Essentials of formal logic

Preface

This little book has been compiled for beginners who intend to complete a full course of philosophy in two years. In such a course Formal Logic is supposed to be finished by the end of the first three months. This requirement demands not a treatise, but a text-book on Formal Logic, which will comprise the essentials of the subject and serve as a basis for further development and illustration in the hands of an experienced teacher.

Conciseness is one of the chief aims of the book. This characteristic respects the individuality and freedom of the teacher, while for the sake of the student, thoroughness, it is to be hoped, is not sacrificed. Hence controverted points and sometimes examples which the judicious teacher no doubt will suggest are omitted.

The author gratefully acknowledges his indebtedness to the admirable Latin works of J. S. Hickey, O. Cist., and C. Frick, S.J. Some of the examples illustrative of the forms of reasoning have been taken or adapted from the more exhaustive treatise in English of G. H. Joyce, S.J.

Fordham University, Feast of St. Michael, 29th Sept., 1917.

Contents

Preliminary Notions

PHILOSOPHY— Definition— Divisions— Educational and Cultural Value — Ethical Value — Relation between Philosophy and the Christian Religion 1

LOGIC — Natural and Acquired — Definition — Material and Formal Objects — Correctness and Truth of Thought — Divisions 6

Chapter I

SIMPLE APPREHENSION AND ALLIED NOTIONS — Definition of Simple Apprehension — Subjective, Objective and Representative Character — Other Names for — Matjerial and Formal Objects — Comprehension and Extension — Mental Processes involved in Simple Apprehension 11

Chapter II

CLASSIFICATION OF SIMPLE APPREHENSIONS- IDEAS — A. According to their Origin — B. According to the Objects which they represent — Direct and reflex universal Ideas — Predicables and Predicaments — C. According to the Perfection with which they represent their Objects 19

THE OUTWARD EXPRESSION OF IDEAS— Signs- Definition — Division — Words — Categorematic — Syncategorematic — Terms — Division — Supposition of terms 30

Part II THE SECOND ACT OF THE MIND — JUDGMENT Chapter I

THE NATURE OF JUDGMENT — Definition — Prerequisites—Matter and Form — Division of Judgment — Proposition — Subect, Predicate, Copula — Nature of the Copula — What it expresses — Division of Propositions — Quantity and Quality of Propositions 35

Chapter II

LAWS THAT REGULATE THE DISTRIBUTION OF SUBJECT AND PREDICATE— Applied to A, E, I, O Propositions — Simple, Complex and Compound Propositions — Reduction of Compound Propositions to their Logical Forms 43

MODAL PROPOSITIONS— Definition— Division ... 47

Chapter IX

INDUCTION— Analytic and Synthetic Judgments— Problem of Induction — Definition of Induction — Steps in the Process, Observation, Hypothesis, Verification,

Generalization, Basic Principles of Induction — Causality— Uniformity of Nature — Two Kinds of Induction — Ultimate Justification of Induction 75

METHODS OF INDUCTION— Agreement— Difference — Residues — Concomitant Variations 81

Chapter II RULES OF METHOD— Rules for Study 94 FINIS

FORMAL LOGIC

Preliminary Notions

1. PHILOSOPHY. The word "philosophy" means the love or study of wisdom. By "wisdom" the ancients meant the knowledge of all things human and divine which make for right living, as well as the causes by which these things are related or hang together. Hence the aim of philosophy is to answer, in as far as reason is capable of doing so, the last zvhy of all things that are. Philosophy is therefore usually defined : The science of all things from the point of view of their highest or last causes, in so far as this knowledge can be attained by the light of natural reason.

2. EXPLANATION OF THE DEFINITION— "Science" is a knowledge of a thing through its cause. A cause in its widest sense is that by which a thing is, becomes, or is known. Philosophy, then, is a science because, like all other sciences, it furnishes us with a systematized body of truths which, resting ultimately on self-evident principles, are united to one another like the links of a chain by an orderly process of demonstration.

"of all things" — Each of the other natural sciences treats of some special department of things, as chemistry, astronomy, medicine, etc., while philosophy takes in a larger field of vision. It embraces the sum total of all things in one complete view.

