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“ Logic should expound the laws of thivking, and universal grammar the laws of speech, apart from their special modifications, in any given language.” logic treats only of those laws or conditions to which objects of sense are subjected in the mind,” and hence it is called an à priori science. “It unfolds the laws of the intellectus ipse, and gives no account of the representations of the senses as such.” “ The appetite for finding out laws from facts, causes from effects, necessary truths from fleeting occurrences of the day, puts in its claim to gratification, which is as legitimate, if less imperious, as that of the animal nature for food and sleep." “ He who loves to see the processes of his mind reduced to their laws and causes, to him are logical studies a pleasure—to him they bring fruit." Logic has its use also in improving the condition of men; it teaches, or perhaps I may only say, may be made to teach them to think.” “Every art and science has the right to form its own terms; but necessity alone can justify the exercise of it.” “I see no cause to deviate materially from the ordinary distribution into three parts, the first teaching of conception, or the power of forming general notions; the second of judgment, or the power of deciding whether two notions agree or not, and the third of syllogism, or the power of drawing one judgment from another.” When men think logic explains the laws according to which their thoughts run, a knowledge of these laws and principles, independent of ulterior profit, is always gratifying; and, inasmuch as the clear understanding of what is right is always useful for the avoidance of what is wrong, logic is a useful instrument in thinking. But it requires to be remembered that it gives the forms of knowledge, not of matter.

The foregoing paragraphs give in brief the chief ideas which are regarded as necessary for introductory explanations. They constitute an abstract of the author's view of the nature, province, divisions, relations, and uses of logic; and the expository portion of the book commences with a series of observations on conceptions, based chiefly on Leibnitz and Wolf, of which the following paragraph exhibits a concise summary :

“ The impression which any object makes upon the mind may be called a presentation."

TABLE OF NOTIONS.

Confused
Clear (cognitions)

S Adequate
Presentations

Distinct

Inadequate
Obscure

Symbolical

Notative “ There are no less than five steps which must be taken by every one who fully and fairly realizes a general notion. 1. Comparison is the act of putting together two or more single objects, with a view to ascertain how far they resemble each other. 2. Reflection is ascertainment of their points of resemblance and the points of difference. 3. Abstraction is the separation of the points of agreement from those of difference, that they may constitute a new nature, different from, yet including, the single objects. 4. Generalization is the recognition of a class of things, each of which is found to possess the abstracted marks. 5. Denomination is the imposition of a name that shall serve to recall equally the genus or class, and the common nature. The first part of logic explains that power of the mind which groups single objects into classes, so that the classes have names and attributes of their own. Its principles are these :-(1) The nature of every higher notion is found in the lower ; consequently (2) the name of the higher may always be applied to the lower,—thus man may be called an animal, because the marks of life and sensation which distinguish animals are found in him; (3) the higher notion (genus) includes the lower notion (species) with other species, and is therefore of wider extension than it; but the species implies more marks, has a fuller definition, than the genus, and is said, therefore, to be of deeper intension than it; (4) that set of marks which distinguishes any species from the species in the same genus is called its specific difference; (5) the whole nature of a species is ascertained, and its definition given, when the properties of the genus and those which make the specific difference are brought together; (6) we ascend from lower conceptions to higher by throwing away specific differences, i. e., by abstraction. We descend to lower ones by resuming the marks we have thrown away, i, e., by determination; (7) in a system of subordinate genera each must contain the individuals included in the lowest;(8) co-ordinate species cannot contain the same individuals; (9) the conception of an object consists of the aggregate of its marks, with the notion of existence superadded; (10) singular objects are invariably referred to and viewed through general conceptions; (11) a conception is complete and adequate when it can be resolved at pleasure into its implied marks by definition, and into its contained species by division; (12) two marks which stand to each other as positive and privative, like wise and unwise, are called contradictory, because it would be a contradiction in terms to assign them at the same time to the same object. Two marks are called contrary, when it is known à posteriori, by experience, and not à priori, by the very form of expression, that they cannot belong to the same objectmas wise and wicked, wurm and frozen.

