THE SCIENCE OF LOGIC;
OR,
AN ANALYSIS OF THE LAWS OF THOUGHT.
BY REV. ASA MAHAN,
AUTHOR OF AN "INTELLECTUAL PHILOSOPHY,"
"A TREATISE ON THE WILL," ETC.
"Words are things;
A small drop of ink, falling like dew upon a thought,
Produces that which makes thousands, perhaps millions, think."
First published at
NEW YORK:
A. S. BARNES & CO., 51 & 53 JOHN-STREET.
1857.
[Copied with no changes by Rick Friedrich in September 1998.]
PREFACE.
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WHENEVER, in the development of any particular science there has been a misapprehension of its appropriate sphere, and especially when wrong principles have been introduced in development, a reconstruction of the whole science is of course demanded. The following treatise has been prepared in view of the assumption, that both these defects exist in important forms in the common treatises on this subject--treaties in which Dr. Whately's is one of the most prominent representatives. Every one is aware, that any given intellectual process having for its object the establishment of truth, may fail of its end for one or more of the three following reasons:
1. The process may be based throughout upon a misconception of the subject treated of.
2. Invalid premises may be introduced as the basis of conclusions deduced.
3. Or there may be a want of connection between the premises and the conclusions deduced from them.
All are equally aware, also, that every valid process is not only free from each of these defects, but possessed of the opposite excellences. In examining any such process, then, three questions are or should be always put, to wit: Has the author rightly apprehended his subject? Are the premises sound? Is there a valid connection between the premises and conclusions? In answering such questions, everyone feels the need of valid criteria by which he can determine whether the process is or is not valid in each of these particulars, and in one no less than in either of the others. The following treatise has been prepared upon the assumption, that the true and proper sphere of logic is to furnish all these different criteria, and thus to meet in full the real logical necessities of the human mind.
The common treatises are constructed upon the assumption that its true and proper sphere is to meet this want in the last particular only, that is, to furnish criteria by which we can distinguish valid from invalid deductions from given premises, and that irrespective of the character of the premises themselves. If we are right in our assumption--and the question whether we are not right, is fully discussed in the Introduction--then an enlargement of the sphere of the science beyond what is aimed at in ordinary treatises is demanded, and so far the science needs a reconstruction.
All such treatises that we have ever heard of--with one exception, "Thomson's Laws of Thought," which has never been reprinted in this country--have been constructed throughout upon the assumption, that "all negative propositions and no affirmative, distribute the predicate," and that in converting a universal affirmative proposition we must change its form from a universal to a particular; as, "All men are mortal,"--"Some mortal beings are men." Let us now suppose that as far as affirmative propositions are concerned, the above principles hold only in respect to a single class, while, in all other cases, such propositions as well as negative ones do, and from the nature of the relations between the subject and the predicate must, distribute the predicate as well as the subject. In that case undeniably, a reconstruction of the whole syllogism is demanded.
Now the truth of each of the above statements can be rendered demonstrably evident on a moment's reflection. Why is it, that in the proposition, for example, "All men are mortal," the subject only is distributed, and that its converse is, "Some mortal beings are men?" The reason is obvious. The term men represents a species of which the term mortal represents the genus. In other words, the former term represents what is called inferior, and the latter its superior, conception. The term mortal being applicable to a larger number of objects than the term men, must be understood, in the above proposition, as representing only a part of its significates. Such proposition, or course, can be converted, but by limitation, that is, changing its form from a universal to a particular. It is only in reference to this one class of propositions, however, that the principles under consideration do or can hold. When the sphere of the subject and predicate are, from the nature of the terms themselves, equal--as they are, in all cases but in reference to the single class referred to--then affirmative propositions distribute the predicate on the same principles that negative ones do.
We will mention here for illustration but a single class of propositions of this kind--the mathematical. In every universal affirmative proposition throughout the entire range of this science, the predicate as well as the subject is distributed; the converse as well as the exposita being universal also. This holds equally in regard to the principles and subsequent deductions of the this science. What is the converse, for example, of such propositions as the following? "Things equal to the same things are to one another,"--"The square of the hypothenuse of a right-angled triangle is equal to the sum of the squares of the two sides,"--"6 + 4 =10,"--"X = Z," &c.? The whole science of logic has been constructed upon principles of distribution and conversion, which would utterly mislead us, if applied to any of the universal affirmative propositions throughout the entire range of the science of the mathematics, or to any propositions but one of the single class above named.
In respect to the different figures of the syllogism, also, it has been laid down as holding universally, that the second yields only negative, and the third only particular, conclusions. This also holds true when, and only when, the propositions belong to the single class above named. In all other cases, we can obtain universal affimative or negative conclutions, in each and all The figures alike. Take the following for examples:
FIG. I. FIG. II. FIG. III.
M = X; X = M; M = X;
Z = M; Z = M; M = Z;
.: Z = X. .: Z = M. .: Z = X.
Every one will perceive at once that each of the above syllogisms is of equal validity, and that the converse of the conclusion is in each case universal, as well as the exposita.
The dictum, too, under which the syllogism has been constructed will be found to be applicable only to arguments constructed entirely from the single class of propositions named. These facts being undeniable, every one will perceive that science demands a reconstruction of the syllogism throughout. This we have attempted to do, and trust we have accomplished to the satisfaction of all who shall acquaint themselves with the following treatise. Before venturing to give our deductions in the important particulars now before us to the public, we submitted them to numbers of scientific men in whose judgment we have great confidence. From these we have received such expressions of approbation as to inspire us with the assurance, that these deductions will stand the test of the most rigid scientific scrutiny, which is most cordially invited.
The doctrine of fallacies, treated of in Part II., we have aimed to simplify by proper definitions, logical division, and arrangement of the whole subject, so as to render the doctrine luminous throughout and its principles of ready application in the reader's mind.
Almost no portion of the teatise does the author regard as of higher importance than the doctrine of method, as elucidated in Part III. We judge that the public will perceive that an important scientific want is there met.
In furnishing the examples presented in Part IV. we have had two special objects in view--to present fundamental suggestions in regard to important questions in science; and to furnish examples for criticism of corresponding importance. If, in any case or in all cases, it should turn out that we have erred in reasoning or in any other particular, and the error shall be discovered by the application of the principles previously elucidated, the great end of the work is answered, and the examples will still have their proper place in the work, just as they would if cited from another author as examples of fallacy in reasoning, or of error or defect in any other particular.
In the perusal of the following treatise the public will perceive that we are much indebted to three authors--Mr. Thomson, whose work we had never seen till we had progressed in our own to the very place where important citations from his first appear--Kant, whose treatise, in our judgment, excels by far in important respects any other that we have met with--and Sir William Hamilton, to whom the science of logic, and the author of this treatise especially, is more indebted than to any other author--the father of the science, of course, excepted. It is with the utmost gratification that we would record the fact, that in almost every particular in which we have departed from the beaten track in the development of the science, we are sustained throughout by such high authority as Sir William Hamilton. With these suggestions, the following treatise is commended to the careful examination and candid criticism of the public.
CONTENTS.
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INTRODUCTION.
Necessity of a correct definition of Logic.
All things occur according to rules.
Logic defined.
Relations of Logic to other sciences.
The idea of Logic developed in a form still more clear and distinct.
Divisions of Logic.
Correctness of the above definition verified.
Logic as distinguished from Esthetics.
Accordance of the above conception of Logic with that given by Kant.
Accordance of the above idea of Logic with that set forth by Sir William Hamilton.
Inadequate and false conceptions of this science.
1. The syllogistic idea.
2. Conceptions of Dr. Whately and others.
3. The idea that "the adequate object of Logic is language."
General division of topics.
PART I.--THE ANALYTIC.
CHAPTER I.--ANALYTIC OF CONCEPTIONS AND TERMS.
SECTION I.---Of Conceptions.
Conceptions defined.
Origin and constituent elements of Conceptions.
Error commences, not with Intuitions, but Conceptions.
Universal characteristics of all valid and invalid Conceptions.
Spontaneous and Reflective Conceptions.
First and second Conceptions.
Matter and sphere of Conceptions.
Individual, generic or generical, and specific or specificial Conceptions.
Highest genus and lowest species.
Empirical and rational Conceptions.
Presentative and representative Conceptions.
Abstract and concrete Conceptions.
Positive, privative, and negative Conceptions.
Conceptions classed under the principle of unity, plurality, and totality.
Inferior and superior Conceptions.
Concrete and characteristic Conceptions.
Laws of thought pertaining to the validity of Conceptions.
Particular, general, and abstract Conceptions.
Individual, specificial, and generical Conceptions.
Presentative and representative Conceptions.
Concrete and characteristic Conceptions.
Inferior and superior Conceptions.
Empirical and rational Conceptions.
SECTION II.---Of Terms.
Singular and common Terms.---Significates.
Relations of Logic to Terms.
CHAPTER II.--OF JUDGMENTS
SECTION I.---Of Judgments considered as Mental States.
Matter and form of Judgments.
Quantity of Judgments, universal, particular, individual or singular.
Quality of Judgments, affirmative, negative, indefinite.
Relation of Judgments, categorical, hypothetical, and disjunctive.
Remarks on these Judgments.
Categorical Judgments.
Disjunctive Judgments.
Modality of Judgments, problematical, assertative, contingent, necessary (appodictical)--Remarks.
Theoretical and practical Judgments.
Demonstrable, and indemonstrable or intuitive Judgments.
Analytical and synthetical Judgments.
Criteria of all first Truths.
Kant's definition of analytical and synthetical Judgments.
Tautological, identical, and implied Judgments.
Axioms, Postulates, Problems, and Theorems.
Corollarys, Lemmas, and scholia.
Criteria of Judgments, or characteristics of all valid Judgments.
General Criteria.
Particular and special Criteria.
Judgments relative to all valid Conceptions.
Individual (single), Particular, and Universal Judgments.
Individual Judgments (affirmative).
Individual Judgments (negative).
Particular (plurative) Judgments.
Universal Judgments (affirmative).
Universal Judgments (negative).
