two and three from five, we will not see any remainder. But if we want to retain a memory of the subtraction, the sentence ‘The remainder is nothing,’ and the word ‘nothing’ which it includes, is by no means useless. For the same reason, a remainder can even be correctly described as ‘less than [15] nothing,’ when a larger number is subtracted from a smaller one. The mind invents for itself remainders of this sort for the sake of the science as a whole, [n.38] and because [n.39] it wants to recall them into the memory whenever necessary. Every name is related to something named, and even if what is named is not always a thing existing in the real world, for the sake of the science as a whole it will be legitimate to say ‘thing’ instead of ‘that which is named,’ as if it makes no difference whether the thing really exists, or is a mere fiction. [n.40]

2.7. Positive and negative names.

2.8. Contradictory names.

2.9. Common names.

Next, some names are common to a number of things, e.g. ‘person’ or ‘tree’; others are peculiar to individual things, e.g. ‘the author of the Iliad’, ‘Homer’, ‘this person’, or ‘that person’. But a common name is called a universal, because it is the name of a number of things taken individually, and not because it is the name of all of them taken together collectively. E.g. ‘human’ is not the name of the human race, but of each member of it: Peter, John, and all other humans separately. So the name ‘universal’ is not the name of some thing existing in the universe, nor of an idea, nor of some phantasm formed in [18] the mind, but it is always the name of some word or name. So that when it is said that an animal, or a rock, or an image, [n. 41] or anything else is a universal, this is not to be understood as meaning that any person, rock, etc. was, is, or could be universal; but only that the words ‘animal’, ‘rock’, etc. are universal names, i.e. names common to a number of things; and the concepts in the mind corresponding to them are images or phantasms of individual animals or other things. Hence, in order for us to understand the force of ‘universal’, there is no need for any faculty other than the imagination, by which we remember that words of that sort have brought into the mind sometimes one thing, sometimes another. Among common names, some are more common than others, the more common being the names of more things, the less common of fewer. So, ‘animal’ is more common than ‘human’, ‘horse’, or ‘lion, because the former includes all the latter; therefore the more common name, in relation to the less common name included under it, is usually called the genus or general, whereas the latter is said to be its species or special.

2.10. Names of first and second intention.

2.11. Universal, particular, individual, indefinite.

Fourthly, some names have a definite or determinate signification, whereas for others it is indeterminate or indefinite. The first type of name, with a determinate or definite signification, is one which is the name of only one thing, and it is called an individual — for example, ‘Homer’, ‘this tree’, ‘that animal’. The second type is one which is prefixed by the word ‘every’, ‘any’, ‘both’, ‘whichever’, or the equivalent. It is called a universal, because it is the name of each and every one of the many things to which it is common. Such names have a definite signification because hearers conceive in their minds the thing which the speaker wants them to conceive. A name is of indefinite signification, firstly, when it is prefixed by the word ‘some’, or ‘a certain’, or something equivalent, and it is called a particular. Secondly, a common name [n.42] is called indefinite when it stands by itself, without any note either of universality or particuliarity — for example, ‘man’, or ‘stone’. Both particular and indefinite names are of indefinite signification, because hearers do not know what thing the speaker wants them to understand as being referred to. Therefore in speech the names indefinite and particular should be considered equivalent.

2.12. Univocal and equivocal names.

A distinction is usually also made between univocal and equivocal names. Univocal names are those which always signify the same thing in a sequence of reasoning. Equival names are ones which are sometimes to be understood in one way, sometimes in another. For example, one would call the name ‘triangle’ univocal, because it is always taken in the same sense; whereas ‘parabola’ is equivocal, since it sometimes denotes an allegory or analogy, [n.43] and sometimes a geometrical figure. Every metaphor is overtly equivocal; but this distinction is not between names themselves, but between those who use them, because some people use words properly and in their strict senses (in order to elicit the truth), whereas others misuse them for decorative effect, or in order to deceive.

2.13. Absolute and relative names.

Fifthly, some names are called ‘absolute’, and some ‘relative’. Relative names are those which are imposed on things because of some relationship — for example, ‘father’, ‘son’, ‘cause’, ‘effect’, ‘similar’, ‘dissimilar’, ‘equal’, ‘unequal’, ‘master’, ‘servant’, etc. Names which are not imposed on things in order to signify a relationship are called ‘absolute’. Just as I said above that universality should be attributed to words, and not to things, the same is to be said about the other distinctions between names — that is, it is not things which are univocal, or [21] equivocal, relative or absolute. There is a further distinction between names into concrete and abstract; but I shall discuss this in the proper place, [n.44] since it concerns propositions, and cannot apply unless something is affirmed.

2.14. Simple and compound names.

Sixthly, some names are simple, and others are compound, or joined together. But it is especially important to note that, whereas in grammar one name consists of one word, in philosophy one name is what, taken together, constitutes the name of one thing. For philosophers, the whole of ‘sentient animated body’ is one name, since it is the name of one thing, i.e. the name of each and every animal. But for grammarians there are three names. The distinction between simple and complex names is not that, as in grammar, one name is put in front of another to form a new name. [n.45] Here I call a simple name the one which is most common or universal in each genus; whereas a composite name is one which makes the other name less universal by being appended to it, and it signifies that a number of concepts existed in the mind, and that it is because of these that the additional names have been appended to it. For example, in the concept of a human being (as pointed out in the previous chapter), the primary concept is that it is something extended, and the name ‘body’ is used to notate this thing. So ‘body’ is a simple name — that is to say, it is imposed by virtue of this single primary concept. Then when I see the thing move in such-and-such a way, there arises another concept, by virtue of which it is called an ‘animated body’; and I call this a compound name. But I also call the name ‘animal’ compound, since it is equivalent to ‘animated body.’ In the same way, ‘rational animated body’, and its equivalent [22] ‘human being’, is even more compound. Thus we see that the compounding of concepts in the mind corresponds to the compounding of names. Just as in the mind one idea or phantasm comes on top of another, and then another on top of the one before, in the same way one name has another and yet another added to it, and the result of all these is a single compound name. However, we should be careful not to think that the bodies themselves outside the mind are compounded in the same way. It is not the case that there exists in the real world any imaginable body or entity, which originally has no magnitude; then becomes a quantity through the addition of magnitude, and a dense or rarefied one depending on whether the quantity applied to it is large or small; and then with the addition of shape becomes shaped; and finally with the injection of light or colour becomes shining and coloured — even though quite a few have philosophised in this way.

2.15. The description of a category.

Writers on logic have attempted to classify names (in each genus of things) into hierarchies, [n.46] by subordinating those of narrower scope to those of wider scope. For example, in the genus of body, they put body, taken in itself, in the first and highest place. Then under it they put names of narrower scope by which it is limited and made more determinate, namely ‘animate’ and ‘inanimate’; and ultimately they arrive at individuals. Similarly, in the genus of quantity, they put quantity in the highest place, and below it names of narrower scope such as ‘line’, ‘surface’, and ‘solid’. They generally call these hierarchies of names predicaments or categories. Negative as well as positive names are included in the classification. It is possible to draw up matrices or tables of the categories as follows: [23]

Here it is to be noted that line, surface, and solid are said to be of such-and-such a size (i.e. are capable of being equal or unequal) intrinsically and by their own nature; whereas the others cannot be said to be equal to each other, or larger or smaller, or to have any quantity at all, except by virtue of something else. In the case of time it is line and motion; in the case of speed it is line and time; and in the case of power it is solidity and speed. [24]

Secondly, it should be observed that, in the case of positive names, the lower is always contained in the higher; whereas in the case of negative names, the higher is contained in the lower. [25] For example, ‘animal’ is the name of every human, and therefore includes the name ‘human’ in itself; but since ‘non-human’ is the name of everything which is not an animal, the name ‘non-animal’ which is placed above it is contained by the lower name ‘non-human’. [n.47]

Chapter 3: The Proposition

3.1. Various kinds of sentence.

[26] The connection or knitting together of names gives rise to various kinds of sentence. Some signify people’s desires or affections — for example, questions, which signify a desire for knowledge; so when we ask ‘Who is a good person?’ one name is specified, and we are looking for another name, which we expect from the person we are asking. Again, there are requests, which signify the desire to have something, and promises, threats, choices, commands, regrets, and other indications of other affections. There can also be entirely absurd and meaningless sentences, when there is no sequence of concepts in the mind corresponding to the sequence of names. Thus it often happens to people who want to appear to understand abstruse matters which they do not understand at all, that they utter words which do not hang together. [27] But any stringing together of words, however incoherent, makes a sentence, even if it lacks the purpose of language, which is signification. [n.48] In metaphysical writings, such sentences are almost as common as meaningful ones. For philosophy, the only kind of sentence is what some call a ‘statement’, and others an ‘assertion’ or ‘pronouncement’, but which the majority call a ‘proposition’. That is to say, it is a sentence uttered by people who assert or deny, and is an indication of truth or falsehood.

