Notes to Accompany a Course on Logic by: Brother Francis, M.I.C.M.
Table of Contents Chapter I - What is Logic? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .p. 2 Chapter II - Argument and the Three Acts of the Mind . . . . . . . . . . .p. 5 Chapter III - Signs and Significations . . . . . . . . . . . . . . . . . . . . . . . .p. 9 Chapter IV - The First Act of the Mind: Simple Apprehension . . . . .p.14 Chapter V - The Tree of Porphyry . . . . . . . . . . . . . . . . . . . . . . . . . .p.18 Chapter VI - The Second Act of the Mind: Judgment . . . . . . . . . . .p. 22 Chapter VII - Supposition - Modality - Predicability . . . . . . . . . . . .p. 25 Chapter VIII - The Third Act of the Mind: Inference . . . . . . . . . . .p. 28 Chapter IX - The Categorical Syllogism . . . . . . . . . . . . . . . . . . . . .p. 31 Chapter X - Fruitful Arguments . . . . . . . . . . . . . . . . . . . . . . . . . . .p. 35 Chapter XI - Fruitless and Fallacious Arguments . . . . . . . . . . . . . . .p. 38 Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .p. 42 Additional Readings............................................................................p. 45
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MINOR LOGIC Chapter I –What is Logic? 1.
Logic is the science and art of correct reasoning. (a) Science is knowledge through causes and principles. Scientific knowledge, which results from the methodical pursuit of the causes and principles of things, is more certain, more accurate, better ordered, and more teachable than the ordinary knowledge of common sense. (b)Art is the ability to perform a complex operation successfully, with correctness, facility, and speed. In the case of Logic, the complex operation consists in thinking correctly about important, difficult, and deep matters. (c) The correctness of thought is determined by success in attaining truth and avoiding error. (d)Truth, as the norm of all thought process, means the conformity of mind to reality.
2.
The Properties or Attributes of Logic - Logic is a liberal, reflexive, and normative discipline. (a) A discipline is a skill, or virtue, or any kind of desirable perfection that can be acquired by instruction and training. It comes from the Latin verb disco, discere, which means "to learn," and from it we get the word "disciple." (b)A Liberal Art is a discipline intended primarily for perfecting man as man rather than as a producer of useful tools and services. The Liberal Arts are indeed useful in many ways; but in them utility is a secondary object and ought to be sought as such. There are Seven Traditional Liberal Arts: The Trivium: Grammar, Logic, Rhetoric The Quadrivium: Arithmetic, Geometry, Music, Astronomy (c) Reflexion - Logic is a reflexive science; i.e., its object involves the mind itself and its activities. Reflexion is called a second intention of the mind, which means that it presupposes another and a prior activity called the first intention, by which the mind apprehends an object other than itself presented to it. Every cognoscitive power, even a material one (like sight or touch), can exercise an act of first intention, but only a spiritual power can, in addition to that, also reflect on itself and on its own actions. Logic is, therefore, eminently a spiritual discipline, in as much as it deals in a spiritual manner (reflection) with objects having a spiritual character (reason and its operations). (d)Normative Science - Logic is a normative science; which means that its primary function is to teach us, not how we actually think (a matter for psychology), but rather how we ought to think and avoid error.
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Methodical Knowledge (Scientia)
Of the Real (Factual)
Descriptive e.g. Geography, History
Of the Ideal (Normative)
Explanatory
By Proximate Causes (The Sciences: Physics, Chemistry, etc...)
Useful e.g. The Culinary Science
By Ultimate Causes (Philosophy) Above Utility (The Transcendental Values)
The Good (Ethics)
3.
The Beautiful (Aesthetics)
The True (Logic)
The Divisions of Logic - Logic is divided into two parts: Major Logic and Minor Logic. This book is intended for a course in Minor Logic. (a) Minor Logic is a necessary prerequisite to all philosophy, and in general, to any discipline which depends primarily on the activities of abstract thinking (Theology, Jurisprudence, Theory of Education, Literary and Artistic Criticism, etc.), in contradistinction with those disciplines which deal principally with concrete facts. Even the latter class, including the sciences of observation, experimentation, or statistics, could benefit considerably from the methodical discipline of Logic; yet it must be admitted that men in these fields, can and do proceed a long way in their specialized pursuits, using merely the spontaneous powers of intelligence and rationality, which all men normally attain at maturity. We must, however, add to this, the necessity of liberal education (of which Minor Logic is the most fundamental part) for the perfection and happiness of the individual, as well as for the good of society. Minor Logic supplies the most basic notions and techniques of the art of sound and orderly thinking, the terminology and the method of the craft, so to speak; and besides this it also examines the form of sound argument, and draws out the laws or rules of inference. The norm of Minor Logic is correctness and consistency of thought. 3
(b)Major Logic - While Major Logic is not our immediate concern in this course, still it is necessary for us to know something about it from the beginning of our approach to Logic. While in Minor Logic we restrict ourselves to the mere form of an argument, in Major Logic we are also concerned with its matter (or content). A thinker can be consistent but entirely wrong. This is true of many famous philosophers. In Minor Logic we are satisfied with consistency, that is, the necessary sequence of one judgment from another, of the conclusions from the premises. But in Major Logic we look further into the truth and certitude of premises as well as conclusions. Both branches are known by several different names, emphasizing slight varieties of approach on the part of different authors. Here is a contrasted list of some of the names by which the two parts of Logic are sometimes referred to: Minor Logic: Formal Logic, Material Logic Major Logic: Dialectics, Criteriology, Epistemology, Theory of Knowledge, etc.
Questions and Assignments 1.
Make a list of the important definitions in this chapter. Do some thinking about each. See if you can discover the essence of a definition, and the technique in forming one.
2.
Why is logic a necessary part of Liberal Education? State your position on this matter in the form of a thesis, and defend it using the proper definitions.
3.
Give an example illustrating the difference between Minor and Major Logic.
4.
Be ready to comment on the following: Scientia est recta ratio cognoscibilium. Ars est recta ratio factibilium. Prudentia est recta ratio agibilium.
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Chapter II – Argument and the Three Acts of the Mind 4.
Argument is the verbal expression of a process of reasoning.
Whenever a man is engaged in any kind of human activity his processes of reasoning are at work; and if ever he gives expression to such a process, the result is what logicians call an argument. Thus an argument may be valid or not, and may be used towards a good or bad purpose; yet, regardless of these considerations, it remains fitting matter for the consideration of the logician. Therefore, in order to emphasize the sheer character of an argument as such, we shall deliberately take up one that lacks validity and was employed to a bad purpose. 5.
An Example of an Argument: In the story of the passion of Our Lord according to St. John, we read the following:
“The Jews answered him (Pilate): We have a law; and according to the law He ought to die, “Because He made himself the Son of God” (John 19:7) The sentence uttered by the Jews is an argument; and a great deal has followed upon it. We could have taken other examples at random from almost any kind of book. Arguments are found in fiction and poetry, in books of history, in books about any kind of science or art; they are also found throughout Holy Scripture. They need not be in writing; indeed arguments go on all the time wherever there are men engaged in conversation. On the quality and soundness of arguments, the very texture of our civilization depends. Remembering what was said in the previous chapter about the two parts of Logic, we may now add that any kind of argument belongs to the material object of Logic, while the formal object of Minor Logic consists in the aspect of validity or soundness of arguments. 6.
The Material and Formal Object:
The two terms “material" and "formal" are very much used in Scholastic Philosophy, in ways related but not identical. We have already noticed that the two parts of Logic are sometimes called Material and Formal. We now find that even after restricting ourselves to Formal (i.e., Minor) Logic, we still can talk about a distinction between the material object and the formal object of the same Minor Logic. Having made the student alert to these two important terms ("material" and "formal") so as to be watching for their precise signification whenever they occur again, let us now illustrate by an example their present use.
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The same thing, say an apple, can be the material object for two different sense powers, like sight and smell, but not under the same formality, and therefore not as the same formal object. The formal object of sight is a colored thing; of smell, a characteristic odor. In the same way, the very same reality could belong to the class of things discussed in two or more distinct sciences; and this is exactly what we mean when we say that the thing belongs to the material object of each of those several sciences. Minor Logic shares its material object, first with Major Logic; second, in a way, with psychology (which studies the process of reasoning and its parts as vital acts); and finally, with each of its companions in the Trivium: the three basic disciplines of Liberal Education sometimes called the Arts of Expression. But the formal object of two sciences cannot be the same, otherwise they cease to be distinct. This is an instance of the following axioms of philosophy: I. No two subjects can have in common the same formal object. II. It is by the formal object that one science is distinguished from another. The following comparative scheme emphasizes the distinction and contrast between Logic (in both its parts) and each of the other two disciplines of the Trivium, in terms of their respective formal objects: Grammar is concerned with the conformity of expressed thought (i.e. in language) to the mind. Rhetoric is concerned with the conformity of one mind to another. Logic is concerned with the conformity of mind to reality. 7.
The Three Acts of the Mind:
Inference, Judgment, Simple Apprehension. The most complete unit of reasoning (the cell, so to speak, for Logic) is an inference, which consists in a certain movement of the mind from one or more judgments to another. Since this act of inference is the most complete act of reasoning, it appropriates the very name itself, so that, to a logician, inferring means reasoning. But you cannot make inferences without judgments, nor judgments without concepts arrived at by the simplest act of the mind, which is called simple apprehension. Hence the act of inference being the most complete act of reasoning, contains within it, and can be analyzed into, the two prior and simpler acts: judging and simply apprehending. An example of inference is the one expressed by our example of an argument given in #5. That argument contains judgments like "We have a law" and "He makes himself the Son of God." It also involves other judgments that are not made explicitly. The judgments can be analyzed further into concepts or ideas (as logicians we may call them "terms"), such as "we," "have," "law," "made," "Son," "God". 8.
Syllogism, Proposition, Term:
An inference is something that takes place in the mind and, consequently, so do the elements of which an inference is made up, namely, the immediate elements (i.e. the judgments), and the 6
remote or ultimate elements (the concepts). But the logician can deal with these mental entities only after they are expressed in language. We already know that when an inference is expressed in language, the resulting expression (in Latin oratio) is called an argument. Now we may add that the most important kind of argument is the syllogism. The syllogism is the principal object of Minor Logic; and it is only as parts of a syllogism that propositions (expressing judgments) and the terms (expressing concepts), are studied here. On the other hand, in Major Logic, the proposition becomes the main object of interest. The following scheme gives in summary what has been said about the three acts of the mind and their corresponding expressions in language, adding the perfection proper to each act: In the Mind First (and simplest) Act: Simple Apprehension (Terminates in concepts or ideas) Second Act: Judgment Third Act: Inference
In Language
Proper Perfection
Terms
Clarity
Proposition
Truth
Argument (Principally the Syllogism)
Validity
Provocative Questions 1.
A proposition may be defined as the expression of a complete assertion; and, therefore, as a sentence which can be called true or false. Apply this definition to the following two sentences: "How are you?" and, "I'm fine." Give other examples of sentences that are, and sentences that are not, propositions.
2.
Give three more examples of an argument like the one in #5 (try to choose examples which are significantly different.)
3.
Find other examples of different sciences sharing (in whole or in part) the same material object.
4.
State some of the implicit propositions in the arguments of #6.
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9. “The Oratio Scheme”: Sounds produced by the human voice may signify something
By Nature eg. weeping, laughing, sighing etc.
By Convention
Inarticulately e.g. screams, applause, wailing whistling
Ordinativa (Aims at effecting a result which could be)
Attention Response (Vocativa) (Interogativa)
Action
To a Superior (Deprecativa)
Enunciativa (Aims at declaring a thought)
Sympathy
To an Inferior (Imperativa)
Imperfecta
Definition (of a concept)
Articulately (Speech Proper or in Latin, Oratio)
Perfecta
Proposition
Arugument
Division
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Chapter III - Signs and Signification 10. Definition of the Term "Sign": "A sign is a medium between a mind knowing and a thing known." This will do for an initial definition. We shall restate it in a fuller and more articulate form at the end of this section. Applying this definition, we see immediately that the words of a language are signs (to one who knows that language, of course, for otherwise they are just things). I see or hear the word "horse" and I think of horses, as I would if I were in a stable looking at them. I sit in a lecture hall listening to a talk on Astronomy, and my mind travels across the universe, from galaxy to galaxy, for no reason other than words uttered by the lecturer. Were it not for those words, my mind would likely have been on entirely different matters, while the stars are moving in their circuits and the astronomer in a deep contemplation of them. There are other kinds of signs than the words of a language. A monument is a sign; a religious habit is a sign; the Sacraments are signs; the Liturgy, to a large extent, is made up of symbols, other kinds of signs; the Flag is a sign; and, of course, there are the ubiquitous traffic signs. The famous Book of Sentences by Peter Lombard (contemporary and friend of St. Bernard, usually referred to as the Master of Sentences), a comprehensive textbook in four volumes used by all the Catholic universities for centuries, and commented upon by all the great Scholastic thinkers including St. Thomas and St. Bonaventure, was divided in its subject matter into two main parts: Things and Signs. Indeed, if we stop to think about it, everything could be used also as a sign. We are taught in Holy Scripture that the sun, the moon, and the stars were made "for signs, and for seasons" (Gen. 1:14). And throughout the Psalms and the rest of Scripture, especially in Our Lord's teaching, we get a sense that God intended to teach eternal truths through sensible objects functioning as signs or symbols. Yet while everything could be used as a sign, not every sign is a thing, at least, not anything besides its very function of merely signifying. This statement points out one of the deepest problems of philosophy, in fact a mystery that goes deeper than the entire order of nature. Yet, all knowledge of reality would become impossible, were there not signs that are not also things. Such a sign is an idea or a concept. We may now restate our initial definition and say that a sign is what conveys to a cognitive faculty a knowledge of something other than itself; whether or not it has a reality of its own, i.e., apart from this matter of signifying. 11. The Division of Signs: The first thing a logician does with a subject is to define it; and the second, is to divide it from one point of view, or, perhaps from several ones. We are going to study these two important techniques of Logic, Definition and Division, in another chapter; but we can say even now, that definition makes a subject more intelligible, and division, more familiar. And when we come to divide, we 9
review our definition, because it supplies us with the significant aspects under which the subject under consideration, by its very nature, tends to divide. Since a sign is a medium of knowledge between mind and reality, there ought to be as many essentially different kinds of sign as there are different kinds of relations between the sign and the mind to which it signifies. From its relation to the thing signified, a sign may signify by nature or by convention. Smoke is a natural sign of fire, but the siren of the fire alarm is a conventional one. On the other hand, from the point of view of its relation to the mind, a sign may signify mediately or immediately. A sign signifies mediately when signifying does not exhaust its reality. The sign is a thing on its own apart from whether or not it is signifying. It must be known as a thing before it can function as a sign. A statue is this kind of a sign. This is usually called a medium ex quo. In opposition to which we have the medium in quo, namely, a sign which is such a sheer sign, that it has no other reality to be known prior to its signifying. Its complete reality consists in signifying. For reasons which will be explained later, this kind of sign is also called "The Formal Sign". It can occur only in the experience of knowing; and therefore, no example can be sought out in any other order. The concept, or the idea, is a formal sign - a medium in quo. All that we have been saying, along with some new additional explanations and illustrations, will be given in the scheme immediately after this section. But before we come to this important scheme, let us say by way of summary, that Logic presupposes a doublefold signification: concepts are signs of things, and words are signs of concepts, and through concepts, also of things. Both the concept and the word are signs; but not the same kind of sign.
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12. The Sign Scheme: A Medium (Something between two others)
Sign: Medium of Knowledge (One of the two is a knowing power)
Arbitrary (Signify by convention) e.g. Red light: a sign for Stop)
All other Kinds of Media (Neither of the two terms is a knowing power e.g. Money (exchange) Roads (media between places) The Mail; Ships; Ambassadors; Merchants Natural
Not an Image (Red: a sign of ripe cherries) Not an Image (A word)
Somewhat an Image (An Onomatopoeic Sound) e.g. “buzz” Mediate Signification (Medium ex quo) e.g. A Statue
An Image
Immediate Signification (Medium in quo) e.g. A Concept
13. Univocity, Equivocity, Analogy: Usually in an argument the same word is repeated more than once; in a syllogism, necessarily so. Now the supreme and paramount rule for validity is that the word should not change its signification within the same argument (at least not in a way to invalidate the force of the reasoning). The attribute of a word preserving entirely the same signification is called Univocity. The contrary defect is called Equivocation. In Logic, equivocation must be avoided as much as possible. Now equivocation in the strict sense can occur in the kind of sign that the word is, but not the kind of sign that is a concept. (Why?). Any word may be given more than one meaning and used in more than one way. (Try to find examples). But if a concept became equivocal, it is really not one but two distinct concepts, which must then be distingnished. But a concept may be analogous, which means that, remaining one and the same concept, it applies in different ways to different orders of reality. Analogy, and other technical matters relating to the signification of terms, shall be dealt with in the future; but let us affirm now in anticipation, that certain kinds of analogy, under determinable conditions, do not destroy the validity of an argument. 11
In the following section, #14, another chart or scheme will, it is hoped, make a little clearer some of the things we have just been saying. It will be referred to as the Analogy Scheme. 14. The Analogy Scheme: The Word may signify either:
One and the same concept
Same in all its inferiors (Univocity)
Not same in all its inferiors (Analogy in the strong sense)
Proper only to one (Analogy of attribution)
Two or more different concepts (Equivocation) In the large sense of the term
Related (Similarity or Analogy in the weak sense)
Unrelated (Strict Equivocation)
Proper to both inferiors (Analogy of Proportion -the strongest kind of Analogy)
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Questions and Assignments
1.