Judgments pertaining to the object of inferior and superior Conceptions.
Judgments pertaining to the objects of characteristic Conceptions (affrimative).
Judgments relative to objects of characteristic Conceptions (negative).
Hypothetical Judgments.
Hypothetical Judgments classed.
Criteria of such Judgments.
Disjunctive Judgments.
SECTION II.--Of Propositions.
Quality and Quantity of Propositions, &c.
Distribution of Terms.
Of Opposition.
Of the Conversion of the Predicate.
Quantification of the Predicate.
Parti-partial Negation.
Criteria by which Propositions properly falling under these different classes may be distinguished from each other.
CHAPTER III.--ANALYTIC OF ARGUMENTS OR SYLLOGISMS.
SECTION I.--Argument defined and elucidated.
Diverse Forms of the Syllogism.
SECTION II.--The Analytic and Synthetic Syllogism.
These distinct forms of the Syllogism elucidated.
SECTION III.--Figured and Unfigured Syllogisms.
Principles and Laws of the Unfigured Syllogism.
The Canon of this Syllogism.
General Remarks upon this form of the Syllogism.
SECTION IV.--The Firgured Syllogism.
This form defined.
Common assumption on the subject.
Influence of Assumptions.
Principles determining the distribution of the Predicate.
Fundamental mistake in developing the science of Logic.
Division of the present subject.
I. Those forms of the Syllogism which have been commonly treated of as including all forms of the categorical argument, to wit: those forms in which the terms employed are related to each other as Inferior and Superior Conceptions.
Preliminary Remarks upon this Form of the Figured Syllogism.
Only proximate conclusions obtained.
1. The principle of Extension and Intension, or of Breadth and Depth, as applied to the Syllogism.
2. Import of Judgments (Extension and Intension--Naming).
3. Direct and indirect conclusion.
4. Character of all the propositions employed in this form of the Syllogism.
Letters to be employed.
Canon and Laws of this Form of the Syllogism--Conditions on which we can obtain the different classes of Conclusions above named; that is, A, I, E, O.
Universal Affirmative Conclusions.
Universal Negative Conclusions.
Particular Affirmative Conclusions.
Particular Negative Conclusions.
All valid Conclusions deduced upon principles which accord with those above elucidated.
Analysis of the above relations.
The Canon of this Syllogsim.
Moods of the Syllogism.
Figure of the Syllogism--Form defined.
Number of the figures of the Syllogism.
Major and Minor Terms and Premises.
Order of the Premises.
Final abolishment of the Fourth Figure.
Opinions of Logicians upon the subject.
Our Reasons for the abolitions of this Figure.
Special Characteristics and Canon of each of the three Figures.
Figure I.
The Canon illustrated.
Figure II.
Canon of this figure.
Figure III.
Canon of this figure.
Absurdity of reducing the Syllogism of the other Figures to the first.
Nature of the Conclusions obtained in this form of the Syllogism.
Kind of arguments which appropriately belong to the different Figures.
A more brief view of this subject.
A scientific determination of the real number of Legitimate Moods in this form of the Syllogism.
Conditions of valid deductions of any kind in this form of the Syllogism.
Universal affirmative conclusions.
Particular affrimative conclusions.
PART II.--THE DIALECTIC, OR DOCTRINE OF FALLACIES.
CHAPTER I.--INVALID CONCEPTIONS.
CHAPTER II.--THE DIALECTIC--INVALID JUDGMENTS.
CHAPTER III.--THE DIALECTIC--FALLICIES OF REASONING.
PART III.--THE DOCTRINE OF METHOD.
PART IV.--APPLIED LOGIC.
INTRODUCTION.
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Necessity of a correct definition of Logic
Every science has a sphere peculiar to itself. Its end or aim also, in the occupancy of that sphere, is equally special and peculiar. The mathematics, for example, have an exclusive sphere, end, and aim, and metaphysics others equally special and exclusive. To enter intelligently and with the rational hope of the highest profit, upon the study of any particular science, its peculiar sphere, and special aim in the occupancy of the same, must be distinctly apprehended. Now while the sphere and aim of most of the sciences have been definitely determined, the opposite is most strikingly true in regard to logic. It would be difficult to name any two philosophers, with the exception perhaps of Kant and Sir William Hamilton, who fully agree in their ideas and definitions of this science.
By some it is defined as the art, by others as the science and by others still, as "the science and art of thought, and not the laws of reasoning, constitute the adequate object of the science." This definition, as the reader will readily perceive, is really identical with the following given by Kant: "This science of the necessary laws of the understanding and of reason in general, or of (what amounts to the same thing) the mere form (laws) of thinking in general, we name logic." These last two definitions, as we apprehend them, we regard as strictly correct, and as presenting the only true and adequate conception of the proper sphere and aim of the science. We will now proceed to elucidate the above definitions as we understand them, and to do so by giving our own independent definition of the science. As preparatory to this end, we would invite special attention to the following extract form our own work on Intellectual Philosophy.
"All things occur according to rules.
"'Every thing in nature,' says Kant, and this is one of his most important thoughts, 'as well in the inanimate as in the animate world, happens, or is done, according to rules, though we do not know them. Water falls according to the laws of gravitation, and the motion of walking is performed by animals according to rules. The fish in the water, the bird in the air, move according to rules.'
"Again: 'There is nowhere any want of rule. When we think we find that want, we can only say that, in this case, the rules are unknown to us.'
"The exercise of our intelligence is not an exception to the above remark. When we speak, our language is thrown into harmony with rules, to which we conform without, in most instances, a reflective consciousness of their existence. Grammar in nothing but a systematic development of these rules. So also, when we judge a proposition to be true or false, or to be proved or disproved, by a particular process of argumentation, or when we attempt to present to ourselves, for self-satisfaction, or to others for the purpose of convincing them, the grounds of our own convictions--that is, when we reason, our intelligence proceeds according to fixed rules. When we have judged or reasoned correctly, we find ourselves able, on reflection, to develop the rules in conformity to which we judged and reasoned, without a distinct consciousness of the fact. In the light of these rules we are then able to detect the reason and grounds of fallacious judgments and reasonings.
"Logic defined.
"The above remarks have prepared the way for a distinct statement of the true conception of logic. It is a systematic development of those rules in conformity to which the universal intelligence acts, in judging and reasoning. Logic, according to this conception, would naturally divide itself into tow parts--a development of those rules to which the intelligence conforms in all acts of correct judgment and reasoning, and a development of those principles by which false judgments may be distinguished from the true. A treatise on logic, in which the laws of judging and reasoning are evolved in strict conformity to the above conception, would realize the idea of science, as far as this subject is concerned. Logic, to judging and reasoning, is what grammar is to speaking and writing. Logic pertains not at all to the particular objects about which the intelligence is, from time to time, employed, but to the rules or laws in conformity to which it does act, whatever the objects may be.
"Relations of Logic to other sciences.
"In the chronological order of intellectual procedure, logic is preceded by judging and reasoning, just as speaking and writing precede grammar. In the logical order, however, it is the antecedent of all other sciences. In all sciences the intelligence, from given data, judges in regard to truths resulting from such data: we also reason from such data for the establishment of such truths. Logic develops the laws of thought which govern the action of the intelligence in all such procedures. As a science, it is distinct from all other sciences. Yet, it permeates them all, giving laws to the intelligence in all its judgments and reasonings, whatever the objects may be about which it is employed."
The idea of Logic developed in a form still more clear and distinct.
It will readily be perceived, we judge, that the above definitions and statements have made a somewhat near approach, to say the least, to the true idea of the science under consideration. To place the subject in a light still more clear and distinct, we would observe, that there are certain cognitions, certain processes of thought, which are universally regarded as valid for the truth of what is therein referred to. We examine, for example, the process of thought (statements and demonstrations) by which we are conducted to the conclusion, that the square of the hypothenuse of a right-angled triangle, is equal to the sum of the squares of its two sides. We affirm that, on account of what is contained in said process, that proposition is to be held as true; in other words, the process itself is valid for the truth of what is therein referred to. On the other hand, there are other processes which are not thus valid. What is true is sometimes professedly established by processes not at all valid for its reality, and through other processes what is not true is often affirmed to have been established as a reality. All processes of the first class are held as valid, and the two last named are regarded as invalid procedures of the intelligence. In each process alike, the valid, as well as the invalid, the intelligence has acted in accordance with certain fixed laws or principles, which we are able to determine. To develop, that is, determine, define, and elucidate these laws, and thus present universal criteria of valid and invalid procedures of the intelligence, when the object of such procedure is truth, is, as we understand the subject, the true and exclusive sphere and aim of logic as a science.
Divisions of Logic.
Logic, as a science, consequently divides itself into two parts:
1. A systematic development of those principles or laws to which the intelligence accords in all valid intellectual processes, processes whose object is truth.
2. A similar development of those principles to which the intelligence conforms, in all invalid processes of the class under consideration. Such is logic as a science, in the sense in which we understand the subject and in which we shall attempt to realize the idea. No one will dissent from the above conception, but upon a single assumption, to wit, that the sphere assigned to the science is too extensive, that sphere including all that has been commonly referred to the science and some things else supposed not to pertain to it. That this is the true and proper sphere of the science, we argue form the following considerations.
Correctness of the above definition verified.
1. The above definition gives a perfect unity and definiteness to our conceptions of the science, the very unity and definiteness which characterize all correct definitions of any other science. The truth of this statement is self-evident.
