An Aristotelian Essay on Error

Things exist or come to be either by nature or by thought, and, in each case, either of necessity or for the most part or occasionally. Nature, if not impeded, acts always in the same way; but it may be impeded, and in that case it fails to so act. It is the same for thought, for at times man^[1] fails to attain the end posited by thought or fails by thinking falsely. At times man does not beget man but a monstrosity, and he does not always conclude rightly but makes mistakes. Whether the cause of error is matter or ignorance or some other agent need not be considered at present, but it is evident that error exists or comes to be, and in various ways. Further, we speak of error as being that which acts or thinks, but we also speak of it as being the effect of that which acts or thinks, or the habit or state of mind of the agent. Thus, false thinking is an error (hamartia), and to so think is to err or to commit an error (hamartanein); and, similarly, b0ad behavior or bad mixing of ingredients is an error, and to so behave or to so mix the ingredients is to err. Again, a two-headed calf as an error is an effect contrary to nature (hamartema), and so is a false proposition, which is caused by thinking.

Now, the failure in nature may be caused by something in the subject having that nature, or by something external to the subject. A seed failed to germinate because it was defective, or it failed because it was planted too deep; and a man failed to get to his meeting because he overslept, or because he was prevented. Leaving error by lifeless nature aside, let us discuss error in which thought participates—not every kind of error but only that kind which arises because of thought or from thought and hence that kind the cause of which is at least partly in the agent who thinks. For error caused by an external agent is called “misfortune” or “mishap,” and it is a mishap if the harm is small but a mis­ fortune if the harm is great; and the harm may be of the mind or of the body or of both. Deprivation of property, too, may be regarded as something harmful, for the deprived person feels such loss, and so too is the untimely loss of a child or other incidents of this sort.

From what has been said, it might appear that what is erroneous because of thought or from thought is or has a bad result, but what is right (which is the contrary of the erroneous) is or has a good result. But this is not always the case; sometimes what is erroneous results in something good, but by accident, and what is right results in some­ thing bad, also by accident. One may lose his way and not arrive at his destination, but he may escape the assassin who is waiting for him; and he may reason falsely but arrive at a true conclusion from false premises. It is evident, then, that (a) erroneous activities as such are bad and their effects, which are errors, are only by accident good, and that (b) right activities as such are good and their effects (successes) are only by accident bad.

Now systematic activities which require thought are of three kinds: theoretical, practical, and productive, and one may err in each of them, and in a number of ways; and the same applies to the effects of those activities. Scientifically, then, one may say that errors are of three kinds, as many as there are kinds of sciences with respect to aim; for theoretical sciences aim at truth, productive sciences aim at things produced, which should be good, and practical sciences aim at action, which should be right.^[2] So we may call these kinds of errors “theoretical,” “productive,” and “practical.” Errors may be unsystematic also, as we shall see later.

Generically taken, there are as many kinds of error as there are kinds of rightness; for error and rightness are contraries and corresponding to one contrary there is one and only one other contrary. Specifically, however, there are more kinds of error than kinds of rightness; for in many cases rightness is like a mean, and each mean lies between extremes, but there is more than one extreme. Corresponding to bravery there is cowardice and rashness and corresponding to generosity there is stinginess and also wastefulness. Further, there may be continuity between extremes, but there is only one mean; for the mean is like a line’s midpoint, and there is only one such point, but deviations from the mean are many, like the other points on the line. It is well said, then, that a man attains the mean in one way only, but he may fail to do so in many ways; for error partakes of the indefinite. Similar remarks seem to apply to activities of thinking; for one may think that a brave man is a coward, but he may also think that he is rash.

Logically taken, there are additional errors corresponding to rightness; for, besides errors by commission, there are errors by negation or omission. The contrary of acting rightly is acting erroneously; but not acting at all, too, may be an error, and this error is not a contrary but a contradictory of acting rightly; it contradicts right action. Similarly, one may harm a man who needs help, but he may also ignore the helpless man; and to do so is to contradict the help the man needs. Further, the contrary of “all men are mortal,” which is true, is “no man is mortal,” which is false; but “ten men are not mortal” and “half of men are not mortal,” too, are false, and these are not contraries of “all men are mortal” but contradict the true statement.

Universally, then, if A’s behavior is right and is opposed to B’s behavior, B’s behavior is contrary to that of A (and in more than one way) or not contrary but contradictory to that of A (also in more than one way).

