3 acts of mind in logic

Philosophy: The Three Acts Of The Mind And My Major International Business

Guidelines for the Short Final Paper:

Content: The content of the paper will center on the three acts of the mind.

Subject Matter: Considering your major ( International Business), or a contemplated major, relate the three acts of the mind to either 1) the process of learning your major, or, 2) how you will use the principles you have learned in your major in performing the duties of your job on a daily basis

Evaluation: This instructor expects that the writing done in this course will meet certain standards. Students will incorporate Standard English usage, punctuation, grammar, and the like. Do not use slang terms or the "Urban Dictionary." No text or IM abbreviations are to be used whatsoever.

I will look for The Three Acts of the Mind – Simple Apprehension, Judgment, and Reasoning to be used, and used correctly. If they are not, appropriate deductions will be made.

The applicable sections of the Writing Intensive Course grading rubric will be used for the final paper. This rubric follows.

Length: The paper must have at least 2 pages minimum, and not more than 3 pages maximum of body text. Word-process the paper in Times New Roman Font, which will produce 21 – 22 lines of body text per page. This means that there must be from 40 to 44 lines minimum to 60 to 66 lines maximum of body text in the paper.

Format: This paper must be double-spaced throughout. If there are blank lines, they will not count toward meeting the length requirement. I will count lines if the paper appears to be short! You can use APA or MLA to document your sources. Sources should include Kreeft’s Socratic Logic, and at least one other outside source. Students may quote and cite Professor Porter’s handouts for a second source.

Writing Intensive Courses Grading Rubric: Faculty will use both sections of the rubric when grading at least one writing assignment within their course. Faculty determines available points for the Course Content section and the categories to be used. This section’s points are to total 60. Points are already determined for the Writing Skills section and all categories are to be used. Faculty may select any percentage in the appropriate range for each category when awarding points for the final paper grade.

Contents:

1) Socratic Logic by Peter Kreeft

a. The Two Logics

b. All Logic in Two Pages: An Overview (B)

c. The Three Acts of the Mind (B)

d. The First Act of the Mind: Understanding

e. The Problem of Universals

2) Gene Odening Presentation on the Trivium

a. Discussion on Cognition

b. Discussion on Grammar

I would like to recapitulate some of the concepts that were discussed at the end of the first logic

saves lives podcast. The first hour was mainly Brett and I discussing historical topics to present

some context to the narratives we’ve come to study and understand, but the last half hour we

delved into the most important aspect of the essence of logic and the rules associated with it. I

had prepared for reviewing and applying the fallacies last week to the Steve Shives presentations

we’ll be going over in later episodes, but I felt as though I might’ve lost some people with some of

the concepts presented towards the end of the podcast as I hadn’t planned to present those in

particular, which created a sort of disharmonious blend of many different ideas that might be hard

to piece together. I would like to concisely clarify some of those concepts, as they are vitally

important to understanding what logic is, what the Trivium is, and how it’s a basic description of

the mind. This short introduction is necessary to understand what an informal fallacy is, as

concept formation applies directly to the improper usage of language which creates faulty

arguments. The above table of contents is for further reading into the concepts I’ll be divulging in

this brief, but substantive description.

The ideas of logic are built upon a foundation of how the mind processes information. From

observation, we have observed three types of responses to sense stimuli. The first type would be

called the primary level, that of a direct-sense experience involving one stimulus and one

automatic response, or reflex, with no attendant memory. An example would be a doctor testing

out your reflex by applying a mallet against your knee. Your knee automatically responds to the

stimulus, with no attendant conscious action on your part. The second level is called the

perceptual level. This involves the first level, but adds a brain to the nervous system and

subsequently a memory associated with discrete units of stimulus. This memory allows us to

connect stimulus together in a causal recognition. An example would be the behavioral

conditioning of animals, whereby which they can respond to a sound or a gesture through their

sense of hearing or sight, and because of their memory they can respond, automatically, to the

behavior that has been conditioned based on the stimulus. This is automatic as well, but has a

level of complexity due to the memory of the stimulus.

The last level is the conceptual level, and builds upon the first two. This allows us to abstract, from

memory, perceptual instances and differentiate the unique characteristics associated with a

sensed phenomenon or thing in reality. An example would be using our five senses to perceive an

apple, and then form a concept that extracts the unique characteristics that are universal to all

apples, and use a symbol or sound to communicate this abstract concept to others. This level is

not automatic – it has a degree of freedom often called free will. Free will is the ability to judge,

accurately or inaccurately, the unique characteristics of a concept.

Concept formation is the foundation upon which logic is built, and it’s the beginning of the first

stage of the Trivium, which we call the General Grammar stage. I mentioned concept formation

mixed in with a host of other concepts that might’ve presented some confusion to the listeners, so

let me briefly and basically explain why this idea is so important to logic and the Trivium, and why

this is necessary to understand before we dive into applying fallacies to the language people use.

Concepts are immaterial ideas. They have no extension in space and time – you can’t measure it.

They rest upon an interaction of electrochemical machinery and impulses, but that only allows for

the potential for this phenomenon we call conscious reason, it doesn’t state what thought we will

have or how our ideas match up with reality or other people’s thoughts. Concept can be loosely

traced back to the Medieval Latin word conceptum, “draft, abstract” or classical Latin “(a thing)

conceived”. It comes from the past participle of concipere, concept, which means “to take in”.

