Socratic Logic PDF - Edition 3.1

I: The First Act of the Mind: Understanding Section 1. Understanding: the thing that distinguishes man from both beast and computer (P) (This section is more philosophical than logical, but it is important because it fleshes out the positive a...

I: The First Act of the Mind: Understanding Section 1. Understanding: the thing that distinguishes man from both beast and computer (P) (This section is more philosophical than logical, but it is important because it fleshes out the positive alternative to nominalism and provides the essential philosophical foundation for Aristotelian logic.) As we have already reported, a new species of human has appeared: one that does not know the difference between a human mind and a computer, between "natural intelligence" and "artificial intelligence." Some of these people even teach philosophy! For centuries there have also been some people - many of them philoso- phers - who say they do not know what the difference is between a human being and an ape. After all, apes seem to reason quite well sometimes. If you put an ape in a pit with a dozen wooden crates, he might figure out how to get out by piling up the crates against a wall in the form of a stairway, whereas some humans would not figure that out. But there is one simple, observable behavior that clearly distinguishes humans from both computers and animals: asking questions. Computers never question their programming (unless they have been programmed to do so); com- puters never disobey. They have no will, therefore no will to know. And animals, though curious, cannot ask formulated questions; their language is too primitive. There is a story that Aristotle, after one of his lectures, was disappointed that his students had no questions afterwards, so he said, "My lecture was about levels of intelligence in the universe, and I distinguished three such levels: gods, men, and brutes. Men are distinguished from both gods and brutes by question- ing, for the gods know too much to ask questions and the brutes know too little. So if you have no questions, shall I congratulate you for having risen to the level of the gods, or insult you for having sunk to the level of the brutes?" Logic specializes in questioning. The three most basic questions humans 36 I. THE FIRST ACT OF THE MIND: UNDERSTANDING ask arc: What, Whether, and Why, i.e. What is it? Is it? and Why is it? These are dealt with in the three parts of logic. The part that most clearly distinguishes humans from computers is the first: understanding a "what," an "essence," the nature of a thing. Computers under- stand nothing; they merely store, process, relate, and regurgitate data. You don't really think there is a little spirit somewhere inside your hand-held calculator, do you? But the world's most complex computer has nothing qualitatively more in it than that, only quantitatively more. An amoeba is closer to understanding than a computer, for it has some rudimentary sensation of feeling (e.g. it detects food). A baby often goes around pointing to everything he 1 sees, asking "What's that?" The baby is a philosopher. "What's that?" is philosophy's first question. (Look at any Socratic dialogue to see that.) The act of understanding, or "simple apprehension" as it is technically called produces in our minds a concept. (Sometimes we use the word "idea" as synonymous with "concept," but at other times we use the word "idea" more broadly, to include judgments and arguments as well as concepts.) We do not merely understand concepts, we understand reality by means of concepts. Our concept of a house is our means of understanding the real house. The real house is physical, but our concept is not. The house is independent of our mind, but the concept of it is not: it is in our mind. If all we understood was our own concepts, we would not understand objective reality. Concepts are amazing things. They can do what no material thing in the uni- verse can do. They can transcend space and time. No body can be in two places 1 The use of the traditional inclusive generic pronoun " h e " is a decision of language, not of gender justice. There are only six alternatives. (1) We could use the grammatically mis- leading and numerically incorrect "they." But when we say " o n e baby was healthier than the others because they didn't drink that milk," we do not know whether the antecedent of "they" is "one" or "others," so we don't know whether to give or take away the milk. Such language codes could be dangerous to baby's health. (2) Another alternative is the politically intrusive "in-your-face" generic "she," which I would probably use if I were an angry, politically intrusive, in-your-face woman, but I a m not any of those things. (3) Changing "he" to "he or she" refutes itself in such comically c l u m s y and ugly revisions as the following: "What does it profit a man or woman if h e or she gains the w h o l e world but loses his or her own soul? Or what shall a man or w o m a n give in exchange for his or her soul?" The answer is: he or she will give up his or her linguistic sanity. (4) We could also be both intrusive and clumsy by saying " s h e or he." (5) O r we could use the neuter "it," which is both dehumanizing and inaccurate. (6) O r w e could c o m b i n e all the lin- guistic garbage together and use "she or he or it," which, a b b r e v i a t e d would sound like " s h... it." I believe in the equal intelligence and value of w o m e n , but not in the intelligence or value of "political correctness," linguistic ugliness, grammatical inaccuracy, conceptual confusion, or dehumanizing pronouns.  