3.2. The definition of a proposition.

A proposition is a sentence consisting of two names joined by the copula, by which speakers signify that they conceive the second name to be the name of the same thing as the first name. Another way of putting it is to say that the first name is included in the second name. For example, the sentence ‘A human is an animal’ is a proposition, in which two names are joined by the copula ‘is’. This is because those who utter it signify that they think that the second name ‘animal’ is the name of the same thing as the name ‘human’; or, in other words, that the first name ‘human’ is contained in the second name ‘animal’.

The first name is usually called the ‘subject’, or the ‘antecedent’, or the ‘contained name’, and the second the ‘predicate’, or the ‘consequent’, or the ‘containing name’. In most languages, their connection is either flagged by a word like ‘is’, as in the proposition ‘A human is an animal,’ or by some inflection or ending of the word, as in the proposition ‘A human walks.’ This has the same force as ‘A human is a walking thing,’ and the ending which makes the difference between ‘walks’ and ‘walking thing’ [n.49] is a sign that these names are conceived as being joined together, or that they are names of one and the same thing. However there are (or certainly could be) some languages which have no word at all corresponding to our ‘is’. Instead, they construct propositions simply by putting one name after the other. [28] It is as if we were to say ‘a human an animal’ instead of ‘a human is an animal,’ since putting the names in this precise order can be enough to indicate how they are connected. The fact that they lack the word ‘is’ does not make them any the less ideal for philosophising. [n.50]

3.3. Subject, predicate, and copula; and abstract and concrete.

So in every proposition, three things need to be considered: the two names (the subject and the predicate), and their being joined together. The names conjure up in the mind a thought of one and the same thing. Their being joined together leads us to think of the cause of these names being imposed on that thing. For example, when we say ‘Body is movable,’ although we think the thing itself which is designated by both names, the mind is not content to stop there, but goes on to enquire what it is to be a body or to be movable. In other words, it enquires what differences this thing has from other things, by virtue of which it has been given these names, and other things not. And people who enquire what it is to be something (e.g. to be movable, to be hot, etc.) are looking for whatever there is in things which causes their names.

From this arises the distinction between names (which we touched on in the previous chapter) into concrete and abstract. A concrete name is one which is the name of some particular thing which is assumed to exist, and which is sometimes called the supposit, and sometimes the subject, or the hypokeimenon in Greek; for example, ‘body’, ‘movable’, ‘moved’, ‘figured’, ‘a cubit in length’, ‘hot’, ‘cold’, ‘similar’, ‘equal’, ‘Appius’, ‘Lentulus’, and the like. An abstract name is one which denotes the cause of the concrete name in the thing which is assumed to exist; for example, ‘being a body’, ‘being movable’, ‘being figured’, ‘being of a certain quantity’, ‘being hot’, ‘being cold’, ‘being similar’, ‘being equal’, ‘being Appius’, ‘being Lentulus’, and the like; or names which are equivalent to these, which are usually [29] called abstract names, such as ‘corporeality’, ‘movability’, ‘motion’, ‘heat’, ‘cold’, ‘similarity’, ‘equality’, and (to adopt Cicero’s [n.51] terminology) ‘Appiety’ and ‘Lentulity’. Infinitives are of the same kind, since ‘to-live’ and ‘to-be-moved’ are the same as ‘to-be alive’ and ‘to-be moved’. [n.52] Abstract names denote the cause of the concrete name, not the thing itself. For example, when we see something, or conceive something visible in our minds, the thing appears or is conceived not as at a single point, but as having parts at various distances from each other, that is, as extended through a certain volume of space. So, since we have decided to call a thing conceived in this way a body, the cause of its name is that it is an extended thing, or extension, or corporeality. Similarly, when we see something appear in different places at different times, and call it moved or transported, the cause of this name is the fact that the thing is moved, or its motion.

The causes of names are the same as the causes of our concepts, namely a certain power, or action, or affection of the thing conceived, or (as some put it) its modes. In fact their commonest name is accidents; but I do not mean the term in the sense in which an accident is contrasted with something which is necessary; but they are called ‘accidents’ because they are not things themselves, or parts of things, but accompany things themselves in such a way that (extension apart) they can disappear or be annihilated, but not abstracted from things.

3.4. Uses and abuses of abstract names.

There is another difference between concrete and abstract, namely that the former are prior to the latter. This is because a proposition can be put together out of concrete names; but abstract names cannot exist without a proposition, since they arise from the copula. [n.53] In ordinary life, and especially in philosophy, abstract names are extremely useful; but they are also liable to serious abuse.

Their usefulness consists in the fact that [30] without them it is almost impossible for us to reason, that is, to calculate the properties of bodies. Suppose we want to multiply, divide, add, or subtract a colour, a light, or a speed. If we double or add them by means of concrete names, by saying (for example) that a hot thing is double a hot thing, or a bright thing is double a bright thing, or a moving thing is double a moving thing, we have not doubled properties, but the hot, bright, moving bodies themselves — which is not what we wanted to do.

The abuse consists in the following. Some people see that increases or decreases in quantity, heat, or other accidents can be considered (i.e., as I have said, entered into the accounts), without considering the bodies or subjects they belong to. This is called abstracting them, or making them exist independently of the latter; so they talk of accidents as if they could be entirely separated from bodies. This is the origin of the gross errors of certain metaphysicians. For example, from the fact that thought can be considered without considering the body, they have wanted to deduce that there is no need for a thinking body; and from the fact that quantity can be considered without considering body, that quantity can also exist without body, and body without quantity, so that a body becomes of a particular size only after quantity is added to it. This is the source of all those meaningless words such as ‘abstract substances’, ‘separated essence’, and the like. There is also the jumble of words derived from the verb ‘to be’, such as ‘essence’, ‘essentiality’, ‘entity’, ‘entitative’, and ‘reality’, ‘aliquiddity’, and ‘quiddity’. Such words are inexpressible in languages where the function of the copula is carried out, not by the verb ‘to be’, but by adjectival verbs [n.54] like ‘runs’, or ‘reads’, etc., or by mere juxtaposition of names. [n.55] Peoples which have such languages are as capably of philosophising as any other, and without any need for [31] their philosophy to include the words ‘essence’, or ‘entity’, or any other such barbarisms.

3.5. Universal and particular propositions.

There are many distinctions between different kinds of propositions. The first is that some are universal, some are particular, some are indefinite and some are singular; and this distinction is usually called that of quantity. A universal proposition is one in which the subject is governed by a sign of a universal name; for example ‘Every human is an animal.’ A particular proposition is one in which the subject is governed by the sign of a particular name; for example ‘Some human is learned.’ An indefinite proposition is one in which the subject is a common name without any special sign, such as ‘Humans are animals,’ or ‘Humans are learned.’ A singular proposition is one in which the subject is a singular name; for example, ‘Socrates is a philosopher,’ or ‘This man is black.’

3.6. Affirmative and negative.

The second distinction, which is called that of quality, is between the affirmative and the negative. An affirmative proposition is one in which the predicate is a positive name; for example, ‘A human is an animal.’ A negative proposition is one in which the predicate is a negative name; for example ‘A human is a not-stone.’

3.7. True and false.

A true proposition is one in which the predicate contains the subject, or in which the predicate is the name of everything of which the subject is the name. For example, ‘A human is an animal’ is a true proposition because whatever is called ‘human’ is also called ‘animal’. And ‘Some human is sick’ is true, since ‘sick’ is the name of some human. A proposition is called false if it is not true, or if its predicate does not include its subject; for example ‘A human is a stone.’