Generically taken, there can be as many, or almost as many, kinds of theoretical errors as there are principles in a theoretical science, and those principles are: indefinable concepts, definitions, hypotheses, axioms, and reasoning.^[3] The axioms and hypotheses in a theoretical science, in its primary sense, are assumed to be true of necessity; and the definitions in that science are assumed to be of objects which exist or can exist. First, we shall consider a theoretical science in its primary sense. Let us assume here that a concept is either of a thing which cannot be defined, such as quantity, or of a thing which can be defined, such as a man or a triangle or virtue. We are using the term “definition” strictly for definable things which are indivisible with respect to essence and are not composites like a white man, and each of these things may be taken generically or specifically, e.g., it may be a man or an animal, a triangle or a polygon. Such a concept, then, is indivisible with respect to essence and cannot be true or false, for truth or falsity is attributed to a combination of two concepts. One may then raise the problem how there can be an error with respect to a concept, say the concept of a triangle or of a substance.

Since a concept, whether definable or indefinable, is of a thing which is indivisible with respect to its essence, the problem is not whether one errs in combining things, but whether one acquires or fails to acquire a concept at all; for, to combine concepts, the ability to do so erroneously or rightly presupposes the possession of concepts to be com­bined, whereas to acquire a concept, there is the problem whether one has or does not have the ability to do so. That ability is the intellect (or intuition, if you wish), and if it is lacking for some reason, one fails to acquire the concept; and it is evident that there exists such ability, otherwise theoretical knowledge would be impossible, for such knowl­edge is universal and is possible only by means of concepts which are universal.^[4] Now that ability may fail to be in a man either permanently or not permanently; and if not per­manently, it may not yet be developed or it may have been lost. Color-blindness is permanent, and a color-blinded person must fail if he tries to acquire the concept of redness or of greenness; a child may try to get the concept of quantity and fail, but the child may succeed later; and a man may lose an acquired concept because of injury or amnesia or some other reason, and that loss may be temporary or permanent.

Whether the failure to acquire a concept should or should not be regarded as an error depends on how error with respect to a concept is defined and not on fact. What is important, however, is the fact that success in acquiring each of two concepts required in science is presupposed, whether one succeeds or fails to combine those concepts rightly. Speaking analogically, however, one may say that acquiring a concept is to failing to acquire that concept as combining two concepts rightly is to combining those concepts erroneously; but acquiring and failing to acquire are contradictories, whereas combining rightly and combining erroneously are contraries. If, then, one wishes to regard failure to acquire a concept as an error, there will be, generically taken, as many kinds of theoretical errors as there are kinds of principles in a theoretical science, but if not, there will be almost as many.

We may now turn to error in a definition, for a definition seems to lie between an indefinable concept and a com­ position of concepts to which truth or falsity may apply. For a concept and the definition corresponding to that concept (this applies to concepts which have corresponding definitions) have the same meaning, yet a definition, which is a composite of concepts, is not true or false. The definition “a three-sided plane figure” is not true or false. But although definitions are neither true nor false, they are not just composites but certain kinds of composites; and since such composites are formed according to certain principles, those principles may be violated. Hence errors with respect to definition are possible. Some possibilities may be given. The parts of a definition must be ordered in one way only; but those parts may be ordered in many ways, and so error is possible.^[5] For example, “a three-sided plane figure” is a definition, but “a plane three-sided figure” is not a definition (or an erroneous definition, if you wish). Again, the parts of a definition must be proper to the category under which the defined thing lies, but one may err if he does not use such parts. For example, “a white man” cannot be a definition, for whiteness as a quality is not a proper differ­ entia of a man or of any substance. Again, one may omit certain required parts or may use superfluous parts in a composite which he regards as a definition. For example, one may regard “a three-sided quantity” or “an equilateral triangle with equal angles” as a definition; but these are not definitions. Again, one may regard as a definition a composite from which a contradiction follows, like the composite “a triangle with non-intersecting altitudes,” but the object signified by this expression cannot exist. It is evident from these cases that one may err with respect to definition.

A problem arises. One may be able to recognize things coming under a species and yet fail to give analytically their definitions; but then he does not know the things scientifically. Does he then have a concept of them? But in a theoretical science one should have the definitions. If not, then there is some error, for mere recognition is possible even through accidents; so if one does not have the definition, whether we regard him as having incomplete or con­ fused or accidental knowledge makes no difference, for theoretically he still errs. And if, according to Aristotle, each thing has a unique definition, one can understand why scientific knowledge is very difficult to possess,^[6] for pro­ceeding from the proper principles and seeking the causes through demonstration further add to the difficulties of knowing the right definitions.

