an our intuitive conception, sequences that actually are random appearas if they are nonrandom. For example, the average basketball playermakes about 50 percent of their shots, similar to the probability of gettingheads. Thus, there is a reasonably good chance of making four, five, oreven six shots in a row if 20 shots are taken in a game. In other words,chance favors the appearance of what sports fans call a hot-hand,!” whichis, in fact, nothing more than a streak typical of a random sequence.
The erroneous notion that random processes should alternate moreand streak less is responsible for two false perceptions: (1) the cluster-ing illusion, and (2) the gambler’s fallacy. In this context, the term clus-ter refers to a clump, either in time or space, of similar events. A clusterof similar outcomes in a random time series gives the illusion of a trendthat has momentum and this creates the false expectation that the trendshould persist. The gambler’s fallacy is the equally false expectation thata cluster of similar outcomes should not occur, and when one does, itgives rise to the false expectation that a reversal is due. The gambler’s fal-lacy is exemplified by a person who thinks a tail is more likely after astring of heads.
It is an observer’s prior beliefs about a process that determineswhether he will fall prey to the clustering illusion or the gambler’s fal-lacy. Suppose a person is observing a process that is, in fact, random butdoes not realize that it is. That person will tend to fall prey to the clus-tering illusion if they hold a prior belief that the process is nonrandomand that it should manifest trends. Sooner or later a streak occurs, and100 > METHODOLOGICAL, PSYCHOLOGICAL, PHILOSOPHICAL, STATISTICAL FOUNDATIONS
the prior belief is confirmed. The observer has fallen prey to the cluster-ing illusion.
In contrast, if the observer has a prior belief that the process is ran-dom, it is more likely that they will fall prey to the gambler’s fallacy.Sooner or later a streak occurs, for example four heads in a row, which isthen followed by a tail. Although this would be quite normal in a randomprocess, the appearance of the tail reinforces the false belief that a tailwas due. Therefore, when a process is truly random both the observerwho thinks the process is nonrandom and believes that trends (clusters)should occur and the observer who thinks the process is random and thatthe trends should reverse will have their beliefs rewarded. In truth, whena process is random both observers’ expectations are false. Randomwalks have no memory, and prior outcomes have no effect on subsequentevents.
The clustering illusion can also occur in a spatial context. The percep-tion of illusory shapes in random data is simply another manifestation of afalse expectation about randomness. The false expectation is that randomdata should not display any hint of organization or form. Any departurefrom this expectation is interpreted, falsely, as a sign of a nonrandomprocess at work. A case in which illusory spatial patterns in random dataencouraged the formation of erroneous perceptions occurred during theWorld War II bombing of London by German V-1 and V-2 missiles." Thenewspapers ran maps of missile impact sites, and readers had the immedi-ate perception that the strikes were clustered. This gave rise to an equallyfalse, after-the-fact interpretation that impact patterns were evidence ofan effort by the Germans to avoid hitting certain parts of London, which inturn spawned fallacious causal reasoning. Londoners came to believe thatthese areas were spared V-2 attacks because they housed German spies.However, a formal analysis of the missile impact sites showed that theywere entirely consistent with a random pattern.
A more recent example of illusory spatial clustering that fosterederroneous causal reasoning was the so-called cancer-cluster hysteria inCalifornia. People became alarmed if the number of diagnosed cases ofcancer of a particular type (e.g., lung cancer caused by asbestos) was farabove average in their community. It turns out that clusters can occur bychance. What is not apparent to the statistically unsophisticated is this:Given 5,000 census tracts in California and 80 possible environmental can-cers, there will be some tracts in which the number of cancer cases will befar above average simply due to chance. In some cases, such clusters re-ally are attributable to environmental toxins, but not always and notnearly as often as intuition would suggest.
This brings us back to TA and the appearance of orderly patterns likedouble tops, head-and-shoulders bottoms, and so forth. The occurrence ofThe Illusory Validity of Subjective Technical Analysis 101
such shapes is not consistent with an intuitive notion of data produced bya random process. Such data is erroneously presumed to be completelyhaphazard and shapeless, so, we jump to the conclusion the patterns mustbe the by-product of a nonrandom process that is not only amenable to vi-sual analysis but that the patterns themselves are useful for making pre-dictions. As Roberts showed, random walks can easily trace the patternsthat subjective technicians hold so dear.
In summary, people have a hard time telling when a set of data is ran-dom or not. Because the mind is predisposed to the perception of orderand adept at inventing stories that explain why that order exists, it is notat all mysterious that the pioneers of TA would find patterns and trendsin price charts and then invent theories about why such patterns shouldoccur. Methods more rigorous than visual analysis and intuition areneeded to find the exploitable order that may exist in financial marketfluctuations.
THE ANTIDOTE TO ILLUSORY KNOWLEDGE:THE SCIENTIFIC METHOD
 
This chapter examined many ways we can be fooled into adopting erro-neous knowledge. The best antidote ever invented for this problem is thescientific method, the subject of the next chapter.The ScientificMethod and
TechnicalAnalysis
 
 
practiced, much of TA is a body of dogma and myth, founded on faithand anecdote. This is a consequence of the informal, intuitive meth-ods used by its practitioners to discover patterns with predictive power.As a discipline, TA suffers because it is practiced without discipline.Adopting a rigorous scientific approach would solve this problem.The scientific method is not a cookbook procedure that automatesknowledge discovery. Rather it is “a set of methods designed to describeand interpret observed or inferred phenomena, past or present aimed atbuilding a testable body of knowledge open to rejection or confirmation.In other words, (it) is a specific way of analyzing information with thegoal of testing claims.”! This chapter summarizes its logical and philo-sophical foundations and discusses the implications of its adoption byTA practitioners.
[ve central problem is erroneous knowledge. As it is traditionally
THE MOST IMPORTANT KNOWLEDGE OF ALL:A METHOD TO GET MORE
 
“Of all the kinds of knowledge that the West has given to the world, themost valuable is the scientific method, a set of procedures for acquiringnew knowledge. It was invented by a series of European thinkers fromabout 1550 to 1700.” Compared to informal approaches it is unsurpassedin its ability to separate fact from falsehood. The dramatic increase in our
103104 METHODOLOGICAL, PSYCHOLOGICAL, PHILOSOPHICAL, STATISTICAL FOUNDATIONS
understanding of and control over the natural world over the last 400years attests to the power of the scientific method.
The method's rigor protects us from the frailties of mind, which oftenimpair what we learn from experience using less formal methods. Al-though informal knowledge acquisition works well for many of the obvi-ous truths of daily living, sometimes what seems obvious is not true. Itwas obvious to the ancients that the sun revolved around the earth. It tookscience to show this was false. Informal observation and intuitive infer-ence are especially prone to failure when phenomena are complex orhighly random. Financial market behavior displays both.
Historically, TA has not been practiced in a scientific manner, but thisis now changing. In academia and the business world, a new breed ofpractitioners, known as quants, have been adopting a scientific approach.Indeed, some of the most successful hedge funds are using strategies thatcould be called scientific TA.
Unsurprisingly, many traditional TA practitioners have resisted thischange. Vested interests and habitual ways of thinking are hard to aban-don. No doubt there was opposition when folk medicine evolved intomodern medicine, when alchemy progressed into chemistry, and whenastrology advanced into the science of astronomy. Rancor between tradi-tional and scientific practitioners is to be expected. However, if history isany guide, traditional TA will, in the end, be marginalized. Astrologers, al-chemists, and witch doctors still practice, but they are no longer takenseriously.
THE LEGACY OF GREEK SCIENCE: A MIXED BLESSING
 
The Greeks were the first to make an effort at being scientific, thoughtheir legacy proved to be a mixed blessing. On the positive side of theledger was the invention of logic by Aristotle. The formal reasoning proce-dures he developed remain a pillar of today’s scientific method.
On the negative side were his faulty theories of matter and motion. In-stead of being generalized from prior observations and tested againstfreshly observed facts, as is the practice in modern science, his theorieswere deduced from metaphysical principles. When observations con-flicted with theory, Aristotle and his disciples were prone to bending thefacts rather than altering or abandoning the theory. Modern science doesthe opposite.
Aristotle ultimately realized that deductive logic was insufficient forlearning about the world. He saw the need for an empirical approachbased on inductive logic—observation followed by generalization. Its in-The Scientific Method and Technical Analysis 105
vention was his most significant contribution to science. However, hefailed in the application of his own invention. At his institution of higherlearning, the famed Lyceum in Athens, Aristotle and his students mademeticulous observations on a wide range of natural phenomena. Unfortu-nately, the inferences they drew from these facts were biased by Aris-totelian dogma and often based on inadequate evidence.’ There was toomuch theorizing from too little evidence. When facts contradicted favoredfirst principles, Aristotle would contort the facts to conserve the principle.
Ultimately the Aristotelian legacy would prove to be an obstruction toscientific progress. Because his authority was so great, his flawed theorieswere transmitted as unquestioned dogma through the next 2,000 years.This hindered the growth of scientific knowledge, or at least the sort ofknowledge that we now characterize as scientific.’ In a like manner, theteachings of TA’s pioneers like Dow, Schabacker, Elliott, and Gann havebeen passed along unquestioned and untested. Just as there is no room fordogma in science, neither should there be in TA.
THE BIRTH OF THE SCIENTIFIC REVOLUTION
 
“Science was the major discovery, or invention, of the seventeenth cen-tury. Men of that time learned—and it was a very revolutionary discov-ery—how to measure, explain, and manipulate natural phenomena in away that we call scientific. Since the seventeenth century, science hasprogressed a great deal and has discovered many truths, and it has con-ferred many benefits that the seventeenth century did not know, but ithas not found a new way to discover natural truths. For this reason, theseventeenth century is possibly the most important century in humanhistory.”®
The revolution began in Western Europe around 1500 in an atmos-phere of intellectual stagnation. At that time, all knowledge was based onauthoritarian pronouncements rather than observed facts. The doctrinesof the Roman Church and the dogma of Greek science were taken as lit-eral truths. On Earth, objects were assumed to be governed by Aris-totelian physics. In the heavens, the laws invented by the Greekastronomer Ptolemy and later endorsed by the Church were thought torule. The Ptolemaic system held that the earth was the center of the uni-verse and that the sun, stars, and planets orbited about it. To the casualobserver, the facts seemed to agree with the Church’s orthodox theory.
Everyone was happy until people began to notice facts that con-flicted with these accepted truths. Artillerymen observed that projectileshurled by catapults and shot from cannons did not fly in conformity with106 METHODOLOGICAL, PSYCHOLOGICAL, PHILOSOPHICAL, STATISTICAL FOUNDATIONS
Aristotle’s theory of motion (Figure 3.1). The objects were repeatedly ob-served to follow arced paths—a distinct departure from the trajectorypredicted by Greek theory, which would have had them fall directly toearth as soon as they left the apparatus. Either the theory was wrong orthe solders were deceived by their senses. The notion of testing the valid-ity of a theory by comparing its predictions with subsequent observationsis fundamental to the modern scientific method. This was an early step inthat direction.
Also, at that time, observations of the heavens began to collide withthe Church’s theory of an Earth-centered universe. Increasingly accurateastronomical measurements revealed that planets did not move as the the-ory said they should. For a time, bewildered astronomers were able topatch up the Church’s theory to make it agree with observed planetarypaths. As discordant observations occurred, new assumptions were addedto the theory, in the form of smaller orbits revolving about a planet’s prin-cipal orbit. These ad hoc fixes, called epicycles, permitted the theory toaccount for the troublesome observations. For example, epicycles wereable to explain why planets were sometimes seen to move backwards(retrograde motion) rather than follow a continuous path across the sky.Over time, a succession of epicycle fixes transformed the fundamentallyincorrect theory of an Earth-centered universe into an unwieldy mon-strosity of complexity with epicycles upon smaller epicycles upon evensmaller epicycles.
A landmark in scientific history took place when the telescope ofGalileo Galilei (1564-1642) showed that four moons circled the planetJupiter. This observation contradicted Church orthodoxy that all celestialobjects must revolve around the Earth. Galileo’s findings would havecalled for the rejection of deeply held beliefs and the destruction of theChurch’s view of reality. Religious authorities were not about to face thesefacts. Though Galileo had originally been given permission by the Churchto publish his findings, it subsequently withdrew the permission and
Path wer Observed
Path PredictedbyAristotelian Physics
 
FIGURE 3.1 Prediction versus observation.The Scientific Method and Technical Analysis 107
found him guilty ex post facto. As punishment, he was forced to give upastronomy and live out his days under house arrest."
Eventually, the Church’s theory of the heavens was replaced by the farsimpler and more correct Copernican model. It placed the sun at the cen-ter of the universe and managed to explain astronomical observationswith far fewer assumptions. Today we know that the sun is not the centerof the universe, but at the time the Copernican model represented a trueincrease in man’s knowledge of the heavens.
FAITH IN OBJECTIVE REALITY ANDOBJECTIVE OBSERVATIONS
 
Science makes a fundamental assumption about the nature of reality;there is an objective reality that exists outside and independent of thosewho observe it, and this reality is the source of the observer's sensory im-pressions. This faith is the basis of science’s emphasis on observation. It isproperly characterized as a faith because there is no experiment or logicthat can prove the existence of an objective reality. For example, I cannotprove that my perception of a red traffic signal is caused by a light that ex-ists outside of myself rather than by something that arose entirely withinmy own mind.
One might ask why we should make a big deal about a fact that seemsso obvious to common sense. Everyone can see there is a world out there.However, in the eyes of science this issue is a mountain and not a mole-hill, and it points to an important difference between knowing scientifi-cally and knowing intuitively. Science does not accept something as truesimply because it seems to be so. The history of science has shown re-peatedly that the obvious is not necessarily true. Science assumes thetruth of an independent objective reality, not because it is self-evident, butbecause it is consistent with a principle that shapes much of the scientificenterprise—the principle of simplicity.
The principle says simpler is better. Thus, when judging which ofseveral theories is most likely to be true, when all theories are equallygood at fitting a set of observed facts, the principle of simplicity urges usto accept the simplest theory. This is the theory that invokes the fewestand least complicated assumptions. The principle of simplicity, alsoknown as Okaum’s Razor, tells us to cut away a theory’s excess com-plexity. The Copernican model of the universe was preferable to theChurch’s model because it replaced a complex arrangement of epicycleswith one orbit for each planet. In a like manner, if a segment of markethistory can be explained either as a random walk, which assumes very108 METHODOLOGICAL, PSYCHOLOGICAL, PHILOSOPHICAL, STATISTICAL FOUNDATIONS
little, or as an Elliott wave pattern that assumes waves embedded withinwaves, golden ratios, Fibonacci sequences, and a host of other complex-ities, the random walk is the preferred explanation. That is, unless theElliott Wave Principle is able to make more accurate predictions thanthe random-walk theory.
Assuming the existence of an external reality simplifies mattersgreatly. To do otherwise would require a far more complex set of assump-tions to explain why two people, observing the same phenomenon, willcome away with generally the same impression. Explaining why I seeother cars stopping when I see the traffic signal turning red is simple if Iassume that there really is a traffic light out there. However, without thatassumption, many more complicated assumptions would be required toexplain why other motorists stop when I do.
As a consequence of its faith in an objective reality, science holdsthat objective and subjective perceptions are essentially different. Myobjective observation of a red traffic signal and my subjective experi-ence of being annoyed because it will make me late for work are not thesame. Objective observations can be shared with and confirmed by otherobservers. For this reason, objective observations lend themselves tothe establishment of knowledge that can be shared with and confirmedby others. Subjective thoughts, interpretations, and feelings cannot, andthis flaw alone is sufficient to disqualify subjective TA as legitimateknowledge.
THE NATURE OF SCIENTIFIC KNOWLEDGE
 
Albert Einstein once said; “One thing I have learned in a long life: that allour science, measured against reality is primitive and childlike—and yet itis the most precious thing we have.” Scientific knowledge is differentthan wisdom gained by other modes of inquiry such as common sense,faith, authority, and intuition. These differences, which account for sci-ence’s higher reliability, are considered in this section.
Scientific Knowledge Is Objective
Science strives for maximum objectivity by confining itself exclusively tofacts about the world out there, although it is understood that perfectlyobjective knowledge is never attainable. This eliminates from considera-tion subjective assessments that are inherently private and accessible byonly one person. Inner thoughts and emotive states cannot be shared ac-The Scientific Method and Technical Analysis 109
curately with others, even when that is the intent of an artist, poet, writer,or composer. In Naked Lunch, William Burroughs attempts to convey hispersonal experience of heroin. However, I will never know his experienceand may take away from those passages something quite different thanBurroughs’s experience or that of someone else reading it. Scientificknowledge is, therefore, public in the sense that it can be shared with andverified by as many people as possible. This promotes maximum possibleagreement among independent observers.
Scientific knowledge is empirical or observation based. In this wayit differs from mathematical and logical propositions that are derivedfrom and consistent with a set of axioms but need not refer to theexternal world or be confirmed by observation. For example, thePythagorean Theorem tells us that the squared length of the hypotenuseof a right triangle, c, is equal to the sum of the squares of the other twosides a and b or
CH=ae+h
However, this truth was not derived by studying thousands of exam-ples of right triangles and generalizing from those many observations.Rather, it is derived from a set of accepted mathematical postulates.
Scientific Knowledge Is Quantitative
The notion that the world is best understood when described in quanti-tative terms originated with the Greek mathematician Pythagoras [569B.c.-approx. 475 B.c.]. It was his contention that both the world andthe mind are essentially mathematical. The importance science placeson quantification cannot be overemphasized. “Wherever mankind hasbeen able to measure things, which means transform or reduce them tonumbers, it has indeed made great progress in understanding them andcontrolling them. Where human beings have failed to find a way to mea-sure, they have been much less successful, which partly explains thefailure of psychology, economics, and literary criticism to acquire thestatus of science.”*
Observations must be reduced to numbers if they are to be analyzedin a rational and rigorous fashion. Quantification makes it possible to ap-ply the powerful tool of statistical analysis. “Most scientists would saythat if you cannot describe what you are doing in mathematical terms, youare not doing science.”* Quantification is the best way to ensure the objec-tivity of knowledge and to maximize its ability to be shared with andtested by all qualified practitioners.£10 > METHODOLOGICAL, PSYCHOLOGICAL, PHILOSOPHICAL, STATISTICAL FOUNDATIONS
The Purpose of Science: Explanationand Prediction
The goal of science is the discovery of rules that predict new observationsand theories that explain previous observations. Predictive rules, often re-ferred to as scientific laws, are statements about recurring process, suchas ‘event A tends to predict event B,’ but laws don’t try to explain why thishappens.
Explanatory theories go further than predictive rules by telling uswhy it is that B tends to follow A, rather than simply telling us that it does.Chapter 7 will describe some theories advanced by the field of behavioralfinance that attempt to explain why the behavior of financial markets is, attimes, nonrandom. These theories give hope to TA and may explain whycertain methods of TA can work.
Scientific laws and theories differ with respect to their generality. Themost prized are the most general—that is, they predict and/or explain thewidest range of phenomena. A TA rule that is effective on all markets andall time scales would have higher scientific stature than one that worksonly on copper futures on hourly data.
Laws also differ with respect to their predictive power. Those that de-pict the most consistent relationships are the most valuable. All otherthings being equal, a TA rule that is successful 52 percent of the time isless valuable than one that works 70 percent of the time.
The most important type of scientific law is the functional relation-ship. It summarizes a set of observations in the form of an equation. Theequation describes how a variable that we wish to predict (dependentvariable) typically denoted by the letter Y, is a function of (i.e., dependenton) one or more other variables called predictors, usually designated bythe letter X. This is illustrated as
Y= F(X)
Typically the values of the predictors are known, but the value of thedependent variable is not. In many applications, this is because the depen-dent variable Y refers to a future outcome, whereas the X variables referto values that are currently known. Once a functional relationship hasbeen derived, it is possible to predict values for the dependent variable byplugging in known values of the predictor variables.
Functional relationships can be derived in two ways. They can be de-duced from explanatory theories or they can be estimated (induced) fromhistorical data by function fitting (e.g., regression analysis). Currently, TAis primarily constrained to the latter because theories of TA are just nowbeing formulated (see Chapter 7).The Scientific Method and Technical Analysis ait
THE ROLE OF LOGIC IN SCIENCE
 
Scientific knowledge commands respect, in part because its conclusionsare based on logic. By relying on logic and empirical evidence to justify itsconclusions, science avoids two of the common fallacies that contaminateinformal reasoning: appeals to authority and appeals to tradition. An ap-peal to authority offers as proof the statement of a purportedly knowl-edgeable person. An appeal to tradition offers a long-standing way ofdoing things as proof.
To its detriment, much of popular TA is justified on grounds of tradi-tion or authority rather than formal logic and objective evidence. In manyinstances, current authorities merely quote prior authorities who, in turn,quote yet earlier experts and so on back to an original source whoseknowledge was primarily intuitive. Thus the fallacies of authority and tra-dition are mutually reinforcing.
The First Rule of Logic: Consistency
Aristotle (884-322 B.c.) is credited with the invention of formal logic,which evolved from geometry. The Egyptians had been making accuratemeasurements of lines and angles and calculating areas for over two thou-sand years, but it was the “Greeks who extended these basic notions andtransformed them into a compelling system of irrefutable conclusions de-rived from mathematical definitions (axioms).”!°
Formal logic is the branch of mathematics concerned with the laws ofcorrect reasoning that are used to formulate and evaluate the validity ofarguments. In contrast to informal inference, if the rules of formal logicare followed, a true conclusion is guaranteed.
The most fundamental principle of formal logic is the rule of consis-tency. It is expressed in two laws: the Law of the Excluded Middle and theLaw of Noncontradiction. “The law of the excluded middle requires that athing must either possess or lack a given attribute. There is no middle al-ternative. Or said differently, the middle ground is excluded.”!! A state-ment is either true or false. It cannot be both. However, the law is onlyproperly applied to situations that are binary and is easily misapplied tosituations that are not truly two-state.
“Closely related to the law of the excluded middle is the law of non-contradiction. It tells us that a thing cannot both be and not be at the sametime.” A statement cannot be true and not true at the same time. An ar-gument that allows for its conclusion to be true and not true at the sametime is said to be a self-contradictory.
As will be shown in subsequent sections, these laws of logic areused to great effect in science. Although observed evidence, such as the112 METHODOLOGICAL, PSYCHOLOGICAL, PHILOSOPHICAL, STATISTICAL FOUNDATIONS
profitable back test of a TA rule, cannot logically prove that the rule haspredictive power, that same evidence can be used to logically disprove(contradict) the assertion that the rule is devoid of predictive power. Bythe Law of Noncontradiction, this indirectly proves that the rule does pos-sess predictive power. This method of proving empirical laws, called themethod of indirect proof or proof by contradiction, is the logical basis ofthe scientific method.
Propositions and Arguments
Logical inference takes two distinct forms: deduction and induction. Wewill consider each separately and then see how they are used together inthe logical framework of modern science, the hypothetico-deductivemethod. However, before considering these forms of inference some defi-nitions are in order.
e Proposition: a declarative statement that is either true or false some-times referred to as a claim. For example, the statement The head-and-shoulder pattern has more predictive power than a randomsignal is a proposition. A proposition differs from other kinds ofstatements that do not possess the attribute of truth of falsity such asexclamations, commands, and questions. Therefore, only proposi-tions may be affirmed or denied.
e Argument: a group of propositions, one of which is referred to as theconclusion, which is claimed to follow logically from the other propo-sitions, called premises. Thus, an argument asserts that its premisesprovide the evidence to establish the truth of its conclusion.
Deductive Logic
As mentioned earlier, the there are two forms of logic, deductive andinductive. This section considers deductive logic; the next considersinductive.
Categorical Syllogisms. A deductive argument is one whose premisesare claimed to provide conclusive, irrefutable evidence for the truth of itsconclusion. A common form of deductive argument is the categorical syl-logism. It is comprised of two premises and a conclusion. It is so namedbecause it deals with logical relations between categories. It begins with apremise that states a general truth about a category, for example All hu-mans are mortal, and ends with a conclusion that states a truth about aspecific instance, for example Socrates is mortal.The Scientific Method and Technical Analysis 113
Premise 1: All humans are mortal.Premise 2: Socrates is a human.Therefore: Socrates is mortal.
Notice that the arguments first premise establishes a relationship be-tween two categories, humans and mortals: All humans are mortal. Thesecond premise makes a statement about a particular individual memberof the first category: Socrates is a human. This forces the conclusionsthat this individual must also be a member of the second category:Socrates is mortal.
The general form of a categorical syllogism is as follows:
Premise 1: All members of category A are members of category B.Premise 2: X is a member of category A.Therefore: X is a member of category B.
Deductive logic has one especially attractive attribute—certainty. Aconclusion arrived at by deduction is true with complete certainty, butthis is so if and only if two conditions are met: the premises of the argu-ment are true and the argument has valid form. If either condition is lack-ing, the conclusion is false with complete certainty. Therefore, a validargument is defined as one whose conclusion must be true if its premisesare true. Or, said differently, it is impossible for a valid argument to havetrue premises and a false conclusion.
In summary, conclusions arrived at by deduction are either true or false.If either valid form or true premises are lacking, then the conclusion is false.If both are present, the conclusion is true. There is no middle ground.
It is important to note that truth and validity are two distinct proper-ties. Truth, and its opposite, falsity, are properties that pertain to an indi-vidual proposition. A proposition is true if it conforms to fact. Becausepremises and conclusions are both propositions, they are aptly character-ized as either true or false. The premise All pigs can fly is false. Thepremise Socrates is a man is true as is the conclusion Socrates is mortal.
Validity is a property that pertains to the form of an argument. Inother words validity refers to the logical relationships between the propo-sitions comprising the argument. Validity or lack thereof describes thecorrectness of the logical inference linking the premises to the conclu-sion, but validity makes no reference to the factual truth of the argument’spremises or conclusion. An argument is said to be valid if, when itspremises are true, its conclusion must also be true.
However, an argument can be valid even if is composed of falsepropositions so long as the logical connections between the propositions$14 METHODOLOGICAL, PSYCHOLOGICAL, PHILOSOPHICAL, STATISTICAL FOUNDATIONS
 
FIGURE 3.2 Euler circles.
are sound. The categorical syllogism that follows has valid form becauseits conclusion is logically compelled by its premises, yet its premises andconclusion are clearly untrue.
All humans are immortal.Socrates is a human.Therefore, Socrates is immortal.
Because validity has nothing to do with matters of fact, validity canbest be demonstrated with arguments or diagrams of arguments, calledEuler circles, which make no factual references whatsoever. In a Euler di-agram, the set of elements comprising a category is represented by a cir-cle. To show that one category, such as sports cars, is a subset of the moregeneral category—cars in general—the circle representing sports cars re-sides within the larger circle representing cars. See Figure 3.2.
Figure 