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NOTE: If you are unfamiliar with Realistic Epistemology (Theory of Knowledge), it is suggested you read An Introduction to Epistemology, or at least read What is Philosophical Realism? before reading this essay. by Jonathan Dolhenty, Ph.D.
The Nature of Induction Knowledge is the goal of all thinking and the possession of truth is knowledge. Remember, there is no such thing as "false knowledge." The only way we can achieve truth and knowledge is through correct thinking. That's why it's important to know the impact of ideas, judgments, and inferences. Judgments are made up of ideas and truth is contained in judgments. A mere comparison of ideas, however, will not always allow the mind to express their identity or non-identity. Some simple facts, of course, can be known by immediate observation: "It is raining outside"; "That man just fell off the steps"; "This cat is black"; and so on. Some axiomatic (self-evident) truths can be known by a mere analysis of the ideas involved in the judgment: "There is no such thing as a square circle"; "One and one equal two"; "A thing is what it is"; and so on. The primary truths of the principles of Contradiction, Identity, and Excluded Middle are of this latter type. The great bulk of scientific truths, however, demand a process of reasoning to establish their truth. That is why it is necessary to understand the laws of consistency in the various forms of argumentation. Science cannot be acquired except through an extensive use of the reasoning powers of the mind. Formal and Material Truth A sufficient and accurate knowledge of the different forms of argumentation will insure correct thinking and the avoidance of error. This will guarantee that the conclusions of an argument will be valid. These conclusions will be valid if they are consistently drawn from true premises. A conclusion will be consistent when it flows with strict logical necessity from the premises as given. If the premises of an argument are, in fact, true, and the conclusion follows logically from these premises, we can rest assured that the conclusion will be true. We distinguish between the formal truth and the material truth in an inference. The formal truth of an argument consists in the correct arrangement of the premises, so that the conclusion follows with logical necessity. The material truth of an argument consists in the truth of the premises as statements of facts. Both formal truth and material truth are required in order that the conclusion be true with certainty. A knowledge of the rules of correct thinking will guarantee the formal truth of a conclusion. These are the rules of logical thinking studied as deductive argumentation. The conclusion of an argument can be true with certainty if the rules of correct thinking are strictly observed and the premises (the judgments) are known to be true. But what will guarantee the material truth of the premises as statements of facts? The answer, of course, is that the material truth of all factual statements can only be discovered by a close observation and study of reality itself. Let's consider the following arguments.
The above syllogisms (arguments) are both formally correct. They are identical as to their figure and mode and both conclusions are consistently drawn from the premises as given. It becomes immediately apparent, however, that both conclusions cannot be true, since a vampire bat cannot be both a bird and a mammal as these terms are employed. While both syllogisms are formally correct, they are not both materially correct. The material truth is missing in the major premise of the first argument. It is not true that "all animals that fly are birds." The premises of the first syllogism led to a false conclusion. The conclusion of the second syllogism is true because both the premises are materially true. We cannot determine the truth of the premises in these arguments by a mere comparison of the ideas contained in the judgments which make up the premises. These truths are not self-evident. Nor can we establish the truths of the premises merely by immediate and limited observation. Establishing the truth of the premises involves a more complicated set of procedures. These procedures we call the scientific method. The material truth of virtually all factual statements can only be discovered by a close observation and study of reality (or nature or whatever). Reality is very complicated and our natural world is a complex and mysterious part of reality. Only when the facts and laws of nature, for instance, are proved to be true can we be sure that the premises of most of our arguments are true. It is no easy task and the scientist performs labor that is both tedious and time-consuming. The scientist uses a scientific methodology in his work. Each science has its own subject matter and its own method of discovery and proof. There is no single methodology that can be called the scientific method. The methods of the physicist are not those of the historian. The methods of the political scientist and sociologist are not those used by the astronomer or the geologist. Although the specific methods used by various branches of empirical science may differ, the laws of thought and the fundamental principles of scientific methodology are the same for all sciences. Logic, the science of correct thinking, is not concerned with the specific methods used by any special science. It is, however, within the province of logic to investigate the fundamental principles of the methodology which all sciences must use at all times and in every process of scientific research. Scientific Methods A method is the proper arrangement of our mental processes in the discovery and proof of truth. Generally speaking, we recognize two fundamental methods. One is called synthesis and it proceeds