We humans take in stimulus through our five senses, and through our nervous system and

memory we can abstract, Latin for “to draw from, to drag out of”, in other words, to extricate or

extract properties, qualities, and characteristics that we observe from the thing perceived. This is

what means it to form a concept. An example would be the apple; we can sense certain

characteristics that are in common to many different apples like colors, shapes, sizes, and tastes.

From this, we can create a concept about what makes an apple. In order to do that, there are two

properties of concept formation that are critical to philosophy and classical, Aristotelian logic.

These properties are abstraction and universals.

As I mentioned, to abstract something is Latin for to lift out of, or to extract from something

characteristics from the thing being perceived. You can think of it as our mind’s ability to compare

and contrast information to find what makes things alike or different. From this property, we can

identify what I mentioned in the first podcast as key, differentiating factors; qualities and

properties that make something truly unique compared to the other things we perceive in reality.

Those unique characteristics, through abstraction, are called universals. Universals come from the

Latin uni, one, versal, with respect to many. In other words, universals are properties and qualities

that can be said about many things that exist. An apple is a round fruit with red, yellow, or green

skin and firm white flesh. A tree is a plant that has branches, bark, and a root system. The

following examples can be said about all apples and all trees. How did I identify those

characteristics? I perceived many different apples and trees, and I was able to abstract the unique

characteristics that all apples and trees have in common. This is what we call essence in

Aristotelian logic. We see many different types of apples and trees, but we don’t see the nature of

the apple or tree, its appleness or treeness. Through abstraction, we bring all apples and trees

under one concept “apple” or “tree”, held in our mind, and communicated through language.

What definition does is to take concept formation one step further and ask you to use multiple

concepts to define new ones. It asks you to define a term, which is a word or group of words or

phrase that identifies a concept, and asks you to define it using other concepts. Man is a rational

animal. So we understand the concept man, rational, and animal all separately. But, when you

combine them together you use multiple concepts to define what is implied in the concept of

man. In other words, you’re breaking the art of abstraction into its component parts, like a

physicist reducing a force down to its component parts, to help identify the characteristics that

make something truly unique and universal. You can think of it, loosely, as the formula logicians

use to help identify the universal essence to a concept. The way this is done is by identifying the

genus, or the general characteristics that are in common to man, in contrast to the specific

difference, or the properties that make man different. In this case, the genus would be animal,

and the specific difference would be rational. Man is a rational animal. From this, you can glean

what question this answers, thereby relating it to what category, in existence, this belongs.

So now we have a very basic understanding of what a concept is, and how it relies on two

properties to create a concept; abstraction and universals, which identify the essence of a

concept, and the “formula” used to define concepts (definition of concept = genus + specific

difference). Once we identify the essence of a concept, the universal, we tend to group them into

categories based on the unique characteristics of the concept. In the general grammar stage,

Gene Odening presented a definition of existence, which is every substance, action, attribute, and

relationship that is, was, or ever will be. This definition relates to the concepts of existence;

substance is every noun and pronoun, actions are verbs, attributes are adjectives and adverbs, and

relationships are prepositions and conjunctions. An apple is a round fruit with red, yellow, or

green skin and firm white flesh. Now, as you continue to break concepts down, by definition, to

include all of the real, perceivable aspects a thing or entity might have in existence, you end up

with Aristotle’s ten categories of being. An example would be the concept of an apple. The apple

is a fruit, but what’s a fruit? A fruit is a seed-bearing structure that develops from the ovary of a

flowering plant. But what’s a plant? Plants are multicellular eukaryotes. As you continue to ask

more questions about what something is, you lose comprehension but gain extension; in other

words the terms have less meaning but apply to more and more things in reality. Aristotle was the

first to abstract to the most general categories that represent all real things that exist – abstracted

from sense perception and understood and communicated through language.

If we go back to the apple example, we can apply the definition of an apple to the general

categories of being, or the definition of existence. An apple is a fruit-(substance) with-

(relationship) red-(attribute), yellow-(attribute), or-(relationship) green-(attribute) skin-

(substance) and-(relationship) firm-(attribute) white-(attribute) flesh-(substance). This simple

example can be extrapolated to all types of definitions and be shown to relate to the categories of

reality and the definition of existence.

We have a clear line from how our minds interpret stimulus, to developing concepts using

abstractions to identify universal essences in things, to formulating definitions and relating the

most general categories of reality to which all real things belong and showing how language

relates to those basic categories. This is the total subject of general grammar. The long, arduous

terminology can be summed up by saying our mind compares and contrasts information it has

perceived from our five senses, and makes a judgment, through language, as to what something is

or not. Now, in the general grammar stage your listeners will be familiar with the 5 W’s + How.

Who, what, where, when, why, and how. These questions effectively answer to the concepts of

existence by identifying one of the main constituent categories implied in existence. Similar to the

physicist metaphor, we’re doing the same thing here with logic. I broke down what the general

grammar stage is based on how we develop and define a concept, which leads up to the five

simple questions we ask to start gathering and categorizing data. This is how the mind works.

