Elements of logic

Introduction

1. Definition of Logic. — Logic is the systematic study of the order to be observed in judging, reasoning, and other processes of thought in order to arrive at the knowledge of truth. This' definiti< >n sh< iws us :

( 1 ) the materials (material cause) of the logical order;

(2) their elaboration (formal cause) ;

(3) the purpose of this elaboration (final cause).

2. Materials of Logical Order. — In some sense, these materials are acts of the mind, like apprehension, judgment, ratiocination (reasoning) ; but strictly speaking, only apprehensions are the material object of logical order (3).

(1) By apprehension the mind represents to itself one thing or many things, without either affirming or denying anything. Concepts, the product of apprehension, are expressed by names or terms.

(2) To establish a relation of identity or non-identity, of agreement or non-agreement, between the objects of two concepts, in affirming or denying one object of another is to judge. A judgment is expressed in a proposition.

(3) To reason is to combine two or more judgments so as to form a new one. The complete ordinary expression of this simplest exercise of reasoning is the syllogism.

3. The Formal Cause of the Logical Order. — The formal object of logic, or the point of view from which logic regards the acts of the mind, is their adaptability to certain processes of thought which are called either particular sciences or philosophy. These processes imply stages. The mind must grasp the numerous aspects of reality one after another before co-ordinating the fragmentary explications. Judgment is the first step in combining ideas; judgments in their turn become the materials of reasoning; an isolated piece of reasoning does not suffice to produce adequate knowledge of things, but several reasonings become materials of a scientific system. This rational arrangement of ideas constitutes the logical order properly so called : ""the order which reason constitutes for its own acts".

4. Difference between Psychology and 1 _,xC. — Many different sciences may be concerned with one and the same subject, if they study different properties in it, and, consequently, consider it from different points of view. They are then said to have a common (that is, undetermined) object, but each has its own formal (or determined) object. Psychology, too, has in part for its (material) object the act of human reason, but it does not study them under the same aspect (formal object) as logic does. Psychology sees in them vital acts, of which it seeks the nature and origin. Logic considers them in so far as they are cognitions of objects, objective representations, abstract and universal, furnishing the matter of the relations which reason formulates in judgments and reasonings, and arranges in a scientific system.

In psychology, as in all the sciences of the real, order is the necessary condition of science; but logic has this order for its object. Its proper object is the form itself of this scientific construction.

5. Final Cause of Logical Order. — The systematization of the .process of reasoning has an ulterior aim: to make our knowledge true.

Before explaining how logic directs its operations towards the true, it must be recalled that truth and error are qualities of the judgment, and not of the concept. As long as we merely speak of some one object by itself — e. g., the sun or a chimera — no one can say that we speak truly or falsely. Truth or error belongs to the statement that the sun exists, that the chimera exists. 1

Now, how can a science, logic, lead us to the knowledge of the truth? Evidently, logic could not in this sense supply the place of all the particular sciences.

Each science enlightens the mind about the particular object with which it concerns itself; and consequently, anyone who had studied all of them would be marvellously equipped for always forming true judgments.

But, besides this initiation into the whole of truth by the successive and collective study of the particular sciences, there is an initiation of another kind, viz., the preparation afforded by a more general science. Thought naturally proceeds from the simple to

1 See General Criteriology, n°. 6.

INTRODUCTION 5

the complex. Now simplicity and universality always go together in our knowledge. The most general sciences, then, are those the object of which is the most simple and, for that reason, best enables us to comprehend the more complex objects to which it is applicable.

■Logic is a general science in the sense that ii regulates the content of all other sciences and subjects them to its laws in their construction. Its object, of extreme simplicity and boundless in extent, is the being of reason.

6. Difference between Logic and Metaphysics. — Another science, having all being for its object, also deserves to be called a general science, because it rules all knowledge: this is metaphysics. Metaphysics and logic are both concerned with all being (common material object), but under different aspects (proper formal object). The object of metaphysics is real being considered formally in its real quiddity, invested with real attributes.

Logic has for its object the same being, formally considered in its mental objectivity, invested with attributes of reason which it acquires in thought and in virtue of thought.

Everything real (existing or possible) is intelligible. Now the real, when it becomes the object of a mental conception, inevitably participates in the attributes which are inherent in the exercise of thought: as a mental object, it becomes abstract and universal. Between abstract, universal objects relations are established which under the concrete and particular conditions of existent things are impossible : such a mental object becomes the attribute of another object of thought which plays the part of subject in regard to the former; the content and extension of ideas give rise to relations of identity or of exclusion; judgments are produced, chains of reasoning are forged, and all the while the material of these various intellectual operations is being, not real being, independent of thought, but the being of reason, i. e., being under the aspect and with the characteristics which mental conception communicates to it.