Synthesis is essentially a method of deduction. The sciences which use this method primarily are referred to as deductive sciences. Mathematics is an obvious example. Mathematics begins with a few basic ideas and axioms and carefully builds up a profound and complicated science of truths. Mathematics itself does not rely primarily on observation and experimentation. The second method is called analysis and it proceeds
Analysis is essentially a method of induction. The sciences which use this method primarily are referred to as inductive sciences. These sciences are analytical and experimental. Such sciences as chemistry, biology, anthropology, physics, sociology, and so forth, are examples of inductive sciences. Sometimes we also refer to these sciences as the empirical sciences because their predominant methodology is empirical, that is, based on material or physical reality as known by the senses. It should not be thought, however, that the inductive sciences are exclusively inductive. Most, if not all, of the inductive sciences use deductive methods, such as mathematics for instance, in their normal operations. They are called inductive sciences because they are primarily inductive, not exclusively so. Also, it should not be thought that deduction and induction are in any way opposed to one another. They are both valuable methods for arriving at truth. They actually assist one another in uncovering and discovering truth. Induction Induction is the legitimate inference of universal laws from individual cases. It is a process of abstraction and generalization, based on an understanding of the nature of the reality under observation and on a perception of the relation of cause and effect. As you know, our minds form abstract and universal ideas of things after contemplating individual things themselves. In a similar manner, our mind also forms abstract and universal laws from contemplating individual phenomena in the natural world. The mind does not have to examine every single instance of the phenomena in our world to formulate these general laws, any more than our mind must examine every single thing in the world to form an idea of that thing. We can form these general laws because we understand the nature of the reality under observation. Consider the boiling point of water. At sea level, the usual temperature at which water boils is 212 degrees F. This is a general law regarding the boiling point of water. How was this determined? Certainly not by taking every bit of water in the world down to sea level and actually boiling it. But it was observed in each and every instance that water was heated at sea level (other things being equal), that when the temperature rose to 212 degrees F., the water boiled. It was then concluded that it is in the nature of water to act in this way. Since the nature of a thing is the same everywhere, it was concluded that water will at all times and everywhere at sea level boil under identical conditions and all things being equal. It is, therefore, a law based on the nature of water as the cause of this effect (the boiling). The complementary relationship between induction and deduction can be clearly seen in the example given above. The general law is established by the method of induction, based on observation and analysis, and abstraction and generalization. Now that we have the general law, the law can be applied to all further cases by the method of deduction, the method of synthesis of applying a general rule to particular cases. Both induction and deduction are necessary for truth. Induction gives us its discovery. Deduction gives us its proof. We argue first from the effect to the cause, and then we argue from the cause to the effect. Here is a very simple illustration of scientific methodology:
While the above may be an over-simplification of what scientists actually do, it does provide a bare outline that is easily understood by non-scientists. It is very close to the actual methodology of empirical science. The general law we formulated in the Fifth Step is the result of an abstraction based on cause and effect, the nature of the things being the cause and the phenomena observed being the effect. Science has been increased by a new law, and the mind of man has been enriched by a new truth. If the new general law agrees with the facts, it is true. If not, it is false. Scientific laws are expressed in definite categorical statements. As you should know by now, truth is only found in categorical judgments which are an actual representation of facts as they exist independent of the mind. The laws of science, like the universal ideas, are not mere figments of the thinking mind. They are representations of reality. The Logical Foundation of Induction Induction is the main method employed by most of the empirical sciences. We go from the concrete, individual cases of phenomena to the general, abstract, and necessary laws which govern the phenomena. It is obvious from just a cursory glance at the scientific achievements over the past hundred years that inductive methods are very important. But what are the logical foundations of induction? What are the principles upon which induction is grounded? The first principle upon which the inductive method is grounded is the Principle of Causality. The