As a last note, the history of philosophy is basically a history of man’s ability to abstract and create

universal concepts. There is a philosophic war about the reality of universals that has been going

on since the beginnings of philosophy. This is effectually what was destroyed towards the end of

the 19 th

and the beginning of the 20 th

centuries with the new psychology and radical empiricism

that denied metaphysics for a mechanized viewpoint of the human being, which continues today

through philosophies and scientific endeavors such as cybernetics, and transhumanism. If people

are interested in understanding the “war on universals” I will refer them to the contents in the

beginning of this document and follow the link to “The Problem of Universals”.

Section 3. The two logics (P) (This section can be omitted without losing anything you will need later on in the

book. It's here both to satisfy the advanced student's curiosity and to sell the

approach of this book to prospective teachers who may question its emphasis on

Aristotelian rather than symbolic logic, by justifying this choice philosophically.)

16 INTRODUCTION

Almost four hundred years before Christ, Aristotle wrote the world's first logic

textbook. Actually it was six short books, which collectively came to be

known as the Organon, or "instrument." From then until 1913, when Bertrand

Russell and Alfred North Whitehead published Principia Mathematica, the

firstclassic of mathematical or symbolic logic, all students learned Aristotelian

logic, the logic taught in this book.

The only other "new logic" for twenty-four centuries was an improvement on

the principles of inductive logic by Francis Bacon's Novum Organum ("New Or-

ganon"), in the 17th century, and another by John Stuart Mill, in the 19th century.

(Inductive reasoning could be very roughly and inadequately defined as

reasoning from concrete particular instances, known by experience, while

deduction reasons from general principles. Induction yields only probability,

while deduction yields certainty. "Socrates, Plato and Aristotle are mortal, there•

fore probably all men are mortal" is an example of inductive reasoning; "All

men are mortal, and Socrates is a man, therefore Socrates is mortal" is an exam•

ple of deductive reasoning.)

Today nearly all logic textbooks use the new mathematical, or symbolic,

logic as a kind of new language system for deductive logic. (It is not a new logic;

logical principles are unchangeable, like the principles of algebra. It is more like

changing from Roman numerals to Arabic numerals.) There are at least three

reasons for this change:

(1) The first and most important one is that the new logic really is superior

to the old in efficiency for expressing many long and complex arguments, as Arabic

numerals are to Roman numerals, or a digital computer to an analog computer, or writing in

shorthand to writing in longhand.

However, longhand is superior to shorthand in other ways: e.g. it has more

beauty and elegance, it is intelligible to more people, and it gives a more per•

sonal touch. That is why most people prefer longhand most of the time - as most

beginners prefer simpler computers (or even pens). It is somewhat similar in

logic: most people "argue in longhand," i.e. ordinary language; and Aristotelian

logic stays close to ordinary language. That is why Aristotelian logic is more

practical for beginners.

Even though symbolic language is superior in sophistication, it depends on

commonsense logic as its foundation and root. Thus you will have a firmer foun•

dation for all advanced logics if you first master this most basic logic. Strong

roots are the key to healthy branches and leaves for any tree. Any farmer knows

that the way to get better fruit is to tend the roots, not the fruits. (This is only an

analogy. Analogies do not prove anything - that is a common fallacy - they only

illuminate and illustrate. But it is an illuminating analogy.)

Modern symbolic logic is mathematical logic. "Modern symbolic logic has

been developed primarily by mathematicians with mathematical applications in

mind." This from one of its defenders, not one of its critics (Henry C. Bayerly,

in A Primer of Logic. N.Y.: Harper & Row, 1973, p.4).

Mathematics is a wonderful invention for saving time and empowering sci•

ence, but it is not very useful in most ordinary conversations, especially philo•

sophical conversations. The more important the subject matter, the less relevant

The two logics 17

mathematics seems. Its forte is quantity, not quality. Mathematics is the only

totally clear, utterly unambiguous language in the world; yet it cannot say any•

thing very interesting about anything very important. Compare the exercises in

a symbolic logic text with those in this text. How many are taken from the Great

Books? How many are from conversations you could have had in real life?

(2) A second reason for the popularity of symbolic logic is probably its

more scientific and exact form. The very artificiality of its language is a plus for

its defenders. But it is a minus for ordinary people. In fact, Ludwig Wittgenstein,

probably the most influential philosophical logician of the 20th century, admit•

ted, in Philosophical Investigations, that "because of the basic differences

between natural and artificial languages, often such translations [between natu•

ral-language sentences and artificial symbolic language] are not even possible

in principle." "Many logicians now agree that the methods of symbolic logic are

of little practical usefulness in dealing with much reasoning encountered in real-

life situations" (Stephen N. Thomas, Practical Reasoning in Natural Language,

Prentice-Hall, 1973).

- And in philosophy! "However helpful symbolic logic may be as a tool of

the . . . sciences, it is [relatively] useless as a tool of philosophy. Philosophy aims

at insight into principles and into the relationship of conclusions to the princi•

ples from which they are derived. Symbolic logic, however, does not aim at giv•

ing such insight" (Andrew Bachhuber, Introduction to Logic (New York: Appleton-

Cenrury Crofts, 1957), p. 318).

(3) But there is a third reason for the popularity of symbolic logic among

philosophers, which is more substantial, for it involves a very important differ•

ence in philosophical belief. The old, Aristotelian logic was often scorned by

20th century philosophers because it rests on two commonsensical but unfash•

ionable philosophical presuppositions. The technical names for them are "epis-

temological realism" and "metaphysical realism." These two positions were held

by the vast majority of all philosophers for over 2000 years (roughly, from

Socrates to the 18th century) and are still held by most ordinary people today,

since they seem so commonsensical, but they were not held by many of the

influential philosophers of the past three centuries.

