7. In treating of Dialectics, the main purpose of a textbook is to teach pupils how to reason correctly themselves, and readily to detect flaws in the false reasonings of others. To this practical purpose we shall almost exclusively confine ourselves. Setting aside, therefore, all other details usually insisted on in works on Formal Logic, we shall here treat of reasoning only, and of a few such preliminary matters as must be understood before the reasoning process itself can be properly explained. We shall therefore treat, in Chapter I., of simple apprehensions and judgments, and, in Chapter II., of reasoning itself.
8. We shall consider: 1. The nature of simple apprehentions 2. The most important distinctions regarding ideas, and 3. Judgments, together with the expression of them in propositions.
ARTICLE I. THE NATURE OF SIMPLE APPREHENSIONS.
9. Simple apprehension is the act of perceiving an object intellectually, without affirming or denying anything concerning it. To apprehend is to take hold of a thing as if with the hand; an apprehension, as an act of the mind, is an intellectual grasping of an object. The mind cannot take an object physically into itself; but it knows an object by taking it in intellectually, in a manner suited to its own nature; forming to itself an intellectual image, called a species of the object. The act of forming this mental image is called a conception, and the fruit of it, the image itself, is the concept, idea or notion of the object. The word simple added to apprehension emphasizes the fact that the apprehension neither affirms nor denies the existence of the object; it affirms nothing and denies nothing, it simply conceives the idea of the object.
10. This intellectual image should not be confounded with the sensible image, or phantasm, which is a material representation of material objects, and which is formed by the imagination, by means of the material organ of the brain. The difference between these two images is great, and distinction between them is of vital importance in Philosophy. For instance, I intellectually conceive a triangle by apprehending a figure enclosed by three lines and thus having three angles. My notion or idea contains this and nothing more; it is very precise, and every one who conceives a triangle conceives it exactly the same way. But when I imagine a triangle, I cannot help imagining it with sensible material accidents, as being of such or such a size and shape, a foot long at one time, a mile long at another. The picture may be vague, various pictures of triangles may be blended together; but it can never be universal, representing all possible triangles, as my idea does. This imagination is a phantasm. True, phantasms are often called 'ideas' by English writers; in fact, the whole school of Berkeley, Hume, and their followers fail to trace any difference between them; it is the fundamental error of their pernicious philosophy. Thus, for instance, Huxley maintains that God, the soul of man, etc., are unknowable and unthinkable,{1} because we can form no phantasm of them. This makes them simply unimaginable, not unknowable nor unthinkable; we know what we mean when we speak of them. (On the difference between ideas and phantasms see, further, Logic, by Richard Clarke, S.J., c. vi.)
Our ideas are expressed by words, or oral terms; the ideas themselves are often called mental terms.
ARTICLE II. DISTINCTIONS REGARDING IDEAS.
11. Logicians go into much detail on a variety of distinctions with respect to ideas; it will be sufficient for our present purpose briefly to notice a few of them.
A first distinction lies between abstract and concrete ideas. A concrete idea expresses a subject, e.g., 'this gold,' 'some men,' 'all flowers'; or a quality as belonging to a subject, 'heavy,' 'virtuous,' 'fragrant.' An abstract idea expresses a quality by itself, drawn forth, as it were (abstraho, I draw away), from the subject to be separately considered, e.g., 'heaviness,' 'virtue,' 'fragrancy.'
12. A second distinction exists between singular, particular, and universal ideas. An idea is singular if it expresses a definite single object, e.g., 'this book,' 'that army,' 'that gold,' 'James,' 'the Angel Gabriel,' 'the United States,' meaning this one country.
An idea is particular if it represents one or more objects without determining which, e.g., 'a man,' 'an army,' 'a Nero,' 'a spirit,' 'three books,' 'some states.'
An idea is universal when it expresses a note or notes common to many objects, found in each of them, no matter how much those objects may differ in other respects; e.g., 'animal' and 'rational' are notes common to all men; they are conceived in the universal idea 'man,' and each of them corresponds to a universal idea. The term note designates anything knowable in an object.
13. All universal ideas can be ranked under five heads, called the five heads of predicables, because it is always in one of these five ways that a universal idea is predicated of an object.
1. What is apprehended as common to many objects, found in each of them, and therefore predicable of them all in exactly the same sense, may be the whole nature, the essence of those objects, i.e., all that without which those objects cannot exist nor be conceived. For instance, it is the nature or essence of all men to be 'rational animals'; unless I conceive an object as being both 'rational' and 'animal,' I do not conceive a man at all. This common essence of a class is called a species. The species, therefore, is defined as all that constitutes the common nature or essence of a class of objects; e.g., 'man,' 'rational animal.'
2. The universal idea may express a part only of the nature common to many objects. Thus, when I conceive 'animal,' I conceive only a part of man's nature, a part found in other species of objects as well, viz., in brutes. 'Rational' is the other part of man's nature, and it is not found in brutes, but it distinguishes man from the brute. Now, that universal concept which seizes upon what is common to different species is the idea of the genus; e.g., 'animal' is the genus, to which belong the two species 'man' and 'brute.'
3. On the other hand, the universal concept which expresses the peculiar note by which one species differs from another species of the same genus is styled the specific difference; e.g., 'rational' is the specific difference of the species man as distinguished from the species brute.
4. When the concept expresses something that flows or results so necessarily from the very essence that the essence cannot exist without it, and that note never exists but in such an essence, such note is called a property or attribute of that essence. Thus, 'the power of laughing,' 'the power to express one's thoughts by articulate speech,' cannot be found but in a being that is both animal and rational, and they result as natural consequences from its compound nature. The use of them may be accidentally impeded, as is that of reason itself in the infant and the idiot; but they belong to human nature as such, as distinct from other natures, and are therefore properties of man, proper or peculiar to man. Properties need not be conceived in order to apprehend the nature from which they flow; thus, to conceive man, I need not think of his risible power.
5. Lastly, the universal may express what is found in one or many individuals of a class, or even perhaps in all of them, yet in such a way that it could be absent without the individuals' ceasing to be of the same nature. In that case it expresses an accident of the species. For instance, a man may be white or black, tall or small, gentle or fierce, young or old, a European or an American; all these are accidental notes of man. All men are larger than ducks; and yet, if a dwarf should be born, who, when full-grown, should not be so large, being nevertheless a rational animal, he would be truly a man, his particular size being only an accident, not a property of his essence.
14. When we conceive a note common to two or more genera, e.g., 'living,' which note belongs to animals and to plants alike, we have then a higher genus, of which the former genera may be considered as the species. 'Body' expresses a still higher genus; for it is predicated not only of living but also of non-living substances, such as stones and metals. Subtance, itself is the highest genus, to which not only bodies but also spirits belong.
Reversing the process, we may start with the highest genus, say 'substance,' and call 'material' and 'immaterial' substances, or 'body' and 'spirit,' its species. The species 'body' becomes next a subordinate genus, of which 'living,' or 'organic' and 'inorganic' will be the two species. Of 'organisms,' as a new subordinate genus, the species will be 'sentient' and 'non-sentient,' 'animals' and 'plants.' Of 'animals' we have two species, 'rational' and 'irrational,' 'man' and 'brute.' We have various species of 'brutes,' but not of 'man'; for, while brutes have very different natures or essences, and, flowing from these, very different properties, all men have the same essence and the same properties; these differ not in kind but in accidental degrees of perfection. Therefore 'man' is not a genus, but the lowest species; 'animal' is his proximate or lowest genus. The genera and species between the highest and the lowest are called subaltern, subordinate, or intermediate.
15. This ramification of a highest genus into subaltern genera and species is presented to the eye in the Porphyrian tree. The trunk of the tree contains the genera and the species, the branches the specific differences, the top exhibits individuals.
I.e., substance is corporeal or incorporeal; corporeal substance, called matter or body, is organic or inorganic; an organic body or organism is sentient or insentient, etc.
THE PORPHYRIAN TREE.
16. In connection with universal ideas we must explain, as matters of the very highest importance in Logic, the comprehension and the extension of an idea. Comprehension means the total signification, all the notes comprehended or contained in an idea; thus, the concept 'man' comprehends the notes 'animal' and 'rational'; 'animal' itself means 'sentient, living, material substance.'
Extension means the total number of individuals to which the idea extends or applies; the extension of the concept 'man' is all men, that of 'animal' is wider still, extending to all men and all brutes. It is thus apparent that the greater the comprehension of an idea is, the less is its extension, and vice versa; because the more numerous the qualities apprehended, the fewer the individuals that will possess them all; thus, the genus 'animal' has more extension but less comprehension than the species 'man.' 'Animal' has more extension than 'man,' because there are more animals than men; it has less comprehension because the term 'animal' signifies fewer notes than 'rational animal' or 'man.'
When a term is taken in its full or widest extension, it is said to be distributed; it denotes then every one of the objects to which it can apply. Thus, when we say 'all men are creatures,' we mean 'every man is a creature.' Terms expressing particular ideas (No. 12) are undistributed; e.g., 'gold is found in California ' -- i.e., 'some gold.'