2. While the sphere here assigned to the science possesses not only perfect unity and definiteness, but also exclusiveness, occupying no department properly pertaining to any other science, it also has throughout a fixed and definite relation to all the other sciences, that is, it is what the science of logic should be, the true and proper antecedent to them all. It does not profess to teach what is true or what is false, in any sphere occupied by any one of the sciences; but it does aim to develop those laws and principles, by which we can determine whether any given procedure in the development of any of the sciences, is or is not valid for the truth of what is referred to in such process, and why such procedure is or is not thus valid. This is precisely what no one of the science professes, or aims, in any of its appropriate departments, to accomplish. Yet what this science aims to accomplish, is just what is needed, in all the sciences alike, in all intellectual processes having truth for their object and aim. We certainly need criteria by which valid processes may, in all cases, be determined and distinguished form those which are not valid. Hence we remark,
3. That this idea when realized meets a fundamental want of universal mind, a necessity which no other science does or can meet. The navigator, when abroad upon the ocean, no more needs tables and instruments by which he can determine his latitude and longitude, than does universal mind, educated mind especially, criteria by which it can judge correctly of the character of its own intellectual processes. Logic, as now defined, aims to meet this universal want, and when realized, does most fully and perfectly meet it. When its sphere is contracted within narrower limits than is here assigned to it, a fundamental want of universal mind is so far left unmet, and that when we gave no science, which, while moving in its proper sphere, does or can meet that want.
4. No adequate reason can be assigned, why any department of the sphere of this science, as above defined, should be assigned to logic, and any other department excluded from it. Nor can any other science be named to which the department excluded, can properly be assigned. We might, with the same propriety, include the latter department in our definition of the science and exclude the latter.
5. All treaties, or most, at least, attempt to realize the full idea of the science, as above defined, though not unfrequently in palpable contradiction to the fixed aim of the science, as previously defined in such treaties. The science is sometimes so defined, for example, that the only fallacies properly falling under its cognizance, are those belonging to one class exclusively, to wit, inferences deduced from premises whether true or false, with which they (the premises) have no logical connection. Yet, when such treatises come to treat of fallacies, they discuss not only this, but every other class of fallacies, and attempt to give us universal criteria by which valid intellectual processes may be distinguished from those which are not valid, the very sphere and aim of logic, as above defined. Hence in these illogical treatises, fallacies are discussed under three classes--the strictly logical, that is, those which fall within the proper sphere and cognizance of logic, as defined--the semi-logical, those which partly do, and partly do not, belong to the defined sphere of logic--and the non-logical, those that logic, as defined, has no business with whatever. It is just as wide a departure from all true principles of scientific procedure, to treat of non-logical fallacies, in a treatise on logic, as it would to include a treatise of arithmetic in a system of geometry. All fallacies are really and truly logical fallacies, or only a certain class of them should be discussed in a treatise on logic.
Logic as distinguished from Esthetics.
It may do something to render still more distinct and definite our conceptions of this science to compare its sphere and aim with those of another, the science of esthetics. This last has been commonly defined as the science of the beautiful in nature and art. As pertaining to mind, its appropriate sphere is the creations of the imagination, the object of which is to blend the elements of thought, not in harmony with things as they are, but with the ideas of beauty, grandeur, sublimity, perfection, &c. Esthetics, as a science, aims to develop those laws and principles in conformity to which this faculty must act, in order to realize the end referred to, to show what kind of elements must be blended into a given conception, and how they must be blended, so as to realize these ideas. Thus it presents criteria by which we can distinguish the truly beautiful from that which is not, in other words, the valid from the invalid procedures of the imagination.
The true and proper aim of the understanding and judgment, on the other hand, is to blend the elements of thought given by the primary faculties into conceptions and judgments in harmony with things, not as they might or should exist, but as they do exist. Logic aims to give those criteria by which we can distinguish those procedures of these faculties which are to be held as valid for realities, from those which are to be held as not thus valid. Esthetics might, with some approach to truth, be defined as the logic of the imagination, while logic proper has for its sphere the procedures of the understanding and judgment, in all processes the aim of which is to realize in processes of intuition, conception, judgment, and reasoning, the idea of truth.
Accordance of the above conception of Logic with that given by Kant.
The perfect accordance, in all essential particulars, of the conception of logic above developed, with that given by Kant, will appear manifest to all who are acquainted with his treatise on this science. To evince that accordance, we need only, cite the following passages from that treatise: "In logic we want to know," he says, "not how the understanding is and thinks, and how it has hitherto proceeded in thinking, but how it shall proceed. It is to teach the right use of the understanding," &c. Further on, after giving precisely similar distinctions between esthetics and logic that we have done, he presents the following division of the latter science, a division which must have its exclusive basis in a conception of the science strictly identical, in all essential particulars, if not in all others, with that which we have given: "We shall consequently have two parts of logic: the analytic, which propounds the formal criteria of truth; and the dialectic, which comprises the marks and the rules, by which we can know, that something does not agree with them. In this sense the dialectic would be of great use as a cathartic of the understanding." He then goes on to show that all other conceptions of the science not accordant with this are "improper" and "wrong."
Accordance of the above idea of Logic with that set forth by Sir William Hamilton.
In connection with the fact that Sir William Hamilton accords in general with conception of logic as given by Kant, the accordance of the idea of the former with that which we have presented will be made sufficiently manifest through the following paragraph selected from his article on Logic, found in his Discussion on Philosophy and Literature, p. 136, as published by the Harpers:
"We shall not dwell on what we conceive a very partial conception of the science, that Dr. Whately makes the process of reasoning not merely its principle, but even its adequate object, those of simple apprehension and judgment being considered not in themselves as constituent elements of thought, but simply as subordinate to argumentation. In this view logic is made controvertible with syllogistic. This view, which may be allowed in so far as it applies to the logic contained in the Aristotelic treatises now extant, was held by several of the Arabian schoolmen; borrowed from them by the Oxford Crackenthrope, it was adopted by Wallis; and from Wallis it passed to Dr. Whately. But, as applied to logic, in its own nature, this opinion has been long rejected, on grounds superfluously conclusive, by the immense majority even of the peripatetic dialecticians; and not a single reason has been alleged by Dr. Whately to induce us to waver in our belief, that the laws of thought, and the laws of reasoning, constitute the adequate object of the science. This error, which we cannot now refute, would, however, be of comparatively little consequence, did it not--as is notoriously the case, in Dr. Whately's Elements--induce a perfunctory consideration of the laws of those faculties of thought; these being viewed as only subsidiary to the process of reasoning."
The object of logic, we repeat, is not to reveal or affirm what is true or what is false in itself, that being the exclusive province of the various special departments of mental operation. Its exclusive object, on the other hand, is to develop and elucidate those laws of thought by which we can determine whether any given intellectual process, whatever its object may be, a process which professedly reveals and establishes the truth in respect to the object to which it pertains, is or is not valid for its truth, and why it is to be held as thus valid or not valid.
Inadequate and false conceptions of this science.
It will add somewhat to the distinctness and definiteness of our conceptions of this science, to compare the conceptions which we have set forth, with certain others which we regard as inadequate or wrong. Among these the following only demand special notice.
The syllogistic idea.
The first which we adduce is what may not inappropriately be denominated the syllogistic idea, that which affirms that the exclusive object of this science is to develop the laws of reasoning, that is, to state what, in a process of reasoning, are and must be the relations between the premises and conclusion, when the latter does or does not necessarily follow from the former. A very few considerations only are requisite to show how fundamentally inadequate this idea is to represent the true and appropriate sphere of this science. Take, as examples, the following syllogisms:
All men are mortal;
George is a man;
Therefore, he is mortal.
The conclusion, in this instance, is not only true, but it results as a necessary deduction from the premises. Take now another of a different character:
All mortal beings are men;
Every brute is a mortal being;
Therefore, ever brute is a man.
Here we have a false conclusion. It has the same necessary logical connection with the premises, however, that the conclusion of the former syllogism has. Again:
All bipeds are mortal;
All men are mortal;
Therefore, all men are bipeds.
In this case a true conclusion is deduced from premises with which it has no logical connection. Further:
All mortal beings are men;
All brutes are men;
Therefore, all brutes are mortal beings.
Here, also, we have a conclusion which is true in itself, but which is deduced from premises, both of which are false, and with which it has no logical connection. Again:
All animals are mortal;
All men are mortal;
Therefore, all men are animals.
In this syllogism, all the propositions are true; but the conclusion has no logical connection with the premises from which it is deduced. Once more:
All mortal beings are men;
George is a mortal being;
Therefore, he is a man.
The conclusion in this case is true, and is necessarily connected with the premises. Still there is a fallacy in the argument, one premise being false.
We have in the five last syllogisms, five different kinds of fallacies, and it would seem that the science of logic ought to give us principles by which we can determine, in each case alike, what is the nature and character of the fallacy, and why it is to be regarded as such. Yet with the first and last of the five, logic, according to the present definition, has nothing whatever to do. There being, in these cases, a necessary connection between the premises and conclusion, every condition required by the science has been fulfilled, and its mission is at an end in respect to them. At the same time, we have no other science to which it pertains to trace out the source of the fallacy in either case, and tell us where it may be found, and why it should be regarded as a fallacy. Numbers three, and four, and five, only, are logical fallacies, according to this definition, and would properly be designated as fallacies in reasoning by the science, as thus defined.
Of the six syllogisms, in three of them, numbers one, two, and six, the conclusions have a necessary connection with the premises, and the argument throughout, in each case, alike fulfills all the conditions of the science, as now defined: in the other three, though in the last two of them the intellectual procedure is fundamentally fallacious, and the propositions all true in the first, the whole of these syllogisms, we say must be classed together under the same category in a treatise upon this science, a treatise developed in strict consistency with such an idea of its exclusive sphere and design. Now we affirm that logic, when developed according to the true conception of its entire and proper domain and adequate aims as a science, will not thus confound things which so fundamentally differ.
In numbers one and two, each conclusion has the same necessary connection with its premises, yet the process of thought is in the first case valid for the truth of the conclusion, and not valid in the last. In the last four syllogisms, there is the same want of validity, whether the conclusion is true or false. Suppose we ask for the reason or grounds of the difference. To answer such an inquiry our investigations must, in every case take a wider range than the mere consideration of the logical connection between the premises and the conclusion, and must in all instances take into account the conceptions represented by the various terms of the syllogisms, the judgments represented in the propositions of which the syllogisms are constituted, and the connections between the premises and the conclusion in the same.