(The following summary should not scare off beginners; it is much more

abstract and theoretical than most of the rest of this book.)

The first of these two presuppositions, "epistemological realism," is the

belief that the object of human reason, when reason is working naturally and

rightly, is objective reality as it really is; that human reason can know objective

reality, and can sometimes know it with certainty; that when we say "two apples

plus two apples must always be four apples," or that "apples grow on trees," we

are saying something true about the universe, not just about how we think or

about how we choose to use symbols and words. Today many philosophers are

18 INTRODUCTION

skeptical of this belief, and call it naive, largely because of two 18th century

"Enlightenment" philosophers, Hume and Kant.

Hume inherited from his predecessor Locke the fatal assumption that the

immediate object of human knowledge is our own ideas rather than objective

reality. Locke naively assumed that we could know that these ideas "corre•

sponded" to objective reality, somewhat like photographs; but it is difficult to

see how we can be sure any photograph accurately corresponds to the real object

of which it is a photograph if the only things we can ever know directly are pho•

tographs and not real objects. Hume drew the logical conclusion of skepticism

from Locke's premise.

Once he limited the objects of knowledge to our own ideas, Hume then dis•

tinguished two kinds of propositions expressing these ideas: what he called

"matters of fact" and "relations of ideas."

What Hume called "relations of ideas" are essentially what Kant later called

"analytic propositions" and what logicians now call "tautologies": propositions

that are true by definition, true only because their predicate merely repeats all or

part of their subject (e.g. "Trees are trees" or "Unicorns are not non-unicorns"

or "Unmarried men are men").

What Hume called "matters of fact" are essentially what Kant called "syn•

thetic propositions," propositions whose predicate adds some new information

to the subject (like "No Englishman is 25 feet tall" or "Some trees never shed

their leaves"); and these "matters of fact," according to Hume, could be known

only by sense observation. Thus they were always particular (e.g. "These two

men are bald") rather than universal (e.g. "All men are mortal"), for we do not

sense universals (like "all men"), only particulars (like "these two men").

Common sense says that we can be certain of some universal truths, e.g.,

that all men are mortal, and therefore that Socrates is mortal because he is a

man. But according to Hume we cannot be certain of universal truths like "all

men are mortal" because the only way we can come to know them is by gener•

alizing from particular sense experiences (this man is mortal, and that man is

mortal, etc.); and we cannot sense all men, only some, so our generalization can

only be probable. Hume argued that particular facts deduced from these only-

probable general principles could never be known or predicted with certainty. If

it is only probably true that all men are mortal, then it is only probably true that

Socrates is mortal. The fact that we have seen the sun rise millions of times does

not prove that it will necessarily rise tomorrow.

Hume's "bottom line" conclusion from this analysis is skepticism: there is

no certain knowledge of objective reality ("matters of fact"), only of our own

ideas ("relations of ideas"). We have only probable knowledge of objective real•

ity. Even scientific knowledge, Hume thought, was only probable, not certain,

because science assumes the principle of causality, and this principle, according

to Hume, is only a subjective association of ideas in our minds. Because we have

seen a "constant conjunction" of birds and eggs, because we have seen eggs

The two logics 19

follow birds so often, we naturally assume that the bird is the cause of the egg.

But we do not see causality itself, the causal relation itself between the bird and

the egg. And we certainly do not see (with our eyes) the universal "principle of

causality." So Hume concluded that we do not really have the knowledge of

objective reality that we naturally think we have. We must be skeptics, if we are

only Humean beings.

Kant accepted most of Hume's analysis but said, in effect, "I Kant accept

your skeptical conclusion." He avoided this conclusion by claiming that human

knowledge does not fail to do its job because its job is not to conform to objec•

tive reality (or "things-in-themselves," as he called it), i.e. to correspond to it or

copy it. Rather, knowledge constructs or forms reality as an artist constructs or

forms a work of art. The knowing subject determines the known object rather

than vice versa. Human knowledge does its job very well, but its job is not to

learn what is, but to make what is, to form it and structure it and impose mean•

ings on it. (Kant distinguished three such levels of imposed meanings: the two

"forms of apperception": time and space; twelve abstract logical "categories"

such as causality, necessity, and relation; and the three "ideas of pure reason":

God, self, and world.) Thus the world of experience is formed by our knowing it

rather than our knowledge being formed by the world. Kant called this idea his

"Copernican Revolution in philosophy." It is sometimes called "epistemological

idealism" or "Kantian idealism," to distinguish it from epistemological realism.

("Epistemology" is that division of philosophy which studies human know•

ing. The term "epistemological idealism" is sometimes is used in a different way,

to mean the belief that ideas rather than objective reality are the objects of our

knowledge; in that sense, Locke and Hume are epistemological idealists too. But

if we use "epistemological idealism" to mean the belief that the human idea (or

knowing, or consciousness) determines its object rather than being determined

by it, then Kant is the first epistemological idealist.)