Understanding at the same time, but a concept can. Suppose someone asks you whether you think San Francisco or Boston is the more beautiful city. You understand the question, and you answer it. Your mind compared (and therefore was present to) two cities 3000 miles apart - at once! Your concepts did what your body cannot do. Though your body is unimaginably tiny compared with the universe, your concept of the universe is greater than the universe! For if you understood the word "universe," your thought 'surrounded' the universe - the same universe that surrounds your body. You did that by having a concept of the universe. Concepts have at least five characteristics that material things do not have. They are spiritual (or immaterial), abstract, universal, necessary, and unchanging. 1. Concepts are spiritual (immaterial, non-material). Compare the con- cept of an apple with an apple. The apple has size, weight, mass, color, kinetic energy, molecules, shape, and takes up space. The concept does not. It is "in" your mind, not your body. It is not in your brain, for your brain is part of your body. It has no size, so it cannot fit there. (If you say that it does have size, the size of an apple, then you must say that your brain must get as big as an elephant when you think of an elephant.) It has no weight, for when you stand on a scale and suddenly think the concept "tree," you do not gain the slightest amount of weight. In contrast to the concept "apple," the word "apple" is just as physical as an apple. It takes up space on the page, and it is made of molecules. The spoken word also is made of molecules: wave-vibrations of sound of a certain size and shape. But between these two material things - the apple and the word "apple" - there is the concept. That is the only reason why we can use the word "apple" to mean the physical apple we eat. We use one physical thing (the word "apple") as a symbol of another physical thing (the apple we eat), and that mental act, or mental relation, that we set up is not a third physical thing. It is a concept, and its meaning is the real apple even though its being is not the being of an apple. (It is not in space, has no molecules, etc.) The concept's meaning is "a physical fruit that grows on apple trees, has red or green skin, etc.," but the concept's being is not physical (material), but spiritual (immaterial). Our having the concept of an apple is dependent on our having a physical body, of course: it is dependent both on the eye, which perceives the apple, and on the brain, which works whenever we have a concept. If we had never seen an apple, we would never have a concept of one, and if we had no brain we could not think the concept of an apple. But the concept is not just the physical apple or the visible word or even the sense image, which is somewhere between a physical and a spiritual thing. (We will see the difference between a concept and a sense image more clearly in the next few paragraphs.) The sense image is like a scouting report sent out by the intellect. The intellect is like a king who stays in a soul-castle and sends out scouts (the senses) to report to him what^s going on in his kingdom. Or, to change the image, the intellect is like a para- 38 I. THE FIRST ACT O F THE MIND: UNDERSTANDING lytic in a wheelchair who directs a blind man where to push him. (In this image, the intellect is symbolized paradoxically, by the physically sighted paralytic and the senses by the blind pusher.) The two are interdependent. When a thing is known, it acquires a second existence, a mental existence; the thing becomes a thought. If familiarity did not dull us, we would find this utterly remarkable, unparalleled in all the universe. No galaxy, no physical ener- gy, no cell, no animal can do this; only a mind can give a thing a second life. Every language speaks of the human mind or intellect, as doing something more than the (animal) senses do: as going "deeper" or "below the surface" or "penetrating" what is sensed like an X-ray; as going beyond appearances to reality, beyond seeing to understanding. (Thus the irony in a blind poet or "seer" like Homer, John Milton, or Helen Keller "seeing" more than sighted people.) Only because we distinguish between appearance and reality do we ask ques- tions. There would be no philosophy and no science without this distinction. 