We will take the first syllogism in illustration. In this syllogism there are three conceptions represented by the terms men, mortal, and George. On examination they will be found to possess certain fundamental characteristics common to all others which appear in judgments really and truly valid for the reality and character of the objects to which they pertain, and which consequently distinguish all conceptions which must be held as true from those which must not, as elements of such judgments, be thus held. Relations equally fundamental and peculiar will be found to obtain between the subject and predicate in each of the premises of such a syllogism, and also between the premises themselves and the conclusion deduced from them. The characteristics of the conceptions, on the one hand, and those of the relations between the subject and predicate in each of the premises, and between said premises and the conclusion deduced from them, on the other, characteristics and relations which may be determined and defined, constitute the laws of thought by which all valid judgments and processes of reasoning may be distinguished from those which are not valid, inasmuch as all valid processes do and must possess throughout these identical characteristics, and all not valid must be thus regarded, for the reason that they violate these rules in some particular or other, some in the relations affirmed to exist between the subject and predicate in one or the other of the premises, or in both together, and others because they are constituted of invalid conceptions.
Now why should it be affirmed that one class of these laws of thought come within the appropriate sphere of logic, and that either of the others should be excluded from it? No reason whatever can be assigned for such an assumption. If any individual should accomplish what is needed in regard to any one of these departments, the relations between the premises and conclusion in processes of reasoning, for example, he would so far meet one important logical demand of universal mind. If, when he has done thus much, he should put forward the claim, that he has occupied the entire sphere of the science of logic, he would simply reveal the fact that he entertains too limited conceptions of that science.
Conceptions, judgments, and deductions from judgments presented as premises, these together, we repeat, constitute the proper sphere and object of this science. Its object is to develop and elucidate those laws of thought by which valid conceptions, valid judgments, and valid deductions, can be distinguished from those which are not valid, and by which it can be shown in what respects and for what reasons any given intellectual process is or is not thus valid.
Conceptions of Dr. Whately and others.
"Logic," says Dr. Whately, and we will give the definition in full, "in the most extensive sense which the name can with propriety be made to bear, may be considered as the science, and also as the art, of reasoning. It investigates the principles on which argumentation is conducted, and furnishes rules to secure the mind from error in its deductions. Its most appropriate office, however, is that of instituting an analysis of the process of the mind in reasoning; and in this point of view, it is, as has been state, strictly a science; while, considered in reference to the practical rules above-mentioned, it may be called the art of reasoning. This distinction, as will hereafter appear, has been overlooked, or not clearly pointed out by most writers on the subject; logic having been in general regarded as merely an art; and its claim to hold a place among the sciences having been expressly denied."
In the above paragraph there are, as shown most indubitably by Sir William Hamilton, at least three important errors.
The first that we notice is an historical one, the statement, that logicians have generally considered logic as an art, and not a science, whereas in the language of the author just named, "the great majority of logicians have regarded logic as a science, and expressly denied it to be an art. This is the oldest as well as the most general opinion."
The next error that we notice pertains to the nature of logic itself. It is in fact in no proper sense and art of reasoning, its fundamental aim, as far as reasoning is concerned, being not to teach us how to reason, but to enable us to judge, upon scientific principles, of processes of reasoning. We all know that an individual may be an excellent and scientific judge of processes of reasoning, and practically a very bad reasoner. Yet science tends to render practice more perfect. In this indirect and secondary sense logic is an art of reasoning.
The third and last error that we notice, is that of a too limited and inadequate conception of the true sphere and consequent full aim of the science. The error to which we now refer, consists in this supposition that the laws of reasoning, instead of the laws of thought, constitute the real sphere and object of the science. This error we have already exposed in another connection. Nothing in addition is therefore required on the subject.
The idea that "the adequate object of Logic is language."
As Dr. Whately proceeds in his elucidation of what he regards as the true and proper conception of this science, he has fallen into another important error, an error which has been so fully and so well exposed by Sir William Hamilton, that we will simply present his statement of it together with his exposition of the same, without any additional remarks of our own:
"But Dr. Whately is not only ambiguous; he is contradictory. We have seen that, in some places, he makes the process of reasoning the adequate object of logic; what shall we think, when we find, that, in others, he states that the total or adequate object of logic is language? But, as there cannot be two adequate objects, and as language and the operation of reasoning are not the same, there is, therefore, a contradiction. 'In introducing,' he says, 'the mention of language, previously to the definition of logic, I have departed from established practice, in order that it may be clearly understood, that logic is entirely conversant about language; a truth which most writers on the subject, if indeed they were fully aware of it themselves, have certainly not taken due care to impress on their readers' (p. 56). And again: 'Logic is wholly concerned in the use of language' (p. 74).
"The term logic (as also dialectic) is of ambiguous derivation. It may either be derived from logoV (endiaqetos), reason, or our intellectual faculties in general; or, from logoV (proforicos), speech or language, by which these are expressed. The science of logic may, in like manner, be viewed either--1. As adequately and essentially conversant about the former (the internal logoV, verbum mentale), and partially and accidentally, about the latter (the external logoV, verbum oris); or, 2. As adequately and essentially conversant about the latter, partially and accidentally about the former.
"The first opinion has been held by the great majority of logicians, ancient and modern. The second, of which some traces may be found in the Greek commentators of Aristotle, and in the more ancient Nominalists, during the middle ages (for the later scholastic Nominalists, to whom this doctrine is generally, but falsely attributed, held in reality the former opinion), was only fully developed in modern times by philosophers, of whom Hobbs may be regarded as principal. In making the analysis of the operation of reasoning the appropriate office of logic, Dr. Whately adopts the first of these opinions; in making logic entirely conversant about language, he adopts the second. We can hardly, however, believe that he seriously entertained this last. It is expressly contradicted by Aristotle (Analyt. Part i. 10, par. 7). It involves a psychological hypothesis in regard to the absolute dependence of the mental faculties on language, once and again refuted, which we are confident that Dr. Whately never could sanction; and, finally, it is at variance with sundry passages of the Elements, where a doctrine apparently very different is advanced. But, be his doctrine what it may, precision and perspicuity are not the qualities we should think of applying to it."
General division of topics.
We have now sufficiently indicated our own conception of the science under consideration. The way has thus been prepared to enter intelligently upon the elucidation of the different departments of our subject, which we shall treat of under the following general arrangement of topics:
I. The necessary laws of thought to which the intelligence does and must conform in all valid conceptions, judgments, and deductions, or processes of reasoning. This department of the science is denominated by Kant, the Analytic. For the sake of convenience we shall include what we have to say on this topic, under this same general title.
II. The doctrine of fallacies which the philosopher just named denominates the Dialectic, and which we shall attempt to elucidate under the same title.
III. The doctrine of Method, or the rules in conformity to which all scientific procedures should be conducted.
IV. Certain general and specific applications of the principles elucidated, applications adduced for the purpose of exemplifying the importance of the science, and the manner of applying its principles.
The first two topics embrace the entire field of logic considered as a science. The last two are presented for the purpose of elucidation.
LOGIC
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PART I.
THE ANALYTIC.
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CHAPTER I.
ANALYTIC OF CONCEPTIONS AND TERMS.
SECTION I.---OF CONCEPTIONS.
Conceptions defined.
A CONCEPTION, or notion, is a mental apprehension of some object or objects, and apprehension which we express by such terms as George, man, tree, plant, animal, &c. Such apprehensions we represent by the general term conception.
Origin and constituent elements of Conceptions.
Knowledge, with the human intelligence, begins not with conceptions but with intuitions, or a direct and immediate perception of the reality of objects. As shown in the Intellectual Philosophy (A System of Intellectual Philosophy, by Rev. Asa Mahan, pp. 476. New York, A. S. Barnes & Co.), and as now generally admitted by philosophers, the faculties of intuition, or original perception, are three,---SENSE, the faculty of external perception, the faculty which perceives the qualities of external material substances--CONSCIOUSNESS, the faculty of internal perception, the faculty which perceives and apprehends the operations or phenomena of the mind itself--and REASON, which apprehends the logical antecedents of phenomena perceived by Sense and consciousness, to wit, truths necessary and universal, such as space, time, substance, cause, personal identity, the infinite, &c.
In intuition each particular quality or phenomenon, together with its logical antecedent, is given singly and by itself. From the nature of the case, it cannot be otherwise, the quality being, in all instances, the object of direct and immediate perception or apprehension. By this we would not be understood as affirming that different qualities may not each be the object of simultaneous perception with others. This we believe. Yet, as each quality is itself individual and single, and is the object of direct and immediate perception, such quality must be originally given singly and by itself. The same holds true of the logical antecedent of such quality, as given by reason. Each quality has its special logical antecedent; and as the quality is originally given singly and by itself, the same must be held equally true of its logical antecedent. The logical antecedent of the reality of the quality of extension, for example, is that of an extended substance, quality necessarily supposing as the condition of its existence, the reality of substance, it being impossible to conceive of the reality of the former, without supposing that of the latter. The same holds true of all other qualities, or phenomena, of every kind.
The origin and constituent elements of conceptions of every kind now admit of a ready statement and explanation. When a quality is perceived, and its logical antecedent apprehended, we have a secondary operation of the intelligence, an operation in which the apprehension of the quality and that of its logical antecedent are united into a conception of a particular object. As other qualities of the same object together with their logical antecedents are perceived and apprehended, they are blended into the same conception, which thus becomes more or less complete, as it more or less fully represents its object. Thus if the object is material, for example, a conception of it is formed as a body existing in time and space, and having definite extension, form, color, &c. On the perception of subjective phenomena, we obtain, in a similar manner, the conception of mind, as a substance possessing the powers and susceptibility of thought, feeling, and voluntary determination. All the elements which do or can enter into conceptions must be given by the primary faculties referred to, as these are the only original sources of cognition. The function which thus blends the original elements of thought (intuitions) into conceptions, is denominated the understanding; and logic, so far as it pertains to conceptions, is the science of the laws of the understanding.
Error commences, not with Intuitions, but Conceptions.