The "bottom line" for logic is that if you agree with either Hume or Kant,

logic becomes the mere manipulation of our symbols, not the principles for a

true orderly knowledge of an ordered world. For instance, according to episte•

mological idealism, general "categories" like "relation" or "quality" or "cause"

or "time" are only mental classifications we make, not real features of the world

that we discover.

In such a logic, "genus" and "species" mean something very different than

in Aristotelian logic: they mean only any larger class and smaller sub-class that

we mentally construct. But for Aristotle a "genus" is the general or common part

of a thing's real essential nature (e.g. "animal" is man's genus), and a "species"

is the whole essence (e.g. "rational animal" is man's species). (See Chapter III,

Sections 2 and 3.)

Another place where modern symbolic logic merely manipulates mental

symbols while traditional Aristotelian logic expresses insight into objective real•

ity is the interpretation of a conditional (or "hypothetical") proposition such as

20 INTRODUCTION

"If it rains, I will get wet." Aristotelian logic, like common sense, interprets this

proposition as an insight into real causality: the rain causes me to get wet. I am

predicting the effect from the cause. But symbolic logic does not allow this com-

monsensical, realistic interpretation. It is skeptical of the "naive" assumption of

epistemological realism, that we can know real things like real causality; and

this produces the radically anti-commonsensical (or, as they say so euphemisti•

cally, "counter-intuitive") "problem of material implication" (see page 23).

Besides epistemological realism, Aristotelian logic also implicitly assumes

metaphysical realism. (Metaphysics is that division of philosophy which inves•

tigates what reality is; epistemology is that division of philosophy which inves•

tigates what knowing is.) Epistemological realism contends that the object of

intelligence is reality. Metaphysical realism contends that reality is intelligible;

that it includes a real order; that when we say "man is a rational animal," e.g.,

we are not imposing an order on a reality that is really random or chaotic or

unknowable; that we are expressing our discovery of order, not our creation of

order; that "categories" like "man" or "animal" or "thing" or "attribute" are

taken from reality into our language and thought, not imposed on reality from

our language and thought.

Metaphysical realism naturally goes with epistemological realism.

Technically, metaphysical realism is the belief that universal concepts corre•

spond to reality; that things really have common natures; that "universals" such

as "human nature" are real and that we can know them.

There are two forms of metaphysical realism: Plato thought that these uni•

versals were real things in themselves, while Aristotle thought, more common-

sensically, that they were real aspects of things which we mentally abstracted

from things. (See Chapter II, Section 3, "The Problem of Universals.")

The opposite of realism is "nominalism," the belief that universals are only

man-made nomini (names). William of Ockham (1285-1349) is the philosopher

who is usually credited (or debited) with being the founder of nominalism.

Aristotelian logic assumes both epistemological realism and metaphysical

realism because it begins with the "first act of the mind," the act of understand•

ing a universal, or a nature, or an essence (such as the nature of "apple" or

"man"). These universals, or essences, are known by concepts and expressed by

what logic calls "terms." Then two of these universal terms are related as sub•

jects and predicates of propositions (e.g. "Apples are fruits," or "Man is mor•

tal").

"Aristotle never intended his logic to be a merely formal calculus [like

mathematics]. He tied logic to his ontology [metaphysics]: thinking in concepts

presupposes that the world is formed of stable species" (J. Lenoble, La notion de

I'experience, Paris, 1930, p. 35).

Symbolic logic is a set of symbols and rules for manipulating them, with•

out needing to know their meaning and content, or their relationship to the real

world, their "truth" in the traditional, commonsensical sense of "truth." A

The two logics 21

computer can do symbolic logic. It is quantitative (digital), not qualitative. It is

reducible to mathematics.

The new logic is sometimes called "propositional logic" as well as "mathe•

matical logic" or "symbolic logic" because it begins with propositions, not

terms. For terms (like "man" or "apple") express universals, or essences, or

natures; and this implicitly assumes metaphysical realism (that universals are

real) and epistemological realism (that we can know them as they really are).

Typically modern philosophers criticize this assumption as naive, but it

seems to me that this is a very reasonable assumption, and not naive at all. Is it

too naive to assume that we know what an apple is? The new logic has no means

of saying, and even prevents us from saying, what anything is!

And if we cease to say it, we will soon cease to think it, for there will be no

holding-places in our language for the thought. Language is the house of

thought, and homelessness is as life-threatening for thoughts as it is for people.

If we should begin to speak and think only in nominalist terms, this would be a

monumental historic change. It would reverse the evolutionary event by which

man rose above the animal in gaining the ability to know abstract universals. It

would be the mental equivalent of going naked on all fours, living in trees, and

eating bugs and bananas. (Could monkeys have evolved by natural selection

from nominalists?)

While it may be "extremist" to suggest it, such a mental "devolution" is not

intrinsically impossible. And changes in logic are not wholly unrelated to it.

Already, "internet logic," or the logic of spontaneous association by "keywords,"

is replacing "genus and species logic," or the logic of an ordered hierarchy of

objectively real categories. To most modern minds, those last seven words sound

almost as archaic as alchemy or feudalism. Many criticize them as ideological•

ly dangerous. These critics dislike categories because they "feel that" (that

phrase is a category confusion, by the way) classifications, and universal state•

ments about classes such as "Hittites could not read Hebrew," constitute "preju•

dice," "judgmentalism," "oppression," or even "hate speech."