2. Concepts are abstract. The English word "abstract" comes from the Latin abstraho, "to draw (traho) from (ab(s))" or "to drag out of." Our mind extricates, or separates, something from something else. What is this something? When we form a concept, we abstract one aspect of a concrete thing from all its other aspects - e.g. the size of a flower (when we measure it), or its color (when we paint it). No one can physically or chemically separate the size from the color, or either one from the whole flower; but anyone can do it mentally. We can abstract, or mentally separate, adjectives from nouns. Animals sim- ply perceive "green-grass," but even the most primitive men mentally distin- guished the green from the grass; and this enabled them to imagine green skin, or red grass, even though they had never seen it. And once they imagined these things, they set about making them, e.g. by dying their skin green from the juice of grasses, or painting pictures of red grass with dye made from beet juice. (When he was two, my son made the thrilling discovery that he could make "pur- ple doo-doo" by mixing up blue and red Play-Doh R in the shape of a hot dog.) Technology and art both flow from this human power of abstraction. The most important act of abstraction is the one by which we abstract the essential from the accidental. By having a concept we can focus on the essence and abstract from the accidents. Some people are reluctant to do this. Their con- versation is utterly concrete - and utterly boring. You want to scream at them, "Come to the point!" These people have few friends, for to have friends you must learn to abstract, i.e. select, set apart, or pick out, the things that interest both them and you. Abstraction fosters friendship - a concrete payoff! Abstractions have received bad press in the modern world. Too bad. The next time you hear someone say "I'm a concrete, practical person, and I hate abstractions," remind them that babies are very concrete - and uncivilized. Abstract ideas do not move us as much as concrete things do. Intellectuals, who live with abstractions, are often practically ineffective dreamers and rarely "movers and shakers" of men, because men will not usually live and die for  Understanding 39 abstractions that move only our mind - even stirring abstractions like "liberty, equality, fraternity" or "democracy" or "freedom" - but for concrete things that move their loves, like their families or their buddies next to them in the trenches. 3. Concepts are universal. Ask a child what he wants and he may answer, "Everything!" He has formed a universal concept. (Most concepts are only rel- atively universal, not absolutely universal like "everything" or "something" or "being") E.g. "tree" is a universal concept because it is a concept of not only that one tree in your yard, but of all trees. "Beauty" is a universal concept, and when we judge whether San Francisco or Boston is more beautiful, we judge both cities by the universal concept "beauty" (or "beautiful city"). The literal meaning of "universal" is "one with respect to many" (unum ver- sus alia). This means that a concept, while remaining one - one essence, one meaning - nevertheless is true of many things, predicable (sayable) of many things, applicable to many things. This oak and that oak and that maple are all "trees." We can truly apply the concept "tree" to any and every possible and actual tree that ever was, is, or will be. The concept signifies something common to many different things. This oak and that oak are different in size, and oaks and maples are different in shape of leaves and taste of sap, but all are trees. All share the same common essence, or essential nature. That is what we are seeking to know when we ask "What is that?" Only the concept gets at this one-in-many, this common essence in many different things. It is not in sense perception that we see this universal. We per- ceive only individual men and women, who are either tall or short, either old or young, but "human being" is neither male nor female, neither tall nor short, nei- ther old nor young. "Human nature" does not look male or female, tall or short, old or young. It does not "look" at all; it "means." Appearances are particular; but essences, or meanings, or the natures of things, are universal. You cannot touch them or feel them; you can only understand them. They are known by concepts. 