The words ‘true’, ‘truth’, and ‘true proposition’ are equivalent. Truth is predicated of words, not things; and even though the true is sometimes contrasted with [32] the apparent or the fictitious, it must apply to the truth of a proposition. So when it is denied that the image of a person in a mirror, or a ghost, is a ‘true’ person, this is because the proposition ‘A ghost is a person’ is not true; for even though a ghost might not be a true ghost, it cannot be denied. [n.56] Therefore truth does not belong to a thing, but to a proposition. As for the saying of the metaphysicians, that being, unity, and truth are identical, this is worthless and silly. For who does not know that ‘person’, ‘one person’ and ‘true person’ denote the same thing?

3.8. True and false belong to language, not things.

It follows from this that there is no place for truth and falsehood except in living beings which have the use of language. If animals which lack language see the image of a person in a mirror, they can be affected in the same way as if they had seen the actual person, and therefore cringe or fawn at it in vain. However, they do not take the thing as true or false, but only as similar — and in this they are not deceived. So just as humans owe good reasoning to properly understood language, they owe their errors to badly understood language. And just as the human race alone is graced by philosophy, only humans are subject to the shame of absurd dogmas. As was once said of Solon’s laws, language is rather like a spider’s web: weak and fussy wits get stuck and entangled in words, whereas strong wits break through them.

It can also be deduced from this, that the first truths of all arose from the wills of those who first imposed names on things, or accepted names imposed by others. For example, it is true that humans are animals, just because of the arbitrary decision to impose those two names on one and the same thing.

3.9. Primary and non-primary propositions, definitions, axioms, postulates.

[33] The fourth distinction is between primary and non-primary propositions. A primary proposition is one in which the predicate is a name which explains the subject by means of a number of names. For example, in the proposition ‘A human is a rational, animated body,’ precisely what is contained in the name ‘human’ is stated in greater detail by the names ‘rational’, ‘animated’, and ‘body’ joined together. It is called primary, since it is the first in any piece of reasoning, because nothing can be proved unless the name of the thing being enquired about is already understood. However, primary propositions are nothing other than definitions, or parts of definitions; and these alone are the starting-points of any demonstration — in other words, they are truths generated by the will of speakers and hearers, and hence indemonstrable. There are some who add certain other propositions, which they call ‘primary’ or ‘principles’, namely axioms or common notions. However, they are not really principles, because they can be proved (even if their self-evidence means that they do not need to be proved). But an even stronger reason for not accepting them as principles is that there are people who make a big noise, and thrust on us, under the name of ‘principles’, many things which are not known to be true, and are sometimes even false, because they think that anything they happen to believe to be true is obviously so. In addition, certain postulates are often included as principles, for example, that a straight line can be drawn between two points, and other geometrical postulates. These are indeed principles, but principles of technique or construction, not of science or demonstration.

3.10. Necessary and contingent propositions.

Fifthly, propositions are divided into necessary propositions (that is, necessarily true), and propositions which are true, but not necessarily so, which are called contingent. A proposition is necessary, when it is impossible to conceive or imagine anything at any time of which the subject is its name, without the predicate also being the name of the same thing. For example, ‘A human is an animal’ is a necessary proposition, because [34] on any occasion when we suppose the name ‘human’ to apply to some particular thing, the name ‘animal’ will also apply to the same thing. A contingent proposition is one which can be true at one time, and false at another time, for example, ‘All crows are black.’ It might happen to be true today, but false at some other time. Again, in every necessary proposition, the predicate is either equivalent to the subject (as in ‘A human is a rational animal’), or part of an equivalent name (as in ‘A human is an animal’). For the name ‘rational animal’, or ‘human’, is a compound of the two names ‘rational’ and ‘animal’. But this is not the case with contingent propositions. Even if it were true that ‘Every human is a liar,’ the word ‘liar’ is not part of the compound name to which the name ‘human’ is equivalent. So the proposition will not be called necessary, but contingent, even if it is contingently the case that it is always true. Consequently, necessary propositions are those which are timelessly [n.57] true.

This provides another reason why truths obviously belong to language and not to things. Certain truths are eternal, since it will always be true that if something is a human, then it will be an animal. But it is not necessary that humans or animals should exist to eternity. . . .

Sections omitted

Chapter 4: The Syllogism

4.8. What there is in the mind corresponding to a syllogism.

[44] The thought in the mind corresponding to a direct [n.58] syllogism is as follows. First, you conceive a phantasm of the thing named, together with its accident or affection on account of which it is called by the name which is the subject of the minor proposition. [n.59] Then there comes into your mind a phantasm of the same thing, together with the accident or affection on account of which it is called by the name which is the predicate of the same proposition. Thirdly, your thought goes back to the thing named, together with the affection on account of which it is called by the name which is in the predicate of the major proposition. Finally, when you remember that all these affections are of one and the same thing, you conclude that the three names are also names of the same thing — in other words, that the conclusion is true.

For example, suppose the following syllogism is constructed: a human is an animal, an animal is a body, therefore a human is a body. There comes into your mind an image of a person talking or discussing, and you remember that what presents itself to you in this way is called a human. Then there comes into your mind the same image of the same person moving of their own accord, and you remember that what presents itself to you in this way is called an animal. Thirdly, there recurs the same image of the person as occupying a certain place or space, and you remember that what presents itself to you in this way is called a body. Finally, when you remember that the thing which [45] was both extended in respect of place, and moved in space, and used speech was one and the same, you also conclude that the three names ‘human’, ‘animal’, and ‘body’ are names of the same thing, and hence that the proposition ‘A human is a body’ is true.

From this it is obvious that, although we have in our minds a concept or thought corresponding to a syllogism consisting in universal propositions, animals which cannot use names have no equivalent, since, in syllogising, it is essential not only to think about the thing itself, but also to think successively about the different names which are used for our different thoughts about the thing.

Sections omitted

Chapter 5: Erring, falsehood, and sophistries

5.1. The difference between erring and falsehood; and how the mind can err without the use of words.

[49] Error occurs not only in affirming and denying, but also in sensing, and in people’s silent thinking. Error occurs in affirming and denying, when people attribute to a thing [50] a name which is not a name of the thing. For example, suppose we see an image of the sun, both reflected in a river, and directly in the sky. If we attributed the name ‘sun’ to both of them, we would have to say there were two suns. This can only happen to humans, since other animals do not have the use of names. It is the only kind of error which deserves the name of falsehood, since it arises, not from sensation or from things themselves, but from rashness in making a judgment. For names are established by the human will, and not by ‘species’ of things. [n.60] Consequently, when people make false assertions, it is their own fault for departing from the agreed names of things. They are not deceived by things or by their senses, since they do not see that the thing they see is called the ‘sun’, but they willed it.

Errors in sensation and thinking occur when a present imagination gives rise to the imagination of something different (as when we see the image of the sun in the river, and imagine that the thing of which it is the image is in that place); or when we imagine things as past which did not happen in the past, or things as future which will not happen in the future (as when we see swords, and imagine that there has been or will be a battle, because they are usually associated); or when we hear promises, and imagine the intentions of the person making the promise; or, finally, when we observe a sign, and imagine the wrong thing as being signified.

Errors of this sort are common to all things endowed with senses. But in this case too, we are not deceived by our senses or by the things which we sense, but by ourselves, since we imagine things which do not exist, and assume that things which are only images are something more than mere images. But neither things nor imaginations can be called ‘false’, since they truly are what they are. And in so far as they are signs, they do not promise anything which they do not deliver, since they do not promise anything — [51] it is we who make promises to ourselves on the basis of them. For example, it is not that clouds promise rain, but that we see a cloud, and promise rain on the strength of it.

So, in order to guard against errors arising from natural signs, first of all (and before doing any reasoning), we should consider ourselves as ignorant about conjectural matters of this sort. Then and only then should we start reasoning; for such errors arise from lack of reasoning. The other errors (which consist in the falsity of affirmative or negative propositions) are the defective products of bad reasoning. So it is with these that I shall be mainly concerned, since they are contrary to philosophy.