As intuition, in all instances, pertains directly, immediately, and singly to its respective object, the fact of such intuitive perception must always be held as valid for the reality of its object. A denial of this principle is a formal impeachment of the validity of the intelligence, as a faculty of knowledge, and nullifies all attempts at knowledge of every kind. All forms of scientific procedure also have their basis in the assumed truth of this principle, the validity of intuition for the reality of its objects. Nor can any reasons be assigned for the assumption that any one class of intuitions should be regarded as thus valid, and others not. No principles, therefore, are required to enable us to distinguish valid from invalid intuitions.
One universal division of conceptions, however, is that of true and false. Here valid and invalid cognitions first appear in the process of thought, and hence the necessity of valid criteria by which the one class may be distinguished from the other.
Universal characteristics of all valid and invalid Conceptions.
The universal characteristics which distinguish all conceptions which should be held as valid for the reality and character of their respective objects, from conceptions which should not be thus held, may now be very readily and distinctly pointed out.
1. All conception which embrace those elements only, which have been really and truly given by intuition relatively to any object, must be held as valid throughout for the reality and character of such object.
2. All conceptions also must be held as thus valid which embrace such intuitions exclusively, together with their necessary logical antecedents. If the intuition is thus valid, so must all its necessary logical antecedents and consequents be. Of this there can be no doubt.
3. All conceptions, on the other hand, which embrace any elements not thus given in respect to the objects of said conceptions, must be held as not valid for such objects.
The truth of the above principles is self-evident. The only question to be determined is, how may we know when a given conception has one or the other of the above characteristics? To accomplish this end is the object of the following distinctions and elucidations.
Spontaneous and Reflective Conceptions.
There are two states in which each conception may be contemplated--to wit, as it first appears in the intelligence through the spontaneous action of the understanding; and as it appears when each element embraced in it has been the object of the distinct reflection, and the entire conception, with all its constituent elements, is presented in consciousness in a distinct and reflective form. All the elements embraced in the conception, in its reflective, is really found in it when in its spontaneous form. In the latter state, however, each element is given obscurely and indistinctly. In the former, in a form distinct and well defined, as a part of the whole conception.
First and second Conceptions.
Another important distinction between conceptions, a distinction for which we are indebted to Sir William Hamilton, and which was first developed, as he states, by Arabian philosophers, is that of first and second conceptions. "A first notion" (conception), says the writer above named, "is the concept of a thing as it exists in itself, and independent of any operation of thought, as John, man, animal, &c. A second notion is the concept, not of an object as it is in reality, but of the mode under which it is thought by the mind, as individual, species, genus, &c. The former is the concept of a thing--real--immediate--direct; the latter is the concept of a concept--formal--mediate--reflex." In other words, when a conception is contemplated as immediately pertaining to its object, as it is in itself, and that without reference to other conceptions, it is denominated a first conception. When it is contemplated in its relation to other conceptions, and as being capable of being classed with, or separated from them, then it is denominated a second conception. When, for example, we contemplate the conceptions represented by such terms as John, man, animal, &c., not as merely pertaining to some object, or class of objects, but in reference to the mode or form in which they pertain to them, that is, as individual, species, or genus, and consequently as capable of being classed with others which pertain, in a similar manner, to their object, these, we repeat, are denominated second conceptions. It is with conceptions of this class especially that logic, as a science, has to do. Phenomena must be classified, before their laws can be determined. So with conceptions. Before the laws of thought can be determined, thought itself must be classified by reflection.
Matter and sphere of Conceptions.
By the matter of the conception is meant, the intuitions actually included in it. By the sphere of a conception, we mean the number of individuals embraced under it. The conceptions represented by the term John, for example, as to its matter, represents all the elements given by intuition, in respect to this individual, and as to its sphere, is limited to this one person, it being applicable to none other. The conception represented by the term man, as to its matter, represents all intuitions, and those only which are common to all individuals of the race; and as to its sphere, it comprehends every such individual.
"The matter and sphere of a conception," as Kant observes, "bear to one another a converse relation." The more elements (intuitions) a conception embraces, that is, the more it contains so far as its matter is concerned, the less number of individuals does it represent, that is, the narrower is its sphere, and vise versa.
The greatness or narrowness of the sphere of a conception depends upon the number of individuals which take rank under it.
Individual, generic or generical, and specific or specificial Conceptions.
Conceptions which pertain to individuals are denominated individual conceptions. Those which pertain to kinds which embrace, not individuals as such, but sorts or classes of individuals (species) under them, are denominated generic or generical conceptions. Those, on the other hand, which pertain to the sorts (species) which are contained under the generic or generical conception, are denominated specific or specifical conceptions. The individual conception embraces all the elements given by intuition relatively to the one object to which it (the conception) pertains. The generic conception embraces only the intuitions which are common to all the specific conceptions which rank under it, and to all the individuals which rank under its various specific conceptions. The specific conception embraces all the elements of intuition belonging to the generic, and also all that belong to the particular class which it represents, and which are not found in the class from which the former is separated.
Highest genus and lowest species.
It is evident that a conception may be generic relatively to another and lower conception, and itself specificial, relatively to one pertaining to a higher genus. Thus the conception represented by the term man, is generic relatively to those which pertain to different orders of the race, and at the same time, specificial relatively to that of a higher genus represented by such terms as rational beings, including as a genus men, angels, &c.
A genus which is not a species is called the highest genus. A species which is not a genus, is called the lowest species. The following remarks of Kant upon this subject are worthy of special regard:
"If we conceive of a series of several conceptions subordinate to one another--for example, iron, metal, body, substance, thing--we may obtain higher and higher genera; for every species is always to be considered as a genus with regard to its inferior conception. For instance, the conception of a man being generical with regard to that of a philosopher, till we at last arrive at a genus that cannot be a species again. And one of that sort we must finally reach; because there must, at last, be a higher conception, from which, as such, nothing can be further abstracted without the whole conception vanishing. But in the whole series of species and of genera there is no such thing as a lowest conception of species, under which no other conception or species is contained; because one of that sort could not possibly be determined. For, if we have a conception, which we apply immediately to individuals, specific distinctions, which we do not notice, or to which we pay no attention, may exist in respect to it. There are no lowest conceptions, but comparatively, for use, which have obtained this signification, as it were, by convention, provided that we are agreed not to go deeper in a certain matter.
"Relatively to the determination of the specifical and of the generical conception, then, this universal law--There is a genus that cannot be any more a species; but there are no species but what may become genera again--holds good."
Empirical and rational Conceptions.
Intuitions are also classed as empirical and rational. All intuitions derived through perceptions external and internal, that is, through the intuitions of sense and consciousness, are called empirical, being derived through experience. Those, on the other hand, which sustain the relation of logical antecedents to empirical intuitions, such, for example, as the intuitions of space, time, cause, substance, &c., are denominated rational intuitions, being the intuitions of that faculty or function of the intelligence denominated the reason.
Now conceptions, the leading elements of which are intuitions of qualities of substances material and mental in the world within and around us, qualities which are the objects of perception, external and internal, are called empirical conceptions. All such conceptions are constituted of two classes of elements, the empirical and rational, that is, intuitions of sense and consciousness, on the one hand, and of reason on the other, all such objects, for example, being apprehended as substances or causes existing in time and space, &c., and as possessed of certain qualities and attributes. The latter class of elements are given by immediate perceptions, external or internal, and the former by the reason. Such conceptions are denominated empirical.
When the rational intuition becomes itself the object of reflection and abstraction, and the intelligence apprehends its object in a distinct and reflective form, as it is in itself, and in its relations to objects of empirical conceptions, we then have what is denominated rational conceptions: those of time, as the place of events; of space, as the place of bodies; of substances, as the subjects of qualities; and of causes, as the origin of events, &c. Rational conceptions sustain to the empirical the relations of logical antecedents, the reality of the objects of the latter being conceivable and possible, but upon the condition of that of the objects of the former class. Thus the reality of body is neither conceivable nor possible, but upon the supposition of the reality of space. So of time relatively to succession, of substance relatively to qualities, and of cause in respect to events. If there is no space, no time, no substance, or causes, there can be no bodies, succession, qualities, nor events. The conceptions of space, time, substance, cause, &c., are therefore denominated the logical antecedents of those of body, succession, qualities, and events. So in all other instances.
Presentative and representative Conceptions.
Sir William Hamilton has classed all our knowledge under two divisions--that which is derived by direct and immediate intuition of the qualities of objects--and that which pertains to such qualities mediately, through consciousness of sensations, for example. Of the first kind are our intuitions of the primary qualities of matter, those which belong to matter as such--for example, extension, form, &c. Our intuitions of the secondary qualities, such as taste, smell, and sound, are not direct and immediate, but indirect and mediate, that is, through the consciousness of sensations. Such intuitions are therefore called representative. Our intuitions of the secundo-primary qualities, on the other hand, those qualities which distinguish one class of material substances from another, such, for example, as gravity, cohesion, &c., are partly presentative and partly representative.
Conceptions constituted of presentative intuitions may be called presentative conceptions. Those constituted of the other class would then be denominated representative. The same conception may partake partly of one, and partly of the other character.
Abstract and concrete Conceptions.
Conceptions also are properly classed as abstract and concrete. The former pertain to some single quality given by intuition, irrespective of the particular object to which such quality belongs, or to which the intuition pertains--conceptions represented by such terms as redness, whiteness, roundness, rightness, &c.
Concrete conceptions pertain to their objects as they actually exist, and combine all the elements given by intuition relatively to such objects--conceptions expressed by such concrete terms as George, man, animal, &c.
Positive, privative, and negative Conceptions.
Conceptions which embrace those intuitions only which are actually given by intuition in respect to their objects, and refer to their objects as actually possessed of the qualities which such intuitions embrace, are called positive; such conceptions, for example, as are represented by such terms as sound, speech, a man speaking, &c. Conceptions which pertain to their objects as void of certain qualities which might be supposed to have been given by intuition as pertaining to the object, are denominated privative conceptions; conceptions, for example, expressed by such terms as deafness, dumbness, a man silent, &c. When, on the other hand, the conception pertains to its object, as merely void of certain characteristics, or as by no possibility possessed of them, then it is denominated a negative conception. Such conceptions are represented by such terms as a dumb statute, a lifeless corpse, &c.
