LOGIC.

OBJECTS OF LOGIC.

THE

HE objects of Logic, as of Grammar and Rhetoric, are partly theoretical and partly practical; partly to give you general ideas concerning the nature of names; assertions, the foundations of reasoned truth, and the various departments of thought and inquiry; partly to warn you against the fallacious tendencies of the human mind, and to teach you the conditions that must be observed in all departments of thought and inquiry before you can attain to true conclusions. Men may reason correctly without knowing Logic, as they may write correctly without knowing Grammar, or convince an assembly without knowing Rhetoric: these things are done every day without a conscious knowledge of any rules whatsoever; but Logic teaches you the ultimate An assertion requires, in the first place, that nature of what you are reasoning about, of the there should be two things mentioned; it is not instrument that you employ, and of the grounds possible so to mention a single object as that whereon you rest when your reasonings are sound. it shall be a matter of belief or disbelief. Thus, And this knowledge is both interesting and profit-fire burns,' 'gold is yellow,' 'bread is nourishing, able. It may not guide you to great discoveries; 'the sun is the centre of the planetary motions' it may not preserve you from all errors of reason- -each contains at least two things or notions ing; it will not eradicate all the fallacious tenden- coupled together. Fire is one thing, burning is a cies of your mind, but it will help. different thing, if there be any meaning or anything to believe in the assertion. But the mention of two things is not enough; the two names of 'gold,' 'yellow colour,' do not make an assertion of themselves; the asserting power is conferred by the verb 'is;' and we shall find that every assertion requires a verb, or that the verb is the part of speech which completes the force of an assertion, or has the power of causing belief or disbelief in the human mind.

The science of Logic has had two great starts in history, both originating in practical necessities. The first was given by Aristotle, the second by John Stuart Mill. The Deductive Logic of Aristotle was suited to the wants of the Athenian people in their Public Assembly and Courts of Law. An audience met to hear a question argued and to form an opinion, have to be guarded against specious inferences from their accepted beliefs; it is good for them to know the correct As an assertion, therefore, requires the mention forms for the application of general principles to of two things, 'every proposition must contain two particular cases, and the ways in which these forms terms. Of these two terms, the one that is spoken most readily become obscured so as to cheat them of is called the subject; what is said of it, the into erroneous conclusions. This, in the main, was predicate; and these two are called the terms (or the practical side of Aristotle's logic. In like man-extremes), because, logically, the Subject is placed ner, the Inductive Logic of Mill was suited to the first, and the Predicate last; and in the middle interest in modern research. Mill did not invent the copula, which indicates the act of judgment, as the canons of valid induction or the conditions of by it the Predicate is affirmed or denied of the valid hypothesis: these had been acted upon more Subject.'-Whately. Thus, in the above instance, or less vaguely by reasoners in all times, and had 'gold,' the thing spoken of, is the subject; 'yellow,' even been formulated by men of science; but the predicate; and 'is,' the copula. The verb 'to Mill was the first to conceive the idea of including be' is the most universal copula, and every other them within the domain of Logic, and referring mode of affirmation or denial might be reduced to them to the fundamental principles of reasoning. it. Agreeably to their origin, the practical value of Deductive Logic is to help in securing consistency; of Inductive, to help in securing truth.*

NAMES, CLASSES, AND PROPOSITIONS. Both Deductive and Inductive Logic profess to exhibit the ultimate grounds of Belief; and all

communications between men of matter for belief or disbelief are made through the instrumentality of language, and in the form of what we call in common speech Assertions, in Grammar, Sentences, and in Logic, Propositions.

A matter of belief is something that we can act upon; something that will enable us to do one thing for the sake of attaining some other thing. When we say 'bread is nourishing,' we do more than announce an object, 'bread,' and a property, nourishing' we tie these two things together with a bond of union which rouses the activity of the human mind, and causes it to set to work in some given course. Belief is the state preliminary to action, or the state disposing to action when some given emergency arises; and assertions or propositions are the subject-matter of this faith or belief.

The present paper follows the arrangement and treatment of the subject in Professor Bain's Logic, to which the reader is referred

for fuller information.