Principle of Causality is an extension of the Principle of Sufficient Reason and the Principle of Sufficient Reason leads logically to the Principle of Causality. The Principle of Sufficient Reason is an extension of the dual Principles of Identity and Contradiction. As you may recall, these primary or first principles are self-evident and need not be proved. In fact, they cannot be proved. If these principles are not accepted as true and valid, all discussion ceases and nothing more can be discovered. The Principle of Identity states: "A thing is what it is." Common sense insists on this as do philosophy and empirical science. The Principle of Identity then gives rise to the Principle of Contradiction which states: "A thing is what it is, and it can be no other thing at the same time in the same respect." The Principle of Contradiction gives rise to the Principle of Sufficient Reason, which states: "Everything must have a sufficient reason to be what it is." This only makes sense, for if something had no sufficient reason for its existence, it would have no existence and it would be nothing. If a thing could exist without sufficient reason, it would exist and not exist at the same time, that is, if a thing exists, it must have a sufficient reason why it exists and why it is this particular thing rather than another thing. This principle leads logically to the Principle of Causality, which is one of the logical foundations of induction. Since the Principle of Sufficient Reason is so important to an understanding of the Principle of Causality and is so often misunderstood by many modern philosophers and scientists, let's consider this principle a little bit more in detail:
At this point you may be asking yourself why we have gone into such detail about the Principle of Sufficient Reason, a principle which common sense and good philosophy accepts as self-evident and necessary. The reason is because this principle has either been denied by many modern thinkers, probably due to their misunderstanding of it, or it has been ignored by modern thinkers, many of whom are not acquainted with it. But the Principle of Sufficient Reason is vital to an understanding and justification of the Principle of Causality, which itself has been questioned and sometimes even denied by some non-realistic philosophers. Everything in the physical universe is in a continual state of change. Everything in the physical universe is, therefore, not necessary in its reality. We say that each "thing" or "being" in the physical universe is contingent, that is, it does not exist out of necessity; it is perfectly possible for any physical thing or being to not exist. The main purpose of empirical science is to discover and prove the causes which produce these physical things or beings, and then express these causes in general laws. Since the concept of cause, as we use it in realistic philosophy, is so commonly misunderstood today, it becomes necessary to discuss both the nature of and the kinds of causes which are active in the production of a thing. This will momentarily take us out of the science of logic into the science of metaphysics, one of the major branches of realistic philosophy. A created being comes into or emerges into being. The created being has its first origin in creation, which is an action proper only to an Infinite Uncreated Being, and which produces a being in its entirety out of nothing. This is the first beginning of all created being. While it is true that bodily substances, such as we are, can generate other bodily substances like us through biological reproduction, the fact is that the root-origin of this process is found in creation. The emergence of being is called becoming. Becoming, looked at in itself and statically, is a combination of the accidentals called action and passion. You may recall that action is an accidental being which determines a reality as doing something, as producing an effect. It is an answer to the question: "What does it do?" Also recall that passion or reaction is an accidental being which determines a reality as undergoing something, as affected by some action. It is an answer to the question: "What is happening to it?" When we consider substantial change or substantial becoming we mean that the beings changed are substances, and that one being ceases to be while another emerges. We do not mean that the process of change is a substance. The process as such is an accidental, a sort of composite or cooperative accident of action and passion. Becoming, considered in regard to its end or purpose, is a process of cause and effect. Beings that emerge as a result of creation are caused beings, and are themselves the effects of creation. Beings which become by reason of change or motion are also caused beings and are themselves the effect of the generation which makes them emerge. A cause is anything that contributes in any way to the producing or the maintaining of a reality. An intrinsic cause is that which is within the being caused. An extrinsic cause is that which is not within the created being, but which lends an influence or activity to the producing or maintaining of that being. Let's consider the marble statue of Thomas Jefferson. Without some stuff, in this case the marble, this statue could not exist. The stuff or material out of which a bodily creature is made is therefore a contributing factor to its being. It is, in other words, a cause. In this particular case we call it the material cause. This cause is intrinsic because it is right in the finished statue. Obviously, only