One may err with respect to axioms also, for axioms are (a) indemonstrable combinations of terms, (b) necessarily true, and (c) necessary for demonstrated knowledge, and one may erroneously think that statements which are not such combinations are axioms. Such statements may be theorems, or the contraries of axioms, or the contradictories of axioms, or any false statements, or true but not necessary statements, or not proper to a science, or necessarily true and indemonstrable statements but not sufficiently universal to be axioms. Thus, certain Greek philosophers regarded as axioms such statements as “it is possible to be and not to be at the same time and in the same respect,” “all things are in a state of flux,” and “motion is impossible”; and when some modern mathematicians regard certain infinite series, such as 1 + .1 + .01 + .001 + etc., as having definite values, they must assume the false axiom that what is potential is actual.^[7]

Similar errors may be committed with respect to hypotheses, for a hypothesis is defined as a statement which is true and indemonstrable in a science, and a statement introduced as a hypothesis may not be true, or not indemonstrable, or not proper to the science, etc. What about a false hypothesis? It is often introduced, if it “works.” But if scientific knowledge is of that which is necessary and is arrived at through the cause, it cannot follow from a false hypothesis so such a hypothesis—if it is to be called “hypothesis” at all— is what Aristotle calls “positive ignorance” and is not a part of a science but is dialectical in scientific activity, and such activity is not a part of a science. Science in the main sense is demonstrated knowledge through proper and true and necessary principles, and knowledge is a quality but is neither an activity nor necessarily dialectical.

Errors committed when one tries to reason are of many kinds. Now, reasoning in logic takes the form of a syllo­gism, and in science the kind of syllogism used is called “demonstration.” A syllogism is a set of three statements, and two of these are called “premises,” but the third follows from the premises and is called “a conclusion.” The premises are posited as true, and the conclusion which follows must be true if the premises are true. A demonstration is a syllogism in a science, and the conclusion follows from the principles of that science through one or more syllogisms. It follows, then, that the conclusion of a demonstration is of necessity true, for the principles of it are of necessity true. The statements laid down as principles may be false, but this is another matter; and in such a case, one may think that he is demonstrating, but the syllogisms he is using are not demonstrations as these have been defined, or else, one may call them “false demonstrations.” Since in a demonstration a conclusion follows from premises through reasoning, error in a science may lie in the premises or in what is taken as a conclusion or in the reasoning, for the conclusion may be false, or it may not follow from the premises, or the premises may not be true, either both or just one of them. Further, there is the problem whether the conclusion is known through the cause, for the conclusion may be true and follow from true premises, but one may be mistaken as to the cause of the conclusion. An example may illustrate the point. The equality 2 + 2 = 4 is known by the mathematician; what is known by the mathematician is true; therefore, the equality 2 + 2 = 4 is true. It appears, then, that the equality 2 + 2 = 4 is true because it is known by the mathematician. But the equality is true not because the mathematician knows it, for it is true because of the nature of numbers, even if no mathematician exists. It is evident, then, that in a science many kinds of errors are possible in a syllogism used or in what appears to be a syllogism; so let us consider them more explicitly. But first, some definitions and abbreviations will be laid down.

A paralogism is defined as an expression which appears to reason from the premises to a conclusion but does not. A paralogism is sometimes called “a false syllogism” or “a false demonstration” or “false reasoning.” A theorem is defined as a statement in a science which is not a principle but a con­clusion which follows causally from principles through one or more demonstrations. Let us use “AB” as an abbreviation for “A is predicated of every B,” and “AeB” as an abbrevia­ tion for “A is predicated of no B.” We use the word “predi­ ca ted” in such a way that, if ‘A is predicated of B, AB is true. From logic, AC follows from AB and BC, and AeC fol­lows from AeB and BC. Also, AeC follows from BeA and BC, for AeB follows from BeA, and AeB and BC imply AeC. Again, AC and BC imply Ab, where “Ab” means that A is predicated of some B. Other syllogisms may be formed in the three figures, but they need not be exhausted here.

A premise in a demonstration is either a principle or a conclusion of another demonstration. If it is posited as a principle, the kinds of errors possible in such a premise have already been considered. If it is a conclusion or posited as a conclusion, the kinds of errors possible in such a premise are the same as those of a conclusion or what appears to be a conclusion, and so their discussion belongs to the discussion of errors with respect to a conclusion.