Find examples illustrating every terminal category of the Analogy Scheme #14.
2.
In accordance with the same Analogy Scheme, how would you characterize the behavior of the underlined term in each of the following instances: A. John has a wrist watch and John ought to watch his manners. B. The song of children and the song of Angels. C. The music of the spheres. D. Dates are too sweet and I cannot learn history because I cannot remember dates. E. Not only is Mary devout; her conversation also is devout. F. Habit as the tenth category and habit as a species of quality. G. A live wire and a live party. H. A noble person and a noble deed. I. The real grass and its real green.
3.
Think of other examples illustrating the Sign Scheme #12.
4.
Think about the following proposition: Univocity is easily attainable in mathematics but not in all science.
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Chapter IV - The First Act of the Mind: Simple Apprehension 15. The first act of the mind, as we already know, is called "Simple Apprehension" whose result is an idea or concept in the mind. Simple Apprehension is defined as: an act by which the mind becomes cognizant of an essence without afirming or denying anything about it. But what do we mean by "Essence"? Essence is reality as understandable (a more technical word would be "intelligible.") The definition of "Essence" could be said differently but it would amount to the same thing. Essence is the answer to the question "What is it?" From the Latin word for "what" it is sometimes called, quiddity from "Quid est," which in turn is the Latin for the Greek original of Aristotle: το τι εστι The essence, therefore, is the meeting ground of mind and reality. It is that thing of the concept which is real; it is also that of reality which is intelligible. To every essence there is a name, and that makes up all the words of language. Now ready for another important definition: A word is every articulate sound that conventionally signifies a concept, and through the concept a reality. Now a great deal of man's quality (I could almost say all of it) depends on the concepts that occupy his mind. If you could cast on a screen all the concepts in a holy man's mind, you would discover that he is a saint and why. Lofty concepts raise man's thoughts to higher things; and clear and ordered concepts are the beginning of all sound reasoning. This is our assignment in this part of the course: To achieve Clarity, Definiteness, Order and Accuracy in all the important concepts of our minds. In Logic we prefer to call the words "terms," for two reasons. First, it emphasizes their functions in a proposition and in an argument. And second, because the word "term" applies just as much to the elements of a judgment in the mind as to those of a proposition. In the most important kind of proposition, namely the Categorical Proposition, the two main terms are called "Subject" and "Predicate." Thus in the categorical proposition "Man is rational," the subject is "man" and the predicate is "rational." 16. Supposition: The title of this section, "Supposition," is a technical term, and has nothing to do with what you may "suppose" that it means. To point out the specific sense it has in this part of Logic, some 14
books keep it in Latin Suppositio. The definition of this term will be given in a future chapter, where its entire subject will be discussed more fully; but to get an idea of what it refers to, consider the following examples: "Man" is a monosyllable (The term man has material supposition) "Man" is a universal idea (The same term has logical supposition) "Man" is rational (The same term has real supposition) Notice that in the three sentences the meaning of the term may remain unchanged; that is, the meaning as you may find it in the dictionary; and yet the use of the term as a sign is entirely different in each one. The term as a sign ought to represent something. Now in the first example, the term "Man" just represents itself (if we may call that representation); and, therefore, it is not used really and formally as a sign, but only materially so. This explains the name we gave it: Material Supposition. In the second example, the term functions as a sign formally by representing an idea in the mind. In the third case, which is the most normal and most ordinary use, the term represents a thing or a reality, but through the mediation of the concept. These are not the only kinds of supposition but the most important ones as we shall see later. 17. Comprehension and Extension: Taking the term in its most normal supposition, which is real supposition, we find it representing a class of things through the mediation of its meaning in the mind. For example, the term "white" represents colored things (snow, sugar, salt, paper, cloud, along with other things); but only through the meaning of the term in the mind whereby we know when to apply that term to a thing. Now the simple meaning of the term is called its comprehension; while the class of things to which it applies is called the extension of the term. The comprehension of most terms is complex, in the sense that it can be analyzed into simpler concepts called its "notes." For example, the concept animal contains the following notes: Being, Substantial, Material, Living, Sentient Only one concept in the mind is absolutely simple, i.e. it cannot be analyzed into notes, and that is "being." On the other hand, the same concept "being" is a note in every concept, as we shall see later. Every concept (and therefore also every term) has these two contrasted aspects to be considered: its comprehension and its extension. And on account of this new interesting little technical word we have just learned, namely "note," the comprehension of a term is also called its connotation, and the extension is called denotation. 18. Definition and Division: We are now ready to discuss the two most important operations of this part of our course, name15
ly, Definition and Division. Every complex concept may be defined in terms of simpler concepts; and may also be divided by concepts of lesser extension. Definition may also be divided by concepts of lesser extension. Definition moves in the direction of simpler, more abstract, and, therefore, more intelligible concepts; while division moves in the direction of more concrete, more specific, and, therefor,e more familiar things. 19. Definition: Definition is defined as: an expression expounding the nature of a reality or the signification of a term. The following scheme giving the different kinds of definition will be known as "The Definition Chart". Definitio (Oratio imperfecta exponens...)
Naturam rei (Realia) Extrinsica Intrinsica e.g. 1. The human soul is an incomplete substance created by God for beatitude. 2. A watch is a little mechanical device to indicate the right time. 3. A circle is a plane figure generated by the rotation of a line around one of its ends being fixed. Descriptiva
Significationem termini (Nominalis) e.g. 1. Philosophy is the love of wisdom (Etymological) 2. Belligerent means party to a war. (A more familiar synonym) 3. Here I use “light” as the contrast of heavy. 4. We’ll call this newly discovered particle "proton".
Essentialis
Per Proprium
Per congeriem accidentium
Physica
Metaphysica
e.g. Man is a laughing animal
e.g. Man is a featherless biped
Man is a subMan is a stance composed rational animal of a rational soul and an organic body
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20. Division: Division is an expression distributing a whole into its parts. From this definition of division we know that there must be as many kinds of division as there are different kinds of wholes, or of the relation of whole and part. Parallel with nominal definition, which merely attaches one fixed meaning to a term, we have normal division, which distributes and distinguishes the different meanings of one and the same term. But more important than that is the distinction between the real whole and the logical whole. The logical whole is the same as the universal; it is the relation between the concept "man" and all men. Thus a real whole cannot be predicated of its parts; for example, a house cannot be predicated of one of its walls or windows; but a logical whole can, since the concept man may be predicated of Peter, and of Paul, and of any other man. The counterpart of a logical whole is called a subjective part; thus Peter is a subjective part of the logical whole "man," because we can say "Peter is a man," and thus make Peter the subject with the logical whole as predicate. Other distinctions will be shown in the following scheme, to be known as "The Division Chart": Divisio
Per accidens (ratione alterius)
Per se (ratione sui ipsius)
1. subjecti in accidentia 2. Accidentia in subjecta 3. Accidentis in accidentia
Division nominis (Distinctio)
Divisio toti potentialis (Totum Logicum)
Univocum e.g. Animal as of tiger, lion, etc.
Analogum e.g. Being as divided into the 10 categories
Non-entitativum Integrale e.g. Man into head, neck, etc.
Potestativum e.g. The soul into its powers and faculties
Entitativum (Being into essence and existence)
Non-essentiale Physicum e.g. Man into a rational soul and an organic body
Divisio rei
Divisio toti actualis (Totum Reale)
Essentiale Metaphysicum e.g. Humanity into rationality and animality
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Chapter V - The Tree of Porphyry 21. Porphyry and the Hierarhy of Concepts: The philosopher Porphyry (a Syrian Neo-Platonist who lived in the third century of our era and died at Rome in A.D. 301) wrote one of the most famous text books in history: an introduction to the categories of Aristotle, known by its Greek name Isagoge (which means Introduction). This book exerted tremendous influence throughout the Middle Ages, and was, among other things, the starting point for the great controversy with regard to the problem of universals. While in many ways not an admirable man, Porphyry was nevertheless an able teacher, and has been mentioned almost unexceptionally in all Logic books since his time, because of a successful pedagogical device known as the Tree of Porphyry. The Tree of Porphyry is an arrangement of the most important concepts of philosophy, in such a way as to express vividly a certain hierarchy of universality that orders and significantly relates these concepts to each other. Since reflection on the activities of thought is not easy without such a pictorial device, Porphyry's pedagogical invention proved to be almost indispensable for the conveying of a great part of the terms, principles, and techniques of Logic. We have to wait until the next page before we can take a look at the Porphyrian Tree, because it needs an entire page all of its own. But we can begin immediately to say a few things about it. The most basic principle governing the arrangement of the Porphyrian Tree consists in placing a logical whole above its subjective parts, which is the same thing (if we still remember what was said previously) as placing a more universal concept above a less universal one. From this a considerable part of the technical language of logicians is derived, as for example, when they say that one concept is higher than another. Let us take one example to illustrate the principle on which the Tree of Porphyry is constructed. Take the two concepts "animal" and "animate". An animal is a living material body possessing the powers of sense life; an animate is a living material body whether or not it is endowed with sensation. Every animal is an animate, but not every animate an animal. Therefore, the concept "animate" should be placed above the concept "animal" on the Porphyrian Tree. Now comparing these two concepts we find that on the score of their comprehension the concept animal has more that the concept animate, since it has sensation in addition to all the notes of the latter. On the other hand, from the point of view of extension, it is "animate" that has the larger extension. And so without needing to examine other instances we can draw he following conclusion: In general, addition to the comprehension of a concept results in the contraction of its extension.
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22. The Tree of Porphyry in the Category of Substance. Logical Terms Supreme Genus............................Substance Differentia..................Composite
Simple
Higher Genus.........Body
Spirit
Differentia..........Living
Non-Living
Higher Genus.....Animate
Mineral
Differentia..........Sentient
Non-Sentient
Genus.................Animal
Plant
Differentia..........Rational
Non-Rational
Species...............Man
Brute
Individuals........Peter (First Substance)
John
X
23. Some Observations Immediately Suggested by the Porphyrian Tree:
a. The Porphyrian Tree is like a tree planted in the sky with its branches spreading earthward. b. The logical terms "Genus" and "Species" may be used in a relative sense, namely, every higher concept can be called a genus in relation to one immediately placed under it as its species. c. But in the stricter sense, only that concept is called species which is a complete essence; namely, one which cannot be differentiated further except by accidental notes like "man". d. No generic concept can be placed over "Substance". "Being" is not a genus because it cannot be contracted by a note not already somehow part of its comprehension. e. A concept to be defined must be considered under the aspect of a species (at least in the relative sense), and definition consists in finding, first, a genus under which the concept falls; and second, the differentia which distinguishes it within that genus. f. Strictly speaking, neither "Substance" nor "Individual" can be defined. Neither of them can be treated as a species.
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g. Neither definition nor division can proceed ad infinitum. Division must terminate with individual things, and definition with the Supreme Genera. 24. The Supreme Genera or the Ten Categories: Everything that can exist in itself, or on its own, falls under the supreme genus "Substance". But there are other realities which presuppose the existence of something else in order to exist in it (or rather in-exist, and more technically, to inhere). Such, for example, is the color green. Grass is substance, but green is not. Grass can exist on its own, but green needs something like grass in order to exist. How many types of such realities, or even of conceivable things, can there be? Aristotle says that besides the supreme genus "Substance" there are nine supreme genera of accidents. And the total is called "The Ten Categories of Aristotle". They are: Substance, Quantity, Quality, Relation, Action, Passion, Time, Place, Disposition, and Habitus St. Thomas, commenting on Aristotle, explains why the categories are precisely the ten enumerated, and none other. On the following page we shall find a scheme manifesting the thought of St. Thomas concerning the number of the categories and their interrelations. It will be known as "The Chart of the Ten Categories." 25. The Rules of Good Definition: 1. A definition must include all that falls under the term defined and must exclude all that must be excluded. 2. The terms in the definition ought to be clearer than the term being defined. 3. The best kind of definition (the essential metaphysical definition) is by genus and differentia; all other types try to imitate this as much as possible. 4. A definition must not be circular; that is, that notion being defined should not enter, not even surreptitiously, into the terms of the definition. 5. In general a definition should avoid negative terms. 6. A definition must be as brief as possible.
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26. The Chart of the Ten Categories: Being (Predicated of all the categories, but only analogously) In itself and as subject of all others
Inhering in a substance (Accident)
In the subject entirely
In the subject partly
Extrinsically
1. Substance Absolutely
Rooted in matter
2. Quantity
Relatively
In the subject as principle
In the subject as term
5. Action
6. Passion
Rooted in form
3. Quality
4. Relation As measure Of time
Not as measure
Of place
10. Habitus
7. Time In relation to other things
Parts in relation to each other
8. Place
9. Disposition
Questions and Assignments 1.
Try to formulate rules for good definition to parallel the rules for good definition given above.
2.
How do you distinguish a logical whole from a real whole? Give examples to illustrate both.
3.
Show how all definitions try to imitate the metaphyical definition. Use the Definition Chart #19 for that purpose.
4.
Take a paragraph in any kind of book and try to allocate all the words under categories.
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Chapter VI - The Second Act of the Mind: Judgment 27. Judgment We read in the Book of Psalms: "The Lord loveth judgment, and will not forsake his saints: they shall be preserved forever." (Ps. 36:28) Is there any connection between that judgment which is loved by God and which leads to eternal life, and the judgment which we are about to study in this chapter? To answer this question let us first examine a few judgments which God certainly loves and which make a difference in whether we do or do not attain to the joys of eternity. "God exists," "My soul is immortal," "Jesus is the eternal Son of God," "Mary is the Mother of God," "God wants all men to be saved in the one true Church approved by Him," "The Pope is the Vicar of Christ and the universal shepherd of all true Christians," "Justice, charity, purity, and piety are virtues, and their opposites are vices whose fruits are the fruits of perdition," etc., etc. All these are judgments and, whether or not they can be arrived at by natural reason, they make use of the same faculty of the mind as any other logical judgment and may form any part of a rational argument. But in what does the essence of a judgment consist? Judgment is defined as an operation of the intellect composing or dividing by affirming or denying. As a second operation of the mind, judging presupposes the first act by which a concept is formed. Now you cannot form judgment with only one concept because you cannot compose or divide until you have at least two; nor is mere composing or dividing of concepts sufficient to form a judgment unless affirmation or denial is also involved. I can compound the concept "mountain" with the concept "gold" to form the new complex concept "gold mountain." I can also divide the concept "spirit" from the concept "clean" to form the concept "unclean spirit." Yet in neither of these two composite concepts is there a judgment. The formal specific difference of an act of judging is the presence of either affirmation or denial, and it is only after affirming or denying that we get in the mind a logical entity that can be significantly qualified as true or false. Hence we may propose an alternative definition for "judgment": an intrinsical descriptive definition per proprium (consult Definition Chart #19): A judgment is the act of the mind which can be significantly qualified as true or false.
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28. The following will be referred to as The Proposition Chart: Propositio
Simplex Categorica (Praedicativa) e.g., Life is short.
Coposita Hypothetica
Aperte
Copulativa Disjunctiva e.g. e.g. I am the Alpha We must and the Omega. have good priests or the faith will be lost.
Exclusiva e.g. Only the Blessed Virgin Mary was immaculately conceived.
Occulte
Conjunctiva Conditionalis e.g. e.g. You cannot If God is for be a Christian use than we and a Communist cannot lose.
Exceptiva e.g. Every being except God, is contingent.
Reduplicativa e.g. Man, as man, desires to know.
29. The Square of Opposition While it is important that the student become familiar with all forms of a proposition as given in the previous section, we must now say that two of those forms enjoy a paramount importance as far as the theory of inference is concerned, and will henceforth monopolize our attention: the simple categorical, and the conditional proposition. The categorical proposition may be divided, from the quality of its copula, into affirmative and negative; and from the quantity of its subject, into universal and particular. There are other divisions and ways of dividing the categorical proposition, bur we may ignore them for the present, in view of our dominant concern at the moment: the discovery of the rules of valid inference. By crossing the two ways of dividing, one against the other, we obtain the fourfold division of categorical propositions which occupy the four corners of the famous Square of Opposition: another pedagogical device like the Tree of Porphyry. It will be given on the next page.
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The Square of Opposition. Every A is B Subalternant A Co ntra dic tori es
es tori c i d ntra o C Subalternate I
No A is B Contraries
E. Subalternant es tori c i d ntra Co
Co ntra dic tori es
Subcontraries
Some A is B
O Subalternate Some A is not B
30. Some remarks and suggestions regarding the Square of Opposition. a. The student is advised to practice formulating propositions of the four types: A, E, I, and 0. b. The four vowels come from the Latin words affirmo and nego. c. A & E are contraries: they cannot be both true. I & 0 are subcontraries: they cannot both be false. A & 0 and E & I are contradictories: they can neither be both true nor both false. d. If the subalternants (A & E) are true, their respective subalternates (I & 0) must also be true; if the subalternates are false, their respective subalternants must be false; in neither case is the converse true. This is a very important relation and we shall talk about it more in connection with hypothetical arguments. e. A term is said to be distributed if its entire extension is meant to be involved in the proposition, otherwise it is called undistributed. In the four propositions above (i.e., A, E, I and 0) a term is distributed only if it is the subject of a universal proposition or the predicate of a negative proposition. See how these rules apply to each of the four types.