Conceptions classed under the principle of unity, plurality, and totality.
Every conception pertains to its object as numerically one--and individual, John; or as many--a multitude; a number of individuals--as John, Thomas, Samuel, &c.; or as a totality, a whole of which each individual is an integral part--a troop of horses, &c. For this reason they are classed under the categories above named.
Inferior and superior Conceptions.
When one conception takes rank as species under another as its genus, as, for example, the conceptions of the various species of fruit-bearing and forest trees ranked under that of the genus tree, the former class of conceptions are denominated inferior, and the latter superior conceptions.
"The inferior conception," as Kant well observes, "is not contained in the superior, for it contains more in itself than the superior, but is contained under it, because the superior contains the ground of the cognition of the inferior." We know the apple-tree, as a tree, for example, through the superior conception represented by the term tree.
Concrete and characteristic Conceptions.
We commonly have two classes of conceptions relatively to the same object,--the one embracing in concrete all the elements given by intuition in respect to the object, and the other embracing those only which peculiarize and distinguish that object from all others. The former class of conceptions we have already designated. The latter may be denominated characteristic conceptions. It is through this conception that objects are distinguished one from another, recognized and classified.
Laws of thought pertaining to the validity of Conceptions.
We are now prepared to state the general laws of thought pertaining to the validity of conceptions. All conceptions, as we have seen, together with all their logical antecedents and consequents, are to be held as valid for their objects--conceptions which are constituted of real intuitions in respect to such objects. Just so far as any conception is constituted of intuitions not thus given, it is not thus valid. These are the general laws. A conception, we would further state, is valid when, and only when, all judgments legitimately deduced from it are themselves valid in respect to their object. How often, for example, when certain judgments are expressed in regard to persons or objects do we hear the reply, "You are totally mistaken in your conception of such person or object;" or, "You are right in your conception," &c. Wrong conceptions lead to wrong misjudgments. Let us now apply them to particular conceptions and to particular classes of conceptions.
Particular, general, and abstract Conceptions.
Particular conceptions are valid when, and only when, such conceptions embrace no elements but actual intuitions, empirical and rational in respect to such objects. Intuitions with all their necessary or logical antecedents and consequents, being thus valid, the same must be true of conceptions into which such intuitions only enter as constituent elements. This holds true, whether the conception relative to its object is complete or incomplete, that is, whether it represents the whole, or only a part of the qualities of its object; for whatever is necessarily implied in the existence of a quality, must be true of all objects to which the quality pertains, and that whether it exists in such objects in connection with other qualities or not.
For this reason, abstract conceptions, with all their necessary antecedents and consequents, must be valid for their objects. General conceptions are valid, when they embrace those elements only which are common to ever particular conception contained under it, and when each of the former embrace those elements only which are actually given by intuition relatively to its object. This for reasons above stated holds true, whether the general conception be complete or incomplete.
Individual, specificial, and generical Conceptions.
What has been said of particular, being applicable in all respects to all individual conceptions, nothing further need be added in respect to the latter.
When individual conceptions ranking under the specificial are valid, the latter are also valid for their objects, when they embrace all the elements contained in the generic, together with all those that are common to all the individual conceptions which rank under the specifical. Thus, for example, the specifical conception represented by the term apple-tree is valid, when said conception embraces all the elements contained in the conception represented by the term tree, together with all those common to all valid conceptions pertaining to all apple-trees of every kind and sort. So of all other specifical conceptions.
Generical conceptions are valid when they include those elements only strictly common to all valid specifical ones contained under the former.
Presentative and representative Conceptions.
Presentative conceptions, those, for example, which are constituted of intuitions pertaining to the primary and secundo-primary qualities of matter, must be valid absolutely for their objects. This is self-evident. All conceptions also, so far forth as they are constituted of such conceptions, are thus valid.
Representative conceptions, on the other hand, can, from the nature of the case, have only a relative validity. Our knowledge of the secondary qualities of matter, for example, is mediate, through the consciousness of sensations. The subjects of such qualities, therefore, are know to us only as the otherwise unperceived causes of such sensations. Our conceptions of them, therefore, are valid in the sense only, that constituted as our sensibility now is, there is in such objects a power thus to affect us. Our presentative conceptions are valid, not for ourselves merely, but for all intelligents. Our representative conceptions are valid only for beings constituted in respect to their sensitivity, as we are, and when in our circumstances, questions which can be resolved only by a reference to general experience.
The same conceptions are often constituted of presentative and representative intuitions, and are, consequently, in corresponding degrees absolutely and relatively valid.
Concrete and characteristic Conceptions.
Concrete conceptions are valid, when they are constituted exclusively of actual intuitions in respect to their object, and when they embrace all the intuitions thus given, and as given.
Characteristic conceptions are valid, when they are constituted of such intuitions of those qualities which belong exclusively to the object of said conceptions, and which are always connected with them. Let A, for example, represent some object or class of objects, and B a quality which belongs to no object but A, and is always present as a constituent element of A. The conception represented by the term B, is valid as a valid characteristic conception of A. When the quality represented by the term B appears, the presence of all that are represented by A may be affirmed.
A conception may often be assumed as valid for ordinary practical purposes, which should not be assumed as the basis of any truly scientific procedure.
Inferior and superior Conceptions.
The rules just stated in respect to individual, specifical, and generic conceptions, embrace all that need be said of inferior and superior ones, the latter being only different forms of representing the former.
Empirical and rational Conceptions.
All empirical conceptions fall directly under the laws and rules already defined and elucidated. We have occasion, therefore, to speak only of the latter class, those which sustain to the former the relation of logical antecedents. If any conception is to be held as valid for its object, all that is contained and implied in its logical antecedents must be regarded as equally valid for the same object. A fundamental element of our conception of body, for example, is that of a substance contained in space, and which occupies space. Whatever, therefore is necessarily implied in the conception of the latter, must be absolutely valid for the object of the former conception. The same holds true of all other rational intuitions. All the necessary logical antecedents of a valid intuition must be just as valid as the intuition itself in respect to the object of said intuition. The validity of the rational conception, therefore, can be denied but upon one assumption, the absolute objective invalidity of all empirical conceptions, together with that of the intuitions of which the former are constituted. This would be an utter and universal impeachment of the intelligence itself, as a faculty of knowledge, and would annihilate the validity of the impeachment itself.
All conceptions conforming to the principles above defined are to be held as valid. All violations, in whole or in part, of any of those principles are to be held as in a corresponding degree invalid. How conceptions became thus vitiated, it will be our object to show, when we come to the Dialectic, the investigation of the sources of fallacy.
SECTION II.---Of Terms.
Very little is requisite in regard to the subject of the present section, to wit, terms. In logic a conception, or notion, expressed in language is called a term. All that is employed for this purpose, that is, to represent the conception, is included in this definition.
It is evident from the above definition, that a term may consist of one, or many words; as, man, or a man on horseback, a horseman, or a troop of horses, &c.
Singular and common Terms.---Significates.
In the science of logic, terms are divided into two classes, singular and common. All terms which represent individuals, or single objects only, are called singular terms, as George, the Hundson, New York, &c. Those, on the other hand, which represent classes of individuals, as man, river, mountain, &c., are called common terms. The individuals which a common term represents are denominated its significates.
Relations of Logic to Terms.
Logic has to do with terms only indirectly, that is, as the representatives of conceptions. What is required in regard to the term is, that, according to its received import, it shall fully and distinctly represent its conception, and nothing more nor less. It must not, according to received usage, represent more no less elements than are included in the conception; for, in such cases wrong, and not the right conceptions are represented.
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CHAPTER II.
OF JUDGMENTS.
SECTION I.---OF JUDGMENTS CONSIDERED
AS MENTAL STATES.
A JUDGMENT is an intellectual apprehension in which a certain relation is mentally affirmed to exist between two or more conceptions. We have in our mind, for example, the conception of body and space. On reflection, we perceive a necessary relation between them, or rather between their objects, a relation of this character, to wit: the existence of the former can be conceived of as possible, but upon one condition, the admission of the reality of the latter. The mind then becomes distinctly conscious of the truth, that body supposes space. This mental affirmation is a judgment. We have in our minds also the conceptions represented by the terms man, on the one hand, and mortal, on the other; we perceive that, as a matter of fact, all that is included in the latter conception, holds true of every individual represented by the former. Mortality is, therefore, mentally affirmed of all men. This mental affirmation, also, is a judgment. So in all other instances. Whenever a certain relation is affirmed to exist between two or more conceptions, or between the objects of the same, this mental affirmation is a judgment.
Matter and form of Judgments.
Logic, as a science, as we have seen, pertains not at all directly to the particular objects about which the thoughts are employed in particular conceptions, judgments, and reasonings, but to the laws of thought itself relating to such objects. So it distinguishes between the matter and form of judgments, and takes cognizance directly only of the latter. The former consists of the special notions or judgments relating to their particular objects, one judgment pertaining to one object, or class of objects, and another to another. The latter, the form of the judgment, pertains to its character relative to other judgments, as affirmative or negative, universal or particular, &c.
Logic, as a science, considers specially the form of the judgment, and has to do with the matter thereof, only so far as to give the universal criteria, by which valid may be distinguished from invalid judgments.
Quantity of Judgments, universal, particular, individual or singular.
When judgments are contemplated relatively to the number of objets of the class to which they pertain, the number which is embraced in the judgment, we then refer to the quantity of judgments, as whether the relation affirmed is conceived of as holding true of all such objects, or of a part of them, or of some one individual. Relatively to quantity, judgments are accordingly classed as universal, particular, and individual, as in the case of those represented by the propositions, "All men are mortal; Some men are mortal; and, George is mortal." In the first case, as the relation is affirmed to hold true universally of all individuals represented by the term man, the judgment is called universal. In the second case, this relation is affirmed relatively to a part only of the individuals represented by this term. The judgment is accordingly called particular. In the last case, the relation is affirmed of one individual only. The judgment is therefore denominated individual. All judgments, as far as the relation of quantity is concerned, may be ranked as universal, particular, or individual.
According to Kant, particular judgments might more properly be called plurative, because they relate to more than one individual. In this he is no doubt, correct, and equally correct, while he expresses such preference, in adhering to common usage.
Individual judgments also are, in logic, treated practically as universal ones, because in the former, equally as in the latter the relation affirmed holds in regard to the whole subject without exception.
Quality of Judgments, affirmative, negative, indefinite.
As far as quality is concerned, their own intrinsic characteristics, judgments are classed, as affirmative, negative, and indefinite. When one conception (the subject) is thought of as coming under the sphere of another (the predicate), as in the judgment, "All men are mortal," all men being in the judgment place in the sphere, or class of mortal beings, the judgment is called affirmative. When one conception is thought of as excluded from the sphere of another conception, as in the judgment, "Mind is not matter," the former substance being thought of as excluded from the sphere or class of material substances, the judgments in that case is called negative. When, on the other hand, a conception is thought of not only as excluded from the sphere of another conception, but as included indefinitely in one excluded from the latter, we then have what is called an indefinite judgment. Thus in the judgment, "The human soul is not mortal," we separate the subject from the sphere or class of the mortal beings, and place it, but indefinitely, in a class excluded from the former, that is, among immortal beings. The distinction between negative and indefinite judgments is important to a correct understanding of the notion of judgments themselves. In logic, however, both are included under one, the negative, and all judgments are classed as affirmative or negative.
Relation of Judgments, categorical, hypothetical, and disjunctive.
When one conception is directly affirmed or denied of another, as in the judgments, "All men are mortal, and, the soul is not mortal," the judgment is denominated categorical. When conceptions are thought of in respect to one another in the relation of antecedent and consequent, as the judgment, "If Caesar was a usurper, he deserved death," the judgment is then denominated hypothetical.
When a conception is thought of as included in one member of a certain division, as in the judgment, "Caesar was a hero or a usurper," "A is in B, C, or D," the judgment is called disjunctive. From the nature of the relation of the subject and predicate in judgments, all judgments must be either categorical, hypothetical, or disjunctive.
REMARKS ON THESE JUDGMENTS
Categorical Judgments.
In categorical judgments, as Kant remarks, "the subject and the predicate make up the matter of the judgment; the form, by which the relation (of agreement or disagreement) between the subject and predicate is determined and expressed, is the Copula," which, when expressed in language, is always--is, or is not. Categorical judgments, as Kant further remarks, "make up the matter of other judgments." With the following remark of this great logician we cannot agree: "But from this we must not think, as several logicians do, that hypothetical and disjunctive judgments are nothing more than different dresses of categorical ones, and can therefore be all reduced to them. All the three judgments depend upon essentially distinct logical functions of the understanding, and consequently must be discussed according to their specific distinction." On a careful analysis of any hypothetical judgments, it will be found, that, in all cases, it is, as stated in the Intellectual Philosophy, a universal proposition expressed in the form of a particular. The proposition, for example, if Caesar was a usurper he deserved death, is nothing more than the universal proposition, "All usurpers deserve death," expressed in a concrete and particular form. A comparison of categorical and hypothetical syllogisms will also show that they are only different forms of the same thing. For example:
All usurpers deserve death;
Caesar was a usurper;
Therefore, he deserved death.
If Caesar was a usurper, he deserved death;
He was a usurper;
Therefore, he deserved death.
The same may be shown to hold true in all the forms which hypothetical judgments assume, and in regard to all the principles and laws pertaining to hypothetical syllogisms. Throughout they are nothing but categorical judgments, or syllogisms stated in particular form.
What has been said in regard to hypothetical judgments being so directly and manifestly applicable to the disjunctive, nothing in addition is required to show that this class also differs only in form from the categorical.
Disjunctive Judgments.
In the language of Kant, "the matter of these consists of two judgments, which are connected together as antecedent and consequent. The one of these judgments which contains the ground" (the subject of the universal categorical) "is the antecedent; the other; which stands in the relation of consequence to that" (that is, the predicate of the universal categorical judgment), "the consequent." The connection affirmed to exist between them is denominated the consequence. The antecedent and consequent in a hypothetical judgment, answer to the subject and predicate in the categorical, and the consequence in the former to the copula in the latter. A few passing remarks are deemed requisite on the following paragraph from Kant:
"Some think it easy to transform a hypothetical proposition to a categorical. But it is not practicable; because they are quite distinct in their very nature. In categorical judgments nothing is problematical, but every thing assertive; whereas in hypothetical ones, the consequence is only assertive or positive. In the latter we may therefore connect two false judgments together, for in this case the whole affair is the rightness in the connection--the form of the consequence; upon which the logical truth of these judgments depends. There is an essential distinction between these two propositions: 'All bodies are divisible, and, if all bodies are composed, they are divisible.' In the former, the thing is maintained directly: in the latter it is maintained on a problematically expressed condition only."
In reply, we remark:
1. That while it is true that "in categorical judgments nothing is problematical, but ever thing assertive, whereas in hypothetical ones, the consequence only assertive," it is equally true, that in both the same thing is asserted, only in different forms. This is manifest, from the fact, that in all hypothetical syllogisms, a categorical may be substituted for the hypothetical judgment (premise), and the argument will stand just as it did before. This we shall see hereafter.
2. Even in those hypothetical judgments which contain "two false judgments," with the connection of necessary consequence between them, a universally valid categorical judgment is always given--a judgment which alone renders valid the relation of consequence referred to. In the judgment, for example, "If Washington was a traitor to his country, he deserved death," we have the two false judgments, and the relation of necessary consequence, under consideration. In this very judgment, however, we have, in reality, the universal categorical one, "All traitors to their country deserve death," and upon the validity of this last judgment depends that of the consequence before us. The same holds true in all other instances.
3. The reason why there is "an essential distinction between these two propositions, all bodies are divisible, and if all bodies are composed they are divisible," is not, as Kant affirms, because a hypothetical proposition cannot be transformed into a categorical one, but because the two propositions before us do not in fact belong to the same class. The judgment, therefore, "If all bodies are composed they are divisible," cannot be transformed into this, "All bodies are divisible." The former judgment, however, may be transformed into this, "All substances which are composed (compounded) are divisible," because that, in these instances, what is affirmed in one case categorically, is affirmed in the other hypothetically. The examples adduced by our author lay no valid basis for the conclusion which he deduces from them.
Disjunctive Judgments.
A disjunctive judgment, is distinguished from all others by this peculiarity, to wit: it is constituted of a certain number of problematical judgments, all of which together sustain such a relation to a certain judgment known to be true, that the object of this judgment must be in one of the numbers referred to, to the exclusion of all the rest. For example, the judgment, which all will admit cannot but be true, that the final determining cause of the facts of the universe in creation and providence, is either an inhering law of nature, or some power out of and above nature, has its basis in the judgment which also must be true, that for the facts named some ultimate reason or cause must exist. A is know to exist. But it sustains such relations to B, C, and D, that it must be found in one of them, to the exclusion of all the rest. Hence the disjunctive judgment. A is in B, C, or D. The same principle obtains in all disjunctive judgments.
The several problematical judgments constitute the matter of the disjunctive judgments, and are called, as Kant observes, "members of the disjunction or opposition." Their mutual relations of disjunction or opposition, that is, the fact that each sustains such relations to all the other, that if it is true, they must be false, and if any of the others be true, each of the rest must be false, constitute the form of such judgments.
Modality of Judgments, problematical, assertative, contingent, necessary (appodictical)
When the connection between conceptions is conceived of as possible, that is, with the conviction that the relation may or may not exist, as in the proposition, "A may be in B," the judgment is called problematical. When the connection is conceived of as not only possible, but as actual, the judgment is called assertative. When the relation is conceived as actual, with the conviction that the facts might possibly have been otherwise, the judgment is denominated contingent; as in the proposition, "A died on yesterday," it being possible to conceive, while it is asserted, that he did die, at the time named, that he is yet alive, or that he died at some other time. When a relation between conceptions is conceived of as not only actual, but the conception is accompanied with the conviction that the facts can, by no possibility, be otherwise than they are, the judgment is said to be necessary or appodictical, as in the judgment, "Body supposes space, or an event, a cause." The contradictory of the problematical is the impossible, a relation which cannot be conceived of as exiting.
Remarks.
1. A judgment may be deemed necessary for either of two reasons--the nature of the relations between the conceptions, or the nature of the evidence in favor of the actual existence of such relations. Of the first class are the judgments, "Every event has a cause," "Two straight lines cannot inclose a space," &c. Of the second, is the judgment, "That the square of the hypothenuse of a right-angled triangle is equal to the sum of the square of its two sides." Judgments of the former class are called primitive, those of the latter, derivative.
2. An assertative judgment, while, from the nature of the relations between the conceptions themselves, it may be, and is contingent, may, relatively to the evidence of the existence of the relations referred to, be necessary. The judgments, "The world exists, and I exist," are of this character. Relatively to the nature of the relations between the subject and predicate in each of these judgments, the judgments themselves are merely assertative or contingent. Relatively to the nature of the affirmations of perception and consciousness, we say that these judgments must be true.
3. A judgment necessary, from the nature of the relations between the subject and predicate, is necessary in the absolute sense--the judgments, for example, "Body supposes space; and succession time," &c. A judgment necessary relatively to the perceptions of sense and consciousness, is said to be relatively necessary; as, for example, "Phenomena supposes substance." A necessary form of this judgment is this: "Substances are as their phenomena." The logical antecedent of the phenomenon of extension is the reality of an extended substance (body). The logical antecedent of the subjective phenomena of thought, feeling, and voluntary determination, is the reality of the self as possessed of the powers of intelligence, sensibility, and will. The above-named phenomena being given, the judgments, "Body is, and Self exists," are necessary, relatively so.