5.2. Seven types of incompatibility between names, all of which result in a false proposition.

Errors which occur in reasoning (i.e. in constructing syllogisms) consist either in the falsehood of one of the premises, or in the making of inferences. In the first case, the syllogism is said to be materially invalid, and in the second case formally invalid. We shall first look at material invalidity, that is, the various ways in which a proposition can be false; and we shall then look at formal invalidity, or the various ways in which it happens that the inference is false when the premises are true.

As I said in Chapter 3, Article 7, a true proposition is one in which two names of the same thing are combined together, and a false proposition is one in which the two names joined together are of different things. Consequently, there are as many ways in which a proposition can be false, as there happen to be ways in which the names combined together are names of different things.

Now, there are four genera of things which have names: bodies, accidents, phantasms, and names themselves. Therefore in every true proposition, it is necessary that the names combined together are both names of bodies, or both names of accidents, or both names of phantasms, or both names of names. Names combined in any other way are incompatible, and constitute a false proposition. I should also add that the name of a thing can [52] be combined with the name of a sequence of names. So there are seven ways in which names are combined together incompatibly.

I shall now give examples of each of these.

5.3. Examples of the first.

In accordance with the first type, propositions are false when abstract names are combined with concrete ones. For example, ‘Existence is a being,’ ‘Essence is a being,’ to ti en einai, [n.61] ‘Quiddity is a being,’ and much more of the same sort to be found in Aristotle’s metaphysics. Similarly, ‘The understanding acts,’ ‘The understanding understands’, ‘Seeing sees’, ‘Body is a magnitude,’ ‘Body is a quantity,’ ‘Body is extension,’ ‘Being a human is a human,’ ‘Whiteness is white.’ It is just as if someone were to say ‘The runner is the running,’ or ‘Walking walks.’ Again, ‘Essence is separated,’ ‘Substance is abstracted,’ and other propositions like them or derived from them (and ordinary philosophy is full of them). For since no subject of an accident (i.e. no body) is an accident, no name of an accident should be attributed to a body, or of a body to an accident.

5.4. Examples of the second.

Propositions like the following are faulty in the second way: ‘A ghost [n.62] is a body or a spirit,’ i.e. a rarefied body. ‘Sensible species fly through the air,’ i.e. they move hither and thither, which is the exclusive property of bodies. Likewise ‘A shadow moves,’ i.e. it is a body. ‘Light moves,’ i.e. it is a body. ‘Colour is the object of seeing, and sound is the object of hearing;’ ‘Space or place is an extended thing,’ and other innumerable examples of this sort. Since ghosts, visible species, sounds, shades, light, colour, space, etc. are present to people who are dreaming no less [53] than to people who are awake, they are not external things, but phantasms of the mind which imagines them. Consequently their names cannot be combined with the names of bodies so as to form a true proposition.

5.5. Examples of the third.

False propositions of the third type are such as these: ‘A genus is a being.’ ‘A universal is a being.’ A being is predicated of a being.’ For ‘genus’, ‘universal’, and ‘to predicate’ are names of names, not of things. Likewise, ‘Number is infinite’ is false, [n.63] since there is no infinite number, but only the name or word ‘number’. When it is not backed up by any specific number in the mind, the name is called ‘indefinite’, but there is no such thing as an infinite number.

5.6. Examples of the fourth.

The fourth type includes false propositions such as these: ‘The size or shape of an object is in reality as it appears to observers;’ ‘Colour, light, and sound are in the object;’ and other similar propositions. For the same object sometimes appears smaller, sometimes larger; and sometimes square and sometimes round, depending on its distance and the medium through which it is seen. But the true size and shape of the thing seen is always one and the same; so the apparent sizes and shapes cannot be the sizes and shapes of the same objects. Consequently, they are phantasms, and in this type of proposition, names of accidents are combined with names of phantasms.

5.7. Examples of the fifth.

The fifth type of mistake is when people say ‘The definition of a thing is its essence;’ ‘Whiteness, or any other accident, is a genus, or a universal.’ For a definition is not the essence of a thing, but a sequence of names signifying our concepts of the thing’s essence. Similarly, it is not whiteness itself, but the word ‘whiteness’ which is a genus or universal.

5.8. Examples of the sixth.

The sixth type of error is committed by those who say ‘The idea of a thing is universal,’ as if there were in the mind some sort of image of a person, [54] which was not an image of any one person, but of ‘person’ and nothing more. But this is impossible, since every idea is both unique, and of one unique thing. Their mistake is to confuse the name of a thing with the idea of it.

5.9. Examples of the seventh.

The seventh type of error is made by those who classify different kinds of being, and say ‘Some beings are beings in themselves, and others are beings only accidentally.’ They say this because ‘Socrates is a human’ is a necessary proposition, whereas ‘Socrates is a musician’ is a contingent proposition; and they make some beings necessary beings, or beings in themselves, and others contingent beings, or beings by accident. But ‘necessary’, ‘contingent’, ‘in itself’, and ‘by accident’ are names of propositions, not of things. So when they say that something is a thing in itself, they combine a name of a proposition with a name of a thing.

The same mistake is made by those who locate some ideas in the understanding, and others in the imagination — as if we had two completely distinct ideas or images of a human: one which came from sensation and is retained in the memory, and another one which is in the understanding when we understand ‘A human is an animal.’ Where they went wrong is that they thought that one idea of the thing corresponded to a name, and another to a proposition. But this is false, since the term ‘proposition’ signifies only the ordering of what is successively observed in one and the same idea of a human. [n.64] So, in order to utter the sentence ‘humans are animals’, we have a single idea, in which we first consider that by virtue of which they are called ‘humans’, and then that by virtue of which they are called ‘animals’.

The falsehood of all these types of proposition is to be revealed through definitions of the names which are combined together.

5.10. The falsehood of propositions is revealed by analysis of terms through continuous definition until simple names or highest genera are arrived at.

On other occasions, names of bodies are combined with names of bodies, names of accidents with names of accidents, names of names with names of names, and names of phantasms with names [55] of phantasms. However, this alone is not enough for us to know immediately whether such propositions are true or not. First we must know the definitions of both names, and then the definitions of the names which feature in the first definition, until continuous analysis brings us to an absolutely simple name. This name will be the highest or most universal in the genus of things in question. And if the truth or falsehood of the proposition is still not apparent, then it is a matter for philosophy, to be investigated by reasoning which starts out from definitions. [n.65] For every universally true proposition is either a definition, or a part of a definition, or demonstrable from definitions.

5.11. The syllogistic fallacy arising from the absorption of the copula into one of the terms.

There are only two ways in which a syllogism can be formally invalid: either it consists in the absorption of the copula into one or other of the terms, or it consists in some verbal equivocation. In both cases, there are in effect four terms; which I have shown cannot happen in a valid syllogism. The absorption of the copula into one or other term is immediately revealed by reducing propositions to pure and explicit predication. For example, ifsomeone argues as follows:

the fallacy is immediately exposed by reduction. If it is expressed as follows:

the four distinct terms are obvious: ‘the hand’, ‘touching-the pen’, ‘the pen’, and ‘touching-the paper’.

[56] But it does not seem that there is enough danger from this sort of sophism for it to be worth pursuing the matter any further.

5.12. The syllogistic fallacy arising from equivocation.

Although it is sometimes possible for equivocation to give rise to fallacies, this does not happen when the equivocation is completely obvious, or in the case of metaphors, since the very word ‘metaphor’ signals in advance that a name has been transferred [n.66] from one thing to something else. However, there are equivocations which are unobvious enough to deceive on occasion. Take the following argument, for example:

The fallacy lies in an equivocation over the word ‘principle’. When Aristotle says, at the beginning of the Metaphysics, that it is the function of first science to deal with principles, by ‘principles’ he means the causes of things, which are certain entities which he calls ‘primary’. But when he says the above primary proposition is a ‘principle’, he means the starting-point [n.67] and cause of knowledge, namely the understanding of words, without which no-one can learn anything at all.

