Elementary logic in 10 chapters. Designed for use in schools, academies and colleges

Front matter

ELEMENTARY LOGIC

IN 10 CHAPTERS.

DESIGNED FOR USE IN

Chapter I. The Subject Defined : Its Analysis And Synthesis

1. The word Logic is derived from the Greek Logos, a word or discourse which has many shades of meaning, and hence the diversity of subjects to which Logic has been applied.

It is not our purpose to enter the fruitless controversy so long waged as to what Logic should or should not embrace, preferring rather to accept the definition generally given and confine it to the scope thus legitimately assigned to it by that definition.

3. Logic has generally been defined as the Science of Reasoning, or the Art of Reasoning, and inasmuch as we must know how to reason before we can practice it, and as the Art thus necessarily embraces the Science, we prefer to define it as the Art of Reasoning, and shall so use it in this treatise.

4. In the analysis of Logic which we propose in the subsequent pages, we shall see that the Dictum of Aristot/e is the groundwork of the syllogism.

In like manner that same great philosopher has given us the principle of contradiction as the groundwork of all reasoning. This principle of contradiction is a primary law of thought, and is generally given in the classification as the first law of thought. The classification of these laws is as follows :

IO LOGIC IN IO CHAPTERS.

PRIMARY LAWS OF THOUGHT.

i. The Law of Contradiction.

2. The Law of Identity.

3. The Law of Excluded Middle.

These laws describe the very simplest truths, in which all people must agree, and embrace all notions which we can conceive. It is impossible to think correctly without them; hence, on them all reasoning must ultimately depend.

We merely refer to them here as the basis of reasoning and give the definition of each, reserving the full explanation and application of these laws till we come to exemplify Logic itself.

1. The Law of Contradiction means that, Nothing can both be and not be.

2. The Law of Identity means that, Whatever is. is.

3. The Law of Excluded Middle means that, Everything must either be or not be.

5. Having defined the subject and given the basis on which reasoning rests, we now propose to give

AN ANALYTICAL VIEW OF LOGIC.

1. Logic is the Art of Reasoning.

2. Reasoning expressed in language is called an argument.

3. The simplest and ultimate form of an argument is the Syllogism.

4. The Syllogism is composed of three propositions, called the Major Premise, Minor Premise and the Conclusion.

5. These three propositions, when legitimately connected in the form of the Syllogism, contain three terms, and only three, which are each used twice, and are called respectively, the Major Term, the Minor Term, and the Middle Term.

LOGIC IN IO CHAPTERS. II

The first two must not be confounded with the Major and Minor Premises on account of similarity of name.

6. A Term is an act of Apprehension.

-j. An Act of Apprehension is a pure conception by the mind of an object apprehended. The mind has three faculties of primary and original knowledge — consciousness, perception and intuition. By consciousness we gain a knowledge ot the empire of mind itself; by perception we cognize the empire of matter; and by intuition we cognize those entities that are neither mind nor matter, such as space, duration of time, personal identity, cause and effect, infinity and substance.

When the mind through either of these primary faculties cognizes anything, as for instance, existence by consciousness, matter by perception, or space by intuition, the act of cognonition in each case is an act of apprehension.

Here we reach the elementary principle — apprehension, the lowest stage in the Analysis of Logic. Here the mind ceases to analyze, to take parts, and begins the opposite process of Synthesis, to build up.

When the mind apprehends an object, i. e., seizes it by apprehension, it seeks a medium to express its act of apprehension. This medium it finds in words which in turn become terms, which in the form of expression become propositions, which, when legitimately connected, form the Syllogism, which is the ultimate form of an argument, and an argument expressed in language is reasoning.

We have thus indicated the process of Synthesis, and in order to make it still plainer, will submit the following :

SYNTHETICAL VIEW OF LOGIC.

i. An Act of Apprehension gives us a Term.

2. The three terms, technically called the Major Term, the

Minor Term, and the Middle Term, when properly arranged, give us the three propositions of the Syllogism.