Logic and social change are not unrelated. Not only our logicians but also

our society no longer thinks primarily about the fundamental metaphysical ques•

tion, the question of what things are, the question of the nature of things.

Instead, we think about how we feel about things, about how we can use them,

how we see them behave, how they work, how we can change them, or how we

can predict and control their behavior by technology. But all this does not raise

us above the animal level in kind, only in degree. The higher animals too have

feelings, and things to use, and sight, and action, and even a kind of technology

of behavior prediction and control. For the art of hunting is an art of predicting

and controlling the behavior of other animals. What do we have that no mere ani•

mal has? The thing that many modern philosophers vilify: abstraction. We have

the power to abstract and understand universals. This is the thing traditional

logic is founded on, and this is the thing symbolic logic ignores or denies.

22 INTRODUCTION

Logic is deeply related to moral and ethical changes in both thought and

practice. All previous societies had a strong, nearly universal, and rarely ques•

tioned consensus about at least some basic aspects of a "natural moral law,"

about what was "natural" and what was "unnatural." There may not have been a

greater obedience to this law, but there was a much greater knowledge of it, or

agreement about it. Today, especially in the realm of sex (by far the most radi•

cally changed area of human life in both belief and practice), our more

"advanced" minds find the old language about "unnatural acts" not only "polit•

ically incorrect" but literally incomprehensible, because they no longer accept

the legitimacy of the very question of the "nature" of a thing. Issues like homo•

sexuality, contraception, masturbation, pedophilia, incest, divorce, adultery,

abortion, and even bestiality are increasingly debated in other terms than the

"nature" of sexuality, or the "nature" of femininity and masculinity. It is not an

unthinkable suspicion that one of the most powerful forces driving the new logic

is more social than philosophical, and more sexual than logical.

Symbolic logic naturally fosters utilitarian ethics, which is essentially an

ethic of consequences. The fundamental principle of utilitarianism is that an act

is good if its probable consequences result in "the greatest happiness for the

greatest number" of people. It is an "if. . . then . . ." ethics of calculating con•

sequences - essentially, "the end justifies the means" (though that formula is

somewhat ambiguous). Symbolic logic fits this perfectly because it is essential•

ly an "if. . . then . . . " logic, a calculation of logical consequences. Its basic unit

is the proposition (p or q) and its basic judgment is "if p then q." In contrast,

Aristotelian logic naturally fosters a "natural law ethic," an ethic of universal

principles, based on the nature of things, especially the nature of man. For its

basic unit is the term, a subject (S) or a predicate (P) within a proposition (p);

and its basic judgment is "all S is P" - a statement of universal truth about the

nature of S and P.

The very nature of reason itself is understood differently by the new sym•

bolic logic than it was by the traditional Aristotelian logic. "Reason" used to

mean essentially "all that distinguishes man from the beasts," including intu•

ition, understanding, wisdom, moral conscience, and aesthetic appreciation, as

well as calculation. "Reason" now usually means only the last of those powers.

That is why many thinkers today who seem at first quite sane in other ways actu•

ally believe that there is no fundamental difference between "natural intelli•

gence" and "artificial intelligence" - in other words, you are nothing but a com•

puter plus an ape. (Having met some of these people at MIT, I must admit that

their self-description sometimes seems quite accurate.)

Aristotelian logic is not exact enough for the nominalistic mathematical logi•

cian, and it is too exact for the pop psychology subjectivist or New Age mystic.

Out at sea there between Scylla and Charybdis, it reveals by contrast the double

tragedy of modern thought in its alienation between form and matter, structure

The two logics 23

and content, validity and meaning. This alienated mind was described memo•

rably by C.S. Lewis: "the two hemispheres of my brain stood in sharpest con•

trast. On the one hand, a glib and shallow rationalism. On the other, a many-

islanded sea of myth and poetry. Nearly all that I loved, I believed subjective.

Nearly all that was real, I thought grim and meaningless" (Surprised by Joy).

Neither mathematical logic nor "experience" can heal this gap; but Aristotelian

logic can. It is thought's soul and body together, yet not confused. Mathematical

logic alone is abstract and "angelistic," and sense experience and feeling alone

is concrete and "animalistic," but Aristotelian logic is a human instrument for

human beings.

Aristotelian logic is also easier, simpler, and therefore time-saving. For

example, in a logic text book misleadingly entitled Practical Reasoning in

Natural Language, the author takes six full pages of symbolic logic to analyze a

simple syllogism from Plato's Republic that proves that justice is not rightly

defined as "telling the truth and paying back what is owed" because returning a

weapon to a madman is no? justice but it is telling the truth and paying back what

is owed. (pp. 224-30). Another single syllogism of Hume's takes eight pages to

analyze (pp. 278-86).

I have found that students who are well trained in Aristotelian logic are

much better at arguing, and at understanding arguments, than students who are

trained only in symbolic logic. For Aristotelian logic is the logic of the four most

basic verbal communication arts: reading, writing, listening, and speaking. It is

the logic of Socrates. If you want to be a Socrates, this is the logic you should

begin with.

The old logic is like the old classic movies: strong on substance rather than

sophistication. The new logic is like typically modern movies: strong on "spe•

cial effects" but weak on substance (theme, character, plot); strong on the tech•

nological "bells and whistles" but weak on the human side. But logic should be

a human instrument; logic was made for man, not man for logic.