4. Relations between concepts are necessary. Every tree necessarily has leaves; every triangle necessarily has three sides. A tree may or may not have many leaves, but it must have leaves. A triangle has to have three sides; that is dictated by its essence, which is grasped in the concept. Thus we can be certain of relations between concepts, as we cannot be cer- tain of material things. We can be certain that a triangle will have 180 degrees in its three angles, but we cannot be certain how tall a tree will be. 5. Concepts are unchanging. Two plus two can never become other than four, but two bunnies plus two bunnies can become more than four bunnies. The concept "blue" can never become not-blue, but the blue sky can become not- blue. The nature of a thing, which is known by a concept, is unchanging; but things, which are known by sense experience, are changing. Humans change; essential human nature does not. 40 I.THERRST ACT O F T H E M I N D : U N D E 1 1 The most i m p o r t a n t o f t h e s e c h a r a c t e r i s t i c s o f " p their universality. " U n i v e r s a l " m e a n s u o n e - i n - m a r ^ i M i | » K many-diverse-somethings" ( " u n i - v e r s a " ) , o n e n a t u r e mfauiK ^ different concrete i n d i v i d u a l s. A s i n g l e c o n c e p t u n 1 |g under one idea. W i t h o u r s e n s e s w e p e r c e i v e h o u s e s i i i i i l p a and colors, but w i t h o u r m i n d w e u n d e r s t a n d | "house." We see m a n y i n d i v i d u a l h o u s e s a n d m a n > r | i M | | - | i ^ doors, roofs, w i n d o w s , a n d p o r c h e s — b u t w e d o n o t $ of the house, the " h o u s e n e s s. " I t i s o n l y t h e u n d e r s t a » i l f c l f houses under the s i n g l e c o n c e p t " h o u s e / ' T h e c o n c e f i # j « i ligible. It brings o r d e r o u t o f c h a o s. 51fl Without it, m e t a p h y s i c s w o u l d b e i m p o s s i b l e. ^ damental branch o f p h i l o s o p h y ; it i s t h e s t u d y o f « study of the laws o r p r i n c i p l e s t h a t a r e t r u e u n i v ^ e r s a M i g l t a K universal concept o f all i s " b e i n g. " E v e r y t h i n g i s ifMfcte n "being" is the m o s t f u n d a m e n t a l c o n c e p t. B e f o r e what a thing is, w e k n o w t h a t it i s a b e i n g. T h e r e i s w The concept o f b e i n g i s i m p l i c i t i n e v e r y o t h e r \ what a house is, w e k n o w w h a t a h o u s e w e (K reality, its s u b s t a n c e. K The concept o f b e i n g i s l i k e t h e g e n i e i n t h e fc>otrti WMwi (j it grows so large t h a t it f i l l s t h e w h o l e s k y. ^ This is crucial t o l o g i c a s w e l l a s p h i l o s o p h y. tf two words, two v e r y c o m m o n y e t v e r y p r o f o u n d 1 i itwskWSi- g fore." "Is" is the f i r s t w o r d t h a t r e l a t e s t w o c o n c e p t s r t i i p ^ tion (the subject a n d t h e p r e d i c a t e ) : " M a n is: m o r t a l iftttuntf 4 "Therefore" is the w o r d t h a t r e l a t e s t w o o r m o r e p> the conclusion) in a n a r g u m e n t : " A l l m e n a r e m o r t a l ^ tal," or "Tomatoes a r e v e g e t a b l e s , a n d v e g e t a b l e s ^ toes are not fruits." U t Is Section 2. C o n c e p t s , t e r m s , ani!i!J fa is different in d i f f e r e n t l a n g u a g e s ; f o r t h e s a m e t e r m.tattlmiE [j is expressed in d i f f e r e n t w o r d s b y d i f f e r e n t l a n ^ i j. « l f p » n made, conventional, a n d c h a n g e a b l e. T e r m s a r e n o t. Ttespp&H 6  Concepts, terms and words / The "problem of universals " 41 translate between different languages: because the same stable term, or unit of meaning, anchors many different words in many different languages. E.g. "love" "carit as" "agape," "lieb," "amor," and "amour" are the same term in six different words. A word is physical and sensible (to the eyes or the ears, or to the touch, in Braille). A concept is not. A term mediates between a concept and a word: inso- far as it is a unit of meaning, it is not something made of matter or perceivable with the senses; insofar as it is expressed by a word, in any language, it is per- ceivable by the senses, like the word "word" in this sentence. The difference between a term and a concept, and the difference between a term and a word, may be difficult to grasp, and it is not crucially important from a practical point of view for the logic student to understand it; but it is crucially important to understand the difference between a concept, a judgment, and an argument; or between a term, a proposition, and a syllogism; or between a word, a sentence, and a paragraph. A term is the most simple and basic unit of meaning. A term is simply any word or group of words that denotes an object of thought. The English word "term" comes from the Latin "terminus," which means "end" A term is one of the two "ends" of a proposition, as the first and last points on a line are the two ends of the line; for a term is either the subject (the beginning) or the predicate (the end) of a proposition, when it is in a proposition. Whether a term is inside a proposition or not. a term is whatever can be used as the subject or the predi- cate of a proposition. "Apples" has the same meaning whether it is in the propo- sition "Apples are fruits" or whether it is outside the proposition and