3. The three propositions, technically called the Major and Minor Premises and the Conclusion, when legitimately connected, form the Syllogism.

4. The Syllogism based upon Aristotle's Dictum is the simplest form of an argument.

5. An argument is reasoning expressed in language.

6. Reasoning expressed in language is the Dictum of the Primary Laws of Thought.

7. The Art of Reasoning, based upon the Primary Laws of Thought, is Logic.

This completes the Synthesis and brings us back again to our subject, which is Logic. Analysis and Synthesis, the two processes of method in the study of Logic, are thus exhibited to acquaint the student with the elements of Logic, their names and /unctions. We will now give a topical review of this chapter, which wc denominate a

SYLLABUS.

We have said that Logic is derived from the Greek Logos, which has many meanings, but is in this treatise defined to be the Ait of Reasoning. That we are indebted to Aristotle for the Law of Contradiction as the groundwork of Reasoning as well the celebrated Dictum the groundwork of the Syllogism. That this Law of Contradiction is a Primary Law of Thought and generally considered as the first of the three Primary Laws of Thought, which are as follows :

1. Contradiction — Nothing can both be and not be.

2. Identity — Whatever is, is.

3. Excluded Middle — Everything must either be or not be. These will hereafter be explained and applied as the

groundwork of ail Reasoning.

Then follows the analytical view of Logic, which shows it to be composed of seven elements, namely: The Art of Reasoning, the Argument, the Syllogism, the Proposition, the Term, the Apprehension, the Conception.

The mind ceases to analyze on the Act of Apprehension and changes to the opposite process of Synthesis, thus combining, 1, Apprehension into Term ; and 2, Term into Proposition ; and 3, Proposition into Syllogism ; and 4, Syllogism into Argument; and 5, Argument into Reasoning; and 6, Reasoning into the Primary Laws of Thought; and 7, the Art of Reasoning into Logic, our subject.

PRACTICAL QUESTIONS.

1. How is Logic defined?

2. Why the Art, rather than the Science of Reasoning?

3. What is the groundwork of Reasoning ?

4. Give the meaning of Contradiction.

5. Name and give the meaning of the other two laws of Thought.

6. What is a Primary Law of Thought?

7. Name the seven elements of Logic as shown in the Synthesis given.

8. Repeat these elements synthetically in order.

9. What is our exact subject ?

10. What branches of learning, must a student understand before he can pursue Logic successfully ?

"thus endeth the first chapter."

ns

Chapter II. The Seven Elements Of Logic Explained

1. An Act of Apprehension, the ultimate element in our analysis of Logic, is a pure conception by the mind of an object apprehended, thus, "to die for one's country is glorious." The words "to die for one's country" constitute the conception because they express exactly what the mind conceives to be "glorious." It takes all these words to express the conception in this proposition, and no more. Sometimes the conception is expressed by one single word, as man is mortal. The word man alone expresses the conception in this case, which is called a simple act of apprehension. Sometimes it is expressed by a number of words as "to die for one's country" as above, which is called a Complex Act of Apprehension. The Indian tribes of the West seem to understand how to express the complex, apprehension as indicated by their Christian names, such as " Old- Man- Afraid-of -his- Horse," " Young A/an - Afraid-of his-Horse," " Spotted Tail" etc.

When the Act of Apprehension is simple it gives us a simple term, and when it is complex it gives us a complex term. It is of the utmost importance that the Act of Apprehension should be a true as well as a pure conception. The greatest care should therefore be exercised in ascertaining in all cases hist what the act of Apprehension is, and also exactly what words should be used to express it, for when expressed in language it becomes one of the thiee terms of the Syllogism. If the Act of Apprehension is in any way faulty it will taint the whole argument.

Let it be remembered that it is not the words but the pure conception of what they express that makes the Act of Apprehension, and this Act of Apprehension makes the Term.

2. A Term in Logic is the Act of Apprehension expressed in language. There are three and only three terms in the Syllogism, and they are technically called the Major, the Minor and the Middle Terms.

EXAMPLE.