"highest or last causes" — This characteristic of philosophical knowledge which aims at answering the last "why" of all reality differentiates philosophy from 1 all other natural sciences. Other natural sciences furnish the more immediate or proximate, but not the ultimate causes of the objects of their study. Hence philosophy helps to satisfy the yearning of the human mind to explore, as far as it is given to reason to do so, the utmost limits of knowledge.

"by the light of natural reason" — In this way is philosophy marked off from sacred or dogmatic theology. The latter takes its facts and truths from divine revelation. Philosophy depends upon the natural human faculties to acquire its data and to deduce conclusions from them.

3. THE DIVISIONS OF PHILOSOPHY. It is divided into:

Logic, which lays down the rules of right reasoning and treats of the means given us by the Author of nature to acquire the knowledge of truth.

Metaphysics, again divided into General and Special. The former, called also Ontology, treats of the properties of Being in general. The latter applies the notions and principles of Ontology to the primary classes of Substance and investigates their natures and properties. It comprises :

Cosmology, which treats of the nature and origin of the visible world, of the laws to which it is subject and of the nature and constituent elements of bodies in general ;

Psychology, which treats of living beings, but principally of the human soul ;

Natural Theology, which treats of God in as far as reason enables us to fathom His Divine nature.

Moral Philosophy, which discusses the principles of morality and the duties we owe to God and to our fellow men, considered both as individuals and as members of society.

FORMAL LOGIC 3

4. EDUCATIONAL AND CULTURAL VALUE OF PHILOSOPHY.

Man has an inborn longing to know the ultimate reasons of things. This longing philosophy in a measure satisfies.

The mental effort which the study of philosophy calls forth imparts, as perhaps no other study does, strength and keenness to the intellectual powers.

It furnishes the mind with a reasoned conviction of the fundamental principles upon which rests all scientific knowledge. It sets forth on reasoned grounds the essential duties of man to his Creator, of the state to its citizens and of the citizens to the state, of man to his fellowmen and to himself.

By the light of sound philosophical principles the divinely authorized teaching of supernatural faith may be more clearly set forth and defended; vital problems of state and private conduct are analyzed and solved ; false theories of philosophers and scientists are criticised and refuted; it unifies the conclusions of the particular sciences; it helps to form soundness of judgment ; it develops men of thought.

5. ETHICAL VALUE OF PHILOSOPHY. It is the nature of thought to find its way into action. "The will of man is by his reason swayed" (Shakespeare). Leo XIII says: "It has been implanted in man by nature to follow reason as the guide of his actions, and therefore, if the understanding go wrong in anything, the will easily follows. Hence it comes about that wicked opinions, whose seat is in the understanding, flow into human actions and make them bad. On the other hand, if the mind of man be healthy and strongly grounded in solid and true principles, he will assuredly be a source of great blessings, both as regards the good of individuals and as regards the common weal."

6. THE RELATION BETWEEN PHILOSOPHY AND THE CHRISTIAN RELIGION.

a. Viewed from different stand-points, philosophy is both independent of, and dependent upon, Theology. It is independent : (a) by reason of its object, namely, "the ultimate causes of all things in as far as they can be known by the light of natural reason", (b) By reason of the source from which philosophical knowledge springs — the light of natural reason.

b. Philosophy is dependent upon Theology (a) in as far as the light of reason, which belongs to the natural order, ought to be subservient to the light of Revelation, which belongs to the supernatural order. Just as the scientifically demonstrated conclusions of chemistry must be reasonably accepted in physics, or as the acknowledged decisions of our Supreme Court are accepted, in legal matters, by other Courts, so should the acknowledged truths of Revelation be accepted by natural science, (b) The guidance of reason which is liable to error, and therefore inferior, ought to submit to the guidance and correction of revealed truth which is absolutely infallible and therefore superior.

"Through the revelation made by the Son of God, a fulness of truth was brought within reach of the human mind of which men had previously no notion. And if it be true, as the ancients had it, that truth is the food of the mind, on which it lives and thrives, the revelation through the Redeemer formed an inexhaustible store from which the human mind might evermore draw new increase of the knowledge which is its life. . . .