Universally considered, if P and Q are premises and R is a conclusion which follows from P and Q, and if a man concludes S from P and Q, where S does not follow from P and Q (it may even contradict R), then he concludes falsely; and even if S happens to be true, what he considers to be a demonstration is a paralogism. Thus AeC does not follow from AB and BeC; e.g., all men are animals, and no dog is a man, but it does not follow that no dog is an animal. Similarly, AB does not follow from AC and BC. Other kinds of paralogisms exist, but they need not be exhausted here.

If one does not conclude falsely, there may be error in the syllogism used because of error in the premises, and the conclusion in such cases may be true or may be false; but in these cases there is no scientific knowledge, for the cause of the conclusion is mistaken. Thus, if AB and BC are true but AeB is used as a premise, then AeC follows from AeB and BC, and AeC is false; if AB and BC are both false, the conclusion AC may be true or may be false; and if BeA and BC are true but BA and BeC are used as premises, the con­clusion AeC is true. Other cases arise, but they need not be considered here.

Errors committed in demonstrations which do not show the cause are hardly discussed in modern times; in fact, modern scientists are hardly aware of such errors, in spite of their importance. Modern mathematicians seem to touch upon this problem in some way when they speak of necessary and sufficient conditions, but their concern is technical and is not directed to the philosophical statement of the problem or to its solution. An example from geometry will illustrate the problem (see Figure 1).

Let ABC be a right triangle and PQ be parallel to CA. Then angles a and m are equal, for they are alternate interior. Similarly, n and m + b are alternate interior and hence equal; and since n is a right angle, m + b is equal to a right angle also Hence a + b = m + b = a right angle; and since c is a right angle, a + b + c = two right angles.

In the above demonstration we have used the fact that c is right, and so one might think that e’s equality to a right angle is necessary for the demonstration. But the fact that c is right is irrelevant and need not be used. So from the above demonstration one cannot know what exactly causes the sum a + b + c to be equal to two right angles. Moreover, the demonstration is not general, for it is limited to right triangles; but every kind of a triangle has the sum of its angles equal to two right angles. The general demonstration goes as follows (see Figure 2).

Let ABC be any triangle and ST be parallel to CB. Then p = c, for they are alternate interior angles. Simi­larly, q = b, for they are alternate interior angles. Hence a + q + p = a + b + c. But the sum a + q + p is equal to a straight angle or to two right angles. Hence the sum a + b + c is equal to two right angles.

It is evident, then, that the demonstration of the the­orem for the right triangle does not show exactly the cause and that the statement of the theorem about it lacks generality. The fact that the right triangle is right does not contribute to the fact that its angles are equal to two right angles, for its angles would be equal to two right angles even if it were not right, as in the case of a scalene triangle. Besides, the second demonstration is more general. The cause of the equality is just the triangularity. But both knowledge of the cause and maximum generality are important and necessary for properties in a causal demonstration, and they should be included if scientific knowledge is to be acquired and if error in such knowledge is to be avoided.

Another kind of error, almost similar to that in the preceding demonstration, may arise from premises which are true, whether of necessity or not; and the conclusion may or may not be of maximum generality. Thus, if D is the defini­tion of an object S, and P is a property of S, then one may conclude DS from DP and PS. But DS is indemonstrable, and P is not the cause of DS; on the contrary, D is the cause of PS. Again, the conclusion “the altitudes of a tri­angle are concurrent” is of necessity true, and it follows from (a) “the altitudes of a triangle are concurrent” is known by a geometer and (b) the fact that what is known by a geometer is of necessity true. But the concurrence of the altitudes is of necessity true not because it is known by a geometer but because follows from certain geometrical principles. If we change “a geometer” to “Einstein,” both premises will lack necessity; for Einstein is mortal, and then the premises may not be true.

One may raise the problem whether errors of a different kind are possible in coming to know particulars to which theoretical objects are applicable, for it appears that, although an attribute of a theoretical object is of necessity an attribute of an individual which is an instance of that object, a particular object is destructible and may not exist, whereas a theoretical statement is of necessity true and eternal. An example may be taken.