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The Different Kinds of Names.

The terms of a proposition, its subject and its predicate, must be names; hence, every proposition must contain at least two names, and it becomes necessary for the logician to consider the nature of names so far as that may affect logic. Other sciences and arts that have to deal with names-Philology, Grammar, Rhetoric-divide names into classes, to suit their particular purposes-Aryan and Semitic; nouns, adjectives, verbs; plain and figurative, stirring and pathetic:

and Logic also makes a division of names to suit its purposes. Two distinctions among names are of value to the logician: the distinction between General and Singular names, and the distinction between Positive and Negative

names.

'A Singular or Individual Name is a name applicable to one thing. A General Name is applicable to a number of things, in virtue of their being similar, or having something in common.'-Bain. Individual or Proper names serve merely the purpose of marking out some one thing from among the multitude of things at large, exactly as could be done by pointing to it with the finger, or in any way indicating it to another person. Such names as England, Nile, Mont Blanc, Niagara, Napoleon, give no information about the things that they denote: they imply no properties or attributes, and may be names of dogs, cats, or prize oxen. Now, Logic having to do with assertions about the properties of things, has little concern with these Singular names, except when it has to keep you consistent in your affirmations regarding whatever they are applied to. The names of interest in Logic are General names-country, river, mountain, waterfall, maneach of which is applied to many different things, in different ages and regions, to indicate what they have in common. General names are said to have a meaning, or connotation: they imply the possession of certain attributes common to all the individuals that they are applied to.

Next for the distinction between Positive and Negative names. This is more subtle, and cannot here be fully explained. When you make an assertion about a subject, you must always by implication deny something: when you say that a bar of iron is hot, you virtually deny that it is cold. Such names as hot-cold, wet-dry, fresh-weary, are called positive and negative names: the one is negative to the other's positive, and positive to the other's negative. If we were to enter fully into this distinction, we should have to shew that nothing is known except by reference to an opposite-a principle called the Relativity of Knowledge; but it is enough for our present purposes to say that in logical operations it is often useful to regard all the things denoted by a general name-man, good—as standing by themselves against all the things that are not-man, notgood, all the things that the general name can not be applied to.

The greater the number of points of community, the smaller the class, and inversely. 'Men' is a smaller class than 'animals,' and the individuals of the class have more in common. Classes are divided into Higher and Lower according to their extent. A higher class is called a Genus with reference to its lower classes, which are said to be Species under it. Animal is a genus, under which man, bird, fish are species. The points wherein one species differs from all other species under the same genus are called its Differentia.

Assertions, or Propositions.

When an assertion is made concerning a whole class, it is said to be a Total or Universal Proposition; when it is made concerning a portion of a class, it is said to be a Partial or Particular Proposition. This is said to be a distinction in the Quantity of Propositions. The logical forms are: All A is B, and Some A is B. In common speech, the quantity is often left indefinite, and one of the reasoner's first considerations should be directed to the real quantity intended. Do 'Honesty is the best policy,' and 'Haste makes waste,' belong to the form All A is B, or to the form Some A is B? Are the assertions universal or partial? Do they apply to all honest actions, to all hasty actions, or to some?

Propositions are also divided into Affirmative and Negative, which is said to be a distinction according to Quality. The above forms are Affirmative. The Negative forms are: No A is B (Universal), and Some A is not B (Particular). The Negative Universal is the complete and uncompromising contradiction of the Affirmative Universal; the Particular Negative is a mild limitation. All Propositions are either Universal Affirmatives, or Particular Affirmatives, or Universal Negatives, or Particular Negatives.

When you affirm anything, you always by implication deny something else, and it is important to know what the various forms commit you to; in other words, what terms are convertible. This gives rise to the logical department called the Conversion of Propositions. Affirmative Particular propositions are simply convertible: if you admit that Some A is B, you are bound in consistency to admit that Some B is A: if some hasty actions are wasteful, then some wasteful actions are hasty. A Negative Particular-Some A is not B-commits you to nothing positive beyond itself. Some B, or No B, or All B, may be A, for anything that it implies. A Universal Negative is simply convertible: if No A is B, then No B can be A-the two classes are mutually exclusive. A Universal Affirmative-All A is B indi-obliges you to admit that Some B is A: but you should be on your guard against admitting that All B is A.