5.13. Sophistries are more often materially rather then formally invalid syllogisms.

In antiquity, the sophists and the sceptics used to attack and poke fun at the truth. But their trickeries depended mostly on materially rather than formally invalid syllogisms. In fact, they were more successful in deceiving themselves than in deceiving anyone else. For example, Zeno’s famous argument against motion depended on the proposition ‘Whatever can be divided into an infinite number of parts is infinite,’ and it is beyond doubt that he himself believed this to be true. But it is false, since to be divisible into infinite parts is nothing other than to be divisible into as many parts as anyone wishes. [57] Even if I could divide and subdivide a line as many times as I wished, this does not necessarily mean that it has an infinite number of parts, or is infinite. However many parts I might have divided it into, their number will always continue to be finite. But if you simply say ‘parts’, without saying how many, you do not yourself set any limit, but leave it to be determined by your hearer. The only sense in which a line can truly be said to be infinite is that it can be divided without limit, and this is how it is usually understood.

But I have said enough about the syllogism, which is, as it were, the first step towards philosophy. I have said as much as is necessary for you to know what every valid argument draws its force from. To pile up everything which could be said would be as superfluous as to give a baby instructions on how to walk (as I said earlier). The skill of reasoning well is acquired, not by instructions, but by practice, and by reading books in which everything is established by strict demonstrations.

I now move to the actual route of philosophy, in other words, the method of philosophising.

Chapter 6: Method

6.1. Definitions of ‘method’ and ‘science’.

[58] In order to know what method is, we must remind ourselves of the definition of philosophy. This was given in Chapter 1, Article 2, as follows: Philosophy is knowledge of phenomena or apparent effects acquired by right reasoning from a conception of some possible means of their production or coming into being; or knowledge of a means of production which actually occurred or could have occurred, from a conception of an apparent effect. [n.68] Therefore the method of philosophising is the most direct tracking down of effects through known causes, or of causes through known effects. [59] And we are said to have scientific knowledge of an effect when we know both that its causes exist; [n.69] and what subject the causes exist in; and what subject they bring about the effect in; and how they do it. So scientific knowledge is knowledge ‘why’, or of causes; whereas all other knowledge is knowledge ‘that’, [n.70] and consists in sensation, or memory, which is an imagination remaining after sensation.

So the first starting-points of our scientific knowledge of everything are the phantasms of sensation and imagination. We know by nature that these exist; but to know why they exist, or what causes they come from, requires reasoning. As I said above, in Chapter 1, Article 2, reasoning consists in composition and division (or resolution). Therefore any method for investigating the causes of things is either compositive, or resolutive, or partly compositive and partly resolutive. The resolutive method is usually called analytic, and the compositive synthetic. [n.71]

6.2. The existence of particulars is better known than that of universals. Conversely, it is better known of universals than of particulars why they are, or what their causes are.

It is common to each method to proceed from what is known to what is unknown — as is obvious from the definition of philosophy I have given. In sensory knowledge, the whole phenomenon is known better than any of its parts. For example, when we see a human, the concept or complete idea of ‘human’ is known first, or is better known than the particular ideas of ‘shaped’, ‘animated’, or ‘rational’. In other words, we see the person as a whole and know that they exist, before we notice these particulars. So in knowledge ‘that’, or that something exists, the investigation begins with the complete idea.

By contrast, in knowledge ‘why’, or in knowledge of causes, that is, in the sciences, the causes of the parts are better known than the cause of the whole. This is because the cause of the whole is compounded from the causes of the parts, [60] and the components must be known before the resulting compound. Here, by ‘parts’, I do not mean the parts of the thing itself, but the parts of its nature. For example, by the parts of a human, I do not mean the head, shoulders, arms, etc., but shape, quantity, motion, sensation, reasoning, and the such like, which are accidents, and which, when compounded, together constitute the whole nature of a human, not the whole physical mass.

This is why it is often said that some things are better known to us, and other things are better known to nature. I do not believe that those who make this contrast think that there is any known thing which is known to nature, even if it is not known to any human being. So when they say ‘better known to us,’ they must be referring to sensory knowledge, and when they say ‘better known to nature,’ they must be referring to knowledge acquired by reasoning. So the sense in which wholes are known better than parts is that those things which have less universal names (which we call ‘particulars’ for short) are better known to us than things which have more universal names (which we call ‘universals’); [n.72] but the causes of the parts are better known than the cause of the whole, or, as is commonly said, universals are better known to nature than particulars are. [n.73]

6.3. What people who philosophise want to know.

People who philosophise have one of two objectives. On the one hand, they may simply be seeking after scientific knowledge as such, whatever it may be; that is, they merely want to acquire as much scientific knowledge as they can, but without any specific question in mind. On the other hand, they may be trying to discover the cause of some specific phenomenon, or at least something specific. For example, they might want to discover the cause of light, heat, gravity, or of a figure to be constructed, and so on. Again, they might want to discover what subject some specified accident inheres in, or which of many accidents are most important for bringing about some specified effect. Or again, they might want to discover how some particular causes in question need to be combined in order to produce a specific effect. Because of this variety of things [61] being investigated, the method to be used is sometimes the analytic method, sometimes the synthetic method, and sometimes both.

6.4. The first part, in which principles are discovered, is purely analytic.

Let us take the case of those who are simply seeking after scientific knowledge as such, which consists in as much knowledge as possible of the causes of all things. Since the causes of all particulars are compounds of the causes of universals or simples, these seekers after knowledge must know the causes of universals (universals being accidents common to all bodies, i.e. to the whole of matter), before they can know the causes of particulars, that is, of the accidents by which one thing is distinguished from another. Again, before the causes of these universals can be known, one must know what the universals themselves are. But since the universals are included in the nature of individuals, they are to be unearthed by reasoning, that is, by means of analysis.

For example, suppose the concept or idea of any particular thing whatever — say, a square. The square will be analysed into ‘plane’, ‘bounded by lines’, and having ‘angles’ which are ‘right-angles’, ‘of a certain number’, and ‘equal’. So we have the following universals which apply to the whole of matter: line, plane (i.e. plane surface), bounded, angle, rectangularity, and equality. Once you have discovered the causes of these, i.e. how they are brought into being, you can put them together to form the cause of the circle.

Again, if you take the concept of gold, analysis will yield the ideas of ‘solid’, ‘visible’, and ‘heavy’ (i.e. the idea of that which has a tendency towards the centre of the earth, or of downward motion), and many other universals which are more universal than gold itself, and which can be analysed in their turn, until you arrive at absolute universals.

By analysing more and more things in the same way, we shall come to know what these universals are, and by knowing their individual causes and compounding them, we shall know the causes of particular things. I therefore conclude that the method [62] for tracking down the notions of universal things is purely analytical.

6.5. The highest causes in every genus are universals known in themselves.

The causes of universals (at least of those which have any causes at all) are obvious in themselves, or, as they say, ‘known to nature’. Consequently they require no method at all, since the one universal cause of them all is motion. Even shape is subordinate, since the variety of all shapes arises from the variety of motions by which they are constructed. On the other hand, a motion cannot be understood as having any cause other than another motion. Nor do the various kinds of things perceived by sensation, such as colours, sounds, tastes, etc., have any other cause apart from motion, both in the objects acting on the senses, and hidden within the sentient beings themselves; and even if it so hidden that it is impossible to know what this motion is like without reasoning, yet it is obvious that it is some sort of motion. It may be that most people need some demonstration in order to understand that all change consists in motion; but this is not the case because of any obscurity in the matter (for it is unintelligible that something should cease from its present state or motion without this being brought about by a motion), but either because ordinary language has been corrupted by the preconceptions of teachers, or because they apply no thought whatever to the search after truth.

6.6. What the method is, which leads from principles which have been discovered to scientific knowledge as such.

So once we know universals and their causes (which are the first principles of knowledge ‘why’), the first thing we have is their definitions, which are nothing other than explanations of our simplest concepts. For example, if you have a correct conception of ‘place’, you cannot be ignorant of the following definition: ‘Place is the space which a body exactly fills or occupies.’ Again, if you have a conception of ‘motion, you cannot fail to know that motion is the loss of one place [63] and the acquisition of another.

Secondly, we have the way they come into being or are constructed; [n.74] for example, that a line is brought into being by the motion of a point, that a surface is brought into being by the motion of a line, that one motion is brought into being by another motion, and so on.