Let P be an individual and let it be assumed that it is a triangular wooden object. Further, let T be any triangle (universally taken), and A be an attribute of any triangle. If P is such as assumed, then the statement AP follows from the premises AT and TP. Since P is a particular object, AP is a particular fact, and, although the fact AT is necessary, AP is not necessary, for P may not exist. One kind of error that may arise, then, is with respect to modality; for one may believe that that which is not necessary is in fact necessary, or that that which is necessary is not necessary. By “modality” I mean the kind of connection between, for example, an attribute and the subject to which it belongs. Thus nine is necessarily and always a square number, a man who is sick is in fact sick but not of necessity nor always, and wood has the possibility of burning when it is not burning. So the three kinds of modalities are connections which are (1) necessary, (2) factual but not necessary, and (3) those with possibility. In a theoretical science, too, one may believe that that which is necessary is not necessary, and perhaps this kind of error, too, should be mentioned there; for many modern scientists and mathematicians make this error. But in a theoretical science there is nothing which may not be; so there can be no error in believing that what is necessary is not necessary. Again, the assumption that P is a triangle may be false, for it rests on the sensation of common sensibles. Such sensation, unlike that of proper sensibles (about which there is no error), may be erroneous, and triangles and all other quantities are common sensibles.^[8] We may add, error with respect to modality may occur not only in mere statements, but also in conclusions through syllogisms; for if the modalities of premises differ, one may err in the modality of the conclusion.

Whether the modalities concerning potentiality are only two or more than two is partly a matter of definition and partly a matter of fact. The expressions “it is possible” and “it may be” have different meanings even if they imply each other;^[9] and there are syllogisms about existing things qua just existing, and such things may not be necessary. Thus “A is possibly B” means that A merely has the potentiality of being B, or that most of the time it is B, and in this sense a piece of wood is potentially a box, or an acorn becomes an oak tree most of the time; but “A may be B” means that the assumption that A is actually B does not lead to a contra­ diction. The problem of modalities need not be discussed here. Aristotle considers it in his Propositions (De lnter­pretatione) and in his Prior Analytics.^[10] In general, then, one may say that error is possible in the modality of a premise or of a conclusion because of false reasoning.

A man may be able to give a verbal demonstration accurately and appear to be perfect in reasoning and causa­tion, but one may wonder whether this is sufficient for sci­entific knowledge; for the concepts in such knowledge may not be clearly possessed, and the same applies to the rela­tions between concepts and to reasoning. For example, one’s demonstration of the concurrence of the altitudes of a tri­angle may appear perfect, but would his concept of an alti­tude, which is a line, be clear? A line should be known scientifically and be conceived as a limit of a surface; and if one is not clear about this, would his scientific knowledge be clear, and if not, should one call this “scientific knowledge” at all? Knowledge, conviction, and other affections and qualities of the soul admit of variation of degree, whether some or all of them, and perhaps error with respect to such affections and qualities is possible.

Errors in theoretical sciences in the main sense have been sufficiently considered here; but there are theoretical sciences in a secondary sense, that is, sciences of things which exist or come to be for the most part, and many productive and practical sciences contain a theoretical part which is of this nature. It has already been pointed out that nature, if not impeded, exists or acts or comes to be always or necessarily in the same way; consequently, things according to nature—and attributes or properties of natural objects are such things—exist or come to be in the same way. But nature may be impeded, and so accidents may result.^[11] Consequently, there are theoretical sciences of things which exist or come to be for the most part, and hence there are causes, too, which exist or come to be for the most part. Thus, if S be a natural object., and A a demonstrable attribute or property which belongs to S for the most part, then the cause of A’s belonging to S will be for the most part and not of necessity. The kinds of errors possible in such a science, then, will be similar in most respects to those in a theoretical science in the main sense, and to these may be added also errors which arise from the modality indicated by the adjective “most.”

Since productive activities require both thinking and production, errors are possible with respect to thinking as well as with respect to production. Now thinking in a productive science is limited to that science qua a science, and the errors which may arise are the same as and perhaps more than those with respect to a theoretical science, whether in the main sense or in the secondary sense (i.e., for the most part); but errors with respect to production arise from the application of that science, or from the choice of materials to make products, or from the products made. Thus if a material is chosen to make rulers, there is the material, the rulers made, and the making of rulers from the material. The same applies to medicine; for there is the diagnosis of a sick man, the same man after being treated, and the treatment of that man. In all, then, errors in a productive science may arise from the following elements: the theoretical, the choice of materials to make a product, the making, and the product made. Since errors in the product made are caused by errors in the choice of materials or by errors because of lack of skill or by both kinds of errors, they need not be mentioned.