Classes, Notions, or Concepts.

Both of the above divisions of names proceed upon the arrangement of things in Classes. Things are arranged in classes, as already cated, on the ground of possessing a common property or properties, a point or points of likeness round things form a class on the ground of their roundness; churches, on the ground of their being public buildings used for religious worship. When the points of agreement in a class are thought of in the abstract, they are said to form a Notion or Concept: being a building, being public, and being used for religious worship, form the concept or notion of a church. The general name is said to denote the class, and to connote the notion or points of community among the individuals composing the class.

The conversion of a Universal Affirmative is practically the most important of these cases. It is a very common fallacy to treat the terms of a universal affirmation as if they were simply convertible. To take a familiar example: the proverb, 'Ill-doers are ill-dreaders,' is often applied as if all ill-dreaders were ill-doers; and the proposition that all Protestants exercise the right of private judgment, as if every one that exercises the right of private judgment were a Protestant, (Bain, i. 114.)

DEFINITION.

the positive notion: assemble representative particulars, and see where they agree. When you wish to give precision to your definition of Solids by defining also Liquids and Gases, you assemble

"

In Bain's Logic, which endeavours to render definition more precise, by expounding its fund-representative instances, and find that Liquids amental canons, this subject is taken up after and Gases yield to the slightest pressure, and Deduction and Induction; but in our slight sketch, have no fixed form, except as given by solid all that we have space for will come in more inclosures.' appropriately here. Logic having to deal with general propositions-that is, with propositions or affirmations concerning classes-it is obviously of the highest importance that those classes should be exactly defined. Now, the definition of a class consists in stating all the properties common to the individuals of the class. You define the class by defining its notion or concept. You cannot draw a ring round all the individuals composing a class, but you draw up a precise statement of a common property or properties, and make no attempt to mark out the boundaries of the class, further than saying that it consists of all individuals possessing the defined propertyor, in other words, all individuals coming under the notion.

DEDUCTION.

The first thing that you naturally do, when you wish either to take stock of what you know and believe, or to discuss the positions of an opponent in debate, is to turn each separate proposition It will not do, however, to fix on notions arbi- round and round on every side, to see what it all trarily out of your mind, and classify the concrete implies. Your next step should be, to consider universe accordingly. You ultimately subject the what may be legitimately inferred or deduced from concrete particulars to the abstract notion, but you propositions that you admit to be true. If you must take the notion in the first instance from the followed our account of the nature of classes, it particulars. Notions consist merely of the points may have occurred to you, that every assertion of resemblance among the members of classes, made concerning a class must be true of every and classes are formed in science upon a strict individual contained in that class, because those principle, which is this: 'Of the various group-individuals, in so far as they are members of the ings of resembling things, preference is given to class, are all alike: an assertion about a class is such as have in common the most numerous and true of every individual possessing the common the most important attributes.' This is the golden properties of the class. Despots are bad rulers,' rule of classifying. Of course, your impression of is a proposition true of every individual possessing the importance of attributes may vary with your the attributes of a despot. When, therefore, you purposes; but in all cases, in any classification admit that despots are bad rulers, you are bound professing to be philosophic, you must bear in in consistency to admit the proposition concerning mind that it is necessary to have some substantial every individual that can be shewn to possess the reason for forming a class, other than mere fancy common attributes of the class. This principle is to put together all individuals having a certain the foundation of Deductive reasoning: and the point of resemblance; also, that the points of Syllogism, as a safeguard against fallacious Deresemblance shall be as numerous as possible, so duction, consists in placing deductive inferences that to name a thing as belonging to a class shall in a form convenient for the application of the give as much information about it as possible. principle.