Part II., on judgment, contains much matter of great value. The sections on definitions, on judgment, &c., are full of acute discussions, and open up a question which requires considerable discussion, and will amply repay study-viz., Ought logic to concern itself with all conceivable forms of predication, or with those only which have actual place in effective thought ? This involves, further, the whole topic of the symbolic notation of propositional forms, and therefore the propriety of extensions of syllogistic processes far beyond those employed and legitimated by the decisions of the Aristotelic logicians. This interesting subject we shall not venture upon in our present paper. We shall find an opportunity more fitting, we presume, when considering and reviewing the works of the most original of the great modern investigators of logical thought (perhaps we should not even say after Sir William Hamilton), Augustus De Morgan, author of "Formal Logic,” &c. We shall, therefore, in the meantime confine ourselves to our expository analysis, and gather together on a subsequent occasion the scattered threads of modern speculations on the syllogism. To proceed :

“Every act of judgment is au attempt to reduce to unity two cognitions.” “A proposition is the expression of a judgment in words." "Every judgment has three parts,—the subject or notion about which the subject is ; the predicate or notion with which the subject is compared; and the copula or nexus, which expresses the mode of connection between them." “ The relation in which the subject stands to the predicate in a judgment, whether as coincident or not coincident with it, we call the doctrine of relation; as to which we find that predicates are of two kinds-substitutes, or definitions, and attributes.

The nature or form of judgments consists

in their having

SUMMARY OF THE ANALYSIS OF JUDGMENTS.

Universal.-Where the whole subject is joined As to wbich (1) QUANTITY. they are

to the predicate; or, either

Particular.—Where part of the subject is

joined to the predicate.
SAs to which 4 formative vtWhere the predicate is decided
QUALITY.

they are
either

Negative. Where the predicate is decided not

to agree with the subject.

Attributive.-Where an indefinite (i. e., an anAs to which

distributed) subject is assigned to the sub

ject; or,
(3) affirmative
RELATION.

Substitutive. Where a definite (i. e., a distrijudgments

buted) predicate is assigned to the subject, are either

which may be substituted for it and serve as

its definition.
EXEMPLARY TABLE OF ALL THE JUDGMENTS.
Sign.
Escample.

Quant. Qual. Rel.
A
All plants grow.

Univ. Affirm. Attrib. E No right action is inexpedient.

Univ. Neg. I Some muscles act without our volition.

Part. Affirm. Attrib. 0 Some plants do not grow in the tropics. Part. Neg. U Common salt is chloride of sodium.

Univ. Affirm. Subst. Y Some stars are all the planets.

Part. Affirm. Subst. “Some judgments are merely explanatory of their subject.” They are called explicative (or analytic) judgments, because they unfold the meaning of the subject without determining anything new concerning it.” Judgments of another class attribute to the subject something not directly implied in it, and have been called implicative (synthetic], because they enlarge or increase our knowledge."

“Part III., Syllogism.-Reasoning," while valuable, has its worth impaired by an air of indecision in the matter of schemes of notation. The author, in 1841, drew up a scheme for himself, constructed from the logical works he consulted; by its publication in 1842, Thomson had the honour of being the earliest among British logicians who explicitly argued in favour of an extension of the theory of the syllogism beyond the scope given to it by Aristotle, and which had been accepted, in general, as the perfection both of system and simplicity. Sir Wm. Hamilton had, it is true, taught for some time-two years or so—a theory of the syllogism differing in detail and extent from that of the ancient expositor of logic, and Augustus De Morgan was about the same time gaining his first notions of a system which extends beyond the common one in several directions. In each of these three methods, thought out and carried on in parallel, not successive lines, an attempt was made to push thought beyond the usual restrictive forms of language, and to acquire the right of stating explicitly in language what is contained implicitly in thought, so that thought, usually subjected to elisions in expression, might have its exact form fully and fairly exhibited by the thoroughgoing quantification of every term. Of these able and independent speculations, Thomson's was first dis

tinctly published, and his system is, we believe, the result of investigations carried on without any consciousness of the course of thought pursued by the great compeers, Hamilton and De Morgan. The scheme and system of the (alas !) late Professor George Boole, LL.D., appears to have been equally independent in its origin, though subsequent in date ;-but of this more in an intended paper on that writer. To the credit, therefore, of publicly initiating the movement for an extension of the common forms of enunciation, which forms so important an element in modern logic, "Thomson of Queen’s” is, we believe, fully entitled, though he has not progressed so far on the way as those who held similar general aims with himself, viz., to add to the authorized contents of the science, and by extend ing to necessitate the remodelling of its details, so as to make it include the entire results of the formal laws of thought.