Errors arising with respect to the theoretical part, whether in the main or in the secondary sense, have already been considered. An engineer, for example, may err with respect to his knowledge of physics or of mathematics if he concludes falsely or uses a false premise to arrive at a conclusion. Similarly, a medical student qua a learner may have what we call “erroneous knowledge” of a premise or may conclude erroneously. It often happens, however, that a product requires for its preservation knowledge of destructive causes; but these causes may not have been considered in the making of that product. In constructing a suspension bridge, for example, the engineer may fail to consider certain geological causes which tend to destroy the bridge, such as wind forces or the nature of the terrain or the like; and in the construction of a house, the kinds of causes which tend to destroy it are even greater in number. Now some destructive causes can come under theory and can be learned, but others are particular or indefinite and so lie outside of theory. Wind velocities are subject to theory, and adequate knowledge of that theory by the engineer would have saved the Tacoma Narrows Bridge in Washington State from being destroyed. But an architect cannot know or foresee all the indefinite individual causes which may destroy a house, but which lie outside of theory. So, in some cases the destruction of a product made is caused, partly or wholly, by an error in the artist; in other cases, the cause is indefinite and no error should be attributed to the artist. But it is not always easy to determine whether it is the artist who made an error or not; for if the destructive causes which are theoretical come under many sciences, one may have to define a particular artist, e.g., an engineer, in such a way as to include knowledge of many sciences.

Errors with respect to that which is to be made may arise from the choice of that which is to be made into some­ thing. Now theoretical knowledge is universal, and the materials to be worked out are particulars;  and it is possible to err in thinking that a particular which is chosen to be worked out comes under the universal which is theoretically know. An engineer may have scientific knowledge of strength of materials and hence of the kind of material required to build a machine or an instrument; but he may err in his choice of the right material, and so the thing produced may not perform its function or may not perform it well. The same applies to the carpenter and to others of this sort. The cause of the error is mainly attributed to the nature of sensation or to inexperience with the materials to be chosen, but it may be due also to the limitations of supply of materials or to other adverse circumstances, like carelessness. Now sensation may be of proper sensibles (colors, sounds, odors, tangibles, flavors) or of common sensibles (numbers, magnitudes, motions). In the case of proper sensibles one cannot be mistaken, but he may be mis­ taken as to that (usually a substance) which underlies a proper sensible, and the properties which are sought in making the product are usually not attributes of proper sensibles but of the subjects which underlie those sensibles. There is no mistake as to the color seen, but there may be a mistake as to the substance which has that color; and a piece of wood may appear to be of a certain kind, but one may be mistaken about it. In the case of common sensibles a mistake is possible, especially in the case of magnitudes. Theoretically, for example, one deals with exact magnitudes; in practice, however, this is hardly possible, for perfect accuracy is unattainable, but the error is usually small. As for errors due to the limitations of supply or to adverse circumstances, the cause is external and is not attributed to the choice of materials; the materials may not be available, or they are available but difficult to attain or to use under certain conditions. If the right material is not available, the artist will knowingly choose, if at all, the best of what is available and hope that the product made will perform its function, but he will not be the primary cause of the error due to such choice; and if he is ordered to make the wrong choice, again he is not the primary cause of the error.

The primary error with respect to the making of a product arises from skill, or better, from the lack of it. We often speak of a bad doctor or a bad carpenter or a bad engineer, and what we mean is that the artist who is called “bad” lacks the skill necessary to make the product rightly, that is, to make the product as it should be made. Now if the term “skill” means the ability—an acquired habit—to make the right product, then the expression “lack of skill” may have two meanings; for it is possible for an artist not to have acquired the skill adequately, and it is also possible for him to have acquired the wrong habit. Whether a wrong habit should be called “wrong skill” or by some other term is a matter of language; but it is evident that inadequate habits and wrong habits in artists, if these are to be called “artists” at all, are distinct from art—i.e., right habits—and that both lead to errors in the making of a product. Lack of skill in either of the two senses, of course, is not the only cause of error in making a product; for there may be external causes also, as in the choice of wrong materials, and also accidental causes.