Two propositions, besides the conclusion, are involved in every legitimate deduction. At the basis of all is your general proposition concerning a class of things, into which form all such general propositions as 'Haste makes waste,' Honesty is the best policy,' may be reduced. Then, before you can proceed to the proposition to be inferred from this-that such and such an action is wasteful, or good policy, you must have an applying proposition to make out that the action belongs to the class concerning which the general allegation is made: that it belongs to the class of hasty actions, or of honest actions. These two propositions are called the Premises of the deduction. When they are formally stated, and followed by the conclusion, thus― All hasty actions are wasteful; This is a hasty action; Therefore, this is a wasteful actionthe whole is called a SYLLOGISM, which, from its etymology, means a joining together of propositions.

The great practical advantage of the syllogism consists in its putting a deduction into a form in

It being premised that you have some justification for forming a class, the first canon is Assemble for Comparison the Particulars coming under the Notion to be defined. You cannot, of course, assemble all the individual instances, but you must assemble 'representative instances sufficient to embrace the extreme varieties' (Bain, ii. 156). If you wish to define a 'solid,' you must bring together, mentally or materially, a large number of representative solids-metals, rocks, woods, bones and compare them, to find out in what they all agree. Having found that they all agree in resisting pressure, applied to change their form, you take this resistance as the notion of the class, and define solids by saying: 'Solids are bodies that resist force applied to change their form.'

Between two such opposed notions as Solid and Liquid, there is often a doubtful margin of particulars that do not belong decidedly to either class. It is difficult to say whether a jelly is a solid or a liquid: it does not lose its form so readily as a liquid, nor does it stand out against pressure like an unquestionable solid. Such cases warn us not to attempt to draw too short a line of distinction: a margin should be left for doubtful cases.

The second canon proceeds upon the principle of Relativity-that every real notion must have an opposite also real. It is: Assemble for Comparison the Particulars of the Opposed or contrasting Notion. It gives greater precision to a notion to define its opposite. In defining the opposite, you proceed upon the same plan as in defining

which its validity or invalidity is at once conspicuous. Both premises are presumed to be true; the syllogism has only to exhibit whether the conclusion is contained in them. As a practical machinery, the syllogism is only a safeguard against inconsistency. As such, it is not without its value. Suppose an orator declaiming about the evils of mob-rule as an argument against an extension of the suffrage, you may be unable to question the truth of the ground proposition that mob-rule is an evil thing; but before you are led away to act upon the conclusion of the orator, you must consider whether you believe the applying proposition-that the new electorate would be a mob.

viewed as a conjunction of terms, and all possible valid conjunctions of terms are elaborately set forth-when, in short, the syllogism is treated mathematically, as a combination of abstract symbols-considerable variety of syllogistic forms is introduced. These we shall briefly state.

Syllogisms are divided by some logicians into three figures, by others into four, according to the position of the middle term, which may either be the subject in both premises, the predicate in both, or the subject in one, and the predicate in the other. The most common case is that in which the middle term is the subject of the major premise, and the predicate of the minor, as in the above example. This is reckoned as the first In elaborating the forms and canons of the figure. When the middle term is the predicate in syllogism, logicians have found it useful to divide both premises, the syllogism belongs to the second each proposition into its two terms, its subject and figure. (No liar is to be believed; every good predicate. As a matter of practice, the best rule man is to be believed; therefore, no good man is a that can be given you is, to reduce every deduc- liar.' Here the middle term, 'to be believed,' is tion to three propositions: an assertion concern- the predicate in both premises.) When the middle ing a class; an assertion that something (an term is the subject in both, it belongs to the third individual or another class) belongs to that class; figure. (There is some anger which is not blameand finally, as a legitimate conclusion, an asser-worthy; every kind of anger is a passion; theretion concerning this something of what the first fore, some passions are not blameworthy.' The proposition asserted concerning that class. When middle term in this case is 'anger,' which is the you have reduced the deduction to this form, you subject in either premise.) In the fourth figure, will then be able to decide by the light of your the middle term is the subject of the minor premown understanding whether you accept the truth ise, and the predicate, of the major. This figure of the premises; and if so, whether they warrant is considered to be merely an awkward form of the the conclusion. A conclusion is often presented first, and no practical value in reasoning. to you as if founded upon one proposition only: thus, This man is a rogue; he is not to be trusted.' But you will bear in mind that there must be two guaranteeing propositions; that in all such cases, one of them must be supposed or taken for granted; and you will exert yourself to discover the lurking premise, so as to state the syllogism in full form. The omitted premise in the above case is: 'No rogue is to be trusted :' a general proposition concerning a class.