All men are mortal.

All Americans are i/ie/i.

All Americans are mortal.

Here '■'■Mortar' is the Major Term, because it includes the greatest number of persons. " Americans " is the Minor Term, because it includes the least number of persons. '■'■Men'''' is the Middle Term, because it is the medium of comparison between the other two terms.

Each of these terms is used twice, and when properly arranged they give rise to the three propositions of the Syllogism, which we next notice.

3. A Proposition in Logic is the legitimate expression of the agreement or disagreement between terms, as Cromwell was a hero ; Brutus was not a patriot. Here agreement is expressed between Cromwell and hero, the two terms, and this makes it a proposition. In like manner disagreement is expressed between Brutus and patriot, and this constitutes it a proposition.

The three propositions, technically the Major and Minor Premises, and the Conclusion, so arranged that the Middle Term is a medium of comparison between the major and minor terms, form the celebrated Syllogism of Aristotle, which we will next explain.

4. The Syllogism of Aristotle is the Procrustean Bedstead of all arguments, the ultimatum of all argumentation, the elementary form and test, the court of last resort, to which all arguments and modes of reasoning must finally come.

The basis of the Syllogism is Aristotle's Dictum, which, literally translated, is this : Whatever may be predicated of a whole class, may be predicated of each individual contained in the class.

Upon this principle the stagirite, that ancient Dialectitian, constructed the celebrated Syllogism which has come down to us unimpaired through a period of more than two thousand years, apd which, now as then, is composed of three propositions, and three terms which have been already explained.

EXAMPLE.

All men are mortal.

All Americans are men.

All Americans are mortal.

The Major Term " 'Mortal" is first compared with "Men" the Middle Term, then Americans the Minor Term is compared with "Men" the Middle Term, and finding that they agree both with the same third term they will agree with each other, hence we compare them directly with each other and declare their agreement, which forms the Conclusion.

5. An Argument consists of two parts, that to be proven, and that by which it is to be proven. That by which it is proven is embodied in the premises ; and that to be proven is embodied in the Conclusion.

When these parts are stated in their natural order and simplest form they constitute the Syllogism. But when they are inverted, so that the Conclusion is stated first, it is called the question, and the premises are joined to it by the word because as the reason.

Q. The basis of Reasoning is the Law of Contradiction with its associate laws of Identity and Excluded Middle, the three forming the " Primary Laws of Thought."

Contradiction is thus explained : Nothing can have, at the same time and place, contradictory qualities, for instance a piece of paper can not be both white and black at the same time and place. It may be white at one time and black at another, and white in one part and black in another, but can not be both at the same time and place. All propositions implying contradictory qualities are impossible and false, and so because they violate this Law of Contradiction.

Identity teaches that everything is itself, and not another, that is identical with itself.

Excluded Middle teaches that there is no middle or third course in affirming things and qualities. When the question is asked as to these things and qualities the answer must be yes or no. If you are asked whether gold be white or not white, you must answer yes or no. You must affirm that it is white or that it is not white. You can not answer the question by saying that it is yellow, although that may be true. Yet it is an excluded middle.

7. Reasoning or Ratiocination is the simple act of the mind by which we deduce the conclusion from known premises which are before the mind, thus having before us the two known propositions as premises to-wit :

All men are mortal.

Washington was a man.

The mind deduces the conclusion that Washington was mortal, although it is not directly affirmed. This mental process is Reasoning.

It matters not to what subject it may be applied, it is Reasoning, for there is but one universal principle of Reasoning. We have no such thing as li Mathematical Reasoning" 2 iS LOGIC IN IO CHAPTERS.

and "Moral Reasoning," as distinct processes; but it is the one principle as above described, whether applied to Mathematics, Physics or Metaphysics. A mind well versed in Mathematics may reason well on that subject, but it must do so according to the one principle of Reasoning.

The reason is the same, whether we reason by the method of Induction or Deduction ; and the Syllogism is equally applicable to both these methods, as will be shown hereafter.

SYLLABUS.