One may raise a problem with respect to intention; for an artist who has both knowledge and skill may intentionally choose the wrong materials or intentionally produce the wrong product. Does he then commit an error? If an artist is said to commit an error because of his lack of ability, then errors because of intention cannot be errors in productive sciences, and perhaps this is the position that should be taken; for we spoke of errors as existing in three kinds of sciences—theoretical, productive, and practical—and if duplication is to be avoided whenever possible, then errors because of intention should not be regarded as errors in productive sciences. Now a productive science must include in its definition a theoretical part; for skill in making a product is impossible if it is not acquired with knowledge of or in accordance with theory, and the artist must have knowledge of at least the fact, if not of the causal fact, as it is stated in the theory which is presupposed in production. Intention, on the other hand, is not a necessary part in production, just as it is not a necessary part in objects of theoretical activity; for intention is concerned with certain ends as ends in themselves, whereas production is concerned with what is useful or instrumental. The discussion of intentional errors, then, should belong to the practical sci­ences only.^[12]

Practical sciences are concerned with activities which are ends or means insofar as they are related to ends; so errors with respect to such activities are errors with respect to ends or with respect to means insofar as they are related to ends. Now in the productive sciences, too, there are ends, but they are qualified ends. For a chair produced by the carpenter is an end, but the chair is produced for a further end which is an end in itself; and a house produced by the architect is an end, but it is produced for comfort or some other such end. In practical sciences, on the other hand, the activities do not result in a product, for they are primarily ends in themselves and hence unqualified ends. A truth discovered by a scientist qua scientist, too, is not a product, unless one wishes to stretch the meaning of the term “product”; and listening to music or behaving at a party or being friendly to a good neighbor or facing the enemy in war is an activity which does not end in a product, except by accident, as in the case of hobbies. A banker may like to make chairs for the sake of just making them, regardless of what happens to those chairs; but in that case one may say that such making has two kinds of ends, a primary, which is an end in itself, and a secondary, which is instrumental. But even in such cases one may distinguish the two kinds of ends and treat each in the science in which it belongs. The kinds of errors in such activities, too, may be distinguished in a similar manner. If the chair produced is bad, the error committed may lie in the making of the chair or in the choice of the material, but if the production of the chair is considered as a hobby and so as an end in itself, that hobby may be overemphasized or chosen at the expense of other urgent or better ends, and the error committed comes under a practical science. In general, since men seek happiness, and since happiness is considered as the end of man, there are corresponding errors when one fails to attain happiness, whether wholly or partly, and such errors come under the practical sciences.

Happiness is defined as an activity of the soul in accordance with virtue throughout life;^[13] if, therefore, one fails to attain happiness, there must be failure with respect to one or more of the causes or elements in that activity, unless accidents intervene; for happiness is a whole and hence analyzable into parts. This is evident from the definition of man also, for he is a rational animal; and the form of man, which is his soul, has a thinking part and also other parts which are common to other animals. Accordingly, man’s practical activities are intellectual and ethical, and so are his virtues and vices; and since happiness is the best end of man, his various activities must be performed in accordance with the various virtues and in the right proportion, i.e., with prudence.

Now the failure of a man to attain happiness is caused partly by himself and partly by external agents. The abilities with which a man is born are not caused by the man himself, for they are inherited at birth, and so any deficien­cies in those abilities should be considered as errors caused not by the man himself but by an external agent, i.e., his father or mother, whether by that part of the latter’s nature which is nonrational or by the kind of life intentionally pur­sued. Such deficiencies, of course, will have an adverse effect on the man’s happiness. Thus, an imbecile or a moron can attain happiness only to a very limited degree. But a man whose abilities vary with respect to their excellence will, for the most part, become happier by developing his stronger abilities than by trying in vain to develop his weak abilities. A man with strong musical abilities and weak mathematical abilities will usually be better off pursuing music than pursuing mathematics. Thus, happiness in the highest sense is hardly attainable, and the extent of attain­ able happiness of a given individual depends partly on his inherited abilities. Leaving external causes of failure aside, then, let us turn to errors caused by an individual man in virtue of his own activities.

What is better is known by reference to what is best; for the better, relative to the worse, is said to be that which is nearer or closer to what is best. Further, one is more likely to succeed in attaining an end or doing so to a greater degree if he has better knowledge of that end. Hence actions which aim at some good are more likely to succeed or do so to a greater degree if the nature of that good is known than if it is not known. This principle is even more evident in productions. To say that one ruler is straighter than another ruler, one must know what straightness is, and such knowledge serves as an ideal according to which one is better equipped to make or judge straight rulers. Similarly, knowledge of the nature of happiness serves as an ideal according to which one is likely to be happier. Accordingly, one who wishes to be happy should study ethics, if this discipline is the science which considers the nature of happiness and the means necessary to attain happiness. Failure to do so, then, is an error (of omission) which lessens the degree to which happiness can be attained.