4. Assertative judgments, like the appodictical, are divided into two classes--primitve and derivative. The judgments, "Body is, and Self exists," are of the first class. The judgment "All bodies attract each other directly, as their matter, and inversely as the squares of their mean distances," is of the latter character.
5. All derivative judgments, as originally given, are problematical, and subsequently become assertative or appodictical, as the case may be; that is, they are originally given as possibly true or false, and consequently as capable of proof, and as wanting it.
Theoretical and practical Judgments.
Theoretical judgments affirm what does and what does not really belong to their objects. Practical judgments, on the other hand, express those forms or rules of action by which certain ends may be obtained, or those actions which ought or ought not to be performed.
Practical principles are treated as theoretical ones, when the question to be argued is, whether the former are, in reality, what they are judged to be. As thus contemplated only, would logic have to do with them.
Demonstrable, and indemonstrable or intuitive Judgments.
A demonstrable judgment is a problematical one, of the class which is capable of being proved. Indemonstrable (intuitive) judgments are those which are immediately certain, and for this reason, incapable of proof.
Judgments of the latter class, since every intellectual process properly denominated reasoning commences with them, are sometimes, and with unquestionable propriety, denominated primitive judgments. Those of the former, being in fact deduced from and evinced by the latter, are called derivative judgments.
Intuitive judgments by which the demonstrable may be evinced, but which cannot be subordinated to others, are called elemental judgments, and also principles, a principle in science being always a judgment which is itself immediately certain, and consequently not evincible through any other judgment.
A demonstrable judgment, when evinced, may become a principle relative to other demonstrable judgments; and a judgment which is derivative in one science, may be an elemental principle in another.
Analytical and synthetical Judgments.
Those judgments whose certainty is immediately evinced from an analysis of, or reflection on the conceptions constituting the subject and predicate of said judgments, are called analytical judgments; those judgments which are evincible only through other and more elementary ones, are called synthetical judgments.
On examination it will be found that all analytical judgments, that is, all judgments whose validity is immediately certain, divide themselves into two classes, and are and must be all comprehended in one or the other of them.
1. Those in which the predicate represents an essential quality of the subject, as in the judgment, "All bodies have extension." It is impossible for us to conceive of a body which has not extension. In the judgment before us, then, the predicate, extension, represents a fundamental element of our necessary conception of body. The judgment has, and must have, immediate certainty, or course. The same holds true in all similar judgments.
2. Those in which the conception represented by the predicate, sustains to that represented by the subject, the relation of logical antecedent, that is, when the reality of the object of the latter conception can be admitted but upon the supposition of that of the former. Of this kind is the judgment, "Body supposes space." The reality of the object represented by the term body, can be admitted but upon the condition of admitting that of the object of the conception represented by the term space. So of the judgments expressed by such propositions as "Succession supposes time; events a cause; phenomena substance," &c. All judgments of this character can but have, of themselves, immediate and intuitive certainty.
Now if we adduce any known indemonstrable judgment which has immediate certainty, we shall find, on examination, that it does, in fact, belong to one or the other of these classes, and that this is the exclusive ground of its certainty. Take, as an illustration, the axiom, "Things equal to the same things are equal to one another." On reflection, it wll be perceived, that the relation of equality among themselves, is the necessary condition of their being equal to the same things. In other words, the conception represented by the words, "equal to one another" (the predicate), is the logical antecedent of that represented by the words, "things equal to the same things" (the subject). Thus we might take up all similar judgments, and all other self-evident ones, and show that they do, in fact, belong to one or the other of the classes above elucidated.
Nor is it possible for us to conceive of any other grounds of the immediate certainty of judgments. In any other conceivable or definable case, the relation between the subject and predicate of the judgment would be such that the judgment would be, at the utmost, only problematical.
Criteria of all first Truths.
We have, then, in the relations before us, the fundamental and universal criteria by which first truths may be distinguished from all others. In all such judgments (first truths) the conception constituting the predicate either exclusively represents elements contained in that represented by the subject, or the former conception sustains to the latter the relation of logical antecedent. There are, and can be, no other first truths but these. The criteria of such truths commonly given, are rather external and circumstantial than intrinsically characteristic, as all scientific criteria should be. We refer to those criteria given by Dr. Reid, and concurred in by philosophers generally, such, for example, as the fact, that all men admit them as a matter of fact in all their reasoning; that even those who deny their validity act upon them; and if denied, the validity of all reasoning fails.
Kant's definition of analytical and synthetical Judgments.
According to Kant, we have but one class of analytical judgments, those in which the relation of identity referred to obtains between the predicate and subject. The other class he represents as synthetical judgments, which, according to him, embrace all judgments in which all the elements of the conception represented by the predicate are not embraced in the that represented by the subject. He accordingly divides synthetical judgments into two classes, the intuitive and problematical, though he gives us no explanations of the reasons why one is intuitive and the other not. In the Intellectual Philosophy, pp. 336-341, we have stated our objections to our author's definition of these two classes of judgments, the analytical and synthetical, and to the use which he has made of the latter. In this connection, we would simply add, that while our definition is just as plain, and of as ready application, as that of Kant, it presents a much more simple and easily understood classification of judgments. If any one, however, should prefer the definition of that philosopher, we would remind him, that in that case, he must divide synthetical judgments into two classes: those in which the conception represented by the predicate is, and those in which it is not, the logical antecedent of that represented by the subject, and that the former class, together, as first truths, and that no other judgments can be classed with them, as such truths. The logical and scientific bearings of each classification will then be, in all respects, the same, and nothing but a verbal difference remains.
Tautological, identical, and implied Judgments.
A tautological judgment is one in which the subject and predicate are identical, either in fact and in form; as, "John is John, Man is man," &c.; or, in all respects, in meaning, so that the predicate is, in no respect, even explicative of the subject; as, "Man is a human being," &c. Such judgments are of no use whatever.
Identical judgments, as distinguished from tautological, are those in which, while there is an identity in fact, there is such a diversity in form between the subject and predicate, that the latter is really and truly explicative of the former. Of this character are all correct definitions; as, for example, a triangle is a figure bounded by three straight lines. Of the same character is the class of analytical judgments, in which the predicate represents some element or quality of the subject; as, "All bodies have extension." Such judgments are, by no means, void of consequence, inasmuch as they render clear and distinct our conceptions of their objects.
An implied judgment is one which is really only another form of another judgment, but which presents some important element of the latter which was not distinctly expressed before. We often say: If this proposition is true, that is also true, because the latter is really implied in the former, that is, is only a different form of stating the same thing. Implied judgments have a very important use; indeed, a statement of them is often indispensable to the production of conviction.
Axioms, Postulates, Problems, and Theorems.
An axiom is an analytical judgment (analytical or intuitive synthetical judgment of Kant) which may be employed as a principle in the sciences in general, that is, a judgment by which other judgments may be evinced. As shown in the Intellectual Philosophy, pp. 257-8, the axioms which constitute the foundation-principles of each of the sciences are essentially identical with those of every other.
Postulates are analytical judgments which can be employed as principles only in particular sciences. Thus the axiom, "Things equal to the same things are equal to one another," is really, though often stated in a somewhat different form, identical with that which lies at the basis of every science that can be named; while the postulate, That a straight line may be drawn between any two points in space," pertains exclusively to geometry and kindred sciences.
A problem is a judgment which appears neither true nor false, and requires an answer to the question, Is it, or is it not true? or presents a number of judgments either of which apparently may be true, an but one can be, and requires an answer to the question, Which is true? or finally affirms that a certain thing may be done, and requires an answer to the question, How may it be done? In problems of the first kind most commonly classed above named, an answer of this kind is most commonly required, to wit, not what is, or what is not true, in the particular cases presented, but how may we determine, what is, and what is not true, in these cases? In the solution of particular problems, in this form, we obtain not only answers to the specific questions presented, but principles by which all other similar questions may be solved. Let us suppose, for example, that an event like the raising of Lazarus from the dead occurs in our presence. The question presents itself, Is this, or is it not a miracle? or, Is this event the result of the direct and immediate interposition of creative power, or of mere natural causes? In the first form, we have a problem of the first class named, and in the other of the second. Suppose, that we are required not merely to give a direct answer to these questions, but to give criteria by which we may know whether the event is, or is not, a miracle, or whether it was the result of a supernatural interposition of creative power, or of natural causes. In giving the solution in this form, we should not only obtain an answer to the specific questions above stated, but should also obtain criteria by which we can, in all other cases, distinguish events resulting from natural causes from real miracles. Suppose, on the other hand, we are required to give a rule, by which a given line may be divided into any specific number of equal parts. We then have a problem of the third class.
Theorems are theoretical judgments capable of proof, and requiring it; as, for example, the proposition, "All the angles of a triangle are equal to two right angles."
Corollarys, Lemmas, and scholia.
Corollaries are the immediate and intuitive consequences of preceding judgments.
A lemma is a judgment previously evinced, and now used as a principle in the demonstration of other judgments. In general it is not native in the particular science in which it is presupposed as evinced, but is taken from some other science, as when some ascertained truth in the science of geology, for example, is employed as a principle in the science of natural theology.
Scholia are explanatory notes or observations appended to evinced judgments, for the purpose of illustration.
CRITERIA OF JUDGMENTS, OR CHARACTERISTICS OF ALL VALID JUDGMENTS.
We are now prepared to give the universal criteria of judgments, or the universal and necessary characteristics of all valid judgments, as distinguished from those which are not valid.
General Criteria.
All universally valid judgments must have the following characteristics:
1. The conceptions constituting the subject and predicate of such judgments must be valid according to the criteria developed in the last chapter.
2. The judgment must be analytical according to the definition above given of such judgments.
Or, 3. It must be evinced as true, by means of judgments which are analytical.
All valid primitive judgments have the first two characteristics. All valid derivative ones have all the three together. Any judgment wanting these characteristics must be held as not valid.
Particular and special Criteria.
As necessarily involved in the above criteria, we present the following and special ones.
Judgments relative to all valid Conceptions.
1. All judgments must be held as valid in which any element of any valid conception is affirmed of the object or objects of such conception. Suppose, for example, that the conception represented by the term m