26 INTRODUCTION

Section 4. All of logic in two pages: an overview (B)

This is one of the shortest and simplest sections in this book, but it is also one of the most

important, for it is the foundation for everything else in logic. If you do not understand it clearly,

you will be hopelessly confused later on. (It is explained in more detail in the next section,

Section 5.)

The ancient philosophers defined Man as the "rational animal." To be human is (among other

things) to reason, to give reasons for believing things to be true.

We can see common forms, or structures, in all human reasoning, no mat• ter what the

contents, or objects, that we reason about. Logic studies those structures.

The fundamental structure of all reasoning is the movement of the mind from premises to a

conclusion. The conclusion is what you are trying to prove to be true; the premises are the

reasons or evidence for the truth of the conclu• sion.

The two basic kinds of reasoning are inductive and deductive. Inductive reasoning reasons from

particular premises (e.g. "I' m mortal" and "You're mortal" and "He's mortal" and "She's

mortal"), usually to a more general or universal conclusion (e.g. "All men are mortal").

Deductive reasoning reasons from at least one general, or universal premise (e.g. "All men are

mortal") usu• ally to a more particular conclusion (e.g. "I am mortal"). Inductive reasoning

yields only probability, not certainty. (It is not certain that all men are mortal merely on the

basis that four men, or 4 million, are.) Deductive reasoning, when correct, yields certainty. (It

is certain that if all men are mortal, and if I am a man, then I am mortal.)

A deductive argument succeeds in proving its conclusion to be true if and only if three

conditions are met. These are the three check points of any deductive argument.

(1) First, all the terms must be clear and unambiguous. If a term is

ambiguous, it should be defined, to make it clear. Otherwise, the two parties to the argument

may think they are talking about the same thing when they are not.

(2) Second, all the premises must be true. You can (seem to) "prove" any•

thing from false premises: e.g. "All Martians are infallible, and I am a Martian,

therefore I am infallible."

(3) Third, the argument must be logically valid. That is, the conclusion

must necessarily follow from the premises, so that if 'the premises are true, then

the conclusion must be true.

All of logic in two pages: an overview 27

(1) A "term" in logic is the subject or the predicate of a proposition (a

declarative sentence). Terms are either clear or unclear. Terms cannot be either true or false. E.g.

"mortal" is neither true nor false. The proposition "All men are mortal" is true, and the

proposition "Some men are not mortal" is false.

(2) Propositions are declarative sentences. They are either true or false.

"True," in commonsense usage, means "corresponding to reality," and "false" means the

opposite. There is no one simple and infallible way of telling whether any proposition is true or

false.

(3 ) There is, however, a fairly simple and truly infallible way of telling whether an argument is

valid or invalid: the laws of logic, which you will learn in this book.

A deductive argument is logically valid if its conclusion necessarily fol• lows from its

premises, invalid if it does not. There are various forms of argu• ment, and each form has its

own inherent rules for validity.

All the rules for each form of argument are natural to that form of argu• ment and to the

human mind. If at any point in this book you think that any of its logical laws contradict what

you already implicitly know by innate common sense, please stop and check; for you must be

misunderstanding either the laws of logic or what you think common sense tells you, for logic

does nothing more than make explicit the rules everyone knows innately by common sense.

Arguments are made up of propositions (premises and a conclusion), and propositions are

made up of terms (subject and predicate). Terms are either clear or unclear. Propositions

(whether premises or the conclusion) are either true or false. Arguments are either logically

valid or invalid. Only terms can be clear or unclear; only propositions can be true or false;

only arguments can be logically valid or invalid.

So the three questions you should habitually ask of yourself when writ• ing or speaking,

and of others when you are reading or listening to them, are:

(1) Are the terms all clear and unambiguous?

(2) Are the premises all true?

(3) Is the reasoning all logically valid?

If the answer to all three of these questions is Yes, then the conclusion of the argument must

be true.

So in order to disagree with any conclusion, you must show that there is either (1) an

ambiguous term, or (2) a false premise, or (3) a logical fal• lacy in the argument such that

the conclusion does not necessarily follow from the premises. (You will soon learn the rules

for judging that.) If you cannot do any of these three things, then honesty demands that you

admit that the con• clusion has been proved to be true. (All this applies to deductive

arguments only; inductive arguments do not claim certainty.)

28 INTRODUCITON

Section 5. The three acts of the mind (B) This section gives you the outline for all of logic. It is an expansion of the pre• vious section

(Section 4) and a summary of the rest of the book.

The basis for the science and art of logic is two facts: the fact that human beings think, and

the fact that thought has a structure. That structure can be clas• sified from various points of

view and for various purposes. For instance, a physiologist or physician might distinguish brain

activity of the autonomic nerv• ous system (e.g. breathing) from activity of the frontal lobes

(self-conscious thought). A moralist might distinguish thoughts that are voluntary, and under our

control, from those that are involuntary, since we are responsible only for what is under our

control. A Marxist would distinguish thoughts supposedly produced by a Capitalist system from

those produced by a Communist system. But from the viewpoint of logic, we distinguish three

kinds of thoughts, three "acts of the mind":

1. Simple apprehension

2. Judging

3. Reasoning

"Simple apprehension" is a technical term. It means basically "conceiving," "understanding," or

"comprehending" one object of thought, one concept, such as 'mortal' or 'man' or 'triangle' or

'triangle with unequal angles.' Animals apparently cannot perform this act of understanding; if

they can, they do not express it in words. Computers certainly cannot do this; a computer no

more understands what you program into it than a library building understands the

information in the books you put into it.