Since happiness is an activity in accordance with virtue, the possession of the virtues is necessary for happiness. First, then, one must perceive that virtue is a good; and if he does not, whether by himself or through another, then he commits a fundamental error. Second, the perception of virtue as a good is not sufficient; for virtue, being a habit, is not inherited but must be acquired, and this takes time and effort and is often or usually accompanied by pain, depending on the individual. The young tend to pursue the pleasures of the senses in excess, and if they come to know that such excess is harmful, they do not necessarily change. For the change from excess to moderation is attended by pain when immediate desires are not fulfilled; and some would rather continue with their incontinence in spite of their knowledge, and in so doing they err. Third, even if one checks such excesses and always acts in moderation, he may err if he is pained by so acting. For he is continent, i.e., pleased by acting moderately but pained by not fulfilling his desire. But happiness is a pleasant activity, whereas the activity of a continent man is partly painful, and the pain arises because of a bad desire. Thus, a virtuous man and an artist differ with respect to their dispositions towards their ends. A good artist will produce a good work of art even if he dislikes his work, but a virtuous man, whose aim is happiness, is usually pleased by acting virtuously.

Means and ends are relative to each other; for means bring about ends, and ends are brought about by means. So in ethical activities, too, ends require or are brought about by corresponding means. One may perceive a certain end as being good, but since that good is still to be brought about, certain means are necessary, and those means require right opinions and ability to act according to them. For means to be brought about are things which may or may not come to be, and the thinking faculty which is concerned with things which may or may not be or come to be is opinion. Now the ability to deliberate rightly concerning the means relative to any given end and act accordingly is shrewdness, and if the end perceived is good, that ability, if it is of the right means, is prudence, whether qualified or unqualified. Prudence is unqualified if the end is happiness but qualified if the end is a part of happiness or some other good, such as bravery or a generous action. Similarly, if the end is good, since means are relative to ends, the means themselves may be qualified or unqualified. But prudence does not choose just any means to achieve a good end; otherwise, a thief who steals to buy a car for his mother, too, would be prudent. If, however, the end chosen is bad, then shrewdness becomes unscrupulousness. So, since a good to be brought about requires the right or the rightly qualified means, it is evident that a prudent man in the unqualified sense is a man who has the ability to deliberate and act rightly concerning what is good or expedient for happiness. And since happiness includes all the virtues, it is also evi­dent that he who is completely prudent has also. all the other virtues and is a good man without qualification. Finally, since shrewdness is necessary for prudence and since folly is the contrary of prudence, folly (or imprudence) in a man is an error, and a man is deprived of happiness to the extent that he is foolish, even if he perceives the right ends.

Does the end justify the means, or better, does a good end justify a bad means? The usual answer is in the neg­ative, but it is simplistic. This problem, stated in a dif­ferent way, is the same as the problem whether qualified means should be used to achieve a good end. Now, we are often faced with a choice of alternatives, each of which is a mixture of good and bad,^[14] and since we must choose one of the alternatives, we cannot escape an element of badness. Consequently, we are faced with a dilemma, and a virtue is required to make the right choice. The safety of an inno­cent man running away from a murderer is a good end, but telling a lie is a bad means. Should a third party tell the murderer the truth and so help him commit murder? This case is not the same as the one in which one robs a bank to buy a car or to have the leisure to study philosophy. Where do we draw the line? This is like the question “Exactly how much should one give to be generous, or drink to be temperate?” The right decision is made by prudence, which is a virtue, and the wrong decision is made by folly, which is a vice and an error.

Errors coming under the three kinds of sciences have been discussed; but there are also errors of a minor nature. One may err in adding figures or spelling a word or bidding in a game, when under similar circumstances he usually acts rightly; and such errors are accidental and very frequent. The harm caused by such errors is usually negligible, but sometimes it is great; for one may fail to see the sign and cause a major accident, or one may curse an annoying stranger and be shot. Other errors of a somewhat minor nature, such as faults or failings, usually have little effect but sometimes are tragic. One may be too ready to be generous, or too truthful, or too proud, or credulous and trusting, like Othello in Shakespeare’s play, and the result may be a tragedy, especially if the agent or patient is a better than average person. Such errors are habits or acts caused by habits, and perhaps their discussion belongs to a practical science. The construction of good dramatic tragedies, too, depends on such minor errors; but its discussion is more proper to poetics, which is a productive science.