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Word Gems 

exploring self-realization, sacred personhood, and full humanity

Dr. Mortimer J. Adler's 

Six Great Ideas

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If we turn now from judgments that we make in the practical
affairs of daily life to the conclusions of historical research, to
the findings, hypotheses, and theories of the investigative sci-
ences, and even to certain branches of mathematics, the same
criteria function to place in the realm of doubt a fairly large
portion of what these learned disciplines offer us as knowledge.
 

This assessment may appear shocking to those who, distin-
guishing between knowledge on the one hand and opinion or
belief on the other hand, regard history, science, and mathe-
matics as branches of organized knowledge, not as collections
of mere opinions or beliefs.

The world "knowledge" for them has the connotation of
truth; in fact, it is inseparable from it. There cannot be false
knowledge, as there can be false opinions and beliefs. The
phrase "true knowledge" is redundant; the phrase "false
knowledge" is self-contradictory.

However, those who hold this view acknowledge that there
is progress in these disciplines. They as well as everyone else
speak of the advancement of learning in all these fields. They
attribute it to new discoveries, improved observations, the de-
velopment of sounder hypotheses, the substitution of more
comprehensive theories for less comprehensive ones, more
elaborate and more precise analysis or interpretation of the data
at hand, and rectified or more rigorous reasoning. Less ade-
quate formulations are replaced by better ones—better because
they are thought more likely to be true, or nearer to the truth
being sought and, therefore, better approximations of it.

In short, all these branches of organized knowledge have a
future, a future they would not have if the present found them
in possession of judgments about what is true or false that had
finality and incorrigibility. To whatever extent history, science,
and mathematics have a future, to that same extent these bodies
of "knowledge" belong in the realm of doubt, not in the realm
of certitude.

I put the word "knowledge" in quotation marks because the
word has two meanings, not one. The same holds for the word
"opinion." The recognition of the two senses in which we use
these words will overcome the shock initially experienced by
those who recoiled from locating history, science, and
mathematics in the realm of doubt, because they are accus-
tomed to regarding them as branches of knowledge, not as col-
lections of opinions or beliefs.

Let us first consider the meaning of the word "knowledge"
that has already been mentioned. It is the sense in which
knowledge cannot be false and, therefore, has the infallibility,
finality, and incorrigibility that are attributes of judgments in
the realm of certitude. Let us call this the strong sense of the
term.

At the opposite extreme from knowledge in this strong sense
is opinion in the weak sense of that term. When we use the
word "opinion" in this sense, we refer to judgments on our
part that are no more than personal predilections or prejudices.
We have no basis for them, either empirical or rational. We
cannot support them by appeal to carefully accumulated evi-
dence or by appeal to reasoning that gives them credibility. We
do not, in short, have sufficient reason for claiming that they
are more likely to be true than are their opposites.

We prefer the opinions to which we are attached on emo-
tional, not rational, grounds. Our attachment to them is arbi-
trary and voluntary—an act of will on our part, whatever its
causes may be. Since we may just as capriciously adopt the
opposite view, unfounded opinions of this sort fall to the low-
est level of the realm of doubt.

In between these two extremes lie judgments that can be
called knowledge in the weak sense of that term and opinion in
the strong sense of that term.

Here we have judgments that are
neither arbitrary nor voluntary, judgments we have rational
grounds for adopting, judgments the probability of which we
can appraise in the light of all the evidence available at the
moment and in the light of the best thinking we can do—the
best analysis and interpretation we can make of that evidence,
again at the moment.

At the moment! The future holds in store the possibility of
additional or improved evidence and amplified or rectified rea-
soning. That fact, as we have seen, places such judgments in
the realm of doubt. They have the aspect of opinion because
they may turn out to be false rather than true, but they also
have the aspect of knowledge because, at the moment, we have
no reason to doubt them. They are beyond reasonable doubt,
but not beyond that shadow of a doubt, from which they cannot
escape because they have a future.

Readers who have followed the argument so far may begin to
wonder whether the realm of certitude is a completely empty-
domain. If not, what sort of judgments can we expect to find
there?

The answer I am about to give applies not only to judgments
we make in the course of our daily lives, judgments ordinarily
made by persons of common sense, even the judgments such
persons may come to make when their common sense is en¬
lightened by philosophical reflection. It also applies to judg¬
ments in the field of mathematics and in some, if not all, of the
empirical sciences.

Truths called self-evident provide the most obvious examples
of knowledge in the strong sense of that term. They are called
self-evident because our affirmation of them does not depend
on evidence marshaled in support of them nor upon reasoning
designed to show that they are conclusions validly reached by
inference. We recognize their truth immediately or directly
from our understanding of what they assert. We are convinced
—convinced, not persuaded—of their truth because we find it
impossible to think the opposite of what they assert. We are in
no sense free to think the opposite.

Self-evident truths are not tautologies, trifling and uninstruc-
tive, such as the statement “All triangles’ have three sides." A
triangle being defined as a three-sided figure, we learn nothing
from that statement. Contrast it with the statement, “No trian-
gle has any diagonals," which is both self-evident and instruc-
tive, not a tautology.