The whole discussion regarding the nature, province, contents, and details of the science of logic is too wide for consideration here, and, as already intimated, we propose to adjourn the exposition of the effects of the critical philosophy on logical studies till we can bring into one view a notice of the recent extensions of formal logic and of proposed additions to its speculative principles and its practical uses. We need only here say that, in the "Laws of Thought,” figure, notation, inference, immediate and mediate, canons of thought and compound forms of thinking, find ample discussion in clear and well-arranged phraseology, in a style more didactic than dogmatic. To the following passages we desire to call the reader's attention, as specimens of clear exposition and terse expression.

“When the state of our knowledge does not warrant us in judging at once whether two conceptions agree or differ, we seek for some other judgment or judgments, that contain the ground for our coming to a decision. This is called reasoning, which may be defined as the process of deriving one judgment from another.” “In some cases we are unable to decide that the terms of the question agree with or differ from one another without finding third, called the middle term, with which each of the others may be compared in turn. This is mediate inference." “ The law on which all mediate inference depends may be thus expressed :-The agreement or disagreement of one conception with another is ascertained by a third conception, inasmuch as this, wholly or by the same part, agrees with both or with only one of the conceptions to be compared.” Hence-(1) “A syllogism will contain three notions, and no more. (2) A syllogism must contain three judgments, and no more. (3) One premise at least must be affirmative. (4) The worst relation of the two terms with a third, that may be established in the premises, shall be expressed in the conclusion. (5) If one of the premises be negative, the conclusion must also be negative. (6) The comparison of each of the two terms must be either with the whole or with the same part of the third term. (7) Neither term of the conclusion must be distributed, unless it has been so in its premise.” These seven general rules are directly evolved from the general canon, and are only so many cautions to employ it properly.

After detailing the usual logical processes of argumentation, and explaining the systems of notation proposed by Lambert, Euler, Hamilton, &c., he follows up the subject by Part IV., on “Applied Logic.” This is perhaps the most original and thoughtful portion of the book,—that portion which really forms its chief characteristic as an addition to modern works on reasoning. Here he gives the best proof that "the sedulous practice of logical analysis will richly reward the understanding with accessions of strength and clearsightedness.” He affirms that the four following questions require to be answered by applied logic:

1. How are the causes of facts to be distinguished amidst a multitude of other facts all open to observation ? 2. How are causes discovered which are less open to observation than their effects ? 3. When should an incomplete enumeration or induction of facts be deemed sufficient, and on what principle? 4. How should new laws be expressed and recorded ?

On these subjects he makes many judicious observations, and the volume concludes with the following paragraph on the utility of logic :

" Let those who wish to possess the intellect they have received from above, in the depth and clearness, the sober composure, the calm activity, which a high degree of culture can alone bestow, venture to study logic in a larger spirit than the merely bistorical. Let them become dialecticians, not in the sense which the sophist attached to that name, but rather in that which the scourge of sophists gave it. Let them not use so excellent a weapon as the reason in mere play, with à guarded point and bated edge ; but let them keep it sheathed, sharpened, and shining, till a battle has to be fought against an error. Let them watch for themselves the processes gone through in completing any science. If the rules given in books are erroneous, let them try to correct, if imperfect to complete them; or if experience verifies their truth and utility, let them be regarded with a degree of trust greater than could have been awarded to them before, when they stood in books, the mere historical record of other men's philosophy. No one who has studied logic in this conscientious spirit has ever found it trifling or useless."

Our analysis of this work has considerably exceeded our original intention ; but we felt unwilling to omit the numerous passages we have quoted, not only because they were evidences of the author's thoughtful and careful acquaintance with the subject, but also because they possessed a special value to all readers for self-culture. To them the perusal will be a delight, and those who peruse this abstract will find the help it gives if they proceed, as we hope they will, to study the work itself. It merits close attention.

Immediately after taking his degree, he was chosen Fellow of his College. He was ordained Deacon in 1842, and having accepted a curacy at Guildford, in Surrey, about thirty miles from London, the Rev. Wm. Thomson, M.A., engaged in active duty as a clergy

Shortly afterwards, being ordained Priest in 1843, he was appointed Vicar of Cuddesden, near Wheatley, in Oxford, a preferment in the gift of the bishop of that diocese. While on a visit to his native town, he preached an Assize Sermon, in the Cathedral of Carlisle, on

· Scriptural Teaching the Safeguard against Crime,” which has been separately printed. In 1844 he was called to Oxford to act_as I'utor in Queen's, of which he subsequently became Dean, Bursar, and, ultimately, Head. In 1848 he was appointed Select Preacher by the University. At the Lent Assizes

man.

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