"The human mind could adopt either of two attitudes towards revelation. It might accept revelation as truth communicated by God, and make this truth

FORMAL LOGIC 5

the criterion and guiding principle of its speculations. If it did this, revelation became an end to which natural knowledge was to be subservient. . . .

"Again, the human mind, in virtue of its natural freedom of election, might abandon the objective standpoint and fall back upon its own subjective resources. It might permit its own reason to deal with revelation in a more unseemly fashion ; it might give reason the first place and revelation the second, so that instead of reason being subject to revelation, revelation should be accommodated to the subjective opinions of the individual ; or, on occasion, entirely denied. This, no doubt, would be a perversion of right order, but just as man can set himself against the divinely-established order in the sphere of morals, so can he set himself in opposition to the divine order in the sphere of knowledge". (Stockl — Hist. Phil., Part II, § 55).

LOGIC

Preliminary NotionB

7. LOGIC is either natural or acquired. The first is that inborn or natural disposition to use one's faculties rightly in the attainment of truth. The second is that same natural disposition cultivated by training. The latter is the subject of the present treatise. It is a necessary study. For untrained reason is liable to err, especially in the solution of more difficult problems.

It may be here noted that any attempt to philosophize at all must presuppose that the human mind can attain truth. The trustworthiness therefore of the human faculties of knowledge must be taken for granted.

That is, they can, by their own nature, attain truth. Otherwise philosophy would be impossible.

8. DEFINITION OF LOGIC. The word \6yo, signifies both "thought" and the expression of thought or language — word. Thought again necessarily represents some object — we cannot think without thinking of something. Logic, then, treats of all three — thought, language and objects. But since in the very nature of things thought comes before language, it follows that Logic treats primarily and directly of thought, and secondarily and indirectly of language and objects.

Since Logic then has primarily to do with thought or the operations of the rational or intellectual powers of the soul, it is usually defined as :

That art and science which directs the operations of reason in the attainment of truth.

9. EXPLANATION OF THE DEFINITION— "Art" — An art is a right method or way of doing

PRELIMINARY NOTIONS 7

something. The thing which logic sets out to do is to point the way to think aright. And the right way to attain this end is indicated by a system of definite rules. In so far, then, as logic sets forth a collection of rules to direct the mind aright in the way to truth, it is an art. We may distinguish, however, the imparting of the mere knowledge of these rules from the actual use of them. The former is called Logica docens, the latter, Logica uteris. Logic is an art in both senses.

"science" — Science, as we have seen, is the knowledge of things through their causes. In as far as logic, then, gives the reasons or causes why the rules it lays down for right thinking are valid, it is a science.

"which directs" — Sometimes men violate the rules of right thinking and reason ill. Hence to prevent this, certain rules of direction must be known and applied.

"operations of reason" — These operations are ideas, judgments, and reasoning. They form the subject matter (material object) of logic. These same mental operations may be the subject matter (material object) of different sciences. But in that case the stand-point from which these operations are viewed (formal object) will in each case be different for the different sciences. Psychology, for instance, considers these operations from the point of view of their nature and origin ; rhetoric with a view of using them for the purpose of persuasion, while it is the province of Logic to direct them as means of attaining truth. To direct, then, the operations of reason towards the attainment of truth, is the formal object of Logic. Hence we say that the same material object may be viewed under different formalities.

To ensure that these operations will issue in truth, two distinct aspects of their truth-giving value must be considered — firstly their conformity to the rules or laws that govern their right procedure as merely subjective acts. This secures their correctness. By correctness is meant freedom from contradiction and inconsistency. Secondly their conformity to objective reality. It is in this sense they are said to be true. Hence it may happen that these operations of reason, or as they are often called intellectual operations, may be correct in their procedure without being true in their content, and true in their content without being correct in their procedure. From this distinction follows the two- fold

10. DIVISION OF LOGIC— MINOR LOGIC (called also Dialectics and Formal Logic), which has to do directly and primarily with the correctness of our thought-operations and secondarily and indirectly with the latter aspect, namely the truth of our mental operations ;

MAJOR LOGIC (also called Critical and Material Logic), which has to do primarily and directly with the latter aspect, the truth, namely, of these same operations, and indirectly and secondarily with their correctness.