The self-evidence of the truth of the latter statement derives
immediately from our understanding of the definition of a tri-
angle as a three-sided figure and from our understanding of the
definition of a diagonal as a straight line drawn between two
nonadjacent angles. Seeing at once that a triangle contains no
nonadjacent angles, we see at once that no diagonals can be
drawn in a triangle.

Our understanding of diagonals also enables us to see at once
that the number of diagonals that can be drawn in a plane
figure that is a regular polygon having n sides (where n stands
for any whole number) is the number of sides multiplied by
three less than that number, the product being then divided by
two.

Sometimes, as in the case of "No triangle has any diagonals,"
the self-evidence of the truth derives from our understanding
of definitions. Sometimes, it derives from our understanding of
terms that are not only undefined but are also indefinable, such
as “part" and “whole."

Since we cannot understand what a part is without reference
to a whole, or understand what a whole is without reference to
parts, we cannot define parts and wholes. Nevertheless, our
understanding of parts and wholes makes it impossible for us
to think that, in the case of a physical body, its parts are greater
than the whole. That the whole body is always greater than any
of its parts is not only true, but self-evident.

Equally self-evident is the truth that nothing can both exist
and not exist at the same time; or that, at a given time, it can
both have and not have a certain characteristic. Our under-
standing of what it means for anything to act on another or be
acted upon gives us another self-evident truth. Only that which
actually exists can act upon another and that other can be acted
upon only if it also actually exists. A merely possible shower of
rain cannot drench anyone; nor can I be protected from the
rain by a merely possible umbrella.

How about the prime example of self-evident truth proposed
in the Declaration of Independence—that all men are created
equal? Clearly, it is not self-evident as stated if the word “cre-
ated" is understood to mean created by God, for the existence of
God and God's act of creation require the support of reasoning
—reasoning that can be challenged. Suppose, however, that the
proposition had been "All men are by nature equal." On what
understanding of the terms involved might that statement be
regarded as self-evidently true?

First of all, we do understand "equal" to mean "neither more
nor less." If, then, we understand "all men by nature" to mean
"all human beings" or "all members of the same species," it
becomes self-evidently true for us that all are equal, which is to
say that no human being is more or less human than any other.

All persons have, in some degree, whatever properties be-
long to all members of the species Homo sapiens. The inequality
of one individual with another lies in the degree to which this
or that specific property is possessed, but not in the degree of
humanity that is common to all.

I have dwelled at some length on this example not only be-
cause we will have to return to it in later chapters dealing with
the idea of equality, but also because the proposition about the
equality of all human beings may have to be defended against
those who advance the opposite view—Aristotle, for example,
who maintains that some human beings are by nature born to
be free, and some are by nature born to be slaves; or the male
chauvinists over centuries past, and even in the present, who
believe that females are inferior human beings.

I think the truth of the proposition about human equality can
be defended against all these errors, but a self-evident truth
should need no defense whatsoever. Hence the proposition,
though true, may not be a good example of self-evident truth.

Another whole class of truths for which certitude may be
claimed consists of those called evident, rather than self-
evident. I do not, as Descartes thought, have to infer my exis-
tence from the fact that I am aware of myself thinking. I per-
ceive it directly, just as I perceive directly the existence of all the
physical objects that surround me. If there is any doubt at all
about the truth of such judgments, it is the merest shadow of
doubt about whether I am suffering a hallucination rather
than actually perceiving.

When I am perceiving, not hallucinating, there can be no
doubt that the objects I am perceiving actually exist. Such judg-
ments have a semblance of certitude that falls short of complete
certitude only to the extent that a shadow of doubt remains
concerning the normality of my perceptual processes.

Whether my perceptual objects exist when I am not perceiv-
ing them is another question, to which I think the true answer
is that they do, but its truth is neither self-evident nor evident.
Reasoning and argument are required to defend its truth. If we
go beyond judgments about the present existence of objects
that we are at the moment perceiving to judgments about their
existence at other times and places, or to judgments about their
characteristics or attributes, we pass from the realm of certitude
to that of doubt. Though we less frequently misperceive than
we misremember, our perceptions as well as our memories give
rise to judgments that are often in error or otherwise at fault.

Judgments that articulate what we perceive or remember take
the form of statements about particulars—this one thing or
that, one event rather than another. We are also prone to gen-
eralize on the basis of our perceptual experience. In fact, the
judgments we are most likely to be insistent about are generalizations from experience. Many of these are unguarded and
turn out to be unwarranted because we have said "all" when
we should have said "some." Even scientific generalizations
sometimes overstate the case. The history of science contains
many examples of generalizations that have been falsified by
the discovery of one or more negative instances.

The falsification that I have just referred to provides us with
one more example of judgments that belong in the sphere of
certitude. When the discovery of a single black swan falsifies
the generalization that all swans are white, our judgment that
that generalization is false is knowledge in the strong sense of
the term—final, infallible, incorrigible. Nothing that might
possibly ever happen in the future could reverse the judgment
and make it true rather than false that all swans are white.

The number of self-evident truths is very small. The number
of falsified generalizations, both those made by scientists and
those made by laymen, is considerable; and the number of
perceptual judgments about the evident truth of which we have
certitude is very large. But it is not the number that matters
when we compare the realm of certitude with the realm of
doubt. What matters is that only judgments in the realm of
doubt have a future, a future in which the effort we expend in
the pursuit of truth may bring us closer to it.