But we still need to find out what sort of motion gives rise to what sort of effects — for example, what sort of motion makes a straight line, and what sort makes a circular one; what sort of motion pushes, and what sort pulls, and by what route; and what sort of motion makes a thing which is seen, heard, etc. to be seen, heard, etc. in various different ways. The method for this enquiry is the synthetic method. For we first have to see what a moving body brings about, if nothing in it is considered apart from its motion; and it is immediately evident that what is brought about is a line, or length. Then it needs to be seen what a long body will make if it is moved, and everyone agrees that it will be a surface — and similarly other effects of motion taken in itself. Finally, in a similar way we need to think about what effects, what figures, and what properties of these figures exist as a result of adding, multiplying, subtracting, and dividing motions of the above sort. And this sort of thinking has given rise to that part of philosophy which is called geometry.

After considering what results from motion taken in itself, we next consider what the motion of one body brings about in another body. In fact there are two cases: in one case the motion can be in the individual parts of the body, without the body as a whole leaving its place; in the other case, a motion brings about the motion of the body as a whole. To take the latter first, if one body collides into another body which is at rest, or which is already moving in a certain way, we need to enquire in what direction and with what speed the first body will move after the collision, and again what motion this second motion will give rise to in a third body, and so on. And this sort of thinking will bring into existence that part of philosophy which is the philosophy of motion.

[64] Thirdly, we come to the investigation of what arises from the motion of parts; for example, how it happens that things which stay the same can appear to the senses as not being the same, but changed. So here the topic of enquiry is sensible qualities, such as light, colour, transparency, opacity, sound, smell, taste, heat, cold, and the such like. But since they cannot be known without knowledge of the cause of sensation itself, the third topic will be to consider the causes of vision, hearing, smell, taste, and touch. The previously mentioned qualities, and all kinds of changes, must be postponed to the fourth topic. These two areas of study together make up the part of philosophy which is called physics.

All four parts include everything in natural philosophy which can be explained by demonstration in the strict sense. If an explanation is to be given of natural phenomena in more specialised areas, for example, why the motions, powers, and parts of the heavenly bodies are as they are, any such explanation must be derived from the four parts of science referred to above, otherwise there will be no explanation at all, but only vague conjecture.

After physics, we must come to moral philosophy, in which we study the causes and effects of the motions of minds, namely appetite, aversion, love, benevolence, hope, fear, anger, rivalry, jealousy, etc. The reason why these have to be studied after physics is because they have their causes in sensation and imagination, which are what we think about when we are doing physics.

It is obvious that all these things must be investigated in the order I have specified, because physics cannot be understood without knowledge of the motion which takes place in the tiniest parts of bodies; nor can this motion of parts be understood without knowledge of the effect of one moving body on another; nor can this be understood unless it is known [65] what is brought about by motion taken in itself. Another way of looking at it is this. Every apparition of things to the senses is determined (i.e. it has the specific characteristics and size which it has) by the combined effect of a number of motions, each one of which has its own particular speed and direction. So we must first investigate [n.75] the directions of motions taken in themselves (which is what geometry consists in); then the directions of motions which have actually been brought into being and are perceptible; and finally the directions of internal and invisible motions (which is the subject matter of physics). Consequently, people who research into natural philosophy, without taking geometry as the starting point of their research, are wasting their time. And people who write about, or lecture on natural philosophy, without any knowledge of geometry, are wasting the time of their readers and listeners.

6.7. The method of civil and natural science is analytic when it goes from sensation to principles, and synthetic when it returns back again from principles.

The connection between civil and moral philosophy is such that the former can be detached from the latter. This is because the causes of mental motions are known, not only be reasoning, but also by the experience of each individual observing their own motions. [n.76] Consequently, those who follow the synthetic method are not the only ones who can attain knowledge of civil philosophy. The synthetic method starts out from the first principles of philosophy, to arrive at scientific knowledge of the desires and disturbances of people’s minds. Following the same route, it proceeds to the causes of the setting up of states, and indeed the necessity of their being set up. After that, it provides scientific knowledge of natural law and of the duties of citizens, and, whatever the type of constitution, of what rights are retained by the state — and everything else which falls within the province of civil philosophy. It can do this because the starting point of politics is knowledge of the motions of minds, and knowledge of the motions of minds consists in scientific knowledge of sensations and thoughts. Nevertheless, people who have never learned the first part of philosophy (geometry and physics) can arrive at the principles of civil philosophy by the analytic method.

Take any question whatever, such as whether such and such an action is just or [66] unjust. By analysing unjust into something that has been done and against the law, and the notion of law into the command of the person who has the authority to coerce, and this authority into the will of people who set up such an authority for the sake of peace, you will eventually arrive at the fact that the appetites and mental motions of human beings are such that they will be at war with one another unless they are coerced by some authority. Absolutely anyone can know this if they go through the experience of introspecting into their own mind. So, having reached this point, one can use the synthetic method to decide upon the justice or injustice of any proposed course of action.

From what I have said, it is now obvious that, for those who seek after scientific knowledge for its own sake, and with no specific question in mind, the method of philosophising is partly analytic and partly synthetic. In other words, it is analytic in so far as principles are discovered on the basis of sensations; but otherwise it is synthetic.

6.8. The method for deciding whether the thing in question is matter or accident.

When we are looking for the cause of some particular phenomenon or effect which is in question, it sometimes happens that we do not know whether the thing we want to know the cause of is matter (i.e. body), or whether it is some accident of a body. In the case of geometry, when we are trying to find out the cause of a magnitude, or a ratio, or a figure, we know for certain that these things (magnitude, ratio, and figure) are accidents. In physics, however, it is not so easy to decide, since it is concerned with the causes of sensible phantasms, which present themselves as the very things of which they are the phantasms, and convince most people that they are.

This is especially the case in phantasms of sight. For example, if you look at the sun, you will have a certain shining idea roughly a foot in diameter, and you will call it the sun, even if you know scientifically that the sun [67] is really much larger. Similarly, a phantasm is sometimes seen as round from a long distance, but square close to. It is therefore perfectly reasonable to wonder this phantasm is matter (or some natural body), or whether it is some accident of a body.

The method for exploring this question is as follows. The properties of matter and accident (which we previously discovered from their definitions by using the synthetic method) are to be compared with the idea itself. If the properties correspond to the idea of body or matter, the idea itself is a body; and if they do not correspond, it is an accident. But matter cannot come into being, or disappear, or get larger or smaller, or be moved from its position by our concentrating on it; whereas the idea comes into being, disappears, gets larger, gets smaller, and is moved at will. Consequently, it is certain that it is not matter, but an accident. And this method is the synthetic method.

6.9. The method for finding out whether a given accident is in this or that subject.

It is sometimes uncertain what subject a known accident belongs to — as in the preceding example, one can wonder what subject the brightness and apparent size of the sun is in. On this question, the method of enquiry is as follows. First, divide matter as a whole into parts, namely the object, the medium, and the sentient being (or whatever division seems most appropriate for any given problem). Then scrutinise each of these parts by reference to the definition of the subject. Eliminate the parts which cannot be characterised by the accident in question. For example, if valid reasoning shows that the sun is larger than its apparent size, the apparent size is not in the sun. Again, the sun is seen at a single definite distance and in a single definite direction; so if its size and brightness are seen at different distances and in different directions (as happens in reflection [68] and refraction), its brightness and its apparent size will not be in the sun itself. Consequently, the body which is the sun will not be the subject of this brightness and size. The same reasoning will result in the elimination of the air and everything else, until nothing is left except the sentient being itself as the only possible subject of the brightness and size.

This method is analytic in so far as the subject is divided into parts, and synthetic in so far as the properties of subject and accident are compared with the accident whose subject we are looking for.

6.10. The method for finding the cause of a given effect.

When an effect is given, and you want to find out its cause, first of all you must get into your mind and think about the notion or complete idea of what the word ‘cause’ refers to; namely that a cause is the sum or total of all the accidents, both in the agents and in the patient, which work together to produce the given effect, so that it cannot be understood how the effect could fail to happen if all these accidents are present, or how it could happen if any one of them is absent.