Many modern authors use the name "Formal Logic" instead of the usual Scholastic term "Minor Logic" and the Aristotelian term "Dialectics". The philosophy of Kant has popularized the term "Formal Logic". But the Kantian concept of this part of Logic is essentially different from the meaning which Scholasticism has assigned to it. In the philosophy of Kant the necessary grooves or laws which the mind must follow in its operations of reason have their origin solely in the mind ; they are of the mind and in the mind.

DIALECTICS 9

We must think, Kant would say, according to these necessary laws because our minds, antecedently to all experiences of reality, are constituted that way.

Scholasticism, on the other hand, accounts for these laws of thought, not because our minds are originally furnished by nature with these necessary laws or "forms", but because we discover through experience that reality which is independent of the mind is constituted according to those laws, and that, too, antecedently to our knowing them.

Kant conceives the laws of thought as "forms" native to the mind and therefore as having no objective value. Hence he calls the science of these "forms" "Formal Logic". Scholasticism admits these laws are in the mind but not of the mind. They are rather engendered in the mind by objective reality. They put us therefore in touch with reality. Hence "Formal Logic" does not mean to Scholasticism what it means to Kantianism.

MINOR LOGIC OR DIALECTICS

11. DEFINITION — Dialectics ( SiaKiymreai ) treats of the processes of reasoning or discursive thought. It may be defined as : A collection of rules scientifically demonstrated by which the intellect is directed to think correctly. Hence the subject matter or material object of dialectics is the "operations of the intellect or reason" ; its formal object is "to direct these operations in the way of correct thinking".

12. DIVISION — Since man is by nature characterized by the power of reasoning, and since reasoning involves judgments and judgments involve ideas, dialectics will treat in turn of each of these mental operations. Again each of these mental processes has its outward expression in language, namely term, proposition, and syllogism. Hence dialectics will treat of "terms", "propositions" and "syllogisms" as the outward signs or expressions respectively of "ideas", "judgments" and "reasoning".

Besides in the pursuit and attainment of truth the human mind, as we shall see later on, naturally proceeds along certain lines, ways or roads. These pathways in the acquisition of truth are explained by what is called Method (fieri. 666t).

To sum up then, Minor Logic or Dialectics will treat of :

I. SIMPLE APPREHENSION OR IDEA AND

TERM

II. JUDGMENT AND PROPOSITION

III. REASONING AND THE SYLLOGISM

IV. METHOD

Part I THE FIRST ACT OF THE MIND- SIMPLE APPREHENSION

Chapter I Simple Apprehension and Allied Notions

13. DEFINITION— Nominal— Simple apprehension (apprehendere) is the act of laying hold of, or grasping something.

Real — The act by which the mind lays hold of an object mentally without affirming or denying anything about it.

EXPLANATION— "The act by which the mind" — Simple apprehension, then, is an act of the mind. As such it must necessarily be something within the mind as in its subject. Hence simple apprehension, as an act of the mind, is said to be something subjective.

"lays hold on an object". Since it is impossible for the mind "to lay hold or grasp" without laying hold of or grasping something, that something is called the OBJECT of simple apprehension. Hence every simple apprehension must necessarily be objective as well as subjective. When the mind "lays hold of" or apprehends an object, it is said to know, to perceive, to become aware of an object.

The object perceived may, of course, have no real existence in nature. It may be only a possible object, as when I apprehend "a golden mountain". Or again, 11 the manner or mode of the object's existence in nature may be quite different from the mode of its existence as perceived by the mind. For instance I may have a simple apprehension of the object "honesty". I perceive "honesty" in and by itself as if it had a manner or mode of existence in nature by itself, yet "honesty" does not exist in nature independently and by itself, but as the quality inherent in some object.

Lastly the object perceived must be represented in some way in the mind ; otherwise we could not discern one object from another. Hence every simple apprehension must needs be representative, that is, its object must in some way be reproduced in the mind. How this reproduction or representation of the object takes place in the mind is not discussed at present. We only assert the fact. Summing up then we arrive at the conclusion that every "simple apprehension" must of necessity be :

A. SUBJECTIVE

B. OBJECTIVE

C. REPRESENTATIVE "mentally". By this word of the definition we

guard against confounding simple apprehension as an act of the intellect with sensitive perception or a sensitive picture in the imagination, which is by philosophers called a phantasm. Imagining is altogether different from conceiving. Sense perception and phantasms men have in common with brutes, while simple apprehension, as an act of the intellect, is the prerogative of man.