Questions and Assignments 1.
Give the most important proposition you can think of in each of the four types. How do the rules of distribution apply to your examples.
2.
Find other examples for all the types in Chart #28.
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Chapter VII - Supposition Modality - Predicability 31. The three notions of this chapter involve aspects of the proposition which deserve some special attention: Supposition, which applies primarily to the subject; modality, to the copula; and predicability, to the predicate in its relation to the subject. If the proposition is "man is mortal," then the supposition of its subject points to that aspect or part of reality where we find the things (namely men) to verify the statement. The point can be made more emphatic by using the same term with a different supposition, as when I say "man is a monosyllable." The modality of that same proposition may be determined by finding out precisely what is meant by that is when we say "Man is mortal"; is he so contingently or by necessity. As for the question of predicability, it goes further still to determine the relation of mortality to man: is it in the essence of man, or part of the essence, or in what relation does it stand in regard to the essence. 32. Supposition The supposition of a term is the precise manner in which it is used as a sign; for example, are we using it to represent concepts in the mind or things in reality, or are we thinking merely of the word itself as an element of language? And if it represents things, does it represent them collectively or taken one at a time? All this great variety of suppositions in the use of the term does not involve any change in the ordinary meaning as found in the dictionary. Hence the signification of terms may be considered as a genus divided into two species: meaning and supposition. The following will be known as The Supposition Chart: Signification of a Term Meaning (as found in the dictionary) Formal Logical (e.g. “man” is a universal idea)
Supposition (its manner of use as a sign) Material (e.g., “man” is a monosyllable)
Real Singular (e.g., this man... the first man...)
Common Absolute Personal (e.g. man forgets) Collective Distributive (Man made all (Men are normal) the works of art)
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33. Supposition and Symbolic Logic. The great difference between traditional Logic and the mathematical parody on it, called Symbolic Logic, can now be brought to light in terms of this matter of supposition. Supposing one were to make the statement that, "All the centaurs are members of the United States Congress." Now since centaurs are merely mythological beings, there exist no entities anywhere corresponding to the term "centaurs". In the language of Symbolic Logic, the term "centaur" represents the null-class, i.e., a class or a set with no members. Symbolic logicians say that all universal statements about the null-class are true, because no one could produce a case to the contrary in refutation of them. But to the traditional logicians all universal affirmative statements of this sort are false for lack of supposition. This may sound like a small point, but it reveals all the chasm between a nominalist outlook, and a logic seriously committed to the truth as conformity to reality. 34. Modal Propositions. A proposition becomes modal, not by modifying the subject or the predicate, but by modifying the copula; since the copula expresses the form of the proposition: the act of judgment. Thus the proposition "Man is subject to infirmities" is a non-modal proposition (called also "propositio de inesse", which means that it merely states that the predicate exists in the subject). This proposition does not become modal when we say "Healthy men are subject to infirmities"; nor when we say "Man is subject to many and grave infirmities"; but it does become modal when we say, "Man is necessarily subject to infirmities." There are four modalities: Necessity, Impossibility, Possibility, and Contingency. The following scheme relating and illustrating the four modalities will be shown as "The Modality Chart". A Categorical Proposition May
merely state as a fact the connection between subject and predicate (Propositio de inesse) e.g., God is Just..
Necessity Of existence
Necessity
also state the kind or mode of connection (Proposition modalis) e.g., God is necessarily Just.
Contingency
Of non-existence
Of existence
Impossibility
Contingency
Of non-existence
Possibility
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Examples of modal propositions: This man may be thinking about heaven. (Possibility) This crime need not have been committed (Contingency) God must continue to think about me. (Necessity) Machines cannot think. (Impossibility) 35. Immediate Inferences: Between modal and non-modal propositions certain immediate inferences can be drawn, and certain fallacies can be committed. Four traditional Latin phrases guide us correctly in these matters: (1) Ab esse ad posse valet illatio. (You may infer validly from the existence of a thing to its possibility.) (The student should be able to supply the translation for the three other phrases.) (2 ) A non posse ad non esse valet illatio. (3) A non esse ad non posse non valet illatio. (4) A posse ad esse non valet illatio. We shall see later that these four propositions are merely a special instance of the rules of inference from a conditional premise. 36. The Five Predicables: The predicables name all the different reasons whereby the predicate, considered as a universal, can be said to apply to the subject as its inferior. The following chart, to be known as the Chart of the Five Predicables, explains why there could be only five such reasons. The Predicate may apply to the Subject as expressing Something Of its essence The complete essence
Outside its essence
A part of the essence
Necessary
I. Species
IV. Property
The determinable part
The determining part
II. Genus
II. Differentia
Contingent
V. Accident (Logical)
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Chapter VIII - The Third Act of the Mind: Inference 37. Inference is reasoning properly so-called; it presupposes the simpler acts of the mind: simple appre-hension by which we obtain concepts, and the act of judging which is expressed in proposition. In inference the mind moves from propositions already known to others not initially known but following upon the known ones by a kind of logical necessity. Inference is thus defined: An act of the mind by which from truths already known the mind comes to know other truths. 38. Division of Inference: Inference can be immediate or mediate; and mediate inference is divided into hypothetical and categorical, so named from the nature of the predominant or leading initial judgment. We have already seen examples of immediate inference, first, in connection with the Square of Opposition; and second, in connection with the modal and non-modal prepositions. As an example of the first kind, we can infer from the proposition, "All men are mortal," the truth of the proposition, "Some particular men are mortal"; or from the affirmation of an A proposition we may validly infer the truth of the weaker proposition. As an example of the second type, from the modal proposition affirming that, "machines cannot think," we may validly infer the truth of the non-modal proposition (or in Latin, propositio de inesse) stating that, "machines do not think." These two examples are enough to convince us that there is such a thing as immediate inference in Logic, even though the two examples given by no means exhaust its varieties. Now while immediate inference can in some sense be called reasoning, and the expression of it be called argument, yet the two terms "reasoning" and "argument" belong more properly to mediate inference, in which one judgment leads to another judgment only through the mediation of one or more other judgments. Here is an example of hypothetical argument, leading with a conjunctive proposition (The Proposition Chart, #28): You cannot be a Christian and a Communist, But you are a Communist; Therefore, you are not a Christian. The student is encouraged to formulate other arguments, leading with the different kinds of propositions found in Chart #28. But, for the purpose of formulating the laws of inference, the major objective of Minor Logic, two types of argument are of paramount importance: The Categorical and the Conditional.
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39. The Syllogism: The Syllogism is the unit of argument: the most perfect expression of the process of reasoning. It is to Minor Logic what the cell is to biology and the atom is to chemistry. It is the object par excellence of Minor Logic. It may be defined as follows: The Syllogism is an argument consisting of three propositions related in such a way that the truth of the third necessarily follows upon the truth of the first two. The example given at the end of the previous section (#38), is also an example of a syllogism. The truth of the first two propositions, “You cannot be a Christian and a Communist,” and “You are a Communist,” necessarily determined the truth of the third, namely, “You are not a Christian”. There are as many kinds of syllogism as there are kinds of arguments, but the ones that will engage our attention most of all in this course are, as we have already intimated, the categorical and the hypothetical syllogisms. 40. The Categorical Syllogism. In the Categorical syllogism (namely one in which all three propositions are categorical), the first two propsitions are called premises and the third is called the conclusion. The syllogism is for the sake of the conclusion, since the premises are known (or at least assumed) to be true; therefore, the conclusion is the most important proposition and most of the terminology revolves around it. In the conclusion there must be two terms: a subject and a predicate. The subject of the conclusion is called the Minor Term, since in a normal proposition it is likely to have a smaller extension than that of the predicate. The predicate, in contrast, is called the Major Term. There can be only one other term in a syllogism and that term must not appear in the conclusion. It is called the Middle Term, since its proper function is to mediate between the two terms of the conclusion in such a way as to manifest the connection between them expressed by the copula. The premise containing the Major Term is called the Major Premise, and is usually stated first; the Minor Premise, mentioned second, must contain the Minor Term. Let us now look at an example of the Categorical Syllogism: Major Premise: All animals are endowed with powers of locomotion. Minor Premise: But the clam is an animal. Conclusion: The clam is endowed with powers of locomotion. Notice that “the clam” is the Minor Term (why?) and is contained in the Minor Premise, that “endowed with powers of locomotion” is the Major Term and occurs in the corresponding premise, and finally that “an animal” appears in both premises but not in the conclusion. It is, therefore, the Middle Term. 41. Conditional Syllogism. The Conditional Syllogism is one whose Major Premise is a conditional proposition. The 29
following argument is a conditional syllogism: Major Premise: If the clam is an animal, then it must be endowed with powers of locomotion. Minor Premise: But the clam is an animal. Conclusion: Therefore the clam must be endowed with powers of locomotion. Notice that the truth of the conditional proposition (the Major Premise) is in an entirely different order from the truth of a categorical proposition: it is not immediately measured by reality. The conditional proposition affirms something not immediately about reality but about two logical entities, namely two propositions; and, therefore, its truth is somewhat independent of the real order; for the statement, "If the clam is an animal, it must be endowed with powers of locomotion" would remain true even if both parts of the proposition were false. This is a very important fact, and we shall have occasions to return to it later. 42. Terminology with regard to Conditional Arguments. Notice that the conditional premise in the syllogism of the previous section (#41) contains two parts, each on its own would be a categorical proposition. The first of these propositions following "If," namely the proposition "The clam is an animal," is called the Antecedent; the second, following "then," is called the Consequent; the logical connection affirmed as existing between the Antecedent and Consequent is called, Sequence. Also notice that what we did in the Minor of that same syllogism was to affirm the Antecedent and then, by virtue of the affirmed Sequence, to go on and infer the truth of the Consequent. This is a valid procedure in a conditional argument. But now let us construct another syllogism: Major Premise: If the car is an animal, then it possesses powers of locomotion. Minor Premise: But the Car is not an animal. Conclusion: Therefore, the car does not possess powers of locomotion. What happened? This time, instead of affirming the Antecedent, we negated it. This cannot be done validly. There are only two valid forms after a conditional Major Premise: in the Minor, either affirm the Antecedent or negate the Consequent. Both of the two other possible alternatives are fallacious.
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Chapter IX The Categorical Syllogism 43. We know that every perfect categorical syllogism is made up of three propositions (called its immediate matter) and of three terms (called its remote matter). This is another way of saying that every syllogism can be resolved immediately into three propositions and, with further analysis, into three terms. Now we are going to state the eight general rules of all valid syllogistic argument; and it will be left to the student to discover the reasons underlying these important rules. But, before reading these rules, refresh your mind on the meaning of the technical term "distributed" as given in #30 e. Laws Governing the Terms of the Syllogism First Rule: Every syllogism must have three terms and no more. Second Rule: The distribution of a term cannot be greater in the conclusion than it is in the premises. Third Rule: The Middle Term must not appear in the conclusion. Fourth Rule: The Middle Term must be distributed as least once in the premises. Laws Governing the Propositions of the Syllogism Fifth Rule: From two affirmative propositions no negative conclusion can be drawn. Sixth Rule: From two negative premises no conclusion can be drawn. Seventh Rule: If one premise is negative, the conclusion must be negative; if one premise is particular, the conclusion must be particular. Eighth Rule: If both premises are particular no conclusion can be drawn. 44. The Figures of the Syllogism and their Special Rules: The Figures of the Syllogism are arbitrarily named from the four different ways the Middle Term can be positioned in the premises. The following scheme gives the conventional numbering of the Four Figures:
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(Note for below: M indicates middle term, S indicates subject, and P indicates predicate.)
Major Premise Minor Premise Conclusion
Fig. I
Fig. II
Fig. III
Fig. IV
M-P S-M S-P
P-M S-M S-P
M-P M-S S-P
P-M M-S S-P
The Special Rule of Figure I M-P S-M S-P The Major Premise must be universal, and the Minor must be affirmative. (The proofs given are brief in order to give the student an exercise in supplying the complete reasons. Please review the laws of distribution given in #30 e.) Proof: If the Major Premise is particular, the Middle Term will then have to be distributed in the Minor, and therefore the Minor must become negative. But if the Minor Premise is negative, the conclusion must be negative, and the Major Term P must then be distributed in the conclusion. But if P is distributed in the conclusion, it must also be distributed in the Minor Premise. But from two negative premises no conclusion can be drawn. Therefore, the Major Premise cannot be particular. And if the Minor Premise is negative, the Major then cannot also be negative, but the conclusion must become negative, thus distributing the major term P in the conclusion without being distributed in the premise; which cannot be. Thus the Minor Premise in the first figure must be affirmative. The Special Rule of Figure II
P-M S-M S-P
One premise must be negative; and the major universal. Proof: If neither premise is negative, the Middle Term would remain undistributed in both premises; which cannot be. Therefore, one premise must be negative. But if one premise is negative, the conclusion must be negative, and the Major Term must be distributed in the conclusion, which cannot be allowed unless it is also distributed in the Major Premise where it is the subject. The only way to distribute the subject of a proposition is to make that proposition universal. Thus in the second figure, as in the first, the Major Premise must be universal. The Special Rule of Figure III M-P M-S S-P
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Proof: If the Minor Premise is negative, the conclusion must be negative which distributes the Major Term P in the conclusion and, therefore, it must then be distributed in the Major Premise, thus making the Major Premise also negative. But this makes both premises to be negative, which cannot be. Therefore, the Minor Premise must be affirmative. Now since the Minor Premise is affirmative, S is undistributed in the premise. Hence the conclusion must be particular. 45. The Fourth Figure: Another point of contrast between traditional Logic and modern Logic is to be found in the different ways they deal with the fourth figure: in traditional Logic it is disregarded, but the modern trend is to give it place beside the other three. Now as far as another possible way of arranging the three terms is concerned, there is no question but that the fourth figure produces just as good a pattern as the other figures; but if taken as representing the structure of another process of reasoning, then Figure IV does nothing more than give us Figure I in an inverse and unnatural order. It will be left to the student to discover why that is so as an exercise. Hence, while we did give the figure along with the others m #44, and we shall soon enumerate the moods belonging to it, still we shall refrain from giving its special rules. 46. The Moods of the Syllogism: The Moods of the syllogism arise from the different ways in which the four types of proposition, namely, A, E, I, and 0 can be combined within the different figures. And since four different things can be taken three at a time in 64 different ways, it would seem that there must be sixty-four moods in each figure. But some combinations are ruled out by the general rules of syllogistic inference (as EEE is ruled out in all figures for having two negative premises), and others are ruled out in the different figures because of the special rules (as lAl is ruled out of the first figure for having a particular major premise). After all these eliminations, only fourteen significant moods survive in the first three figures, and five negligible ones in the fifth. Now these fourteen significant moods, and even the five negligible ones, have been given names concocted in such a way as to convey valuable information about the corresponding mood. Here are the names: First Figure: Barbara, Celarent, Darii, Ferio Second Figure: Cesare, Camestres, Festino, Baroco Third Figure: Darapti, Felapton, Disamis, Datisi, Bocardo, Ferison Fourth Figure: Bamalip, Calemes, Dimatis, Fesapo, Fresison. We shall learn to decipher all the information packed into these deviceful names; but for the present it is sufficient to note that the three vowels represent in the proper order the quality and quantity of Major, Minor, and conclusion. Provocative Assignment: Try to formulate meaningful syllogisms in each of the nineteen moods. 33
Chapter X - Fruitful Arguments 47. Arguments are fruitful if they lead to certitude or prudent opinion concerning important matters not otherwise known. They are fruitless if they lead to mere doubt or ignorance, or to truths either trite or well known apart from the argument. Fmally, arguments are fallacious if they lead to error. This chapter is dedicated to fruitful arguments, the following chapter to the other two varieties. 48. Concealed Syllogism: By far the most important and most prevalent type of argument is the syllogistic form and, when correctly used, it is a fruitful kind of argument, as witness all the sciences, whether demonstrative or dialectical, deductive or inductive. However, the form of the syllogism is not always evident; as a matter of fact it is rarely so. Having studied, therefore in the previous chapter the fourteen significant types of the syllogism, let us proceed now to observe some of the common ways in which the syllogistic form can be concealed. 49. The Enthymeme: An enthymeme is an abbreviated syllogism, namely one, a part of which (usually the Major Premise) is not expressed, but, as the Greek name indicates, is kept in the mind. Here are some examples of the enthymeme: The electron is a physical body, therefore it must have weight. The suppressed major premise: All physical bodies must have weight. First degree murder is punishable by death, therefore this man must die. The suppressed Minor Premise: This man committed first degree murder.
The enthymeme is sometimes called "the rhetorical syllogism"; this is due to the fact that the rhetorician rarely expresses all his premises, either to avoid tediousness, or to conceal weakness in a premise that would become evident once it is made explicit. But it is not true to say that enthymemes are restricted to rhetoric. They are much more common in every kind of literature than the perfect syllogism. Scientists, for example, rarely if ever, give all the grounds of their scientific arguments. A physicist may never once express the principle of causality, and may even deny that he believes in it if confronted with it fully formulated; but he takes if for granted throughout all his arguments. Were an experimental scientist to become interested in the suppressed premises that guide all his reasoning and make his arguments to be syllogistically valid, that scientist would by that very act move from science to philosophy. Now due to an understandable human tendency to reason by means of enthymemes instead of the fully developed syllogism, many of the most important truths by which men live and think remain in the shade and thus never receive the attention due to their importance. It could be truly said that 34
Aristotle's discovery of the complete syllogistic form, led not merely to the discovery of new conclusions, but pointed in the other direction, leading to the discovery and explicit formulation of the great Major Premises of thought, hence, it led also to the discovery of metaphysics. The enthymeme is like a telescope that works in two directions. 50. The Epichirema: The Greek meaning of the word epichirema, which names the peculiar form of argument we are about to study, is an undertaking or an attempt, to be understood m this case as an attempt m the direction of a proof. So the epichirema is an argument in which, instead of giving several syllogisms to prove every pomt that could be at issue, only the main argument is given m perfect syllogistic form, but with words added to one or both of the premises suggestmg how they could be defended or proved. The following is an example of an epichirema: The human soul is spiritual, because it can entertain abstract and universal ideas, But what is spiritual is immortal, being simple m substance; Therefore, the human soul is immortal. It is good exercise for the student to try to put this argument in a fully drawn syllogistic form, using as many syllogisms as are called for. It is obvious that the epichirema is also a way of abbreviating what would be a more tedious argument. 51. The Polysyllogism and the Sorites: The polysyllogism is simply a number of syllogisms arranged in such a way that the conclusion of one becomes a premise of the next one, until the desired conclusion is reached. As such, the polysyllogism is not a new type of argument; but when the intermediary conclusions are not drawn, and only the ultimate conclusion is expressed, then we do get a truly new variety of abbreviated syllogistic form. It is called the Sorites, and the following is an example of it: Happiness consists in the contemplative experience; but contemplation requires peace, and true peace cannot be without justice, and justice is built on truth; therefore, whatever is inimical to truth undermines the happiness of man. 52. The Demonstrative vs. the Dialectical Syllogism: Now that we have seen some of the different ways in which the syllogistic form can be adapted to the exigencies of ordinary discourse, let us proceed to examine the different ways of usimg the syllogism. From the point of view of Logic, the two most important such ways are the demonstrative and the dialectical. In the demonstrative syllogism the premises are known with certitude, and the syllogism is used 35
to reach other truths as conclusions sharing the same certitude, thus extending our knowledge. It is therefore justly defined as: Demonstrado est syllogismus efficiens scire namely, a demonstration is a syllogism producing scientific knowledge in the highest and strictes sense of the term. An example of a demonstrative science is Euclidean Geometry. On the other hand, in the dialectical syllogism, the premises, or at least one of them, are asserted merely tentatively and conditionally, and it is the conclusion which may prove to be false, contrary to the facts, and perhaps even absurd. The dialectical syllogism is encountered everywhere in the Dialogues of Plato, but is not by any means restricted to them. The dialectical syllogism can be conceived in the manner of a conditional proposition, in which the premises taken together are the Antecedent and the conclusion is the Consequent. Remembering the rules of inference governing a syllogism with a conditional Major Premise, we can see why if the conclusion is evidently false or absurd, at least one of the premises must be false; but if the conclusion is true, no inference can be drawn as to the truth or falsity of the premises. 53. Induction vs. Deduction: Deduction is that movement of the mind proceeding from what is more universal to what is less universal, or even to what is perhaps singular; while induction is simply the reverse process. It is obvious that the movement in the syllogism from premises to conclusion is deductive; but before we can start a syllogistic argument we must have universal propositions, which in turn, if we remember that all human knowledge must arise from sense experience of singulars, presupposes that the universal premises necessary for every syllogism must be arrived at inductively. Now there is one kind of induction where the mind from one singular experience perceives a necessary and, therefore, universal truth; and another kind where all the singular cases of a finite class can be examined before generalizing; but the most significant kind is when what is observed is judged to be a property and not a mere logical accident, even if only hypothetically so.
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Chapter XI - Fruitless and Fallacious Arguments 54. Truth and its enemies: Truth is one of the highest values of humanity; and on it many other values depend, including our happiness in time and in eternity. Our Lord and Saviour teaches us the value of truth in word and deed. Of Himself He says: "I am the way, the truth and the life" (John 14:6). He also says: "You shall know the truth, and the truth shall make you free" (John 8:32). And This is eternal life that they may know thee, the only true God, and Jesus Christ whom thou hast sent" (John 17:3). It is true that these and many other similar utterances of Holy Scripture refer primarily to the supernatural truth of revelation, still there is a harmony of all truth such that the truth of the natural order, serves that of the supernatural order and prepares the way for it, while error of any order is opposed to it. We may safely conclude that all the forces in the world which militate against truth, against the attainment, the expression, and the propagation of it, are forces inimical to man and obstructive of his highest purpose. These forces constitute a major part of that evil from which we constantly pray to God the Father to deliver us, when we say in the Our Father: "And deliver us from evil". But what are the forces inimical to truth? We cannot answer this question until we find out all the different planes of truth by which man lives, and in which he seeks to attain his end. Having discovered the tremendous importance of the syllogism as an epitome of the entire thought process, we may rightly expect to find these planes of truth, or type or orders of truths, reflected in the very structure of the syllogism. Thus to the Major Premise correspond all these general and ultimate judgments which over-arch all our thought activities: The universal and self-evident truths of the speculative, as well as of the moral order; the great conclusions as to the reality, existence, and attributes of God; the spirituality and immortality of the human soul; the unity and purposiveness and order of the universe; etc. To the Minor Premise correspond the correct knowledge of the facts of reality: the major facts of history; the true character of persons, things, institutions, and movements, and their relative merits and demerits; etc. And finally to the Conclusion correspond the contemplative appreciation of things and persons, as well as the rules and guides of action. The student is invited to consider if every truth he can think of as a value cannot be reduced to this threefold division as mirrored in the syllogistic form. As examples of the first type, corresponding to the Major Premise, we propose, in the supernatural order, the truths contained in the Credo; and in the natural order, such truths as the principle of causality, and the obligation to serve God and to refrain from acts of injustice. Opposed to the truths of this plane are false religions and false systems of thought. As for the second plane of truth, corresponding to the Minor Premises of the thought process, we propose as examples the true facts about the Church, Freemasonry, the Jews in history, the conspiracy against Our Lord and Our Lady and the Saints, the secret government, etc. Opposed 37
to the truths of this plane is a whole kingdom of darkness, fraud, hypocrisy, misrepresentation, false publicity (including even the universities), lies, calumnies, deception, secrecy where secrecy is not due, etc., etc. As for the third and most important plane of true judgments corresponding to the third and most important part of the syllogism, i.e., the Conclusion, we propose as examples the contemplative and appreciative response of the saints to all that comes within their experience, seeing, as did St. Francis in all things, reflections of the beauty, goodness, love, and sanctity of God the Creator, also those judgments by which men and women dedicate themselves entirely to the service of God and become saints, apostles, virgins, and even martyrs. On a lower level we give as examples those practical and proximate principles of good well-directed actions which conclude the thought process regarding the practical order, and become constructive of the moral order and of all that is good in civilization. The strict logician cannot cope with the entire problem of error and falsehood: it has behind it the world, the flesh, and above all, the devil (that angel of darkness who can turn himself into an angel of light). There is a mystical alliance between wickedness and error, as between holiness and truth. This is why the royal psalmist cries out from the depth of a distressed soul: "0 ye sons of men, how long will you be dull of heart? Why do you love vanity and seek after lying?" (Ps. 4:3). However, if the logician as such is unable to account for our proclivity to error in this our fallen state, he must deal with it when it expresses itself by any kind of abuse of the processes of thought. Such abuse can be of three sorts: 1) By overt violation of the rules for valid inference; 2) By using the rules of inference correctly, but not to the purpose for which thought was intended, namely, to lead man to his proper end and purpose of existence; and, 3) By arguments which have a deceptive appearance of validity without being so in fact. The arguments of this third group are technically referred to as sophisms or fallacies. The first of the three groups mentioned above, namely, the arguments involving an overt violation of the rules of inference, do not need to be separately discussed here. Any one who understood the rules where they were positively expounded, will detect any departure from them in an argument. That leaves the second and third groups to be discussed here, which, by the way, explains the title of this chapter: Fruitless and Fallacious Arguments. 55. Fruitless Arguments: The nominalists, as well as some other philosophers, accuse the syllogism itself of being a fruitless form of argument. They claim that unless you knew the conclusion to be true you could not have affirmed the premises in the first place; and so all that the syllogism can achieve is to give you in the conclusion a part of a larger truth you already possessed. They take advantage of the innocent syllogism: All men are mortal, but Socrates is a man; therefore, Socrates is mortal; by which so many textbooks of logic present the syllogism for the first time in order to illustrate its parts and give the technical terminology. They say that unless you know that Socrates (who is one of the men) is mortal, you could not affirm the major premise: All men are mortal. This argument flies in the face of the evidence. It attributes to human intelligence and its processes an angelic property, contrary to the obvious facts of the matter. Finally, it could be construed to involve several of the fallacies that will be studied in the following section. A child who assents to the axioms and postulates of Euclidean geometry, certainly does not know all the theorems implicitly contained in them, until he had gone patiently through the different syllogistic processes which show him the connection. What is known only 38
implicitly, exists only potentially, and to equate potency with act, is like equating the egg and the chicken, or the acorn and the oak tree. But if the charge of fruitlessness or sterility cannot be levelled against the syllogistic argument, when properly directed, it can with far greater justice be directed at the antagonists of the syllogism. Most of the arguments of such thinkers are frustrated of the fruit proper to constructive and genuine thought, namely, the attainment of ordered truth: the deep, important, destiny-making truth: the perfective truth that makes for contemplation and happiness: the creative truth that builds civilizations. This is supremely true of the travesties on logic in common usage at the universities of our day. 56. Fallacious Arguments: A fallacy (sometimes called a sophism) is a deceptive argument having the mere appearance of validity without being so in deed. A mere violation of a rule of inference is not as such a fallacy, but if the violation is subtle and not easily detectable, then it might deserve the name under a new title. That is why we sometimes hear of the Fallacy of the Four Terms, or of the Fallacy of the Undistributed Middle. Much more often, do we hear of the Fallacy of the Consequent, which involves a violation of the rules of the conditional syllogism, namely, by affirming the Consequent in the Minor, or denying the Antecedent, instead of the contrary procedure which would be valid. In the chapter by Father Bittle given as a sequel to these notes, there is an excellent example of this kind of fallacy. But the fallacies properly so-called, are divided into two classes: Fallacies of Diction and Fallacies of Thought. 57. Fallacies of Diction: Verbal fallacies or fallacies of diction arise out of the limitations of language as a medium of thought expression. Here are the leading ones: 1. The Fallacy of Equivocation involves the use of the same word in two different meanings. When it occurs in a syllogism it is identical with the fallacy of four terms. In the article from Father Bittle which appears as a sequel to these notes, there is an excellent example of this fallacy, where a deceptive argument for idealism or subjectivism revolves around the use of the word "sensible" in two different senses. 2. The Fallacy of Ambiguity. In this fallacy, while the meaning of individual words remains unchanged, the sentence as a whole can be taken in more than one sense. The oracles of Delphi offer many classical examples, but Shakespeare imitates them where he says: "The Duke yet lives that Henry shall depose" (Henry VI). 3. The Fallacy of Illicit Transition involves the more subtle cases of a change of supposition. Thus the argument "Man is a monosyllable, but Andrew is man; etc." is not a fallacy but a joke; but the following argument for the existence of God incurs the censure of illicit transition from the logical to the real order: "I have an idea in my mind of God as the greatest and most perfect being, but a being who exists in thought and reality is greater than one who lacks real existence; therefore, by necessity God must exist in reality."
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58. Fallacies of Thought: 1. The Fallacy of the Accident. This consists in considering as a property of some universal nature what is merely a logical accident of some of its inferiors. It is an abuse of the genuine process of induction, and leads to hasty universal statements which are not true in their sweeping universality. This fallacy is sometimes called "ab uno disce omnes." 2. The Fallacy of the Mere Antecedent. This is sometimes called the Fallacy of the False Cause, or Post hoc, ergo propter hoc." (After this, ergo because of this) It consists in taking for a cause what is merely an antecedent to a thing or event, having no causal connection with it. 3. Ignoratio Elenchi. The Fallacy of Missing the Point in question, and proving what is not at issue. In the chapter from Father Bittle which is immediately to follow, he shows how the idealists, pretending to prove that sensible objects have no real existence, do it by merely pointing to the indisputable fact that they do not have an intentional or mental existence. This is a perfect example of this kind of fallacy. Closely related to this is the fallacy of proving too much, "Qui nimium probat, nihil probat." (He who proves too much, proves nothing) Such would be an argument trying to prove the immortality of the rational soul by an argument which would seem to prove the immortality of plant and animal souls. 4. The Fallacy of the Vicious Circle also known as the Petitio Principii. This consists in surreptitiously including in your premises the very point at issue, or taking for granted what is yet to be proved. Again we go to Father Bittle for an excellent example of this kind of fallacy. Father shows how one way of formulating the fallacy of idealism begins with the premise, "If something has mental existence, it has a purely subjective existence." This premise begs the whole question that is at issue. Another example would be for a materialist to try to prove the non-reality of the soul, because the body suffers no loss of weight when the soul has departed. The argument takes for granted the materialist contention that what has no weight cannot be real. Closely connected with this fallacy is the fallacy of coloring the facts. It is like talking about a man as a criminal before the guilt is proved. Many false theories of science depend on the evidence of statistics, or observations or findings already arranged or disposed in accordance with the hypothesis that is supposed to be on trial. Father Cotter gives a good example from Allers on Psychoanalysis: "Thus psychoanalytical expositions are so formulated that the theories completely color what should be the plain description of a situation, so that what is offered us as a fact and proof of a theory actually already assumes and contains the whole theory." (Allers p.340) By this we conclude our study of arguments and of the valid rules of inference. Like a book on medicine which studies not only normal health, but also those deviations from it called sicknesses, or diseases, so we in this little book on Minor Logic considered the matter of inference from its positive and normal aspect, and also the deviations from what is right, as we did in this last chapter. But let me repeat: the enormous problem of error and its baneful effect on men, can by no means be exhausted by the analysis of its logical aspect. It is deeply tied up with the deeper mystery of iniquity. St. Paul almost gave a definition of sanctity when he said that, "charity rejoiceth with the truth" (I Cor. 13:6). 40
Index Analogy p. 11 #13 Antecedent p. 30 #42 Argument p. 5 #4 Art p. 2 #1 Book of Sentences p. 9 #10 Categorical Propositions p. 14 #15 Categorical Syllogism p. 29 #40 Charts and Schemes Analogy p.12 #14 Definition p.16 #19 Division p. 17 #20 Modality pp. 26, 27 #34 Predicables p. 27 #36 Oratio p. 9 #9 Propositions p. 23 #28 Scientia p. 2 #2 Signs p. 11 #12 Supposition p. 25 #32 Ten Categories p. 21 #26 Comprehension p. 15 #17 Conditional Syllogism p. 30 #41 Connotation p. 15 #17 Consequent p. 30 #42 Contradictories p. 24 #30 Contraries p. 24 #30 Correctness p. 2 #1 Deduction p. 37 #53 Definition p. 16 #19 Demonstrative Syllogism pp. 36, 37 #52 Denotation p. 15 #17 Dialectical Syllogism pp. 36, 37 #52 Discipline p. 2 #2 Distribution p. 24 #30 Division p. 17 #20 Enthymeme p. 37 #53 Epichirema p. 36 #50 41
Equivocity p.11 #13 Essence p. 14 #15 Extension p. 15 #17 Fallacy of the Consequent p. 40 #56 Fallacies of Diction Ambiguity Equivocation Illicit Transition p. 34 #57 Fallacies of Thought p. 41 of the Accident p. 41 the Mere Antecedent p. 41 Ignoratio elenchi p. 41 Vicious Circle p. 41 #58 Figures of the Syllogism p.p. 31, 32 #44 Fruitful Arguments p. 35 #47 Fruitless Arguments p. 39 #55 General Rules of Syllogism pp. 31 #43 Genus p.19 #23 Grammar p. 5 #6 Induction p. 37 #53 Immediate Inference p. 27 #35 Inferences p. 28 #37 Judgment p. 22 #27 Liberal Art p. 2 #2 Logic attributes of p. 2 #2 definition of p. 2 #1 description of p. 5 #6 division of p. 3 #3 Logical Whole p. 18 #21 Major Logic p. 3 #3 Mediumexquo p. 9, 10 #11 Mediuminquo p. 9, 10 #11 Minor Logic p. 3 #3 & p. 26 #34 Modality p. 25 #31 Moods of the Syllogism p. 31 #46 Normative Science p. 2 #2 42
Notes p. 15 #17 Null Class p. 26 #33 Object (Material and Formal) p. 5 #6 Polysyllogism p. 36 #51 Porphyry p. 18 #21 Predicables p. 27 #36 Quadrivium p. 2 #2 Reality p. 9 #10 Reflection p. 2 #2 Rhetoric p. 5 #6 Rules of good definition p. 20 #25 Schemes (See charts.) Science p. 2 #1 Sequence p. 30 #42 Sign, def. of p. 9 #10; div. of p. 9, 10 #11 Simple Apprehension p. 14 #15 Sorites p. 36 #51 Special Rules of Syllogism pp. 31, 32, 33 #44 Species p. 19, 20 #23 Square of Opposition pp. 23, 24 #29 Subalternants p. 19 #30 Subcontraries p. 19 #30 Subjective Parts p. 18 #21 Supposition p. 25 #32, p. 14 #16, p. 25 #31 Syllogism p. 29 #39, 40 Symbolic Logic p. 26 #33, p. 33 #45 Ten Categories p. 20 #24 Term p. 14 #15 Tree of Porphyry p. 18 #21 Trivium p. 2 #2 Univocity p. 11 #13 Word p. 14 #15
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THE DANGERS OF SCIENTISM Dr. Fahkri Maluf If a man were to say to me, “I refuse to use my eyesight except through a microscope,” I might think that the man is queer or crazy, and I would certainly try to avoid his company. Imagine taking a walk with a man who keeps one eye closed, and the other permanently fixed to a microscope! Such a man is worse than blind, for a blind man, who cannot see the stars, talks about them, and eagerly seeks to learn; but the man tied to the microscope neither sees nor seeks. The blind man knows that he is blind and acts accordingly, but the man with the microscope thinks that he is the only one who sees, and if you dare to mention the sky before him, he says, “But where is the sky!”, meaning, of course, that the sky could not exist unless it could be placed in his range of vision. Now if you take this clumsy and most unlikely illustration and translate it from the order of sense to the order of intelligence, you get one of the most common intellectual types today, the type of a mind that will not apply its intelligence except through the scientific method. This type of mind is apt to undermine common sense, on the ground that future scientific discovery might disprove any certainty. It discredits philosophy, because the objects of philosophy (God, the spiritual soul, cause, substance, etc.) cannot be weighed or measured, can neither be reduced to a mathematical formula, nor observed in a test tube. And finally, this type of mind discards all revelation, on the ground that religion is not a channel of knowledge and that its value is purely emotional and unintellectual. This is the attitude of mind that is gradually being recognized as a cultural danger by educators and social thinkers, and is coming to be called “scientism”. Scientism is not the same as science, but is rather an abuse of the scientific method and of scientific authority. Here are some instances to illustrate what I mean by the term “scientism”: Physicists are now being consulted, not only on the development of atomic energy, but also on the morality of dropping atomic bombs. Professional experts must now tell us, not only whether children may be exposed safely to gamma rays, but even, whether children may be exposed to sun light. Experts must decide whether mothers should be allowed to hug their babies. Einstein is teaching, on the grounds of mathematical physics, that God is not personal. Whitehead describes the attributes of God in terms of quantum physics. Bergson builds biology into a false metaphysical religion. Bridgman moves over from the specialized field of high-pressure physics, to define democracy, investigate the foundations of morality, and pronounce on the freedom of the will! I propose to study in this article some aspects of scientism, this cultural disease, which I hold responsible to a large extent for the alarming number of infidels and atheists in modern universities, and for the rise of dangerous beliefs and practices, the absurdities of which could be detected by a child, but not by the involved mind of the “scientific expert” and of those who worship authority. I hope to suggest that the remedy lies in restoring philosophy to its rightful place in education. Philosophy has been called “the Queen of 44
the Sciences,” and indeed, the realm of the sciences left without philosophy is like the kingdom in a state of anarchy. Philosophy defends the fundamental certitudes of common sense, establishes the grounds of morality, prepares the mind for revelation, and restores order in the house of science. Let the reader then be prepared to become more philosophically minded, if this article is to make its point. To begin with, let us observe the place of knowledge in the life of man. Knowledge is the most characteristic activity of man. A man could, without knowledge, fall down from a balcony like a fainting acrobat; but no man could, without knowledge, climb up a balcony like Romeo. When the fainting acrobat falls down, we call that an act of man, because it is a man and not a stone or a log that is falling under the pull of gravity; but when Romeo climbs up, we call that, not only an act of man, but also a human act. Knowledge must be present in every human act: in every art or profession, in humor and in prayer, in virtue and in vice. Man cannot even commit a sin without knowledge. Even man’s beatitude is defined in terms of knowledge, for “this is eternal life: that they may know thee, the only true God, and Jesus Christ, whom thou hast sent” (John 17:3). If, therefore, knowledge plays such a tremendous role in the life of man, and if the consummation of this life in the Beatific Vision consists in the knowledge of all truth, would it not be extremely strange if God had restricted the privilege of knowing to that very small fraction of mankind that constitutes the class of scholars and scientists? As a matter of fact, by far the greater part of our knowledge belongs to the order of common sense. Even the expert scientist could not live one single day in this world, were he to depend exclusively on his expert knowledge in his special field. And besides, both science and philosophy presuppose the great mass of common sense knowledge, and could not proceed without it. If a student comes to a biology laboratory not knowing how to distinguish between a living and a non-living thing, what would stop him from observing the properties of life in a piece of chalk? Also, both science and philosophy use the same knowledge-seeking faculties as we use in acquiring our common-sense knowledge; and therefore, if these faculties were discredited as they function normally in common sense, it is difficult to see how they could be trusted as they function artificially in other fields. A philosopher who cannot distinguish by common sense between his head and his headache, would never acquire that distinction by studying the abstract attributes of substance and accident. Common sense knowledge has some remarkable qualities which are easily lost when knowledge gets to be artificially methodical. To mention just one quality, common-sense knowledge is somehow complete and integral; that is to say, that in common sense, the complete man knows in a certain manner the whole of reality. Common sense knowledge is undivided and unclassified, it is knowledge about God and about the world, about men, animals, plants, seas, lands, time, space, institutions and objects of all kinds. Certain knowledge is mixed with knowledge that is only probable, and knowledge which comes through the senses is not distinguished from knowledge which comes through the intellect. A soldier on the front line, does not say, “Let me abstract from the noises I hear and 45
the sights I see, and reflect on the principle of causality” nor, on the other hand, does he say, “Indeed, I hear all kinds of sounds, and see all kinds of shapes and colors, but I must not make any further inferences.” Common sense is also knowledge within a perspective. Only God, eternal, omnipresent, omniscient, can afford to know too much about too many things, without much reference to a purpose. The man on the front line knows all reality, but only as relating to the thing at stake, his very life. And the man of common sense is constantly on the front line, the line that divides time from eternity; consequently, he must know all things as they relate to the maintenance of his life in this world, and the salvation of his soul in the next. You cannot teach the man of common sense until you get him interested, and you can get him interested only by relating all things to the ultimate purpose of his existence. But common sense knowledge has its limitations, as the man of common sense very well knows. By mere common sense, no airplane can be constructed, and no medical operation can be performed. When the man of common sense needs to build a bridge, he does not go to another man of common sense; instead, he uses his common sense and goes to an engineer. It must be evident, therefore, that if we would have many of the things we consider desirable, common sense knowledge would no longer be sufficient, and scientific knowledge becomes necessary. But the discipline that is required for the acquisition of scientific knowledge makes that wholeness, that completeness of common sense knowledge, impossible on the scientific plane. No man can possess technical scientific knowledge about everything; and therefore, every one must specialize in that part of knowledge needed for his profession, or for his function in society. Further, in contrast with the spontaneity of common sense and the directness with which it envisages its objectives, we find that science requires intricate and roundabout processes for its attainment. This makes it quite possible for man to lose every perspective of relevance, and to proceed along blind alleys of knowledge and research that lead nowhere. And yet all this is unavoidable and follows from the very nature of science. It would be absurd to ask a medical student to justify in terms of ultimate human purposes every single action or assignment required in his general training for his profession. Hence we have another danger of specialized training; namely, when man is trained to know a part of reality, and to deal even with this part in a manner that is systematically artificial, this man develops more as a function than as a person. Hence, it is that science and technology carry the danger of depersonalizing social relations. But man insists on being a person and on being treated as such; and as a person, he insists on his right of somehow knowing all reality and being concerned about his destiny as a complete man. Therefore, once his common-sense perspective gets to be distorted by the artificial mold which frames his mind in a special field, he tends to raise his special and partial science up to the dignity of a universal science. “All reality is made up of material atoms or quantums of energy,” says the physicist. “Reality is a mysterious life force, elan vital,” retorts the biologist, who would see all things from the window of biology. All history is made by economic forces (Marx), or by 46
sexual energy (Freud). These and similar monisms, represent some of the grave dangers of scientism. Then we have what is perhaps the greatest danger of scientism, namely, the philosophy of positivism. The primary interest of the special sciences is not the contemplative understanding and appreciation of reality, but the control of the visible world for practical purposes. In order to harness the powers of nature, all the knowledge needed is knowledge of certain accidental aspects of material things. Such an accident as the quantity of the thing, is all that remains of reality when the real thing is replaced by a measure and is introduced into a mathematical formula. Of course any child could tell you that the quantity of a thing is not its complete reality, but the scientific expert tends to identify the quantity with the whole thing. Hence we get those quantitative ghosts called by such names as, energy, mass, atomic number, wave length, intelligence quotient, etc., floating around the scientific graveyards where the objects of common sense are deeply buried, and parading in the garbs of the real and substantial entities. When this tendency of the sciences is built up into a complete philosophy, a world view, which denies the substance of things, denies the reality of causes, and admits only those surface accidents or appearances of material things which can be measured and made subject to the scientific method, when this thing happens, we get that most negative of all philosophies, namely, ironically enough, the philosophy of “positivism.” Now neither God nor the spiritual soul of man can be made subject to measurement or to test-tube analysis. Therefore, the positivist rejects on principle all metaphysics and all religion. Now, having seen some of the dangers of scientism, let us proceed to study the nature of science. This will lead us to determine whether philosophy is a science. The Greeks and the scholastics considered philosophy the science par excellence, but to the modern mind, this view cannot be taken for granted; it has to be justified. What is a science, and how does scientific knowledge differ from the knowledge of common sense? The most superficial observation reveals to us that what we call sciences possess a certain form and order, i.e., they are organized bodies of knowledge and not random collections of facts. Now this order of the sciences is not imposed on them externally like the alphabetical order of a dictionary. It is an order which mirrors and reveals the order of real things. The sciences have order because they put things together as things flow from common origins, principles, or causes. Science begins as soon as things begin to be systematically and methodically explained, and the more explained things are, the more orderly they appear to be. Man, therefore, can be said to have sciences, because he asks questions and seeks explanations of things that fall within his experience. And man is a great “question-asker.” As a matter of fact, man is the only question-asker in the whole universe. You could almost define man by this property, which flows from his very essence. 47
Now here is the reason why man asks questions. The human mind is made for a reality which is absolute, necessary, and simple, and which contains the sufficient reason for its being. This reality is, of course, God. Once the mind sees God, our intelligence is so thoroughly satisfied that it can raise no further questions, because no problem or mystery remain, either in God Himself, or in anything He caused. But when the human mind is confronted with a contingent reality which does not possess within itself a sufficient reason for its existence, the mind immediately tries to explain this reality, and explaining a thing means reducing it ultimately to a cause or principle which does not need to be explained. To put what we have just said in more philosophic terms, we could say that the mind knows with absolute certainty that there must be a sufficient reason for everything that is. If we didn’t know that, we would never seek the “why” of a growing tree or of a falling apple. Every single science in the world owes its existence to this thirst for explanation, which all men share. This thirst for explanation is in our intellects and not in our senses. Animals never ask questions and never attain science. The stream of sense experience received in my skin from a flowing river does not raise any questions, but the notion of movement abstracted by my mind raises the problem of change, and starts the mind along the track of science. The number of the sciences could be very large, because in addition to the great variety of objects that could be studied scientifically, there is a great variety of aspects from which to study things. A chair, for example, could be studied in physics, in chemistry, and in economics; and man may be studied in anatomy and in politics. In each case, the material object is one, but the formal object different. But this variety of the sciences forms a natural hierarchy. For example, biology is superior to bacteriology, physics to metallurgy, astronomy to navigation, and economics to banking. What determines this hierarchy? The principle of explanation, in which the very essence of science consists. The superior sciences come closer to giving an ultimate explanation. In every case mentioned so far, the superior science explains the principle of the inferior science, and defines its basic concepts. Hence, the inferior science of each pair presupposes the superior science, and depends upon it for being a science at all. Metallurgy presupposes the ordinary laws of general physics (such as the laws of heat and light, the principle of specific gravity, the laws of magnetism, etc.). If one were to stop and give a sufficient explanation of every term occuring in the science of metallurgy, one would have to include the greater part of general physics in every chapter on metallurgy; but, of course, physics is ordinarily taken for granted.
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The hierarchy of the sciences is, therefore, a hierarchy of explanation. But along with this mark, others follow, stemming from it and depending upon it. The superior science is in every case a greater general interest and is valuable as knowledge in itself and for itself, while the inferior science is primarily of practical interest, and is valued on that account. No one studies metallurgy in order to become better educated. Close to the top of this hierarchy, we find such sciences as physics, biology, and mathematics. Yet none of these sciences is ultimate, not even in their respective orders of knowledge. No book on geometry, for example, discusses the nature of quantity, continuity, shape, dimension, point, number, measure, space, etc. Geometry takes all these concepts for granted, just as it also presupposes its axioms and the general method of demonstration. The same could be said about physics and biology with regard to their basic notions and principles, such as the notion of matter, change, mass, energy, entropy, atom, field of force, life, generation, etc. All these sciences, in so far as they are sciences, that is, in so far as they possess any explanatory value, presuppose the superior philosophic sciences of Logic, Cosmology, rational Psychology and Ethics. And these philosophic sciences, in turn, presuppose Ontology or general metaphysics. Ontology is the absolute summit of natural knowledge; it is the one science which does not presuppose any other. Ontology studies all things under the most important aspects of all things. What Ontology studies about being is more important than anything said about that being in any other science. Is there any approach to reality more important than to study a thing in so far as it is one, true, good, and beautiful? Supposing you take a society and remove from it all institutions and persons concerned with the attainment and expression of truth, goodness, and beauty, how much of that society is worth having? Or, let us take the history of man and remove from it the stories of its philosophers, scientists, poets, artists, saints and mystics; how much of what is left of that history is worth studying? As Ontology studies all these attributes of being, it studies things in so far as they reflect the perfections of God; for God alone is supremely one, true, good, and beautiful. Ontology thus establishes the highways on which the mind constantly travels from the world to God, and from God to the world. Moreover, Ontology raises, formulates, and answers, all the most basic problems which torment the minds of men in all ages, and which underlie all great literature. Such problems as the problem of being and of change, the problem of evil, and the problem of knowledge, are solved in ontology as well as is possible for the human mind. But then, have we any right to call Ontology a science? According to modern usage, when we say science, we understand primarily something like physics, bacteriology, or perhaps even sociology. It should be clear however, from our discussion, that the notion of science applies primarily to ontology, secondarily, to the other philosophic sciences, and 49
only in a very weak sense, to the special sciences. But since the discussion has been a little general so far, I would like to illustrate by a concrete example, the contrast between the philosophic and scientific outlooks (using the word “scientific” in accordance with modern usage). Let us suppose that a philosopher and a scientist were to witness together the death of a man; the scientist would ask, “Why did this man die?”, and he would seek an explanation in such things as poison or heart failure. On the other hand, the philosopher perceives immediately a more fundamental problem: he would like to know, not the accidental reason why this man died, but rather why anybody should die at all. The investigations of the scientist might contribute to the sciences and arts of medicine, pharmacy, and perhaps even chemistry; the reasonings of the philosopher, on the other hand, lead to a better understanding of a composite, material being, in contrast with a simple being, and therefore, to a deeper understanding of God and of man. Science goes hand in hand with the practical arts and artcrafts, with medicine, farming, engineering, industry, etc.; while philosophy associates with religion, poetry, and the contemplative arts. Put in the language of philosophy, this difference between philosophy and the sciences can be expressed in the following terms: philosophy seeks the ultimate explanation, while science is satisfied with the proximate causes of things. Now as far as the mind is concerned, proximate explanation is really no explanation at all. It explains only for practical purposes. To know that water can be decomposed into oxygen and hydrogen is useful information in case you are interested in manufacturing either of the two gases, but it certainly fails to explain the mystery of chemical union. Besides, the problems of science presuppose those of metaphysics. Man would not seek the precise cause of malaria unless he knew that things like malaria must have a cause. For, obviously, the scientist does not try to determine whether malaria has a cause, but rather what the cause is. The scientist, obviously, knows that a contingent thing like malaria must have a cause, although he does not develop the notion of a “contingent being” and the notion of a cause, nor does he care, as a scientist, to reason out all the implications of what he implicitly asserts with regard to these notions. Were the scientist to stop and reflect on these matters, he would move out of the field of science and into the field of philosophy. Philosophy, therefore, not only has the title to be called science, but has it to the highest degree: it is, as already intimated, the queen among the sciences. Beginning with Ontology, and running down the hierarchy of sciences, we would get something like the following arrangement: I. Ontology (or general metaphysics) of which the most important part is Theology. II. The Philosophic Sciences (the sciences of special metaphysics): Logic, Cosmology, Rational Psychology, Ethics.
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III. The Mathematical Sciences and the General Sciences of Observation and Experimentation: Arithmetic, Geometry, Physics, Chemistry, Astronomy, Biology, Politics, Economics. IV. All the practical arts and sciences whose primary purpose is not the understanding or the explanation of reality but some practical utility. Their number is very great. They correspond with the variety of crafts and professions, especially those which are intricate enough to require the development of a science or perhaps many sciences. e.g., all the sciences of medicine, engineering, farming, pharmacy, navigation, metallurgy, banking, jurisprudence, electrical engineering, etc. One glance at this table reveals the root reason of scientism. The lowest order in this hierarchy of the sciences is the foundation of our material civilization: it builds our machines, runs our hospitals, and fights our wars. In order to maintain our culture we are bound to devote a great part of our time and attention to the cultivation of these lower sciences. This trend has been crowding out of existence those sciences of the highest two orders, which guarantee cultural unity and a balanced perspective. The general science of the third order, like physics and economics, came to be regarded as the core of liberal education, but these sciences are ordered primarily to the practical interest and not to the speculative. Physics, biology, and economics are not innocent crafts like carpentry and masonry, which require the development of special skills, without distorting the truths of common sense. The latter are sciences of a kind, without being sciences to the limit. And when the mind is made to perform on the plane of science, it must either be led to final and correct answers, or find false substitutes in sophistry and ideological error. We must restore philosophy, religion and common sense as valid means of knowledge, or else we are going to die from the sickness of scientism. It is nice to have a nose on one’s face, but when you see a nose swelling and about to efface the remaining features, you know that there is disease and danger. Culturally speaking, scientism is such a pathological inflation of science, at the expense of all other forms of human knowledge. As for common sense, little can be done for it deliberately. As soon as common sense becomes reflective or methodical, it becomes something else; that is, it becomes either philosophy or science. Common sense cannot formulate or defend its convictions against the attacks of false philosophies and false religions, and therefore, unless the fundamental certitudes of common sense are developed and defended by good philosophy, false doctrines are bound to arise. As for revelation, it is foundationally in God, under His disposition; and, as long as we do not confuse ourselves by perverse use of our natural faculties, God can talk to us and lead us to the saving truth. Our own responsibility consists in using our natural powers 51
according to the purposes intended by God, and God gave us intelligence, primarily, so that we may know Him and love Him, and, secondarily, in order that we may rule the material universe. We are putting a tremendous effort towards the attainment of the second of these objectives, but if we are to be faithful to the first objective, we must restore philosophy to its place in liberal education. Of course, this advice cannot be given except to those who know where to find the one sound tradition of philosophic truth. This tradition is protected, and will always be secure, only in the shadow of the Catholic Church. Here is another confirmation of Christ’s promises, where He says: "Seek ye first the kingdom of God and His justice, and all these things will be added unto you” (Matt. 6:33). Here is another temporal problem, which shall never be solved by those who do not care to discover the kingdom of God, as it exists in this world. If the place of philosophy is usurped by the confusion of all the false doctrines and perverse opinions of all times, then certainly that kind of philosophy will offer no remedy to the confusion of scientism. They say, “You want to bring philosophy back to the modern man; but he already suffers from the complexity and diversity of his interests. Wouldn’t philosophy add just one more item to this complexity?” This is like saying about a man trying to find his way around in a crowded dark room, “Why crowd him further with a lamp”? For that is precisely what philosophy contributes to the complexity of modern civilization: a lighted candle in a crowded dark room.
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Fallacy of Idealism The foregoing review of the trends in modern philosophy was necessarily brief. It will suffice, however, to indicate the maze of contradictory theories which have arisen in this relatively short period of time. Almost every thinker has his own particular brand of theory, more or less at variance with that of his fellow-philosophers. There seems to be hardly a single point on which they all agree, when they begin to expound the details of their system. On the surface, there appears to be nothing but intellectual chaos. Viewed from a broader standpoint, however, by far the majority of these theories and systems will be seen to be more or less alike. They reveal a common parentage and show a common kinship. As such, then, they must possess a uniform trait, a fundamental doctrine identical in them all, which underlies all the variants and forms the root-idea from which they derive their origin and then develop into different philosophies. This uniform trait is idealism, and the root-idea is the idealist postulate. It would be an impossibility to submit every form and variant of idealisim to a critical evaluation. Nor is this necessary. If it can be shown that the fundamental doctrine, the root-idea, of idealism is essentially fallacious, then idealism itself as a system of thought, no matter what its individual shade and shape, will also be shown to be essentially fallacious.
THE COMMON ELEMENT IN IDEALISM Idealism arose out of the difficulty of understanding and explaining how the human mind can transcend itself and know extra-mental reality. The ordinary man sees no difficulty in this; for him there is no problem. He sees houses; he hears sounds; he smells odors; he tastes flavors; he touches objects: these are plain, everyday facts; what more is there to say? The epistemologist acknowledges these facts and he finds his problem precisely in these facts. Certainly we see and hear and smell and taste and touch; but what do we perceive in these psychical acts and how do we perceive these supposedly extra-mental things? The extra-mental objects (if there be such) cannot very well leave their location, travel through the intervening space, pierce the body, and enter the mind in their physical being; the house across the street, for instance, remains across the street, and the red of the rose remains in the rose out there in the garden. And the mind assuredly does not leave the body, flit through space and envelop the star billions of miles away in its physical being; the mind remains here amd the star remains there. How then can the mind perceive things at a distance, or how can things get into the mind? It does not seem to solve the difficulty by referring to the stimuli (light-waves, airwaves, etc.), which are supposed to leave the objects and impinge upon the sense-organs; because then we should perceive these stimuli and not the objects from which they come. That, however, is not the case: we perceive apparently objects and certainly not stimuli. The greatest difficulty lies in the fact of the dissimilarity which exists between mind and matter. The mind is psychical, while the objects are physical, the mind is unextended, while the objects are extended. How can the mind assimilate something so diametrically opposed to its own nature? And how can physical, extended objects impress themselves upon a mind which is altogether devoid of all extension? Can the extended become unextended, or the unextended become extended? Can the 53
physical become psychical, or the psychical become physical? Is this not a contradiction in terms? Since the mind is psychical, it seems perfectly obvious and logical, that nothing but what is psychical can affect the mind and nothing can proceed from the mind . . . but what is psychical. All knowledge, then, since it proceeds from the mind and takes place in the mind, must be purely mental. Physical objects are, therefore, absolutely excluded from knowledge: the objects of knowledge are mental objects, ideas. Consequently, even when we apparently perceive external and extended objects, what we really perceive are ‘mental objects,’ ‘ideas,’ ‘conscious states,’ ‘representations,’ but not physical, extra-mental things themselves. All we can perceive is our ‘ideas’ of things; whether anything corresponds ‘out there,’ extra-mentally, to theses ‘ideas,’ is something we can never actually know. If such extra-mental objects exist, we simply cannot know them because they are physical entities, and the mind is restricted to the mental, the psychical, the ideal, in all its processes. As far as the mind is concerned, its objects have ‘being’ only in so far and so long as they are ‘perceived’: esse est percipi. Such ‘being’ is then not physical, but ideal; and since it proceeds from, and resides in, the mind as its ‘subject,’ it is subjective. All objects of our knowledge are, therefore, ideal and subjective, because they are mental products. This doctrine, that the mind in its knowing can know only its own ‘ideas’ or ‘percepts,’ is idealism; and when this doctrine is accepted as an axiom or postulate, it is the idealist postulate. This line of reasoning, formulated in many different ways, though seldom cast into strict logical form, is basic to idealism. It can be worded thus: Objects, so far as the knowing mind is concerned, exist only when perceived; but perception (‘being perceived’) is a conscious mind-state or ‘idea’; hence, objects are only conscious mind-states or ‘ideas’; consequently their existence or ‘being’ (esse) is nothing but ‘being perceived’ (percipi): esse est percipi. The argument originated with the anithetical dualism existing between the body and mind, as postulated by Descartes.
THE FALLACY OF THE IDEALISTIC POSTULATE Logic is not the strong point of modern philosophers. They disdain the strictly logical formulation of the arguments and prefer the loose language of the essayist. And loose language often hides loose thinking. We can see this clearly in the argument of Berkeley, if we cast his thoughts into strict form. A close analysis will reveal the fallacy underlying his argument. Here are his words: “What are the aforementioned objects [houses, rivers, mountains, and, in a word, all sensible objects] but the things we perceive by sense? and what do we perceive besides our own ideas or sensations? and is it not plainly repugnant that any of these [ideas or sensations], or any combination of them, should exist unperceived?”1 A casual reading of this argument sounds plausible enough; in fact, it almost seems self-evident; and to many this line of reasoning has appeared so transparently and unanswerably obvious, that it has been accepted without question and become the dogma of idealism. It deserves, therefore, to be analyzed more in detail. It will be evident that the conclusions of the idealist argument will have to be that objects cannot exist in reality except when they are perceived, because it is the contention of the idealists that the ‘being’ of objects is their ‘being perceived’. So far as we are concerned, they cease to ‘be’ once they cease to ‘be perceived’. Here is the syllogism: Ideas or sensations cannot exist unperceived; . A Treatise Concerning the Principles of Human Knowledge, p. 259
1
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But sensible objects (house etc.) are ideas or sensations; Ergo, sensible objects (houses etc.) cannot exist unperceived. The fallacy lies in the minor premise: “Sensible objects (houses etc.) are ideas or sentations.” The term ‘sensible objects’ can be taken in two meanings: objects can be called ‘sensible objects’ in the meaning of ‘actually sense-perceived’ and in the meaning of ‘potentially sense perceived’. In the first meaning they are perceived in the act of perception; and in the second meaning they can be perceived. In the first case we have objects which are ‘within’ the act of perception, and in the second case we have objects which are ‘outside’ the act of perception but are capable of being perceived. In either case such objects would be called ‘sensible’. The difference lies in the fact that in the first case these ‘sensible’ objects are considered as ‘perceived’ while in the second case they merely ‘perceivable’. Berkeley confuses the two meanings: he identifies the ‘perception of objects’ with ‘objects of perception’. His argument merely proves that ‘sensible’ objects when perceived, are ‘ideas or sensations’; but it says nothing whatever about such objects when not perceived. All that his argument can prove is that ‘objects are perceived when we perceive them’; and that, though true, is plainly a redundancy and a juggling of words, but no proof that things ‘cannot exist unperceived’. If he contends that the argument also holds in the second meaning, so that there are no sensible objects outside the act of perception which are unperceived, but perceivable, he begs the whole question by presupposing in his premise what is supposed to be the burden of the conclusion. Such a contention is an unwarranted assumption. “Sensible objects are ideas and sensations” when perceived; but that is no proof that they cannot be in and for themselves without being perceived. What idealists prove is merely that ‘sensible objects cannot be perceived as existing without being perceived as ideas or sensations’; but this in no way proves that ‘sensible objects cannot exist without being perceived as existing’. Because objects, when perceived, have now a ‘subjective existence,’ it does not follow that such objects have a ‘subjective existence only’. Things could possibly have an ‘subjective existence’ in the subject when perceived by the subject. In order to establish their case, idealists would have to disprove this possibility; but this their argument fails to do. The fallacy of the idealist argument will, perhaps, be more clear if we cast it into the form of a hypothetical syllogism. It could be made to read in the following manner: If something has a purely subjective existence, it has a mental existence; But perceived objects have a mental existence; Ergo, perceived objects have a purely subjective existence. The major premise contains a true statement: anything that has a purely subjective existence is mind-dependent, because it is produced by the mind; it has, therefore, a mental existence. The minor premise is also true: when objects are perceived, they are perceived by the mind and as such exist cognitionally in the mind; they have, then, a mental existence. But the conclusion does not follow logically from these premises. It is the fallacy of false consequent. The minor premise posits the consequent instead of the antecedent, and that is not logically permissible. If we wsh to avoid this inconsistency and make the minor premise posit the antecedent, the syllogism will read: If something has a purely subjective existence, it has a mental existence; But perceived objects have a purely subjective existence; Ergo, perceived objects have a mental existence. 55
But now the argument does not prove enough. It merely proves that perceived objects have a ‘mental existence’, and that is something which the realist admits; the idealist, however, desires to prove that all perceived objects have nothing but ‘a purely subjective existence’, and since it is his contention that the ‘esse’ of all perceived objects is their ‘percipi’. The argument does not reach that far. Besides, in the syllogism, as now given, the minor premise states that ‘perceived objects’ have a purely subjective existence’. This statement begs the question in dispute, because here the ‘esse est percipi’ is already assumed as true, while the truth of this fact is supposed to be found only in conclusion. There is only one more way in which this argument can be formulated so as to be logically correct and consistant. It could be made to read as follows: If something has a mental existence, it has a purely subjective existence; But perceived objects have a mental existence; Ergo, perceived objects have a purley subjective existence. This syllogism is consistent, but the conclusion is not true. The major premise, as it stands, is again a begging of the whole question. The fact in question is precisely that which assumed in the major premise: Is it a fact that if something has a mental existence, it has a purely subjective existence? This is the very point which the idealist intends to prove by the argument; hence, to assume its truth in the premises is an illegitimate procedure. It is thus seen that the fundamental position of the idealist is untenable, because illogical. He cannot prove that the objects we perceive have only a subjective existence in the mind; for all he knows, they may have a mind independent, objective existence in nature also. And if objects can exist both in nature and in the mind (and no valid reason has been adduced to the contrary), then the fundamental idealist postulate is invalid. D.C. Macintosh has summarized the essential fallacy of idealism in these words: The fallacy may appear as one of equivocation - the common fallacy of ‘four terms’ - as in the following syllogism: What is subjective (dependent on self for existence) is not externally real, but mere idea; all objects of which we are aware are subjective (related to a self which is conscious of them); therefore, all objects if which we are aware are not externally real, but mere ideas. Or, if the equivocation be avoided, the fallacy will remain as that of an ‘undistributed middle term’, as in this syllogism: The unreal objectively is subjective (related to a subject); similarly, all of which one is conscious is subjective (related to a subject); therefore, all of which one is conscious is unreal objectively (mere ideas). Or, more simply, psychological idealism may be said to rest upon a fallacious conversion. From the obvious truth that all elements which depend on consciousness for their existence, such as pains, feelings, desires, etc., are in the subjective relation,i.e., are objects for a subject, it is inferred, by the fallacious process of simple conversion, that all that is in the subjective relation, all that is object for a subject, is dependent on consciousness and this relation to consciousness for its own existence.2
2
The Problem of Knowledge (MacMillan, 1915), p. 95 - Regarding the various kinds of fallacies mentioned in this chapter, see the author’s Science of Correct Thinking (Bruce Publishing Co.).
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THE EGO-CENTRIC PREDICAMENT Every form of idealism, whether dualistic or monistic, rests upon the primacy of consciousness. Things simply cannot be known, perceived, experienced, except by a conscious mind. Consciousness is thus for them the universal condition of all knowledge and also of being. Consciousness constitutes its objects; and if this consciousness maintains its own individuality in the human mind, we have dualistic idealism, and if it is merged in a universal Ego, we have monistic idealism. In either case the ‘object known’ is identified with the ‘subject knowing’. We have seen how Berkeley argues for the oneness of the material reality with the perceiving mind. Bradley argues in a similar fashion for the oneness of all reality with sense-experience. Immaterialism, phenomenalism, absolutism, and every shade of idealism, ultimately base their doctrine on the fact that reality is somehow enclosed within the realm of consciousness, for the simple reason that we cannot perceive objects as existing apart from conscious perception. This ultimate fact, which is the heart of idealism, thus rests on what has been so aptly styled ‘the ego-centric predicament’. Here is Perry’s exposition of the idealist fallacy as based in the ego-centric predicament: No thinker to whom one may appeal is able to mention a thing that is not an idea, for the obvious and simple reason that in mentioning it he makes it an idea. No one can report in the nature of things without being on hand himself. It follows that whatever thing he reports does as a matter of fact stand in relation to him, as an idea, object of knowledge, or experience... “This predicament arises from the attempt to discover whether the cognitive relationship is indispensable to the things which enter into it. In order to discover if possible exactly how a thing is modified by the cognitive relationship, I look for things out of this relationship, in order that I may compare them with instances of things in this relationship. But I can find no such instances because ‘finding’ is a variety of the very relationship that I am trying to eliminate. Hence I cannot make the comparison, nor get an answer to my original question by this means. But I cannot conclude that there are no such instances; indeed, I now know that I should not be able to discover them if there were. “Just in so far as I do actually succeed on eliminating every cognitive relationship, I am unable to observe the result. Thus, if I close my eyes, I cannot see what happens to the object; if I stop thinking, I cannot think what happens to it; and so with every mode of knowledge. In thus eliminating all knowledge, I do not experimentally eliminate the thing known, but only the possibility of knowing whether that thing is eliminated or not. This, then, is ‘the ego-centric predicament’. But what does it prove, and how does it serve the purpose of idealism? It should be evident that it proves nothing at all. It is simply a peculiar methodological difficulty. It does, it is true, contain the proposition that every mentioned thing is an idea. But this is virtually a redundant proposition to the effect that every mentioned thing is mentioned - to the effect that every idea, object of knowledge, or experience, is an idea, object of knowledge, or experience. And a redundant proposition is no proposition at all. The assertion that an idea is an idea conveys no knowledge even about ideas. But what the idealist requires is a proposition to the effect that everything is an idea or that only ideas exist. And to derive this proposition directly from the redundancy just formulated, is simply to take advantage of the confusion of mind by which a redundancy is commonly attended. 57
It may be argued, however, that the ego-centric predicament is equivalent to an inductive proof of the proposition that all things are ideas. Every observed case of a thing is a case of a thing observed. Neglecting the redundancy, which is sufficient of itself to vitiate the assertion, we remark that the induction proceeds entirely by Mill’s ‘method of agreement’, which is invalid unless supported by ‘the method of difference’, that is, the observation of negative cases. But the ego-centric predicament itself prevents the observation of negative cases. It is impossible to observe cases of unobserved things, even if there be any. In other words, there is a reason connected with the conditions of observation why only agreements should be observed. But where this is the case the method of agreement is worthless; and the use of it a fallacy.3 Perry’s criticism of the idealist argument from the ego-centric predicament is eminently justified. The argument is essentially fallacious. The only way in which we can become acquainted. with things, is to perceive them or have ideas of them; therefore, if and when and while we know them, they must be ‘percepts’ or ‘ideas’ in our consciousness. The very nature of our knowing demands this. But things could possibly have existence without being perceived and thus be mind-independent in their being; all that the ego-centric predicament can prove is that things cannot be perceived without being perceived, which truth, of course, amounts to a mere tautology. If we now return to Bradley’s idealist argument, it will be evident that it is nothing but a sample of specious reasonong from the ego-centric predicament. He says: “Find any piece of existence, take up anything that anyone could possibly call a fact, or could in any sense assert to have being, and then judge if it does not consist in sentient experience. ...Anything in no sense felt or perceived becomes to me quite unmeaning.”4 Certainly, things ‘in no sense felt or perceived’ must be ‘unmeaning’ to the perceiver or the knower; for how could they acquire a meaning for him, if he did not ‘feel’ or ‘perceive’ them? That would imply ‘knowing’ them without someone knowing them, and ‘perceiving’ them without someone perceiving them. The very fact of cognition always involves the perceiver or knower just as necessarily as the object itself that is to be known; because an object, to be known, must be known by someone. Wherefore, Bradley’s argument only proves that objects cannot exist for a perceiver and a knower without sentient experience; but it says nothing whatever about what objects can or cannot be for themselves outside the knowledge relation, and Bradley’s conclusion that ‘experience is the same as reality’ is thus seen to be entirely unwarranted. The ultimate nature of reality is still an open question. The whole attitude of the idealist, of whatever type he may be, rests upon a confusion of ideas. From the fact that a being, in order to be known, must be perceived within the consciousness of the perceiver in a mental act, he concludes that the ‘realty itself ’ of the being, and not merely its ‘perception’, is mental. Reality would thus be immanent in the knower. The confusion is based on the identification of the ‘reality’ and the ‘perception’ of the object known. It is unquestionably true that the ‘perception’ of an object is mind-dependent and immanent. To assert that an object, when known, can remain unperceived, is a contradiction; and it would also be a contradiction to assert that an unperceived object, when unperceived, can be known. But it is no contradiction to assume that an object, which has a reality of its own, can remain unperceived by the human mind, either temporarily or forever, either in part or in whole. We would simply not know of its existence until 3 4
Present Philosophical Tendencies, pp. 129-131 (Longman’s, Green, and Co.). Appearance and Reality, pp. 144-145 58
such time as it enters our experience. To deny that such an object can exist as an ‘unperceived reality’ means to confuse the reality of this object with the perception of its reality. This is precisely what idealists do, but it is an illogical and dogmatic procedure and therefore fallacious. The foregoing criticism shows that idealism arises out of the ego-centric predicament and that its arguments involve a faulty logic. This, of course, does not prove that extra-mental reality actually exists; it merely shows that idealism has not disproved the existence of extra-mental objects. The question of the existence of such objects, must be solved, not by any a priori, but by an a posteriori method. Facts alone, together with their proper interpretation, must settly the issue; that is the only scientific and philosophic procedure which can lead us with safety to a definite conclusion.
Summary of Chapter IX Most modern theories are a form of idealism. The fundamental position of idealism is fallacious. 1. The element common to all forms of idealism is the tenet that reality lies within the consciousness of the perceiver and the mind cannot transcend its own conscious states. It arrives at this conclusion through the diffficulty of understanding how the mind can perceive objects as a distance and how a psychical mind can conform itself to a physical object. Hence, there has arisen the idealist postulate that the mind in its knowing can know only its own ‘percepts’ or ‘ideas’. The argument can be formulated as follows: Objects, so far as the knowing mind is concerned, exist only when perceived; but perception (‘being perceived’) is a conscious mind-state or ‘idea’; hence, objects are only conscious mind-states, or ‘ideas’; consequently their existence or ‘being’ (esse) is nothing but ‘being perceived’ (percipi): esse est percipi. 2. The Idealist Postulate of idealism is fallacious. Berkley’s argument that esse est percipi is grounded on faulty logic. His term ‘sensible object’ is ambiguous, because he does not distinguish between the ‘sensible’ as perceived and as perceiveable. He merely proves that ‘sensible objects’, when perceived, are ‘ideas or sensations’, so that his proof really amounts to the redundant proposition that ‘perceived objects must be perceived’. The fallacy of idealism thus consists in confusing the statement that ‘sensible objects cannot be perceived as existing without being perceived’ with the statement that ‘sensible objects cannot exist without being perceived as existing’. To assume that the latter statement was true, is a petitio principii. All arguments which tend to prove that all reality must be identified with ‘ideas’ involve either a ‘four-term’ syllogism, or an ‘undistributed middle’, or a fallacious ‘conversion’. 3. The ego-centric predicament, or the difficulty to discover any objects outside the cognitive relationship existing between object and subject, is responsible for the fallacy of idealism. Dualistic and monistic idealism rests upon the primacy of consciousness. Since consciousness is the universal condition of knowledge, it is also assumed that consciousness constitutes the being of all objects of knowledge. Due to the ego-centric predicament, every mentioned thing is an ‘idea’, and from this idealists conclude that everything is an ‘idea’ ’ and that only ideas exist. But this reasoning is fallacious, because it merely proves that objects, if and when and while known, must be ‘percepts’ or ‘ideas’; in other words, ‘things cannot be perceived without being perceived’, which is a redundancy and a platitude. The 59
argument, however, does not prove that objects may not exist in themselves, as mind-independent things, without being perceived. The whole attitude of the idealists is based in the confusion of identifying the reality of an object with the perception of this reality; they fail to distinguish between the ‘knowledge of objects’ and the ‘objects of knowledge’. The foundation of idealism thus rests on faulty logic and on the ego-centric predicament. The existence of extra-mental things is a question which can be settled only by a close analysis of the facts; not the apriori, but the a posteriori method can solve the problem.
READINGS D.C. Macintosh, The Problem of Knowledge, Chs V-IX; D. Card. Mercier, The Origens of Contemporary Psychology, Ch. V; R.B. Perry, Present Philosophic Tendencies, Chs. VI, IX; J. T. Barron, op. cit., Chs. X, XI; P. Coffey, op. cit., Chs. XIX, XX; William James, A Pluralistic Universe, Chs. I-VI; A.J. Balfour, A Defence of Philosophic Doubts, Chs. VI, IX; R.W. Sellars, Critical Realism, Ch. VI; G.E. Moore, “The Refutation of Idealism”, in Mind, 1903.
Plato and Liberal Education I. What is Education Plato conceived education as an art of perfecting man. According to this view, education is possible because man is a perfectible being. Nobody ever talks about perfecting God, because God is not perfectible, but perfect; nor do we ever discuss the education of angels, because, although an angel is not absolutely perfect, he is perfect within his own essence, which means that an angel receives all the perfection that is due and proper to his nature in one instantaneous act. To be sure, there are in the visible world other perfectible things besides man; but even so, the notion of education does not seem to fit the modes of perfectibility of things that are not human. A machine, for example, can be constructed and improved, while a tree attains its proper perfections by growth. Yet we would all hesitate to talk about the “education” of a plant or of a machine; and it would be just as incorrect to speak of the education of an animal. A dog, for example, may be trained; but a dog could never be educated. A dog is trained by being made subject to human purposes and notions, not even remotely entertained by the dog itself. Besides, it is trained, not to become a more perfect dog, more suitable for beastly society, but rather, in order to become more useful or more amusing to man, even if in the process it loses its intrinsic properties and gets to be, not more, but less of a dog. Education remains, therefore, a distinctively human affair, and as such, derives its distinctiveness from man’s peculiar way of growing into his perfections. Like all living things, man possesses within himself a vital principle of growth; but in man, this principle is further determined by rationality. It is by virtue of his rationality that man can consciously entertain his purposes, choose his means, and criticize his own actions. This coincidence of growth and rationality in the same being is a privilege which renders man unique in the whole universe. Plato must have been fascinated by this marvelous blend of qualities in man, this blend of intelligence and growth, for he makes it the central theme of practically all his Dialogues. In these Dialogues we have a most vivid picture 60
of education. In every case we find that education is a growth, a movement from confusion to clarity, from ignorance to knowledge; and also we find that in every case, the student is his own first teacher. The role of the teacher is simply to help the student in his seeking and to guide his steps. The teacher of the Dialogues, usually Socrates, is supposed to be the wise man, the man who has already attained those perfections desired for and by the student. The teacher stands as a proximate exemplar; and, by virtue of the fact that he is supposed to see the end of the road, he can also guide and direct, by ruling out false starts and by suggesting better ones. To put it in a more characteristically Platonic simile, the teacher is a midwife, who assists at the birth of the idea in the mind of the student. We can learn a great deal more about human nature and also about education, by observing with Plato, the way man grows into the attainment of his perfections. In contrast with other intelligent beings (God and the angels), man must accomplish his rationality through effort and discipline. Because human rationality is an accomplishment, it enjoys only a precarious existence. All our human concerns which manifest man’s rationality under any aspect, whether of order, purpose, truth, or beauty (the sciences and the arts, institutions, laws cultural values, etc.), depend for their continued existence upon the disciplined activities of men. Cathedrals do not grow like weeds, and no painting was ever made haphazardly. Every new-born baby is an absolutely new beginning, and every new generation of babies is a terrific challenge and threat to the existing civilization and to the established order of things. Indeed, our life here is an explosive situation! Man is a joining together of the nothingness and am infinity, and it is education which must span the chasm between the two extremes. No wonder that Plato, having understood the nature if education, should view it as the highest social function, commensurate with the whole of life, and absolutely necessary for the perfection of the individual and of society. Plato had such a profound appreciation of the importance of education, that starting to describe the building of a state, he ended up, in his famous Republic, with a kind of super-school on his hands. But there comes a point where we must remind ourselves that, after all, we are with a pagan philosopher, and should be on guard lest we let him mislead us in matters about which we ought to know better. And we do, as a matter of fact, know more than Plato about the origin and purpose of our human existence. Let us, therefore, be on the alert for any possible defects in Plato’s educational theories and practices which might flow from his pagan errors about man. Plato certainly understood that education must be of the whole man, which means of the complete composite of soul and body. He also rightly defended and emphasized the primacy of the soul in matters of education. He knew that the human soul is immortal, and at least vaguely suspected that man’s life-long educational activity finds its consummation in another life. But Plato also held some erroneous doctrines about the soul. It is a well known fact, for example, that he taught that the human soul exists prior to this life. We Christians, on the other hand, know that every individual human soul is created singularly and immediately, at the moment of conception, by a separate act of God. Here we have in this issue what might seem at first glance like a slight difference of belief: but on more careful examination, this disagreement between the Christian and pagan outlooks, reveals such a chasm as can only be explained by the tremendous intervening fact of the Incarnation. Plato can hardly be blamed for missing the point with regard to the fact, the manner, or the purpose of creation. This kind of knowledge requires a far greater intimacy with God than was given to the pagan world. It remains to the immortal credit of Plato that he attained, by mere rea61
son, a clear concept of the kind of reality the human soul is. He knew the soul in its spirituality and in its simplicity; he recognized its power and its dignity; he understood its activity of life in the body, and its activity of knowledge beyond the body; and he proved philosophically, that this kind of being cannot be dissolved or destroyed by natural means. But the same kind of argument led Plato also to believe that the soul could be neither made nor developed by any natural process. He, therefore, concluded that the soul is not only immortal, but also eternal, having no beginning as well as no end in time. The Christian alternative, namely, that the soul is created out of nothing by the omnipotence of God, did not present itself to Plato; for to him, God is neither infinite nor omnipotent, and the very idea of creation out of nothing would have sounded to him as no less that a philosophic absurdity. Plato, therefore, according to his own lights, had to educate a soul which was never created, which had no beginning in time, and no definite destiny for the future. The human soul to Plato is a little sad deity which cannot die, but can lose everything else it ever attained; even to the very memory of its personal identity in previous lives. This unconscious deity is accidentally united to, or rather, imprisoned in a material body, which it must leave after a certain length of time, to be united, perhaps to another body, and to go through the same cycle all over again. This soul has already had more intimate contacts with eternal realities that it has in this life, and therefore must have been in a higher state of perfection than in its present state. Unfortunately, however, it has lost all memory of these perfections and must now make a new start at re-ascending the scales of perfection to lose them again once more. How futile the whole thing must appear when viewed from the total perspective of eternity! And yet, this is as optimistic a view of human existence as the pagan world ever attained. These errors of Plato are at least partly responsible for some of the most obvious defects in his theory of education: depriciation of the body and of sense experience; a false theory of knowledge according to which we learn by remembering what we already knew in a previous life; and, most seriously, a relative disregard of personal values by treating the individual primarily as a function of the state. Yet, in spite of these defects, Plato remains, even today, a great master of the art of teaching, and the leading champion of the very concept of liberal education. It is in this last capacity that we are now primarily interested in Plato, and therefore, let us proceed to examine more specifically what Plato means by liberal education.
II. What is Liberal Education? We are used to distinguishing between two kinds of education: liberal and vocational. But Plato, while recogizing the need of developing the practical arts and professions, reserved the term “education”, at least in its absolute unrestricted sense, to what we would call liberal education. “This is the only training which, upon our view, would be characterized as education: that other sort of training which aims at the acquisition of wealth or bodily strength, or mere cleverness apart from intelligence and justice, is mean and illiberal, and it is not worthy to be called education at all.” From following the thoughts of Plato we get a hint as to the essence of liberal, or in his language, true education, which distinguishes it from all kinds of training for useful skill or for useless cleverness. Liberal or true education is education whose end is man himself. It is the education of 62
man as man. When a man is trained for the perfection of what he makes, he receives vocational training, or, if we call it education, we are using the term in a forced sense; but when a man is trained and instructed for the perfection of what he is and what he does (immanently) within himself, then we may say that he is being educated in the most absolute sense of the term. We may teach a man to become a carpenter, a farmer, a physician, or an engineer. We may also teach a man to become a good man, good not only in the moral sense but primarily in the ontological sense, in the sense of perfected, developed, accomplished, in the sense that he can exercise and apply his faculties coordinately and for their natural purposes. When men are trained vocationally we have every right to expect better products (potatoes, chairs, medical services, or efficient machines), but we have no right to expect better men unless somewhere in our educational plans and activities we aim at the proper perfections of a man. You are as likely to produce a well-constructed bridge by accident and without aiming at it, as you are to produce a well-educated man by a scheme of training thoroughly directed to other ends. It should go without saying and as part of nature’s justice, that in a society where leaders receive specialized vocational training without liberal education, no sound norms can rightly be expected and no human values are secure. When the present trend towards vocational training finally succeeds in overwhelming and washing away the last vestiges of liberal education, we can expect to live in a world of good things and bad men. We shall have, to give one good example, unintelligent and confused leaders, on othe one hand, and excellent atomic bombs, on the other! What are, then, those human perfections which constitute the end of liberal education? Plato’s answer to this question is in a way the major theme of all his writings. If one dares put it briefly and succinctly in one sentence, this is what it would be: man’s proper perfection consists in the knowledge of the absolute good, and in response to beauty. The absolute good is the good-in-itself and the source of the goodness all other things. It is good, not mediately as being the cause of something else, but immediately, ultimately, as being the end to which all other things are means. Man seeks this end, not only by his senses but by his intellect, and can attain it only with his intellect. But man must begin with his sense experience, and gradually advance, through higher and higher aspects of the good, reflected in the world of contingent things, until he is finally ready to see the primal source of all goodness. On the way to this absolute good, beauty is the sign-post. Man, therefore, must begin by learning to respond to beauty as given to the senses and as found in the visible universe, but he must not dwell in it nor let it conceal that invisible beauty it is meant to proclaim. Not all knowledge, therefore, is conducive to the perfection of man, and consequently, not all knowledge has value in liberal education. All the sciences of space and time, of experience and experiment, of statistics and measurements, such sciences as mathematics, physics, chemistry, biology, history, economics, etc., must find their justification primarily in the practical order, in the order of what man makes outside of himself. Man’s perfection consists in a growth from the fragmentary knowledge of sense experience to a unified vision of the mind; and hence all the above mentioned experimental sciences, can figure in the course of liberal education, only in so far as they lead the way to philosophic science; they must be treated as preludes to philosophy. Their end must be the understanding of the eternal truth, first as reflected in the visible world, but finally and consumately, as it is in itself. The climax of liberal eduction consists in philosophy and theology, and all its earlier stages must be ordered to this end, both in the selection of their subject matter and in the 63
mode of their presentation. It is especially remarkable that Plato, who is the greatest pioneer in the field of philosophy, should recognize the necessity of revealed truth, and admit the superiority of such truth over the highest truths of human reason working on its own. Although he was handicapped by an inadaquate pagan religion, he still had the genius to see that those intimate truths of the inner life of God could only be known if God Himself were to reveal them, and that once known, such truths would unquestionably be the crown of all human knowledge, and the summit of wisdom in this life. Thus in the Republic, after making Socrates describe the building of a state by the guidance of reason, Plato makes one interrogator raise the question as to whether any thing is left out. “Nothing to us,” replies Socrates, “But to Apollo, the god of Delphi, there remains the ordering of the greatest and noblest and chiefest things of all.” “Which are they?” asks again the interrogator. “The institution of temples and sacrifices, and the entire service of the gods, demigods, and heroes. . . These are matters of which we are ignorant ourselves, and as founders of a city we should be unwise in trusting them to any interpreter but our ancestral deity. He is the god who sits in the center on the naval of the earth, and he is the interpreter of religion to all manknid.”
III. The Epochs in Plato’s Educational System The key for Plato’s system of education is the Greek word µουσικε (sounds like “musikay”) which has survived in our modern languages in such words as “music” and “museum”. To the Greeks the term had a wider signification, including within its comprehension all the liberal arts. Greek mythology personified the liberal arts, making each one of them a goddess, a Muse, who guides, inspires, and stands as a type and an ideal. Thus we have the Muses of history, poetry, astronomy, eloquence, music, dance, tragedy, comedy, and lyric poetry. The Greeks saw beauty everywhere; whenever reality is known, it reveals rhythm and harmony, and hence education must progressively direct the mind to higher and higher aspects of beauty. The mind rises from beauty in the plane of sheer sense experience, the rhythm and harmony of sounds, shapes, and movements, to the beauty of law and order manifested in the visible world, the music of the spheres; and finally to the source of all beauty, Beauty in itself, the eternal Logos, attained by the art of dialectics. Every one of the arts and sciences is called µουσικε in this sense; and it is in this sense that we must understand the passage in the Republic where Plato makes Socrates say: “When the modes of music change, the fundamental laws of the state change with them.” Corresponding to the different planes of knowledge, we can distinguish four epochs in Plato’s educational plan. Here is a brief description of each of these epochs in their sequence. 1. The first twenty years are concerned mainly with the body and with the organic faculties. The children, as early as the age of three are introduced to mythology; this is meant to train their imagination, and to cultivate love of valor and heroic deeds. The mythology must be purged of any references to the gods which might degrade the concept of divinity in the child. The fact that mythology does not give the factual or historic truth does not matter, but it must be censored and purified from anything that might give a 64
permanantly false impression of reality. Factual truth is not so important at this stage, because it is an intellectual concern, and this stage of education is mainly concerned with the senses. After mythology, follow in sequence: gymanstics, reading and writing, poetry and music, and mathematics, until finally this epoch is rounded off in two years of military training, from the eighteenth to the twentieth year. Plato recognized the imitative tendencies of the soul, and thus he prescribes that the child must be surrounded from early childhood with beautiful objects which embody the truth he will come to understand later on in life. Hence the surroundings and environment are tremendously important in this formative period. 2. The second period, extending from the year twenty to the year thirty, is concerned with the sciences of measurement and understanding. Plato mentions plane geometry, solid geometry, astronomy, and harmonies. He conceives their role as a prelude to dialects. Evidently, he envisaged a patient treatment of these topics, with sufficient time for creative reasoning on the part of the students, and meditations on fundamental truths and notions which prepare the way for philosophy. This is clear from the amount of time he allows for this kind of work, although the amount of facts, principles, experiments, in such a variety of sciences, and in such a short time, that we leave him no leisure for reflection, meditation, wonder, nor for any creative work on his own initiative. Furthermore, the language of these experimental physical sciences today, is so little related to the language and truths of philosophy, that instead of being a prelude to philosophy as Plato intended, these positive sciences stand in our day as a tremendous handicap to philosophic thought. 3. The third epoch, which occupies the years thirty to thirty-five, is concerned with the art of dialectics, “the art which elevates the mind to the contemplation of what is best in existence”. This is the crowning mark of liberal education; the mind’s eye, which so far had been trained only to recognize the reflections of Good, must now be exercised to see the Good itself, the ultimate source of truth and beauty in the universe. To Plato, philosophy was not an organized science, or a system of sciences. The task of organizing truths of philosophy was to be carried out by his disciple Aristotle. This is why Plato was mainly concerned with the art of attaining philosophical knowledge, and this art he called “dialectics”. In our days, we possess not only the fruits of Plato’s and Aristotle’s efforts towards discovery and organization of philosophocal truths. We have, in addition, the results of centuries of collective effort on the part of scholastic philosophers, ending in a body of logically related sciences, full of precise notions, clear definitions, and well established truths. This philosophic tradition was accomplished through gradual steps, beginning with sense experience and common-sense knowledge. We must remember that the individual also must grow to philosophic understanding through the same way. Philosophy is a science, but philosophizing is an art. If we realize this truth suffficiently, we would not depend so exclusively in our teaching on the presentation of philosophic truths as finally and definitely formulated. The dialect method of Plato can still teach us a great deal as to how to teach philosophy effectively, and how to train the student to raise philosophic problems, to attain a realization of a philosophic truth, and to formulate and defend this truth. We can make philosophy much more of a living tradition by reviving the Platonic method, if not the Platonic science of philosophy. 4. The fourth and last epoch, requiring fifteen years of life and terminating at the 65
age of fifty, is a period dedicated to real experience in the world. It is significant that Plato did not try to carry the world into the school; the only way to know what life is, is to go through it. No man is truly wise enough to be entrusted with the destiny of a state until he has seen the real world in the light of universal truth. Philosophic ideas alone may be sufficient for the purpose of philosophic contemplation, but the philosopher-king, must make practical decisions for the common good, who must have more than ideas, namely, experience. Nor would experience without the philosophic discipline and knowledge of the Good suffice, because experience can move on a plane of insignificant facts unless illuminated by the idea of the Good. It is twenty-three centuries since Plato opened his academy and invited the youths of Athens to seek the knowledge of the Good. Since that time, something has happened on our planet; the Eternal Truth, the very Person of Good, has broken the bounds of eternity, plunged into our world, and lived as one of us. If Plato were to come to life today, how would he respond to our tidings of great joy? What would he think of our response?
Mathematics and Christian Education Fakhri Maluf Nothing could be more distinctive of the age in which we live than the overpowering prominence of mathematics. All through the Catholic centuries, arithmetic and geometry constituted all the mathematics that an educated Christian was asked to learn. Even these two subjects were treated from a more contemplative point of view, which made them far more harmonious with other liberal studies. Arithmetic consisted in the study of the properties of numbers; geometry in the study of shapes and figures. When not overdone, and when counter-balanced by the proper correctives from the other types of knowledge, geometry and arithmetic, as they used to be taught, cultivated a few desirable virtues of the mind like clarity and precision, and sharpened the mind for the perception of harmony, rhythm, and pattern in the study of nature and of Holy Scripture. But even then, many saints and sages warned against the seductive clarity of mathematics; for it is not enough for the mind to be accurate and clear; we are bound to ask “accurate and clear about what?” Since in mathematics accuracy and clarity are achieved at the price of the reality and the goodness of the object, it is a danger of the mathematical mind to continue to sacrifice reality and goodness for the sake of clarity in every other field in which man must seek and find the truth. But in our time, education is overwhelmed by mathematics and on more than one score. For, while a contemplative interest in the properties of shapes and numbers is almost completely, extinct, an illiberal and utterly inhuman form of mathematics dominates the years of learning of our boys and girls, almost completely from the very first year of the primary school to the very last year of college. In place of arithmetic and geometry, whose relation to reality is definite and understandable, there is now an indefinite confusion of branches which go by the name of mathematics, the nature of whose objects nobody understands! Such topics as topology, non-Euclidean geometry, Boolean algebra, transfinite numbers, projective geometry; not to speak of other more recognizable subjects like algebra, trigonometry, integral calculus, vector analysis and the theory of equations. These new subjects are not only more confusing but much more difficult to aquire, and therefore much less likely to leave the mind at leisure for other liberal studies. But the predominance of 66
mathematics today is not restricted to those courses which go by its name, because mathematics, in some form or other, in matter or in method, has crept into every other corner of the curriculum. According to the modern positivistic conception, mathematics and not wisdom is considered as the prototype of science. In subjects ranging from physics to education, covering every field of human learning, there is an evident tendency to assimilate all knowledge to mathematical knowledge and to resolve all realities into mathematical formulas. This trend reaches its apex in the development of symbolic logic, in which guise mathematics invades even the field of philosophy, to distort all the basic conceptions of the mind, and to deflect all the activities of thought from attaining their fulfillment in true wisdom, which consists in knowledge about God, by keeping them whirling endlessly around the nihilistic circle of sheer mathematical emptiness. Now in an attempt to determine the influence of mathematics on the mind of a Christian, it would be folly to ignore the fact that after twenty centuries of Christian living, it is impossible to name one single patron saint for mathematics. There are Catholics indeed who occupied themselves considerably with mathematics and as far as we know kept the faith; but I know of no mathematician whose faith burned so brilliantly as to earn him a place among the stars of sanctity. Nor is this a mere coincidence, for any one of us can look into his own mind to find that there is no other kind of human knowledge or human experience which offers less in terms of value for the Christian message than mathematics. Almost all that one needs in the way of mathematics in order to learn all of Holy Scripture and all the Doctors of the Church, does not exceed the ability to count up to a thousand and to distinguish between a vertical and horizontal line. Whatever it is you talk about in mathematics, it is never anything you can carry over to your meditations, or employ in your prayers; it gives you no courage in your moments of despair, and no consolation in your loneliness. In the field of philosophy, mathematics has always been fertile grounds for sophistry. There is hardly any other intellectual interest which has contributed more to confuse men about fundamental truths regarding God, man, and the universe, than mathematics. Just to mention the names of Thales, Pythagoras, Plato, Descartes, Spinoza, Whitehead and Russell, would suffice to convince one even slightly acquainted with the history of thought about the great number of minds that were deceived by the mirage of mathematics, and misled to accept fraudulent substitutes for the saving truth. I believe that an unpredjudiced consideration of the nature of mathematics and of the nature of its objects would reveal clearly that all these charges levelled against the mathematical mind are rooted in the very nature and essence of things. But what kind of a science is mathematics? Is it a practical science which envisages the achievement of a good, or a speculative science which envisages the attainment of truth? A practical science, like medicine or ethics, would be eliminated by the elimination of the corresponding good. For example, if men were indifferent to health and its opposite there would be no criterion for distinquishing between a right prescription and a wrong one, and consequently, medicine would cease to be a science. In a similar way, if men per absurdum were suddenly to become neutral to the attainment of happiness or its opposite, that would be the end of ethics. But what good, if ceasing, would determine the end of mathematics? None whatever, for the simple reason that mathematics prescinds from all good and all value. Mathematics talks the language of a speculative science. It utters propositions which must be either true or false. Now a proposition is true or false depending on whether it is or is not in conformity with reality. Just as a practical science envisages a good to 67
be achieved, which good functions as the criterion for right and wrong precepts in that science, so a speculative science considers some part or aspect of reality, which stands as the measure of truth and falsehood in that science. If there were no stars there would be no astronomy; and theology would be sheer nonsense if God did not exist. But what part of reality would destroy mathematics by being eliminated? What does the mathematician talk about? Is the object of mathematics a creature or a creator? Is it a substance or an accident? Is it something actual or merely potential? Is it changing or changeless? Temporal or eternal? Material or spiritual? Tangible or intangible? If one were to compose an inventory of all the subsisting realities of the whole universe, including God, the angels, men, animals, plants and minerals, would the objects of mathematics be on this list? Am I asking too many questions? Well, here are a few answers whose reasons will either be supplied later, or be left to the reader to discover for himself. Mathematics is a speculative science whose value can only be in the practical order. It has no speculative value, because it does not convey any essential knowledge about any subsisting reality. It is not contemplative knowledge and, therefore, not essentially good for man, because it occupies the intellect with objects that the will cannot love. It is knowledge which does not proceed from understanding, because the mathematical expression of any reality, never conveys any understanding of it. You are not one inch closer to the penetration of the mystery of light and color when you know the number of Angstroms in each of the colors of the spectrum; nor about the nature, cause, or purpose of gravity when you resolve its laws into mathematical formulas. And it does not resolve in wisdom because neither is mathematics concerned with the First Cause, nor does it lead to the First Cause. The manner by which mathematics deals with its objects abstracts completely from any dependence upon God, and as a matter of fact, attributes to these objects a species of eternity and turns them into quasi divinities completely independent in themselves. This explains the autonomous nature of mathematics, according to which, left to itself, it never leads to anything non-mathematical. A mathemetician might be led to think about God by an accidental non-mathematical reason, but never from the very needs of mathematics. As for the object of mathematics, it is not a physical entity but a mental entity; it is not real but ideal. There is nowhere in the world, outside of the mind of a mathemetician, a point without dimensions, a line without width or thickness, or a square root of minus one. But these fictions of the mind are founded on reality, and their foundation consists of the accident of quantity and its properties and relations. Arithmetic is founded on discontinuous quantities or multitudes; geometry on continuous quantities or magnitudes; while algebra is founded on abstract quantity considered generically, prescinding from whether it is number or magnitude and, therefore, potentially capable both of an arithmetical as well as of a geometrical interpretation. Other mathematical objects, more distantly removed from this real foundation of mathematics, are rooted in these simpler elements and in the relations which hold among them. Having experienced the three dimensions by the three variables of an algebraical equation, nothing prevents the mind from creating the fiction of a space corresponding to an algebraical equation of four variables; hence four dimensional space. But what do we know about this accident of quantity, on which is founded, proximately or remotely, every object of mathematics? We learn from philosophy that quantity is an accident of material substances, and that in contrast with the accident of quality, quantity manifests the material and not the formal aspect of these substances. Therefore, the real foundation of mathematics is 68
found in the material aspect of material things. Further, an accident when conceived as an accident always brings you back to its substance; but in mathematics the accident of quantity is conceived as if it were a substance. Further, a material substance moves to the attainment of an end, but the mathematician considers quantity as a substantialized material accident devoid of any principle of change and abstracted from any movement to attain an end. The concrete material substance manifests itself through its sensible qualities by means of which it is known, but the object of mathematics, without being a spiritual substance like an angel, prescinds from all sensible qualities and can be known only by the intellect and not by the senses. Hence we have the apparent paradox that, while the only foundation for the mathematical object is the material aspect of material things, still mathematics represents its objects such as matter could neither be nor be known. For matter is nothing but a principle of change, while mathematics prescinds from change; and matter can only be known through the senses while mathematics prescinds from sensibility. The object of mathematics is therefore an accident parading as a substance, a material reality pretending to be immaterial, an ideal entity which poses for something real. At the basis of all these antinomies is the fact that mathematics arises only when an intellectual mind directs the light of its spiritual intelligence, not for the purpose of contemplating being, but for the purpose of controlling potency. The mathematical object is the shadow that matter casts on spirit. For, when spirit knows spirit, there is not even the foundation for mathematics; when material cognition (sensation) knows material things, the objects of mathematics cannot arise; even when a spiritual being knows matter contemplatively it understands a material substance through its form and its qualities. It is only when a spiritual being concerns itself with matter and for the purpose of sheer control that mathematics finally finds its grounds. But how about the truth in mathematics? If the objects of mathematics are mental entities (entia rationis) what is it that determines the truth or falsehood of a mathematical proposition? What reality stands as the measure to the judgment of the mind? In the classical branches, arithmetic and geometry, the foundation in reality was close enough to preclude any statements that are not justified by the real properties of multitudes and magnitudes. But as mathematics branches out and develops into newer mathematics, and higher mathematics, and purer mathematics, that control becomes less and less until finally the mind remains its own measure. Consistency and not conformity becomes the touchstone of validity. Apart from mathematics, there used to be three other distinct types of knowledge: physical, logical, and ethical. All three led ultimately to God, the physical sciences under the aspect of Ultimate Cause, the logical sciences by way of the Prime Truth, and the ethical sciences by way of the Supreme Good. But in mathematics, the mind reigns supreme, lord of all it surveys. The mind finds in itself a sufficient cause for the kind of being the mathematical entity enjoys. It is the only ultimate measure for the truth of its judgments. It prescinds completely from the aspect of goodness. Of all the intellectual pursuits, mathematics alone does not lead to God. It is like the web of a spider, it proceeds from the very substance of the spider and ends up being its own jail. It gets more involved and more intricate the more it is extended, and, finally, when the web is intricate enough, the new threads do not have to measure up to any real independent distances. From the spider of mathematics, may God deliver us.
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