Now that you know what a cause is, you must examine, one by one, every accident which accompanies or immediately precedes the effect, and which seems to have some connection with it, to see whether or not the effect in question can be understood as happening if it were not present. In this way, those which contribute to the production of the effect will be separated out from those which do not. After you have done this, you should assemble together all those which do contribute, and consider whether it is still possible to understand the effect in question as not happening, even if all these accidents are present at the same time. If that is inconceivable, then this totality of accidents is the complete cause of the effect; otherwise it is not, and you must look for more to add to them.

[69] For example, if we are researching into the cause of light, we start by investigating the external world. We find that whenever light appears, there is always some special object which is the source of the light, and without which it is impossible to understand how there could be light. So some object is the first contributor to the generation of light. Then we consider the medium, and we discover that, even if the object remains the same, the effect fails to happen unless the medium has a certain character, namely that it is transparent. So the transparency of the medium also contributes to the generation of light. Thirdly, I study the body of the perceiver, and I find that light is prevented from occurring by any malfunctioning of the eyes, brain, nerves, or heart (i.e. by obstructions, or sleep, or fainting). So the fact that the bodily organs are in a fit state to receive the impressions of external objects also contributes to the cause of light. Again, of all the things which inhere in the object and can bring about light, action (i.e. some sort of motion) is the only one which cannot be understood as being absent as long as the effect remains. This is because, for something to be able to shine, it is not necessary for it to be of a particular size or shape, nor for the whole body to move from where it is. (It might be said that the cause of light which exists in the sun or any other body, is light; but this would be an absurd objection, since ‘light’ means nothing other than the cause of light — it is as if one were to say that the cause of light is that which exists in the sun and has light as its effect.) So the only remaining alternative is that the action by which light is generated is a motion of parts only, From this it is easily understood that what the medium contributes is the transmission of the motion to the eye; and finally that what the eye and other organs of the perceiver contribute is the transmission of the same motion right up to the heart, or the ultimate organ of sensation. In this way, the cause of light will be compounded [70] from a continuous motion from its source to the source of vital motion, and light itself is a transformation of this vital motion brought about by contact with the other motion. I have included the above merely as an example, since I am going to explain what light is, where it comes from, and how it comes into being at greater length in the proper place. [n.77]

In the meantime, it is obvious that it is necessary to use both the analytic and the synthetic methods for tracking down causes. The analytic method is needed for conceiving the circumstances of the effect separately from one another, and the synthetic method for combining the effects of individual circumstances into a single whole.

Now that I have dealt with the method of discovery, it remains to discuss the method of exposition or demonstration, and the different stages of demonstration.

6.11. In discovery, words function as notes, and in demonstration as signs.

In the method of discovery, the function of words consists in their being notes, which enable us to recall new discoveries to memory. Unless this happens, whatever we have discovered will be lost; and because of the weakness of our memory, it will not be possible to make any progress from our starting points beyond one or two syllogisms. For example, if you concentrate on a triangle placed before your eyes, you will discover that all its angles taken together are equal to two right angles. You can do this by thinking privately about the object of your thought itself, without using any words, whether merely conceived in your mind, or uttered to others. But if you were then to be presented with another triangle different from the first (or even the same triangle, but looked at from a different position), you would not know if it had the same property or not. So every time you were confronted with a new triangle (of which there are infinite varieties), you would have to start thinking about each one afresh. This is made unnecessary by the use of words, since each universal word denotes the concepts of infinitely many individual things. However, as I have already said, they are of value to discovery as notes for aiding the memory, and not as [71] signs for indicating them to others. Consequently, people can philosophise by themselves, without any teacher. Adam managed it. But to expound or demonstrate requires at least two people, and words combined into syllogisms. [n.78]

6.12. The method of demonstration is synthetic.

Teaching is nothing other than leading the mind of the learner along the tracks of one’s own discovery until they know what has been discovered. Consequently, the method of demonstration will be the same as that of enquiry, except that you should omit the first part, namely the one which proceeded from the sensation of things to universal principles. Since the latter are starting points, they cannot be demonstrated; and since they are known by nature (as I said in Article 5, above), they likewise cannot be demonstrated, even if they require some explanation. So the method of demonstration is entirely synthetic, and it consist in the ordering of sentences, starting with primary or absolutely universal propositions which are understood in themselves, and proceeding by a perpetual combining of propositions into syllogisms, until the truth of the conclusion in question is understood by the learner.

6.13. The only primary, universal propositions are definitions.

These principles are nothing other than definitions, and they are of two kinds. Some are definitions of words which signify things of which at least some cause can be understood; others are definitions of words which signify things of which the cause cannot be understood. Of the first kind are body or matter, quantity or extension, motion taken in itself, and everything that is common to all matter. Of the second kind are a particular body, a particular motion, a particular magnitude, a particular figure, and everything else by which one body can be distinguished from another.

Names of the first kind are adequately defined if, using the smallest [72] number of words possible, clear and complete ideas or concepts of the things of which they are the names are conjured up in the mind of the listener. For example, we might define ‘motion’ as the continuous leaving of one place and acquisition of a new one. Even though nothing in motion nor the cause of motion is to be found in this definition, yet simply from hearing those words, the idea of motion will be observed clearly enough in the mind. But in the case of names of things which can be understood as having a cause, that cause or way of being generated must itself be included in the definition — for example, when we define a circle as a shape created by rotating a straight line on a plane.

Apart from definitions, no other proposition should be described as primary; and, strictly speaking, they should not be counted as principles. Thus Euclid’s axioms are not starting points for demonstration, since they can be demonstrated; but since they do not need demonstrating, they have acquired the authority of principles by common consent. As for what are called postulates or assumptions, they are indeed principles, but principles of construction rather than of demonstration, that is, of power, not of science; or to put it another way, they are not speculative theorems, but they relate to action or performing a task. [n.79]

Still less should we regard as a principle anything which is no more than a commonly accepted dogma, such as Nature abhors a vacuum, Nature does nothing in vain, and the such like. They are not known in themselves, they cannot be demonstrated from anything, and they are more often false than true.

But to return to definitions. The reason why I say that those [73] which have a cause and a way of coming into being should be defined in terms of their cause and way of coming into being, is as follows. The purpose of demonstration is scientific knowledge of the causes of things, and of how they come into being. But if it does not feature in the definitions, it cannot feature in the conclusion of the first syllogism derived from the definitions. And if it does not feature in the first conclusion, it cannot feature in any subsequent conclusion. Therefore there cannot ever be any scientific knowledge of it, which is inconsistent with the purpose and intention of the demonstrator.

6.14. The nature and definition of a definition.

Since, as I have just said, definitions are principles, or primary propositions, they are sequences of words; and since they are used to conjure up the idea of something in the learner’s mind, provided that the thing has been given a name, a definition can be nothing other than an explanation of the name through words. But if the name has been given to it by virtue of a compound concept, a definition is nothing other than the analysis of the name into its more universal parts — or example, when we define ‘human’ by saying that a human is rational, sentient, animated body. The names ‘animated body’, etc. are parts of the whole name ‘human’; and this is why definitions of this sort always consist of genus and differentia, so that the first is the differentia, and all the rest stand for the genus. But if a name is the most universal in its genus, its definition cannot consist in genus and differentia. So it must be made by any roundabout form of words which is best suited for explaining the force of the name. Again, it can happen, and often does happen, that merely combining genus and differentia is not enough to produce a definition. [74] For example, the expression ‘straight line’ contains genus and differentia, but it is not a definition, unless we think that a straight line has the definition a straight line is a straight line. However, if there were some single word which was different from these two but meant the same, then these two words would be the definition of the one word. From what has been said, it can be understood how definition itself is to be defined, namely that it is a proposition, of which the predicate is an analysis of the subject, when this is possible, and an explanation of it when this is not possible.

6.15. The properties of a definition.

The properties of a definition are the following:

1. A definition removes all equivocation, and hence the whole multitude of distinctions which are used by those who think that science can be acquired by arguing. For the nature of a definition is to define, that is, to determine the meaning of the name defined, and to separate it from every meaning other than that which is contained in the definition. Hence a single definition replaces all the distinctions which can be made concerning the thing defined.
   