Metaphysics is the universal science of the real.

Logic is the science of the science of the real. 1

1 Tin* relations considered by this philosophical discipline are not the ontological relations upon which the attention of the mind falls im-

7. Is Logic to be Considered a Science or an Art? — Is logic a speculative or. a practical science? Speculative science stops at the knowledge of its object; practical science makes that knowledge subservient to an ulterior action or work. "The end of the speculative is truth ; the end of the operative, or practical, is action." The logician does not study acts of thought merely for the disinterested pleasure of knowing their co-ordination; he puts his science to the ulterior use of directing mental operations. In this sense some hold, and with reason, that logic is a practical science. — Others, taking a higher point of view, say that logic is a speculative science, because the direction of mental operations is itself subordinate to the knowledge of truth. St. Thomas takes this view when he says : ' "In speculative matters the rational dialectic science is one thing . . . the demonstrative, another." 1

Logic is also an art, if by this we understand a body of practical rules, for the guidance of action. 2 mediately, the prima: intentiones, objects of a first abstraction, but the logical relations springing from the combination of- abstract objects to which the reason reflecting returns, sccundce intentiones, objects of second abstraction.

1 Summa Theol, 2a 2* q. 51, art. 2, ad 3.

2 "Other animals", he says, "are prompted to their acts by a certain natural instinct, but man is directed in what he does by the judgment of his reason. For this reason various arts serve for the easy and orderly execution of human acts. For an art appears to be nothing else but a fixed disposition of reason by which human acts arrive at their due end by way of calculated means. Now reason not only can direct the acts of the subordinate parts, but is also adapted to direct its own function. For it is the property of the intellective part to reflect upon itself : the intellect understands itself, and in like manner the reasoning faculty can reason about its own act. As, therefore, the art of building or of carpentry comes from the fact that the reasoning faculty reasons about the act of the hand, and man is thereby enabled to perform acts of this kind with ease and with well ordered effort, so, also, there must be some art by which the act of the reason itself may be directed, by zuhich man may proceed easily and correctly in the very act of reasoning. And this is the art of logic, i. e., the rational science. Nor is it rational only because it is according to reason, which is a common characteristic of all arts, but also because it deals with the very act of the reason as its proper matter. And therefore it seems to be the art of arts, because it directs us in the act of the reason, from which act all acts proceed." Post. Analyt., lect. I.

INTRODUCTION 7

8. Divisions of Logic. — (1) It is usual to divide logic into two branches : formal and real logic. This division, which is of relatively recent date, is very questionable:

(a) It is obviously inspired by certain arbitrary theories of Kant's philosophy. 1

(b) The questions ordinarily discussed in real logic constitute for us the object of a treatise which comes next after psychology, and which we call critcriology (science of the criterion of truth and certitude), or analysis of certain knowledge.

(2) Formal logic is generally divided into three parts, treating respectively of apprehension, of judgment, and of reasoning. This division, which is unimpeachable, is borrowed from the material object of logic. Without rejecting it, we prefer:

(3) Another division, which squares better with the general distribution of every philosophic study 2 and is inspired by the study of logical order by its four causes, efficient, material, formal and final.'-' 1

The study of the efficient cause of logic belongs, properly speaking, to psychology. Here it forms the object of a Preliminary Chapter {Chap. I).

The First Part of the treatise on logic will have for its object concepts and terms, the materials of logical order : The Material Cause of logical order (Chap. II).

The Second Part will have for its object the arrangement of these materials, their deliberate disposition in judgments, reasoning, system, to secure the knowledge of truth : Formal Cause of logical order (Chap. III).

A concluding chapter will have for its object the employment of rational order in the service of science and philosophy: Final Cause of logical order (Chap. IV). 4

1 See Critcriology, n°. 42.

2 Ci. the beginning of an opusculum in logic reckoned among the works of St. Thomas: De totius Logics Aristotclis Summa. Op. XLIV, Procemium. Ed. Parm.

3 Cf. General Metaphysics, fourth part.

4 These four causes of logical order are mentioned in the definition of logic [I] and in the text of St. Thomas: Logic is the "art by which the act of the reason itself [material cause] may he directed [formal cause], by which man [efficient cause] may proceed easily and correctly in the very act of reasoning [final cause]."

CHAPTER I The Efficient Cause of Logical Order

9. Principles and Nature of the Operations of Reason. — The

remote principle of the operations of reason is the human substance composed of body and soul ; the proximate, or immediate, principle is the intellectual faculty. 1

Psychology teaches us that every act has its origin in the senses. While the material thing, which is the object of our sensations, is always determinate, made of particular matter, endowed with particular properties, the object of the concept is abstract and universal, that is to say, is considered apari from the particular attributes which really belong to it in nature (abstrahere, to consider separately), and it thereby becomes universal, or applicable to an indefinite number of individual subjects. This bell, which I see and touch, is made of bronze, it is round in shape, it gives a pleasant sound, it is there on my desk at this moment as I look at it. All this is determinate. Now I am able to think of a bell which abstracts from all these peculiarities, and which will serve to represent to me, at least imperfectly, all bells of whatsoever material they may be made, whatsoever may be their peculiarities of shape or of tone, whatsoever the position in space or the moment of time in which they may exist.

10. Multiplicity of the Operations of Reason. Their Fundamental Identity. — All the operations of reason — apprehension, judgment, and reasoning — are at bottom identical; they consist in the intuition that something is {quod quid est), but they nevertheless present different accidental characters which it is of interest to determine.

I. Apprehension assumes many formalities.

(1) When the mind considers an object independently of its surroundings, the action is called attention.

(2) The attention is directed sometimes to a single note in the object, independently of those with which it is united, sometimes

1 See Psychology, n°. 153.

Till-'. EFFICIENT CAUSE OF LOGICAL ORDER 9

to the whole collection of notes which constitute the essence of

the object, but apart from the notes which individualize it in reality: such acts of the mind arc called abstraction.

(3) Abstraction is the basis of generalization.

( 1 ) Abstraction effects in the mind analysis, i. e., de-composition of the notes of the object known.

(5) When the mind reunites notes previously separated, it makes a synthesis.

(6) When we represent to ourselves two objects in succession and perceive a relation between them, the apprehension — or rather, the double apprehension— is called comparison.

(7) The perception of an existing reality is an intuition. We call it perception as opposed to the conception of things said to be ideal, i. e., things considered apart from their existence.

(8) When the intelligence has for its object the acts of one's own soul, chiefly its spiritual acts, the apprehension takes the name of consciousness.

(9) Distinction is an act by which the mind represents one object to itself as not being the same as a second object. By object we are to understand anything that can be the term of an act of thought (id quod ob-jicitur cognoscenti). 1

II. Judgment consists in attributing one object to another, in seeing that two objects, previously apprehended, have, or have not, anything in common. It is an act of apprehension of which the formal object is the identity between the terms of two antecedent apprehensions (appreheusio complexa, or complexorum — complex apprehension, or apprehension of complex things — as opposed to simple apprehension, apprehensio incomplexa, or incomplex orum) .

IN. Reasoning is a linking-together of judgments. The reasoning faculty compares with a middle term two extreme terms, the. identity of which it does not immediately grasp, with the result of seeing, by the aid of this comparison, whether they are identical or not. This process is also termed ratiocination.

The acts of apprehension under their manifold forms, judgment and reasoning, fundamentally constitute one and the same act

1 On the various types of distinction (real, of pure reason, virtual) see General Metaphysics, n°. 49.

— the apprehension or seeing that something is. They depend upon a single faculty indifferently called intelligence, understanding, or reason.

11. The Abstract Character of Concepts Renders Judgment and Reasoning Possible. — Every being which exists in nature is itself and no other, it is an incommunicable individuality, and it is inconceivable that one real being should be affirmed of another or attributed to another. Socrates is himself, he is no one else; this tree is this tree and no other. 1

How is it, then, that things are affirmed of one another in our judgments? It is because the mind has the power of looking at things without their individualizing notes : it abstracts.

In consequence of this abstractive mode of apprehension, the object of the concept is universal; that is to say, it is found, or can be found, in many other individuals, and can be attributed to them in our judgments (universale in prcedicando) . . -

Therefore, by means of intellectual abstraction, things can be affirmed, or, if we may so express it, are predicable, of one another. Thanks to this power of abstraction, our notions of beings as they are, are attributable to a whole species-, a whole genus; in other words they reproduce characteristics of classes — i. e., of genera and species. Abstraction makes reasoning possible ; for reasoning, as we shall see later, supposes a universal middle term, and universality follows abstraction — abstrahi ad quod sequitur intentio universalitatis.

1 See General Metaphysics. "Particulars are not predicated of other [objects], but other [objects are predicated] of them." Aristotle, Prior Analytics, I, 27.