The student is advised to make himself thoroughly acquainted with these seven elements before proceeding further. Let him learn that an Act of Apprehension is the elementary principle — the ultimate element.; that it is all important that this should be a true conception as well as a pure one ; that this is determined by the primary laws of Thought; that the law of Contradiction declares that a thing is or is not — it can not be and not be. Identity proclaims that whatever is, is; that if a thing is it is ; and Excluded Middle declares that there is no middle course, that a line is either straight or not straigt; it can not be a third thing between straight and crooked. It may be difficult at first to distinguish between the meanings of the Law of Contradiction and the Excluded Middle — the meaning of Contradiction is at once self-evident. The meaning of Excluded Middle is equally as evident, but not so readily perceived.

Let it be rememembered that an Act of Apprehension expressed in language is a term ; that terms make propositions and propositions make the Syllogism, and the Syllogism is the form of every argument, and every argument is reasoning expressed in language, and the performance of all this is the art of reasoning, which is Logic — our subject.

LOGIC IN TO CHAPTERS. 19

PRACTICAL QUESTIONS.

1. Repeat by name the seven elements in order.

2. What is an act of Apprehension ?

3. What is a Term ? How many kinds?

4. What is a logical proposition ?

5. Of what is the Syllogism composed ?

6. Explain the three Primary Laws of Thought

7. Explain Ratiocination.

LOGIC IN IO CHAPTERS.

Chapter III. Logic As The Art Of Reasoning

1. We have already seen that we are indebted to Aristotle for the Law of Contradiction as the basis of Reasoning, as well, as the Dictum, the basis of the Syllogism. In like manner, we are also indebted to him for the very ground work of all sciences. That venerable stagirite and profound dialectitian about 350 years B. C. declared: "All science must set out from something already known ; in a word, must have its first principles or grounds (dp%ai), which are not themselves science, but the result of immediate cognition" which he distinguishes from strict science, but calls it certainty. (See Anal., Part I., 1.; Eth. Nic. V., 3.) Dr. Thomas Reid, the great common-sense Philosopher, uses the very same expression (dp%ai) as the first principles of science. We may not wonder then, that Aristotle is called the master mind of antiquity, since he has given us the basis of the Syllogism, of the Reasoning, and of all sciences. Logic was denominated by Aristotle as dialectic, and was considered by Plato as the regulator of all sciences, the all-comprehensive science whose object is eternal truth, and is therefore possible and knowable only to God; yet, the true ideal at which the soul of man should ever aim in order to become Godlike.

2. We now propose to erect our superstructure on the threefold foundation given by Aristotle. For other foundations hath no man fhan that of the first principles of sciences, the Laws of Thought, especially that of Contradiction, and the dictum of the Syllogism, the great "instrument of all demonstration."

Before we can reason at all we must know; must know whereof we reason ; must know that we ourselves exist, and that the external world exists; n.ust know the ego and the non-ego.

3. Our Beneficent Creator has so constituted us that we know these ground principles, and we know them in such a way as to require no proof of them. They are immediate cognitions, mental axioms. This original knowledge is given as the capital stock for the acquisition of more knowledge ; and it is not the property of a few philosophers, but is, as Dr. Reid says, the common sense and heritage of all the race.

Consciousness is the root of our knowledge. It is a witness to the mind of its operations. It testifies to the knowledge obtained by the mind through both the internal and external perception, so that we are conscious of the internal acts and states of our own minds, and conscious of the perception of the external world. This knowledge we cannot doubt. It is a certainty, a self-evident certainty. Here we begin.

4. We begin with the known and proceed to the unknown, the only method for the acquisition of knowledge.

The human mind, endowed with this original stock of knowledge, knows that it knows. It apprehends its own acts and states, and also external objects. This constitutes an Act of Apprehension, the simplest and ultimate element of Logic. The mind utters this Act of Apprehension in language, and then it becomes a term. The mind, having two such terms before it, proceeds by its own processes to declare that these terms agree or disagree. For instance, we have the two terms line and straight. The first Law of Thought, which is contradiction, declares that the line is straight or not straight. It cannot be both, it must be one and not the other. This peclaration is a proposition either affirmative or negative, according as agreement or disagreement is declared.

5. With propositions thus obtained, and known to the mind to be true, it next proceeds, by one of its faculties called Comparison, to compare others known to be true, and deduce therefrom a third proposition, called the conclusion, which arises out of the known propositions as premises by comparing the two terms, heretofore not known to agree> with the same third term as a medium, with which both having agreed, are now axiomatically declared to agree with each other.

This completes the process of Reasoning, and brings us to . a conclusion known to be certain. Thus starting on our original stock of knowledge, which is certain, we acquire other knowledge, and reduce it at the same time to certainty. We thus go on from one acquisition to another, adding to our faith knowledge, and to our knowledge certainty, throughout the vast domains of science.

It was in this manner, adding round after round of knowledge in spiral ascent up the "Hill of Science," that Aristotle, Descartes, Reid, and Hamilton reached the summit.

6. To know the process now described is to know Logic in its elements; to perform the process is to practice Logic. The former is the Science of Reasoning; the latter is the Art of Reasoning.

We now propose to illustrate the process by an example.

Let it be remembered that we must have some knowledge in order to obtain other. We know who John the Baptist was, and we know what a priest is. But we do not know immediately whether he was a priest or not. Hence we must seek this information through a medium. We know from the Bible that there were many priests, and that all the sons of priests were themselves priests. But the Bible is silent as to John the Baptist being a priest. Yet it tells us that he was the son of Zacharias the priest. Now let us take what we do know, and try to find out what we do not know. We have two terms, Baptist and priest, and we do not know whether they agree or not.

We select another term, to-wit, "Son of a priest," and compare the other two with it, and if they both agree with it, then of a certainity they will agree with each other, for the axiom says so. We thus compare them :

The sons of piiests were themselves priests. John the Baptist was a son of a priest. Therefore John the Baptist was a priest.

We now know mediately what we before did not know immediately, yet we know it as certainly as if we had known it immediately, because the conclusion partakes of the certainty of the premises.

7. Again, the Constitution of the United States provides for the election of the President, and eighteen of our citizens have been President, and enjoyed all the honors and emoluments, of the office. But the Constitution has not declared a single one of them President by name or person ; and if we deny this process of reasoning by mediate inference, we deny facts that are known and acknowledged to be true by the civilized world, to-wit, that each of these eighteen men has been President of the United States during certain periods of time in the Eighteenth and Nineteenth Centuries A.D. The Constitution has only declared that in the election "the person having the greatest number of votes shall be the President." It says nothing about George Washington, Thomas Jefferson, nor James K. Polk as President, yet each of these distinguished men has filled that position. Without mediate inference they could never have been known as Presidents. The process is simply this :

" The person having the greatest number of votes" is the medium of comparison, i. e., the Middle Term. President is the Major, James K. Polk is the Minor Term. The axiom says that things that agree with the same thing agree with each other. Now, if both the Major and Minor Terms agree with the Middle, we may unhesitatingly declare that James K. Polk was President of the United States. Let us try it.

The person having the greatest number of votes shall be President.

The President of the Senate declared that James K. Polk had the greatest number of votes in 1845. Therefore James K. Polk was President in 1845.

Deny this process, and there is no power on earth by which it can be made out that James K. Polk was ever entitled to the office (which he filled with so much credit to himself and profit to the country.)

Wc therefore lay this down, not as a convenient method of reasoning, or one by which men may reason, but as the principle by which they must reason, although in many cases they may not be aware of the fact and may not know the rules and principles by which they reason.

SYLLABUS.

We have presented this chapter in seven sections, and would advise the student to explain to himself the matter contained in each thus :

He should explain the three great principles for which we are indebted to Aristotle, and state what Dr. Reid has said of one of them ; what Aristotle called Logic, and Plato's views of the subject.