The object of sense-perception is always concrete, individual, bound up with matter. It is limited by time, place; it is here and now and this, as this particular triangle (drawn upon the blackboard with yellow chalk). The object of a simple apprehension

SIMPLE APPREHENSION AND ALLIED NOTIONS 13

on the contrary is conceived in the mind as abstracted from all limitations of matter — of nowness, hereness, thisness, size, color, as a triangle conceived as "a plane figure bounded by three straight lines". It is an object common to many individuals, that is, it is universal. The universal is not picturable.

This distinction is fundamental in all sound systems of philosophy. Failure to recognize this distinction has issued both in the past and present in Idealism on the one hand and Sensism on the other.

"without affirming or denying, etc.". "Apprehension" for this reason is called "simple", and is distinguished from judgment. A judgment always says something is or is not something else. Hence an act of judgment always involves two objects of thought, a simple apprehension only one.

Understand well, then, that the simple apprehension is simple not because the object apprehended may not be complex, as "the last-rose-of-summer", but precisely because in its character of simple apprehension we do not affirm or deny anything about it, that is, we do not form a judgment about it.

14. OTHER NAMES FOR SIMPLE APPRE- HENSION. Simple Apprehension is also spoken of as an idea, concept, notion, mental word, mental term. Each of these words but emphasizes some particular aspect of the same thing. Thus while simple apprehension expresses more emphatically the subjective and objective aspect of the first mental act, idea (likeness, picture) lays stress upon its representative value ; concept (conceptus) directs attention to the spiritual generation of the object in the mind. Again, since to apprehend is to know (noscere), to take notice of an object, hence the result of apprehension is called a notion (notus). Simple apprehension is called a mental word, because by it the object is expressed in the mind, and a mental term because the simple apprehension may be viewed as a mental form or likeness of the object, which de-term-ines the mind to know this object rather than that.

It is customary, as it is more convenient in Logic, to speak of ideas rather than of simple apprehensions.

15. THE OBJECT OF AN IDEA. That which the idea represents to the mind is called the object of the idea. Objects manifest themselves to us; that is we know them by certain marks. These marks are called "attributes", "qualities", "forms", "determinations", "notes". For instance the paper I write upon is "white", "rectangular", "thin", "made of linen", "smooth". These are called its "notes", etc. We may come to know a greater or less number of these "notes".

THE MATERIAL OBJECT OF AN IDEA— The object itself, viewed as the subject of all its notes, whether we advert to them or not, is called the material object of the idea.

THE FORMAL OBJECT OF AN IDEA. That same object, viewed as manifesting to the mind certain notes which we here and now actually come to know, is the Formal Object of the idea. The Formal and Material Object are not two really independent objects, but the same object viewed from different points of view.

16. THE COMPREHENSION AND EXTEN- SION OF AN IDEA. By the comprehension of an idea is meant the collection of notes which the idea implies ; by the extension of an idea is meant the number of individual objects to which the idea applies. It follows then as a general rule that as the comprehension of an idea is increased, its extension is

SIMPLE APPREHENSION AND ALLIED NOTIONS 15

decreased, and vice versa, in any series of ideas that have an orderly relation one to the other.

English writers use the term connotation for comprehension and denotation for extension.

17. OTHER MENTAL PROCESSES IN- VOLVED IN SIMPLE APPREHENSION. That we may the better understand what follows, it is necessary to explain certain mental processes which ideas or simple apprehensions involve. They are :

ATTENTION, an act by which the mind directs its powers of thought to one object out of many which lie in its field of vision. To apprehend an object the mind must needs attend to it. Hence every simple apprehension involves an act of attention, whether voluntary or involuntary.

ABSTRACTION, which is a species of attention. It is an act by which the mind withdraws its attention from all other "notes" which naturally co-exist in an object, and fastens it upon one alone. By abstraction the mind does not deny the other notes ; it simply prescinds from them. For instance we may consider the "color" of a flower to the neglect of the "odor", or we may fasten our attention upon the characteristics of the nature of man — "rational" and "animal" apart from the individualizing notes of this particular man. Since the object of a simple apprehension is universal, the mind in conceiving it abstracts from individualizing qualities of that object. Hence an act of simple apprehension involves also an act of ABSTRACTION.

The object in which the "notes" or attributes are found is called the subject, and the note or attribute in itself is called a form, quality, attribute, etc. (Cf. 15).

REFLECTION, an act by which the mind contemplates its own acts or states. Reflection is two-fold:

Psychological Rejection, when the mind regards its own acts, or states as facts or modifications of one's own soul;

Ontological Reflection, when the mind regards its own acts or states not precisely as its own, but as representative of objects.

How reflection enters into an act of simple apprehension will appear in the explanation of INTEN- TION.

INTENTION may be considered subjectively as an act of the mind, or objectively as an OBJECT upon which the mind's eye is riveted. But when logicians use the word "intention" they usually understand it in an objective sense. It is in this latter sense we shall consider it at present.

Intention is two-fold — first or direct intention and second or reflex intention. It may be observed that a clear knowledge of these terms is essential to the understanding of the Scholastic system of philosophy.

These terms express what experience tells us are the two stages through which the mind passes in the formation of universal ideas. An accurate understanding of their meaning may be difficult for beginners. Yet the light which their study will throw on subsequent logical processes will repay our efforts.

A FIRST or DIRECT INTENTION is an object of our first thought or of our first views of things. I become aware by my sense of sight, for instance, of a "triangle". It will be right-angled, or equilateral, or scalene, or isosceles ; it will be drawn with chalk of a certain color; it will be of a certain area; it will be here, now and this. It will have all the individuating "notes" of a material particular "triangle". At the same instant my intellect spontaneously abstracts from this triangle perceived by sense all its individuating peculiarities — its thisness,

SIMPLE APPREHENSION AND ALLIED NOTIONS 17

nowness, hereness, its color, size, etc., leaving before my first direct intellectual gaze only what constitutes a "triangle", namely "a plane figure bounded by three straight lines". This object of thought then, "plane figure, etc.", upon which the mind directly and at first hand rivets its attention, is called a "first or direct intention".

A SECOND or REFLEX INTENTION has for its object something altogether different from that of the "first intention". The object of the "first or direct intention" is some reality as it is in itself set out before and independent of the mind. The object of the second or reflex intention is the CONCEPT in the mind of the object of the "first intention". The "first intention" looks out directly upon its object — "the plane figure bounded by three straight lines". The second intention looks back into the mind for its object, the concept namely of "the plane figure, etc.". The second intention therefore is a concept of a concept. Its object is a concept in the mind.

The concept or idea which the mind forms of the object of the "first or direct intention" — the plane figure bounded by three straight lines — is called a "direct universal". It neither includes the individuating notes nor does it explicitly exclude them. It simply neglects them. Considered abstractedly, it is in itself not yet known to be either singular or universal. Yet the notes it represents really exist independently of the mind.

The concept which the mind forms of the concept of the object of the "first intention" is called a reflex universal, because the formation of such a concept called for a reflex act of the mind. This reflex universal positively excludes all the individualizing notes. Because the mind perceives the Concept within the mind itself in the manner in which it is therein — and the concept is in the mind in a state of abstraction as a result of its first intention. Hence it expresses a certain number of "notes" that are capable of being pluralized in many. The object of thought in the case of the reflex universal embraces both the object I conceive (the direct universal) and the way I conceive it. Hence the reflex universal is a logical or conceptual entity in the mind, but with a foundation in reality.

Examples of second intentions are "animal" as a genus, "man" as a species, "rational" as a specific difference.

It is called SECOND Intention because it necessarily presupposes a First Intention. It likewise presupposes acts of reflection.

ANALYSIS means the act of separating- or taking the elements of a thing apart. Analysis of an idea is the act of resolving an idea into its constituent parts whether in its comprehension or extension. The formation of a simple apprehension which results in a universal idea always involves analysis, because the mind by its power of abstraction eliminates individual or accidental characters.