merely "apples." A term is simply any word or group of words that denotes one object of thought. Terms are never either true or false. Only propositions are true or false. "Apple" is neither true nor false. The proposition "Apples are fruits" is true, and the propositions "Apples are vegetables" is false. Instead of being true or false, terms are unambiguous or ambiguous, clear or unclear. Propositions are ambiguous or unambiguous only insofar as their terms are ambiguous or unam- biguous. You will learn how to change ambiguous terms into unambiguous terms in the chapter on defining terms. Section 3. The "problem of universals" (P) The fact that most terms are universal (predicable of many things) has given rise to one of the classic problems in the history of philosophy, the so-called "prob- lem of universals." First raised by the ancient Greek logician Porphyry, the prob- lem arises when we ask this question: What is there in reality that universal terms refer to - especially abstract universal terms like "beauty" or "humanity**? It is clear that concrete singular terms like "Socrates" or "the moon" refer to 42 I. THE FIRST ACT OF THE MIND: UNDERSTANDING concrete individual entities that exist in a particular space and time; but where and when do we find beauty or humanity, as distinct from this beautiful thing or that human being? We have said that terms express concepts, that concepts arc universal, and that concepts refer to the essences or natures of things. Are these essences uni- versal, like the concepts we have of them? If they are not, then it seems that our concepts of them are not accurate, for they do not correspond to their objects. And in that case, our concepts would dis- tort rather than reveal the true nature of things. But are universals then real things? Is beauty real as well as beautiful things? Does humanity or human nature or the human species really exist in addition to the 6+ billion human beings that have the same essential human nature? Plato thought they did. He called these universals "Forms" or "Ideas" - not ideas in minds but Ideas outside minds, objective Truths; not thoughts but the objects of thoughts. He believed there were two kinds of reality, two "worlds": a world of concrete, material individual things in space and time that we know by our bodily senses, and another world of immaterial universal Forms that we know with our minds through concepts. The "two worlds theory" seems fantastic to common sense and an example of what one philosopher (Alfred North Whitehead) calls "the fallacy of mis- placed concreteness," treating an abstracted aspect of a thing (its essential nature) as if it were another concrete thing. This theory of Plato's is sometimes called "Extreme Realism" because it claims that universals are "extremely real," so to speak - just as real as individual things, in fact more real since they arc timeless and immortal and unchangeable. A beautiful face changes with age, but beauty does not. The theory most totally opposed to Plato's is called Nominalism. The 14th- century medieval philosopher William of Ockham is usually credited for invent- ing the theory, and modern philosophies such as Empiricism, Pragmatism, Marxism, and Positivism have embraced it and made it popular. Nominalism claims that universals are only names (nomini) that we use as a kind of short- hand. Instead of giving each individual tree a separate proper name, we group together, for our own convenience, under the one vague name "tree," all those things that resemble each other in certain ways (e.g. having trunks and branch- es and leaves). But in reality, all trees are different, not the same; not one-in- many ("uni-versal"), but only many. Nominalism seems logically self-contradictory, for if all trees are different, how can it be true to call them all "trees"? The very sentence that says all trees are not really the same presupposes that they are! If universals are only our names for individuals that resemble each other in certain ways, those "certain ways" must be really universal (e.g. all have trunks, branches, and leaves); so we have eliminated one universal ("tree") only by appealing to three others ("trunk,"  The extension and comprehension of terms 43 "branches," and "leaves"). Something in trees must justify our use of a universal term "tree." What is this? Is it their "resemblance" or "similarity"? But they must resemble each other in something. What could this be but their nature, their essence, their treeness, what-trees-really-are? Aristotle, as usual, takes a middle position between these two extremes, and his view accords best with common sense. His position was developed by the Arabic philosopher Avicenna and by St. Thomas Aquinas in the Middle Ages. It is called "Moderate Realism," and it holds that essences are objec- tively real (contrary to Nominalism) but not real things (contrary to Extreme Realism). They are the essential "forms" or natures of things. Forms exist in the world only in individual material things, but they exist in our minds as uni- versal concepts when our minds abstract them from things. It is the very same nature (e.g. humanness) that exists in both states; otherwise our concept of it would not be accurate, would not be a concept of it, of what really is in the things. A universal form such as humanness exists in the world only individu- ally, but the same form or nature exists in the mind universally, by "abstrac- tion" from individuals. So according to Aristotle the Nominalist is right to say that universality is only in the mind, not in things, but wrong to say that there is nothing in reality that is the object of universal concepts. And the Extreme Realist is right to affirm that universals are objectively real and not just names, but wrong to think they are "substances." (Aristotle s technical term for concrete individual things was "substances") They are the "forms" of substances (e.g. the treeness of trees, the humanness of humans, the beauty of beautiful things, the redness of red things). Some are essential forms (like "humanness") which a thing must have in order to be what it is, others are accidental forms (like "redness") which a thing can gain or lose and still remain what it is, as when a tomato changes from green to red. This apparently very technical, abstract, logical dispute has great practical consequences. If universals are more real than individuals, then individuals, and human individuals too, are not primarily important - a convenient philosophy for totalitarians! And if individual things are less real than universals, then the senses do not reveal anything very important, and only the few "brains" who can think very abstractly are wise. On the other hand, if universals are not real at all, then we have the even more radical consequence of skepticism: reality is an unknowable chaos, and all so-called universal truths arc merely subjective and man-made, including all principles of science and ethics. Section 4. The extension and comprehension of terms Every term (and the concept it expresses) has both an extension and a compre- hension. The extension of a term is simply all the real things the term refers to - the 44 I. THE FIRST ACT O F T H E M I N D : U N D E R S T A N D I N G "population" of the term, s o to s p e a k , in t h e w o r l d. E. g. t h e e x t e n s i o n o l is the 6+ billion men w h o exist. O r , if " m a n " is t a k e n e x c l u s i v e l y i n s inclusively, then its extension is 3 + b i l l i o n m a l e s. The "comprehension" o f a t e r m m e a n s t h e t e r m ' s i n n e r m e a n i n g , a s from its external "population." T h e w o r d " c o m p r e h e n s i o n " h e r e d o e s n to our mind's act of c o m p r e h e n d i n g , i.e. u n d e r s t a n d i n g , t h e t e r m , b u t r z the meaning that the term " c o m p r e h e n d s " o r i n c l u d e s w i t h i n i t s e l f. E. g. t l prehension of "man" is "rational a n i m a l. " Sometimes the words " e x t e n s i o n " a n d "intension" are used i n s "extension" and " c o m p r e h e n s i o n. " D o n o t c o n f u s e " i n t e n s i o n , " w h i c l objective meaning of a term, w i t h " i n t e n t i o n , " w h i c h i s t h e s u b j e c t i v e m a person. Another set of two w o r d s s o m e t i m e s u s e d t o m a k e t h e s a m e d i s t i n "denotation" and "connotation." T h e d e n o t a t i o n o f a t e r m i s t h e r e a l fcj refers to; the connotation is all t h e a t t r i b u t e s o r q u a l i t i e s o r c h a r a c t e r i s t i c by it. However, " c o n n o t a t i o n " is s o m e t i m e s u s e d in a d i f f e r e n t a n d n sense, as meaning only those c h a r a c t e r i s t i c s r e f e r r e d t o implicitly, or "I the lines," as nuances or s h a d e s o f m e a n i n g t h a t a r e n o t e x p l i c i t l y p a r term's comprehension. " C o n " m e a n s " w i t h " a n d " n o t a t i o n " m e a n s so literally, "connotation" m e a n s a " m e a n i n g - a l o n g - w i t h. " Another set of two w o r d s s o m e t i m e s u s e d t o m a k e t h e s a m e d i s t i n "meaning" (comprehension) a n d " r e f e r e n c e " ( e x t e n s i o n ). A t e r m ' s " r e f is all the real things the term r e f e r s to. T h e s e t w o w o r d s a r e u s u a l l y u s e d the point that a term can have a m e a n i n g y e t n o r e f e r e n c e a t a l l , e. g. t "unicorn." QUALITATIVE QUANTITATIVE Comprehension Extension Intension Extension Connotation Denotation Meaning Reference The two aspects of terms: The extension (or d e n o t a t i o n o r r e f e r e n c e ) o f a t e r m i s q u a n t i t a t i v e , count all the individual b e i n g s t h e t e r m r e f e r s t o. T h e c o m p r e h e n s i o n ( o sion or connotation or m e a n i n g ) o f a t e r m is q u a l i t a t i v e , n o t q u a n t i t a t i cannot count a term's inner m e a n i n g. Logical divisions, or outlines, a n a l y z e t h e extension of a term. L o g ! in itions analyze the comprehension of a term. The Principle of Inverse R e l a t i o n b e t w e e n E x t e n s i o n a n d C o m p r e h Extension and comprehension u s u a l l y vary inversely. ("Usually" b e c a u :  The extension and comprehension of terms 45 are rare and technical exceptions.) As comprehension increases, extension decreases; as comprehension decreases, extension increases. When we add attributes to increase the comprehension of a term, we add to its meaning but decrease its reference. E.g. "animal" has more extension than "man," for there are only 6+ billion men but trillions of animals, including both rational animals (men) and irrational animals ("brutes"). But "animal" has less comprehension than "man," for "animal" means only "a living and sensing thing" while "man" means "a living and sensing thing with reason." "Beer" has more comprehension than "drink," for it means "drink made from malt and hops." But "drink" has more extension than "beer" for that exten- sion includes milk, water, wine, etc. As terms become more abstract, they lose comprehension and gain exten- sion. Common misunderstandings come about from confusing comprehension with extension. E.g. when we judge that "males are taller than females," or "fish gotta swim, birds gotta fly," we are speaking of the comprehension of the sub- ject term "males" or "fish," not the extension. Not all 3+ billion human males are taller than all 3+ billion human females, of course, but the nature of males is on average to be taller than females. Another example: Aristotle's famous first line of his Metaphysics, "All men by nature desire to know," is not disproved by the fact that some men are in fact uncurious, lazy couch potatoes. Even the couch potato by nature desires to know; he is suppressing his nature at the moment by being hypnotized into thoughtless stupefaction by the boob tube. Perhaps "boob tube hypnosis" is the reason why so many people today will immediately and thoughtlessly reject all "generalizations" like "men are more aggressive than women" as "stereotypes." They are confusing comprehension and extension. They are misinterpreting a statement about comprehension as if it were one about extension, and that is why they think that the fact that Mrs. X is more aggressive than Mr. X disproves the statement that "men are more aggressive than women." They cannot or will not rise to the original statement's level of abstraction and argue with it on its own level. The statement is not about all the individuals that have the nature of male and the nature of female, but about those natures in abstraction from the individuals that have them. Those who reject all generalizations because they can find some exceptions to them are thinking only on the concrete sense level of extension, not on the abstract con- ceptual level of comprehension; they are operating like cameras (sense experi- ence) plus computers (calculating the quantities of extension), but not like human minds (understanding essences, natures, "whats"). The point is important enough philosophically to justify going through it again. When I say "all my books are paperbacks," I am not speaking of the com- prehension of "book," only the extension; for there is nothing in the essential nature of a book that requires it to be a papcrback. But when I say "all men are 46 I. THE FIRST ACT O F T H E MIND: U N D E R S T A N D I N G mortal," I am speaking of the comprehension of "man" and seeing "mortal" in it, for man by nature has an animal body and thus is subject to death. When I say "all my books are paperbacks," I am simply reporting on what my senses tell me about all the concrete individual books I own; and what makes that proposition true or false is not the essential nature of the things it refers to (i.e. books qua books, the essential nature of books), but something accidental, contingent, uncertain, and unpredictable. But when I say "all men are mortal," I am abstract- ing the essential nature of men from the individual men I have met and making a statement about its comprehension that is universal. Universally and necessarily true statements like "all men are by nature mor- tal" are not tautologies. Tautologies are mere repetitions, like "x=x" or "x is either y or not y," or "whatever has legs and toes has toes." "Rational animals are animals" is a tautology; a computer can tell that it is self-evidcntly true. But "all men are mortal" is not a tautology; it requires insight into the comprehension of "man" to know that "all men are mortal" is necessarily true, and some people have that insight while others do not. Computers do not have the power of insight. We need more than computer logic because we are more than computers. There are enough logics around for computers, and not enough for humans.