bodily realities have material causes since spiritual substances are not made of any stuff or material. The marble statue is marble, before, during, and after the sculpting which made it a statue of Thomas Jefferson. The sculpting changed only the shape of the marble. It has not changed the marble substantially, for it is still marble, but it has changed it accidentally. It has, however, given the marble a certain determinateness as a statue, an accidental determinateness. Any determining factor is called, in metaphysics, a form. The sculpting has given the marble an accidental form. The form constitutes or determines a being as a reality and is, therefore, a cause. An accidental form is an accidental formal cause. The statue has many accidental points of determinateness. It is of a certain height (quantity), a certain weight (quantity), a certain color (quality), a certain temperature (quality), and so on. Each of these determinations, down to the last and least and the most insignificant, contributes something to the making of the statue of Thomas Jefferson to be the precise being it is in all particulars. Each of these determinations is an accidental form, and an accidental formal cause. There is an underlying form and formal cause in the statue which makes it a statue of marble. This is the substantial form of marble, the substantial principle which makes marble to be marble and not any other substance. This substantial form is the substantial formal cause of the marble and of the statue made of the marble. There can be in any given unit of substance only one substantial form, only one substantial formal cause. The formal causes, accidental and substantial, are actually in the effect, and that is why we call them intrinsic causes. The intrinsic causes are the material cause (the bodily reality) and the formal causes, both substantial and accidental. The marble statue of Thomas Jefferson was produced by some activity. That which by its activity produces an effect is called the effecting cause of the effect. Sometimes the effecting cause is called the efficient cause and this is the term we will use for this cause. The efficient cause in our example of Thomas Jefferson's statue is the sculptor who carved the statue. This sculptor is the efficient cause of the statue, that is, the accidental shaping of the marble. It should be obvious that the efficient cause is not in the effect, that is, the sculptor is not in the statue. That's why we say the efficient cause is an extrinsic cause. There is another extrinsic cause besides the efficient cause and this is called the final cause. This is the end or the object or the goal or the purpose which the efficient cause intends to attain. The sculptor in our example had some end or purpose in mind which led him to the activity which produced the statue. Perhaps he wanted to express his devotion to Thomas Jefferson. Perhaps he merely wanted to have pleasure in doing something he could do skillfully. Perhaps he wanted to make money or become famous. In any case, the sculptor had some end or purpose in view. This constitutes the final cause of the statue. The final cause, of course, may be multiple. It could be that the sculptor wanted to make money, as well as exhibit his skill and leave something for posterity. Also it is important to note that ends or final causes run in chains or series. We may say, therefore, that the sculptor made the statue of Thomas Jefferson for money, he wanted money to buy food, he wanted food in order to live, and he wanted to live because he was enjoying his life. For the Christian student of metaphysics, of course, all chains or series of final causes tend towards God, who is the ultimate Final Cause and Supreme Good of all. Even the sinner and disbeliever are looking, although mistakenly, for good, and for the Supreme Good. Unfortunately, such people are looking in the wrong place. The four major causes of being, then, can be described this way, and pay particular attention to the bold words:
These four kinds of causes -- material, formal, efficient, and final -- are positive factors in the production of a thing. This production, when it occurs in our physical world, is only a change from one kind of already-existing thing to another kind of thing; it is not the production of a thing out of "nothing," a phenomenon properly called creation in the strict sense of that term. In nature we do not experience creation as such. The empirical sciences are not concerned with anything other than the type of causes experienced in the physical world. Furthermore, the empirical sciences are not particularly interested in free will as a cause; they are generally interested only in the non-free forces which influence material reality. The empirical sciences can be said to concentrate on the non-free material causes that are at work in our physical world. There is an important distinction that needs to be made here between what constitutes a cause and what constitutes a condition. These two concepts are often confused even by professional scientists. A cause, you will recall, is anything that contributes in a positive way toward the production of a thing in its existence and being. A condition, however, is something which enables the cause to produce an effect, without actually contributing toward the production itself. Some examples may help to illustrate this distinction: 1. Pressing the button of a door-bell is a condition for its ringing. But it is the electric current that causes the door-bell to ring. 2. Winding a wristwatch is a condition