   
2. A definition displays the universal notion of the thing defined, so that it is a sort of universal picture, not for the eyes, but for the mind. Just as someone who paints a person makes an image of that person, so someone who defines the word ‘human’ also makes a sort of image of what it is to be human.
   
   
3. There is no need to argue about whether definitions are to be accepted or not. Since it is the only business between teacher and student, if the student understands all the parts of what has been defined which have been analysed through definition, but still refuses to accept the definition, then the controversy stops there and then, since it is just the same [75] as if the pupil refused to learn. But if the student does not understand, then there is something inarguably wrong with the definition, since the nature of a definition consist in displaying the idea of a thing clearly. Principles are either known in themselves, or they are not principles.
   
   
4. In philosophy, definitions are prior to the names defined. This is because the teaching of philosophy begins with definitions, and it proceeds synthetically to scientific knowledge of the compound. Therefore, since definition is the explanation of the name of a compound through analysis, and the procedure goes from the results of analysis to the compound, definitions need to be understood before compound names. Indeed, once the names of the parts have been explained verbally, it is not necessary for the compound name to be composed of the names of the parts. For example, once the names ‘equilateral’, ‘quadrilateral’, and ‘rectangular’ were known, it was not necessary for geometry that the name ‘square’ should exist at all. In philosophy, defined names are used only for the sake of brevity.
   
   
5. Compound names can have different definitions in different parts of philosophy. For example ‘parabola’ and ‘hyperbola’ have different definitions in geometry and in rhetoric. [n.80] Definitions are established and used for a specific body of knowledge. So if in one part of philosophy, a definition suggests a particular name which seems suitable for expounding geometry more succinctly, it is equally reasonable that it should do the same in other parts of philosophy as well. The use of names is private and arbitrary, even when a number of people agree on a particular usage.
   
   
6. No name can be defined by means of just one word. This is because a single word [76] cannot provide an analysis of one or more words.
   
   
7. The name being defined should not re-appear in the definition. That which is defined is the whole compound; but the definition of the compound is its analysis into parts; and the whole cannot be a part of itself.

6.16. The nature of demonstration.

Any two definitions which can be combined into a syllogism produce a conclusion. Since it is derived from first principles, i.e. from definitions, the conclusion is said to be demonstrated; and the derivation or act of combination is called demonstration. Similarly, a syllogism is said to be a demonstration if one of its premises is a definition, and the other is a demonstrated conclusion; or if neither is a definition, but both have already been demonstrated — and so on.

So the definition of a demonstration will be as follows: A demonstration is a syllogism, or a sequence of syllogisms, derived from definitions of names all the way to the final conclusion. It follows from this that every valid piece of reasoning which begins from true principles is a true demonstration yielding scientific knowledge.

As for the etymology of the name ‘demonstration’, it is a literal translation of the Greek apodeixis. The Greeks used the name exclusively for reasoning in which they placed what was to be proved before the eyes, as it were, by drawing specific lines and figures. This is the literal meaning of apodeiknuein, or ‘to show’. [n.81] However, it seems that the reason why they confined the name to this kind of demonstration was because geometry was almost the only discipline which provided scope for such figures, and absolutely the only one in which there was precise reasoning resulting in scientific knowledge. They observed that every other discipline was full of controversy and rhetoric — [77] not because the truth which their practitioners laid claim to could not become apparent without geometrical figures, but because they had failed to establish valid starting-points for their reasoning. So there is no reason why there should not be valid demonstrations in any discipline whatever, provided that definitions are established right from the start.

6.17. The properties of demonstration, and the order in which things should be demonstrated.

The defining characteristics of methodical demonstration are:

1. That every sequence of reasoning is valid, i.e. in accordance with the syllogistic rules specified above.
   
   
2. That the premises of individual syllogisms have already been demonstrated, right back to primary definitions.
   
   
3. That, after the definitions have been arrived at, the procedure is for everything to be taught in accordance with the same method as it was discovered.

To amplify the last point, the first things to be demonstrated are those which are next to the absolutely universal definitions — and this comprises the part of philosophy which is called First Philosophy. Next, there is whatever can be demonstrated by means of motion in abstract — which comprises Geometry. After Geometry, there are those things which can be taught by means of perceptible action, i.e. pushing and pulling. Then one must move more specifically to the motion of invisible parts (or change), and to the study of the senses and of the imagination, and to the internal passions of animals. The passions of humans are of special importance, since they include the fundamental grounds of duty, or of political philosophy, which occupies the final place.

It is obvious that the order of all learning must be as above. What I have said should be taught last cannot be demonstrated unless what I have said should be taught first is already understood. The present Elements of Philosophy is the unique instance of this method. [78] It begins with the next chapter, and the method will be followed throughout the whole work.

6.18. Fallacies in demonstration.

In the previous chapter, I dealt with fallacies arising from the falsehood of premises and from their improper conjunction. There are two more which are exclusive to demonstrations, namely begging the question and false cause. These make you think that what was to be demonstrated has been demonstrated, when in fact it has not been demonstrated at all. Teachers sometimes fall victim to these fallacies, as well as inexperienced students.

Begging the question is when the conclusion to be proved is expressed in different words, and used instead of a definition, or the starting point of the demonstration. So the demonstration is circular, since the thing itself, or the effect, has taken the place of the cause of the thing being looked for. For example, suppose you want to demonstrate that the earth stays motionless at the centre of the universe. If you assume that the cause of this fact is gravity, and if you define gravity as the quality by virtue of which a heavy body tends towards the centre of the universe, then you are wasting your time. For what is in question is the cause of that quality’s being in the earth, and if you cite gravity as the cause, you are taking the thing itself for its own cause.

To illustrate the fallacy of false cause, I shall take a similar example from a certain treatise in which it was to be demonstrated that the earth moves. The author starts from the fact that, since the earth and the sun do not maintain the same relative position, necessarily one or the other must be in motion — which is true. Then he says that the vapours which the sun draws up from the earth and the sea must necessarily be in motion because of this upward motion — which is also true. Then he infers that this is the cause of winds — which must also be accepted as true. He then says that the water of the sea is moved by these winds, and that their motion makes the sea floor [79] revolve by a sort of whipping effect. Finally he concludes that the earth is necessarily in motion. However, this is a fallacy. If this wind were the cause of the earth’s original circular motion, and if the motion of the sun or the earth were the cause of this wind, then the motion of the sun or the earth would have to precede the wind. But if the earth was in motion before the wind arose, then the wind could not have been the cause of the earth’s revolution. But if the earth was at rest, and the sun was in motion, it is obvious that the earth could be at rest despite the existence of the wind. Consequently, the cause of the earth’s motion is not the one he put forward. Fallacies of this sort are very common among physicists, although there can hardly be a more complicated example than the one I have just given.

6.19. Why analytic geometry cannot be dealt with here.

It might be thought that this part of the book on method was the place to discuss the geometrical technique which is called ‘logistic’. This consists in assuming that what you want to know is true, and by reasoning from that assumption, either ending up with something known from which the truth of the assumption can be demonstrated, or with an impossibility, from which it follows that the assumption is false. But the technique cannot be explained here, since it can be understood and applied only by experts in geometry. Indeed, the more theorems individual geometricians have at their disposal, the more scope there is for logistic — so much so, that it is no essential difference between logistic and geometry itself.

The technique has three parts. The first is to discover that what is unknown is equal to something which is known (this is called an ‘equation’); but such an equation can only be discovered by those who have at their command the nature, properties, and transpositions of ratios; [80] the addition, subtraction, multiplication, and division of lines and surfaces; and the extraction of roots — which already requires advanced geometrical skills. The second part is to judge whether or not the truth or falsehood of the matter in question can be derived from the equation which has been discovered; and this requires yet more scientific knowledge. After the discovery of an equation which is suitable for resolving the problem, the third part is to solve the equation, so that its truth or falsehood is evident; and in difficult questions it cannot be done without knowledge of the nature of curved figures. But to have the nature and properties of curved figures at one’s command is the most advanced part of geometry. Besides, there does not happen to be any method for discovering equations, and people’s ability to discover them depends on their natural wit.

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