·

Each figure is divided into moods, according to what are called the quantity and quality of the propositions—that is, according as they are universal or particular, affirmative or negative.

The scheme on next page represents all the legitimate moods-that is, all those where the conclusion follows correctly from the premises. A is the minor term; C, the major; B, the middle term.

The invention of the fourth figure is commonly attributed to Galen, but not on the most satisfactory evidence. It has often been rejected by logicians, on the ground that it is but the first inverted by the transposition of the premises. This, however, is not exactly the case, although, on the whole, it ought to be excluded as alike useless and deformed (Baynes's Translation of the Port Royal Logic, Note 48).

But though this arrangement is practically sufficient, and is founded directly on the fundamental principle of the syllogism, the forms worked out by Aristotle and other logicians are an interesting study. As we have just said, they divide each proposition into two terms. Altogether there must be three, and only three, terms in a syllogism, each being repeated twice in the course of the three propositions. You have the predicate of the leading assertion, the assertion in which you are interested, the conclusion: that is called the Major term. Then you have the subject of this assertion, which is called the Minor term. And most important of all, you have the Middle term: the class involved in the two premises, concerning which the predicate of the conclusion can be asserted, and to which the subject of the conclusion can be asserted to belong. In the syllogism-'No rogue is to be trusted; this man is a rogue; therefore, this man is not to be trusted'' trustworthy person' is the major term, 'this man' is the minor term, and 'rogue' is the middle term.

It can be shewn that syllogisms in any of the above forms are legitimate-in other words, that if the premises are true, the conclusion must be true also; and that no other combinations of universal and particular, affirmative and negative propositions can yield true conclusions.

If, for example, we take the first mood of the first figure-All B is C; all A is B; therefore, all A is C: all animals are mortal; all men are animals; therefore, all men are mortal-the reasoning is seen to be true from the very meaning of language, or is what may be called selfevident. If we say that‘all animals are mortal,' we have already affirmed that every species or class of animals, everything coming under this designation, has the attribute of mortality, men being necessarily included. So that, in fact, the major premise has already affirmed the conclusion, provided only we are sure that the subject of the conclusion (men) belongs to the subject of the major (animal). This assurance is given in the minor (all men are animals), whence the conclusion is made out as a matter of necessity. In

The normal form of the syllogism, when it is arranged according to its fundamental proposition, presents the middle term or connecting class as the subject of the major or grounding proposition, and the predicate of the minor or applying proposition. But while all valid syllogisms may be reduced to this form, yet when the syllogism is

certainty and self-evident nature of the syllogism | manner that the conclusion was really contained depend on this very circumstance, that the conclusion affirms nothing that has not been affirmed in the premises; if it were otherwise, the reasoning would be bad. We cannot step one jot out of the compass of the two premises, but we may affirm in as many new forms of language as we can contrive, the same facts as these have affirmed. The syllogism is a check upon us when we are in danger of thus transcending the premises, which we are sometimes liable to do, from the complications and involutions of language accompanying the statement of facts.

Passing to the other figures, we might, by examining each syllogism in detail, and turning it over on all sides, satisfy ourselves in the same

in the premises. There is, however, another mode of making out the sufficiency of the reasoning in each case-namely, by shewing that all the syllogisms of these figures come under those of the first figure, being in fact proved when they are proved. This is to reduce the succeeding figures to the first, or deduce them from the first. It is the manner of mathematics to avoid independent appeals to fact as much as possible, and make one truth prove all that can possibly come under it, as we may see in Euclid. So logicians shew that an argument in the second, third, or fourth figures may be thrown into a syllogism of the first figure, and thereby acquire the certainty that we have just seen to belong to the cases of that figure.