for its running. But it is the internal mechanism that causes the wristwatch to actually run. 3. Bees carrying pollen from plant to plant may be a condition for fertilization of a plant. But it is the pollination itself that is the cause of the fertilization. You should now be able to see that the Principle of Causality is a part of the logical foundation of the inductive method. Without this principle, the method of induction, and consequently all empirical science, would be useless. There would be no way to arrive at anything approximating what we call scientific knowledge. The pursuit of truth would be a barren enterprise. While the Principle of Causality is vital to the inductive method, by itself it is not sufficient to justify the many claims made by empirical science. The principle itself only requires that every material change have a cause or sufficient reason for its existence. It deals only with those changes in nature which actually happen. It deals only with individual occurrences of physical cause and effect. The Principle of Causality, therefore, can only be applied to each single, individual change that occurs. This is not enough for us and it is not enough for empirical scientists. This brings us to the second principle necessary for the logical foundation of induction: the Principle of the Uniformity of Nature. This principle states that "Nature is uniform in its causality." This means that the same non-free causes under the same conditions will always produce the same results. This principle allows us to formulate general laws which are universal in nature, the same for all times and for all places and under all circumstances. These general laws are the "laws of nature" we accept as scientific knowledge. There are many laws of nature which empirical science has discovered. These laws, of course, existed before scientists discovered them and are, therefore, independent of our minds. Scientists did not "invent" them. These laws of nature allow the empirical scientist to construct theories about the past and also to predict future events in the physical world. One such law of nature, for instance, regards the speed of light which has been found to be a constant in the universe. Wherever you travel in the universe, the speed of light remains the same. There are other laws of nature regarding heat, motion, electricity, and so forth. What justifies the scientist when he says, for instance, that there is such a law as the law of gravity? Obviously, he cannot travel everywhere in the universe, investigating every individual case involving falling bodies. He cannot, in other words, provide a complete enumeration of all instances where the phenomenon of falling bodies occurs. The scientist does, however, accept the law of gravity as a universal law of nature, valid for all times, in all places, under the same circumstances. If induction depended on a complete enumeration of occurrences to justify general laws of nature, induction would be a hopeless methodology. Scientists do accept (as we non-scientists also accept) the universal validity and necessity of properly formulated laws of nature. Scientists say such laws are true even though they have not examined every case where such laws may apply. On what logical grounds can scientists do so? The logical ground is the Principle of the Uniformity of Nature. This principle must be accepted as a necessary foundation for the inductive process. It must be presupposed or scientific knowledge is a sham; the so-called laws of nature are illusory. But how do we know that nature is uniform at all? After all, we have (as scientists have also, of course) only a limited view of all nature and we can only examine a limited number of occurrences of any phenomenon. The key questions and answers concerning this problem are the following: The question is: Why must nature, in its causality, be uniform at all? The answer is: Because the things which make up the natural world are causes which operate with necessity and must always operate in the same way, that is, they operate in a uniform manner. The question is: Why must these things operate of necessity? The answer is: Because their causality is determined by their very essence and their essence must always be the same. The question is: Why is their essence determined so definitely that it must always be the same and cannot change? The answer is: Because they were created by a Being and, in giving these things their essence, this Being endowed them with certain definite powers and tendencies which these things, being non-free agencies, necessarily strive to realize. We can now see that the method of induction rests on two principles, both necessary to establish the truth of propositions resulting from this scientific methodology. These two principles provide the logical foundation for induction. Empirical science bases its universal laws of nature on the causality inherent in the nature or essence of things. It is not necessary for the scientist to examine each and every occurrence of a phenomenon in order to establish a general law of nature. The Principle of Causality and the Principle of the Uniformity of Nature allow the empirical scientist to rise from the particular to the universal and from the contingent to the necessary. These two principles provide the philosophic justification of induction as a true scientific method. Through the method of induction as applied to the physical world around us, truth can be discovered and human knowledge advanced.
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