Explain on what this treatise is founded, and why; also what is said of this original stock of knowledge, its certainty and use. State where all sciences must begin and how, and proceed. How the first element of Logic is obtained; and then elaborated into the Syllogism ; and then give the axiom on which this mediate inference is based. Explain how it was shown that John the Baptist was a priest, and that James K. Polk was once President, and give the Syllogism in each case.

PRACTICAL QUESTIONS.

Let the student explain each of the seven sections.

Chapter IV. Reasoning By Induction And Deduction

1. Reasoning proceeds upon the Primary Laws of Thought as its basis by two methods — Induction and Deduction.

Induction is the method of Reasoning by which we discover laws from individual facts and causes from effects.

Deduction is the reverse method of deriving facts from laws and effects from causes.

To correspond with these two methods, Aristotle made two sorts of Syllogisms, the one Inductive and the other Deductive. The former sets out from particulars already known, and reaches general conclusions. The latter sets out from some general and admitted principle, and reasons to a particular conclusion. These are the only strictly scientific procedures, and we will now illustrate each by an example.

2. We submit as an example a Syllogism of Complete Induction, and reserve what is generally called Incomplete Induction for a more thorough consideration hereafter.

EXAMPLE OF INDUCTION.

Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, and Neptune all revolve around the Sun in elliptical orbits. These are all the planets.

Therefore all the planets revolve about the Sun in elliptical orbits.

The above is on the supposition that these are the only

planets.

EXAMPLE OF DEDUCTION.

All the planets revolve about the Sun in elliptical orbits.

Jupiter is a planet.

Therefore Jupiter revolves about the Sun in an elliptical orbit.

These will serve to illustrate the two methods of Induction and Deduction.

' 3. We propose to treat Induction under the usual divisions of Complete Induction and Incomplete Induction.

We have already given an example of Complete Induction, and will only add that it owes its name to the fact that in this process a complete examination of all the individuals or facts may be made and declared.

Thus, Jesse had seven sons. One had been chosen king, and Samuel was sent to anoint him without knowing which it was. He caused six to pass before him for inspection and refused them all. If he had stopped at this his induction would not have been complete. But he completed it by sending out for David, the lad attending the sheep, and anointing him king.

The Dictum for this kind of Induction is this :

' ' Whatever is true of all the constituent parts is true of the constituted whole. "

4. Incomplete Induction is defined to be that process of induction which takes a part of the individuals or facts known to represent all the remaining ones, and for this reason it has been adjudged not certain in its conclusions.

The name and nature of this method of induction are calculated to impress the mind of the young with the idea that its results are uncertain, yet this is the very process from which the greatest part of all our knowledge is derived, and especially is this true in the sciences. It therefore presents the most interesting question connected with the whole subject of Induction. The question is this: On what principle are inductions deemed sufficient, short of complete enumeration of all the particulars ?

We answer, "Our confidence in the uniformity of Natural

Laws is the principle." This confidence is embodied in the words which we denominate the Canon :

" Under the same circumstances and with the same substances the same effects always result from the same causes." v/

5. All experience teaches us that order, regularity, and uniformity prevail in the universe, in the " cosmos" which means order ; and caprice, chance-work, and uncertainty are excluded. If it were otherwise the universe would crumble into chaos.

While it is conceivable that any one of the natural laws might be reversed — and it is certain that some of them have been miraculously suspended on great and important occasions — yet our reliance upon their permanence is simply unlimited. The thought that there will be no more daylight after to-day; that the water from the spring today would destroy the life which it refreshed yesterday; that a stone would remain suspended mid-air instead of falling, never enters our minds except as an idle whim cr an amusing fancy.

6. Let us examine a few examples of this so-called Incomplete Induction in the light of the canon already announced, and see if it answers fully the question propounded.

Let us first appeal to Mathematics. Euclid, in his 5th Proposition of Geometry, takes a single triangle and proves that its opposite angles are equal, and says not a word about any other triangle. But from this one experiment he proceeds to declare that any and all Isosceles triangles have their opposite angles equal, and the world cries Amen to the conclusion !