A distributed term is applied to all its objects in exactly the same meaning or acceptation. Now, many words are capable of two or three different acceptations: 1. When the meaning of a word is exactly the same, the term is called univocal; as when we give the name of 'box' to a case or receptacle of any size or shape. 2. When the meanings are entirely different, without any connection between them, the term is styled equivocal; as when the word 'box 'is applied, now to a case, then to a blow on the head. 3. When the meanings, are different but connected with one another, the term is analogous; thus the same word 'box' may stand for a case and for the wood out of which cases used often to be made, the box-tree.
ARTICLE III. JUDGMENTS AND PROPOSITIONS.
17. A judgment may be defined as an act of the mind affirming or denying the agreement of two objective ideas. The mind in judging compares two ideas, and consequently the objects represented by those ideas, and affirms or denies that they agree with one another; e.g., 'modesty is praiseworthy,' 'ebriety is not worthy of man.' If, as in these examples, the agreement or disagreement is seen to exist by the mere consideration or analysis of the ideas compared, the judgment is analytic; it is also styled a priori, i.e., formed antecedently to experience; or pure, i.e., formed by pure reason, not learned by sense-perception; or again, it may be called necessary, absolute, or metaphysical; according to the obvious meanings of those terms. But if the agreement or disagreement is discovered consequently on experience, e.g., 'gold is malleable,' the judgment receives the opposite appellations of synthetic, a posteriori, experimental; contingent, conditional; and physical.
18. If a judgment of either kind is arrived at by reasoning, it is mediately evident; if the agreement or disagreement is seen without the aid of reasoning, the judgment is immediately evident. That 'ice is cold,' is an immediate a posteriori judgment; that 'there is nothing without a reason for it,' is immediately known a priori; that 'the sum of the angles of a triangle is equal to two right angles,' is known mediately a priori; the physical laws are known mediately a posteriori.
19. A judgment expressed in words is called a proposition. The subject and predicate together are its matter, and the affirmation or negation its form; the copula is always the verb 'to be' in the present indicative, expressed or implied: 'I see' is equivalent to 'I am seeing,' 'He said' to 'He is one who said,' etc.
That a proposition be negative, it is necessary that a negative word affect the copula. Now, it often requires some reflection to see what word is intended to be affected by the negation: 'No criminal is a happy man' means 'A criminal is not a happy man'; 'A tyrant has no peace' means 'A tyrant is not one having peace.'
20. In propositions it is of the highest importance for correct reasoning that we carefully attend to the extension and the comprehension of the terms used and of the ideas for which they stand.
I. If we consider the extension of the subject, a proposition is styled singular, particular, or universal; according as its subject expresses a singular, particular, or universal idea (No. 12). The form of the term expressing that idea may be misleading, the meaning must be carefully considered. Thus, 'a man is a creature,' 'man is a creature,' 'all men are creatures,' 'every man is a creature,' 'no man is necessary,' are all universal propositions; while 'a man was slain' is particular (for here 'a man' means, not every man, but 'some one man'), and 'that man is generous' is a singular proposition.
II. If we consider the extension and the comprehension of the predicate, we have the following rules:
1. In an affirmative proposition the predicate is taken in its full comprehension, but not (except in definitions) in its full extension. For instance, 'gold is a metal' means that gold has all the notes constituting a metal, but not that it is every metal. We say 'except in definitions,' for in these the defining words, which are the predicate, must have the same extension as the thing defined, expressed in the subject; e.g., 'man is a rational animal,' i.e., 'any rational animal.'
2. In a negative proposition the reverse holds true, i.e., the predicate is taken in its full extension, but not in its full comprehension. For instance, 'a diamond is not a metal' denies that the diamond is contained in the whole class of metals; but it does not deny that it has qualities in common with metals, since it is a substance, material, lustrous, etc., as well as metals. The extension of the subject determines the quantity of a proposition; its quality depends on its form, i.e., on its being affirmative or negative.
21. In reasoning we must distinguish between hypothetical and categorical propositions.
The hypothetical proposition does not affirm or deny the agreement of subject and predicate absolutely, but dependently on some supposition or condition, or with a possible alternative. It is distinguished from the categorical, which directly affirms or denies the agreement between a subject and a predicate without any condition or alternative.
The hypothetical may be of three kinds:
(a) The conditional, consisting of two parts, one of which is declared to be the condition of the other. The part expressing the condition is called the condition or antecedent, the other the conditioned or consequent. If the connection is true, the proposition is true. Thus, 'If you knew God well, you would love him,' is certainly true; 'If you get old, you will be wise,' may be false.
(b) The disjunctive, which connects incompatible clauses by the disjunctive particle 'or'; as, 'A being is either created or uncreated.' The proposition is true, if it leaves no alternative unmentioned.
(c) The conjunctive, which denies that two things can exist or hold true, at the same time; as, 'A being cannot be created and independent.'
{1} Essay on Science and Morals.