Judging is more complex than simple apprehension. Instead of just thinking one concept, like

'man,' it relates two concepts, like "man" and "mortal," to each other by predicating one term

(the predicate) of the other (the subject) in judg• ing that, e.g., "Man is mortal" or "Man is not

a triangle."

As judging is more complex than simple apprehension, reasoning is more complex than

judging. As judging moves from one act of simple apprehension (the subject) to another (the

predicate), reasoning moves from two or more judg• ments (the premises, or assumptions) to

another (the conclusion) in arguing that if the premises are true, then the conclusion must be

true. E.g. "All men are mor• tal, and I am a man, therefore I am mortal," or "A man is not a

triangle, and that is a triangle, therefore that is not a man."

The mental products produced in the mind by the three acts of the mind are:

1. Concepts (the products of conceiving)

2. Judgments (the products of judging)

3. Arguments (the products of reasoning, or arguing)

Distinguishing between the acts and their objects is not crucial for logic.

What is crucial is distinguishing the three acts, and the three objects.

The three acts of the mind 29

These three mental entities (concepts, judgments, and arguments) are expressed in logic as:

1. Terms

2. Propositions

3. Arguments (the most usual form of which is the syllogism)

They are expressed in language as:

1. Words or phrases (less than a complete sentence)

2. Declarative sentences

3. Paragraphs, or at least two or more declarative sentences connected by

a word like 'therefore' which indicates an argument

Examples:

l ."Man"

2. "Socrates is a man."

3. "All men are mortal, and Socrates is a man, therefore Socrates is mortal."

(Logic does not deal with interrogative sentences (questions, like "What time is it?"), imperative

sentences (commands or requests, like "Pass the mus• tard, please"), exclamatory sentences

(like "Oh! Wow! What a hit!"), or perfor• mative sentences (like "I dub thee knight"), but only

with declarative sentences, sentences that claim to state a truth.) Non-declarative sentences are

not proposi• tions.

The difference between logic and language is (1) that languages are man- made artifices and

therefore (2) there are many languages that are different in place and time, while (1) logic is

not made but discovered, and (2) there is only one logic. There is no "Chinese logic" or

"American logic," no "19th century logic" or "20th century logic," or even "masculine

logic"«or "feminine logic," just logic. (What is often called "feminine logic" is intuition rather

than logic: a formidable and invaluable power of the mind but not teachable by textbooks.)

Like mathematics, logic is objective, universal, and unchangeable in its basic laws or

principles. But the forms in which these unchangeable laws of logic are expressed are

linguistic forms, and these forms are changing and varied.

A term has no structural parts. It is a basic unit of meaning, like the num• ber one in math or

like an atom in the old atomic theory (when they believed atoms were unsplittable and had

no parts).

A proposition has two structural parts: the subject term and the predicate term. The subject

term is what you 're talking about. The predicate term is what you say about the subject. The word

"subject" and "predicate" mean the same thing in logic as in grammar.

An argument has two structural parts: the premises and the conclusion. The premises are the

propositions that are assumed. They are the reasons or evidence for the conclusion. The

conclusion is the proposition that you are trying to prove.

30 INTRODUCTION

For instance, in the classic example "All men are mortal, and I am a man, therefore I am

mortal," the argument is everything inside the quotation marks. The two premises are (a) "All

men are mortal" and (b) "I am a man." The con• clusion is "I am mortal." The subject of the

first premise is "men" and the pred• icate is "mortal;" the subject of the second premise is "I"

and the predicate is "a man;" and the subject of the conclusion is "I" and the predicate is

"mortal."

Structural parts of a term: none

Structural parts of a proposition: subject term & predicate term Structural parts of an

argument: premises & conclusion

We can think of the subject and predicate terms as two rooms which togeth• er make up one

floor of a building (say, a town house). Each floor is a proposi• tion. A syllogism is a building

with three floors. The rooms are the parts of the floors, and the floors are the parts of the

building.

1 st premise

2nd premise y. argument

conclusion

These three logical entities answer three different questions, the three most fundamental

questions we can ask about anything:

1. A term answers the question what it is.

2. A proposition answers the question whether it is.

3. An argument answers the question why it is.

1. "What are we talking about? "Man."

2. "What are we saying about it?" "That man is mortal."

3. "Why is it mortal?" "Because man is an animal, and all animals are mor•

tal, therefore man is mortal."

Terms, propositions, and arguments reveal three different aspects of reality:

1. Terms reveal essences (what a thing is).

2. Propositions reveal existence (whether it is).

3. Arguments reveal causes (why it is).

This (above) is the theoretical basis for the practical art of logic. The prac• tical art consists in

discriminating between clear and unclear (ambiguous) terms, true and false propositions, and

logically valid and invalid arguments.

Logic is a (practical) art as well as a (theoretical) science. Therefore it does not only tell us

what is but also what should be; it not only reveals these three fundamental logical structures

but also judges and tries to improve them. For all three can be either logically good or logically

bad: