3.3 makes clear why argument 1 is valid but argument 2 is not.Argument 1 is valid because its conclusion, X is a B, follows necessarilyfrom (i.e., is compelled by) its premises. However, Argument 2 is not validbecause it conclusion, X is an A, is not logically compelled by itspremises. X may belong to category A but not necessarily. The Euler dia-grams portray validity more forcefully than the argument itself becausethe argument alone requires some thinking.
Argument 1
All A’s are B's.
Xis ana.Therefore, X is a B.The Scientific Method and Technical Analysis 415
Argument 1 Argument 2Valid InvalidAll A's are B's. All A's are B's.XisanA. XisaB.Therefore X is a B. Therefore X is an A.
         
Category B
Category B
Category A
X
 
FIGURE 3.3 Valid and invalid categorical syllogisms.
Argument 2
All A’s are B's.XisaB.
Therefore, X is an A.
Conditional Syilogisms: The Logic of Scientific Arguments.Another form of deductive argument, and the one that is central to scien-tific reasoning, is the conditional syllogism. It is the logical basis for es-tablishing the discovery of new knowledge.
Like the categorical syllogism, the conditional syllogism is also com-posed of three propositions: two premises and a conclusion. It is sonamed because its first premise is a conditional proposition.
A conditional proposition is a compound statement that combinestwo simple propositions using the words [f—then. The proposition follow-ing if is referred to as the antecedent clause and the proposition followingthen is referred to as the consequent clause. The general form of a condi-tional proposition is
If (antecedent clause), then (consequent clause)£16 > METHODOLOGICAL, PSYCHOLOGICAL, PHILOSOPHICAL, STATISTICAL FOUNDATIONS
For example:If itis a dog, then it has four legs.
In the example, it is a dog is the antecedent clause and it has fourlegs is the consequent clause. A second example that is closer to the pur-pose at hand would be
If the TA rule has predictive power, then its back tested rate of re-turn will exceed zero.
Our ultimate goal will be to establish the truth of the antecedentclause of these conditional propositions like the preceding example. Aswill become clear, the route to establishing its truth is an indirect one!
The second premise of a conditional syllogism is a proposition that ei-ther affirms or denies the truth of either the antecedent clause or the con-sequent clause of the first premise. Referring to the prior example, thesecond premise could be one of the following four statements:
It is a dog: Affirms the truth of the antecedent.
It is not a dog: Denies the truth of the antecedent.
It has four legs: Affirms the truth of the consequent.
It does not have four legs: Denies the truth of the consequent.
The conclusion of the conditional syllogism affirms or denies thetruth of the remaining clause of the first premise. In other words, the con-clusion references the clause that is not mentioned in the second premise.For example, if the second premise refers to the antecedent clause of thefirst premise, /t’s a dog, then the conclusion would refer to the consequentclause, It has four legs.
An example of a conditional syllogism is as follows:
If it is a dog, then it has four legs.It is a dog (affirms the truth of the antecedent).Therefore, it has four legs (affirms the truth of the consequent).
When a conditional syllogism possesses valid form, its conclusion islogically compelled by the two premises. Moreover, if it has valid form andits premises are factually true, then the conclusion of the conditional sy]-logisms must also be true.The Scientific Method and Technical Analysis 117
Valid Forms of the Conditional Syllogism. There are two validforms of the conditional syllogism; affirming the antecedent and deny-ing the consequent. In an argument that affirms the antecedent, the sec-ond premise affirms the truth of the antecedent clause of the firstpremise. In an argument that denies the consequent, the second premiseasserts that the consequent clause of the first premise is not true. Thesetwo valid forms of argument are shown here. They assume all dogs pos-sess four legs.
Affirming the antecedent:
Premise 1: [f it is a dog, then it has four legs.Premise 2: Jt is a dog.
Valid Conclusion: Therefore, it has four legs.
In this valid form, the second premise affirms the antecedent clauseby stating /t is a dog. These two premises deductively compel the conclu-sion Jt has four legs. The general form of a conditional syllogism in whichthe antecedent is affirmed is
Premise 1: /f A is true, then B is true.Premise 2: A is true.Valid Conclusion: Therefore, B is true.
The other valid form of the conditional syllogism is denial of the con-sequent. In this form, the second premise asserts that the consequentclause of premise 1 is a falsehood. From this, one may conclude that theantecedent clause of premise 1 is also false. This is illustrated by the fol-lowing example:
Premise 1: [f it is a dog, then it has four legs.Premise 2: /t does NOT have four legs.Valid Conclusion: Therefore, it is not a dog.
Denial of the consequent follows the general form:
Premise 1: [f A is true, then B is true.Premise 2: B is not true.Valid Conclusion: Therefore, A is not true.418% METHODOLOGICAL, PSYCHOLOGICAL, PHILOSOPHICAL, STATISTICAL FOUNDATIONS
This is sometimes shortened to
If A, then B.Not B.Therefore, not A.
Notice that this form of argument uses evidence (creature does nothave four legs) to prove that antecedent (/t is a dog) is false. It is this formof reasoning that is used in science to prove that a hypothesis is false. Thehypothesis plays the role of the antecedent. We hypothesize that the crea-ture is a dog. The consequent clause predicts what will be observed if thehypothesis is true. That is, if the creature is truly a dog, then, when it is ob-served, it will be seen to possess four legs. In other words, the conditionalproposition, /f A, then B, predicts that B would be observed in an experi-ment if the hypothesis (A) were in fact true. The second premise statesthat when the observation was made, the observation contradicted theprediction, that is, B was not observed. Given this, we can validly deducethat the hypothesis A is false.
As will be shown in due course, if we can prove that hypothesis A isfalse, we can indirectly prove that some other hypothesis is true. Thatother hypothesis is the new knowledge that we wish to establish as true,for example that a new vaccine is more effective than a placebo or thatsome TA rule predicts more effectively than a randomly generated signal.
Invalid Form of the Conditional Syllogism. An important reasonfor using formal logic is the difficulty people often have when reasoninginformally about conditional syllogisms. Consistent with the numerous bi-ases and illusions discussed in Chapter 2, psychological studies’? haveshown that people tend to commit two fallacies when reasoning aboutconditional propositions: the fallacy of affirming the consequent, and thefallacy of denying the antecedent. An example of the fallacy of affirmingthe consequent is
Premise 1: [f it is a dog, then it has four legs.Premise 2: /t has four legs.Invalid Conclusion: Therefore, it is a dog.
The fact that a creature has four legs certainly does not compel theconclusion that the creature is a dog. It may be a dog. The evidence is con-sistent with the fact that it is a dog. However, the evidence is also consis-tent with other conclusions. It could just as easily be a cow, a horse, orThe Scientific Method and Technical Analysis 119
any other four-legged creature. The fallacy of affirming the consequenthas the general form:
Premise 1: /f A is true, then B is true.Premise 2: B is true.Invalid Conclusion: Therefore, A is true.
This fallacy is a very common error in poor scientific reasoning andone committed in many articles on TA. Consider the following syllogism,which commits the fallacy of affirming the consequent.
Premise 1: If TA rule X has predictive power, then it should produceprofits in a back test.
Premise 2: The back test was profitable.Invalid Conclusions: Therefore, the TA rule has predictive power.
Both of these premises may be true, but the conclusion is not necessar-ily true. With respect to the first premise, it is true that if the TA rule X doespossess predictive power it should back test profitably. In other words, aprofitable back test would be consistent with the supposition that the rulehas predictive power. However, a profitable back test could also be consis-tent with the supposition that the rule was merely lucky. Similarly, just asevidence of four legs is consistent with a dog, it is also consistent with allother four-legged creatures." The fallacy of affirming the consequent is thereason that empirical evidence cannot be used to prove that a hypothesis istrue. As we shall see, one philosopher of science, Karl Popper, contendedthat the scientific method must, therefore, rest on denial (falsification) ofthe consequent, which, as pointed out earlier, is a valid form of inference.
The other fallacy associated with conditional syllogisms is the fallacyof denying the antecedent. It is illustrated here:
Premise 1: [f it is a dog, then it has four legs.Premise 2: It is not a dog.Invalid Conclusion: Therefore, it does not have four legs.
The fact that a creature is not a dog does not preclude its having fourlegs. The general form of this fallacy is
Premise 1: Jf A is true, then B is true.Premise 2: A is not true.
Invalid Conclusion: Therefore, B is not true.120 METHODOLOGICAL, PSYCHOLOGICAL, PHILOSOPHICAL, STATISTICAL FOUNDATIONS
In logical shorthand
If A, then B.Not A.Therefore, not B.
Invalid arguments can be hard to notice when they concern complexsubjects. The best way to reveal them is to plug in commonplace items forA and B and see if the conclusion follows from the premises.
Figures 3.4 and 3.5 summarize the preceding discussion of the condi-tional syllogism.
As mentioned, the great strength of deductive reasoning is its abilityto deliver conclusions that are true with certainty. However, deductivelogic has a great weakness; it is unable to reveal new knowledge about theworld. All that a deductive argument can do is to reveal truths that werealready implicit in its premises. In other words, deductive reasoning canonly tease out truths that were already present in the premises thoughthey may not have been evident.
This is not meant to minimize or trivialize deduction but to clarify itsrole. It may well be that a conclusion implied by the premises is far fromobvious. Great mathematical discoveries are exactly that—the revealingof truths that had been implicit in the axioms of a mathematical systembut that had not been understood prior to being proven. Such was thecase with the much-publicized proof of Fermat’s last theorem. It was first
Valid Invalid
Affirming the Antecedent Denying the Antecedent
If A, then B. WeeA. Not A.Therefore, B. Therefore, Not B.
PFT Mi ie Affirming the Consequent
If A, then B. Lae UeNot B. ceTherefore, Not A. Therefore, A.
 
FIGURE 3.4 Conditional syllogisms: general form.The Scientific Method and Technical Analysis i218
Valid Invalid
Affirming The Antecedent Fallacy: Denying Antecedent
If a dog, then has 4 legs. If a dog, then has 4 legs.It is a dog. It is not a dog.Therefore, has 4 legs. Therefore, not 4 legs.
Denying The Consequent Fallacy: Affirming Consequent
If a dog, then has 4 legs. If a dog, then has 4 legs.Legs not equal to 4. Cwm ekeTherefore not a dog. Therefore dog.
 
FIGURE 3.5 Conditional syllogisms: example.
hinted at in the margin of a book in 1665 but not proven until 1994, by An-drew Wiles and Richard Taylor.
Inductive Logic
Induction is the logic of discovery. It aims to reveal new knowledge aboutthe world by reaching beyond the knowledge contained in the premises ofan inductive argument. However, this new knowledge comes with aprice—uncertainty. Conclusions reached by induction are inherently un-certain. That is, they can only be true with some degree of probability.Thus, the notion of probability is intimately connected with induction.
Induction proceeds in a manner opposite to deduction. We saw that de-duction progresses from a premise expressing a general truth that is held toapply to an unlimited number of instances, All men are mortal to a conclu-sion about a specific instance Socrates is mortal. In contrast, inductive rea-soning moves or, better said, leaps from a premise based on a limitednumber of observed instances to a general conclusion about an unlimitednumber of similar but not-yet-observed instances. Thus, this form of infer-ence is often referred to as inductive generalization. It is in leaping beyondwhat has been directly experienced by observation that induction incursuncertainty—the possibility that its conclusion may be wrong.
Inductive generalization is illustrated by the following:
Premise: Each of one thousand healthy dogs had four legs.General conclusions: All healthy dogs will have four legs.#22 METHODOLOGICAL, PSYCHOLOGICAL, PHILOSOPHICAL, STATISTICAL FOUNDATIONS
The conclusion, in this example, is called a universal generalization,because it asserts that all members of the class dog have the attribute fourlegs. Universal generalizations have the form
All X’s are Y’s.or100 percent of X’s have the attribute Y.
Generalizations need not be universal. Nonuniversal generalizationshave the form
P percent of X’s are Y’s.orP percent of X’s have attribute Y.orX’s have attribute Y with probability P.
Again, we see that probability is inextricably tied to the concept ofgeneralization. In fact, nonuniversal generalizations are also known asprobabilistic generalizations. An example would be: A higher percentageof bulldogs are prone to violence than poodles. This statistically soundnonuniversal generalization"® does not claim all bulldogs are prone to vio-lent behavior, nor does it claim that even a majority are so inclined. How-ever, it does say that, as a group, statistics show that bulldogs have ahigher probability of being dangerous than poodles.
Aristotle’s defeat as scientist was in part attributable to his failure toappreciate that nonuniversal generalizations convey useful knowledge.His fascination with the certainty of deductive proofs led him to restricthis search to universal generalizations. He was unable to see that manyimportant regularities of the natural world are inherently probabilistic.
Induction by Enumeration
The most common form of inductive argument is based on enumeration.It proceeds from a premise that enumerates the evidence contained in aset of observations, and then draws a general conclusion that pertains toall similar observations outside the enumerated set.The Scientific Method and Technical Analysis 123
Premise: Over the past 20 years there have been 1,000 instances inwhich TA rule X gave a buy signal and in 700 of those instances themarket moved higher over the next 10 days.
Conclusion: In the future, when rule X gives a buy signal, there is a 0.7probability that the market will be higher at the end of 10 days.
This conclusion or any conclusion reached by induction is inher-ently uncertain because it extends to observations that have not yetbeen made. However, some inductive arguments are stronger than oth-ers, and hence, arrive at conclusions that are more certain. The strengthof an inductive argument and the certainty of its conclusion dependupon the quantity and quality of the evidence enumerated in itspremise. The more numerous the instances cited and the higher theirquality, the more likely the conclusion will generalize accurately to fu-ture observations.
Suppose that the conclusion about TA rule X had been based on only10 instances with a 70 percent success rate instead of 1,000. In such acase, the conclusion would have been at least 10 times more uncertain."This means we should be less surprised if the signal's future accuracy dif-fers greatly from its historic success rate. In science, the evidence offeredin support of a conclusion is typically evaluated with statistical methods.This allows one to make quantitative statements about the conclusion’suncertainty. This topic is discussed in Chapters 5 and 6.
The strength of an inductive argument also depends upon the qualityof the evidence. Evidence quality is an entire subject unto itself, but suf-fice it to say that some observational methods produce higher quality evi-dence than others. The gold standard in science is the controlledexperiment, where all factors but the one under study are held constant.TA does not permit controlled experiments, but there are better andworse ways to make observations. One issue that is relevant to TA is thematter of systematic error or bias. As will be discussed in Chapter 6, ob-jective TA research is prone to a particular type of systematic error calleddata mining bias if careful steps are not taken.
Also relevant to the strength of an inductive argument is the degreeto which the evidence cited is representative of the kinds of observationsthat are likely to be encountered in the future. An inference about a rulethat generates long/neutral (+1,0) signals that was back-tested only dur-ing rising markets is unlikely to be accurate about the rule’s performancein a declining market environment. Even if the rule had no predictivepower, its restriction to long or neutral positions makes it likely that itwould have generated a profit because it was tested during a rising mar-ket period.#24 METHODOLOGICAL, PSYCHOLOGICAL, PHILOSOPHICAL, STATISTICAL FOUNDATIONS
The most common fallacy of induction is the hasty generalization—an induction based on too little evidence or evidence of poor quality.Rule studies that cite a small number of successful signals as a basisfor concluding that the rule has predictive power are likely to be hastygeneralizations.
THE PHILOSOPHY OF SCIENCE
 
The philosophy of science seeks to understand how and why scienceworks. It explains such things as: the nature of scientific propositionsand how they differ from nonscientific and pseudoscientific proposi-tions; the way scientific knowledge is produced; how science explains,predicts, and, through technology, harnesses nature; the means for de-termining the validity of scientific knowledge; the formulation and useof the scientific method; and the types of reasoning used to arrive atconclusions. '”
That the scientific method is one of man’s greatest inventions and isby far the most effective method for acquiring objective knowledge aboutthe natural world is beyond question. “The part of the world known as theIndustrial West could, in its entirety, be seen as a monument to the Scien-tific Revolution. .. .”'* Humankind’s ability to predict and control the nat-ural world has improved more in the last 400 years, since the scientificrevolution began, than it had in the prior 150,000 years that modern hu-mans, homo sapiens, walked the face of the Earth.
Strange as it may seem, the invention of the scientific method and itsfirst fruits came before it was understood why the method worked as wellas it did. That insight came gradually, over the course of several centuries,as practicing scientists and their erstwhile critics, the philosophers of sci-ence, wrestled with perfecting the method and, in parallel, developed anunderstanding of how and why it worked.
The mere fact that the scientific method did work was not enough. Itwas seen as necessary to understand why. What philosophers found sovexing was the following apparent contradiction. On the one hand werethe great victories of science, such as Newton's laws of motion and gravityand humanity’s expanding technological control over nature. On the otherwas the fact that scientific knowledge was inherently uncertain, becauseconclusions arrived at by logical induction were inherently uncertain.How could so much useful knowledge result from such a flawed methodof inference?
This section discusses the keys steps in the method’s developmentand the milestones in our deepening understanding of how and why itThe Scientific Method and Technical Analysis 125
works. The reader may wish to skip this historical development and go di-rectly to the summary of the key aspects of the scientific method.
Bacon’s Enthusiasm
Without invitation, philosophers poke their noses into all sorts of matters.It’s their nature. They tell us how to act (ethics), how governments shouldrule (political philosophy), what is beautiful (aesthetics), and of greatestconcern to us, what constitutes valid knowledge (epistemology) and howwe should go about getting it (philosophy of science).
The scientific revolution was, in part, a revolt against Aristotelian sci-ence. The Greeks regarded the physical world as an unreliable source oftruth. According to Plato, mentor of Aristotle, the world was merely aflawed copy of the truth and perfection that existed in the world of Forms,a metaphysical nonmaterial realm, where archetypes of the perfect dog,the perfect tree, and every other imaginable thing could be found.
When the revolt against this view of reality finally arrived, it was harshand unremitting.'” The new school of thought, empiricism, resoundinglyrejected the Greek paradigm. It contended that, not only was the naturalworld worthy of study, but that careful observation could lay bare itstruths. A pioneer of empiricism and perhaps the first philosopher of sci-ence was Francis Bacon (1561-1626). “Nature, for Bacon was an openbook that could not possibly be misread by an unprejudiced mind.””° Inhis famous work the Novem Organum (the new tool) Bacon extolled thepower of observation and induction. He held science to be a completelyobjective rational practice that could conclusively confirm or falsifyknowledge simply by observing without bias or prejudice and then gener-alizing from those observations. In many situations, this approach seemedto work.
However, empiricism was not the perfect tool Bacon and his disciplesclaimed, and philosophers made it their business to say why. First, theypointed out that empiricism, an observation-based enterprise, rested on acrucial assumption that could not be confirmed by observation, the assump-tion that nature was uniform over all time and space. That assumption wascritical in justifying the empiricists’ position that if a scientific law was ob-served to hold true here and now it would also hold true everywhere andforever. Because the uniformity of nature assumption could not be con-firmed by observation, it had to be taken on faith. Second, science oftendeals with phenomena and concepts that defy direct observation: atomicstructure, the force of gravity, and electric fields. Though their effects areobservable, these constructs could not be arrived at exclusively by obser-vation and induction. They are better understood as human inventions thatexplain and predict rather than observable physical realities.126 > METHODOLOGICAL, PSYCHOLOGICAL, PHILOSOPHICAL, STATISTICAL FOUNDATIONS
Nevertheless, Bacon’s contributions to the development of the scien-tific method were important. He promoted the idea of experiment andmade room for doubt by taking special note of discordant observations.Both ideas eluded the Greeks.
Descartes’s Doubt
If philosophers are good for anything it’s raising doubt, and no one wasbetter than Rene Descartes (1596-1650). Regarded as the father of mod-erm philosophy and a key figure in the birth of science, Descartes sharedBacon’s skepticism for the authoritarian knowledge of the Greeks and thedogma of the Roman Church. However, Descartes was just as skeptical ofthe claims made by the empiricists about the power of observation and in-ductive generalization. His famous expression, “I think, therefore I am,”expressed the position that science must start by doubting everything ex-cept the existence of the person who experiences doubt. From that pointof solidity, knowledge must be built purely by deductive reasoning with-out being contaminated by error-prone observations made with the imper-fect five senses.
As a consequence of Descartes’ anti-empirical stance and penchantfor theorizing in a factual vacuum, his scientific findings were almostmeaningless.”! However, his contributions to science were lasting. Skepti-cism is central to the scientific attitude. In addition, Descartes’ inventionof analytic geometry paved the way for Newton’s invention of the calculuswhich, in turn, allowed him to specify his famous equations of motion andgravity.
Hume’s Critique of Induction
Another dose of doubt was administered by Scottish empiricist andphilosopher David Hume (1711-1776). His seminal work, the Treatise onHuman Nature, published in 1739, grappled with a central problem ofepistemology: how to distinguish knowledge from lesser forms of know-ing, such as opinions that happen to be true. Prior to Hume’s publication,philosophers generally agreed that the distinction was related to the qual-ity of the method used to acquire the knowledge. What justified callingone bit of wisdom knowledge but not another was the pedigree of themethod of inquiry.”
Philosophers could not, however, agree on the best method of knowl-edge acquisition. Empiricists argued that objective observation followedby inductive generalization was the route to wisdom. Rationalists, on theother hand, contended that pure deductive reasoning from self-evidenttruths was the correct method.The Scientific Method and Technical Analysis 127
Hume took issue with both schools of thought and ultimately evenwith himself. As an empiricist, Hume disparaged the rationalists’ purelydeductive approach because it was disconnected from observed facts.Also, in the spirit of empiricism, Hume said that it was wise to adjust thestrength of one’s beliefs in proportion to the evidence and that theoriesshould be evaluated by the degree to which they matched observation.But then Hume went on to contradict himself by attacking the logical ba-sis of empiricism. He denied the validity of inductive generalization anddisparaged the ability of science to establish causal laws. His searing cri-tique of induction has come to be known as Hume's problem.
Hume’s attack on induction was on both psychological and logicalgrounds. First, he said the belief that induction could establish correla-tive or causal connections between events was a nothing more than aby-product of human psychology. Hume asserted that the perceptionof cause and effect was merely an artifact of the mind. The belief thatA causes B or is even correlated to B, simply because A has alwaysbeen followed by B was nothing more than a habit of mind, and a badhabit at that.
From a logical perspective, Hume claimed that induction was flawedbecause no amount of observed evidence, no matter how objectively col-lected, can compel a conclusion with the force of a valid deduction. More-over, he said that there was no rule of induction that tells us when wehave evidence of sufficient quantity or quality to justify the leap from a fi-nite set of observations to a conclusion about an infinite number of similarbut not yet observed instances. A rule of induction would, itself, have hadto be the result of a prior valid induction made on the basis of an even ear-lier rule of induction, and so forth and so on, ad infinitum. In other words,an attempt to justify induction inevitably rests on an infinite regress—alogically impossible absurdity.
In light of Hume’s attack, supporters of induction retreated to a nar-rower claim saying inductive generalizations were merely correct in aprobabilistic sense. So as evidence accumulates in favor of a relationshipbetween A and B, the probability that the relationship is authentic also in-creases. However, philosophers were quick to point out that a probabilis-tic justification of induction was also flawed. As will be pointed out inChapter 4, the probability that A predicts B is equal to the number of timesthat A was followed by B divided by the total number of instances of A re-gardless of whether it was followed by B.”’ Because the future holds an in-finite number of instances, the probability will always be zero, no matterhow numerous the past observations (any number divided by an infinitelylarge number is still zero).
Thus, Hume and his allies created a paradox. On one hand were theirseemingly valid concerns about the flaws of induction. On the other hand was128 METHODOLOGICAL, PSYCHOLOGICAL, PHILOSOPHICAL, STATISTICAL FOUNDATIONS
the accumulation of stunning scientific discoveries. If science was based onsuch a flawed logic, how could it have managed to be so successful?
William Whewell: The Role of Hypothesis
It took philosophers and scientists two hundred years of watching the sci-entific method succeed to understand how it worked and why it had beenso triumphant. By the middle of the nineteenth century, it was becomingclear that science employs a synergistic combination of inductive and de-ductive logic. In 1840, William Whewell (1794-1866) published The His-tory and Philosophy of Inductive Sciences.
Whewell was the first to understand the crucial role of induction inthe formulation of a hypothesis. Whewell called it a happy guess, He saidthat scientific discovery starts with a bold inductive leap to a new hypoth-esis, but it is followed by deduction. That is to say, after a hypothesis hasbeen induced, a prediction is deduced from said hypothesis. This predic-tion takes the form of a conditional statement:
If the hypothesis is true, then specific future observations are pre-dicted to occur.
When the observations are made, they will either be consistent withthe prediction, thus confirming the hypothesis, or conflict with the predic-tion, thus contradicting the hypothesis.
What is a scientific hypothesis? It is a conjecture of a suspected pat-tern, for example:
X predicts Y.orX brings about Y.
This conjecture is spawned by a scientist’s prior experience—noticingrepeated pairings of X and Y. Once the XY hypothesis has been put for-ward, a testable prediction is deduced from it. This takes the form of aconditional proposition, which is composed of two clauses: an antecedentand a consequent. The hypothesis serves as the antecedent clause, and theprediction serves as the consequent clause. In situations where it ismerely asserted that X is correlated (predicts) with Y the following condi-tional proposition would apply:
IF X predicts Y, then future instances of X will be followed by in-stances of Y.The Scientific Method and Technical Analysis 129
In cases where the hypothesis asserts that X causes Y, the followingconditional proposition would apply:
IF X causes Y, then if X is removed, Y should not occur.
The predictions embodied in the consequent clause of the conditionalproposition are then compared with new observations. These must be ob-servations whose outcome is not yet known. This is crucial! This does notnecessarily mean that the observations concern some future event. It sim-ply means that when the prediction is made, the outcome of the observa-tions is not yet known. In historical sciences like geology, archeology, andso forth, the observations are about events that have already taken place.However, the outcomes have not yet been observed.
If it turns out that future observations of X are not followed by Y or ifremoval of X does prevent the occurrence of Y, then the hypothesis (an-tecedent) is proven to be false by the valid deductive form falsification ofthe consequent.
If X, then Y.Not Y.Valid Deduction: Therefore, not X.
If, however, future instances of X are indeed followed by Y, or if theremoval of X does cause the disappearance of Y, the hypothesis is notproven! Recall