1. How Reasons Connect to Conclusions
Our present task is to develop an understanding
of practical implication, which is the sense of implication that interests
us most in applied logic and the sense of implication we have in mind when
we ask whether P is a good reason for Q.
We have said that in applied logic our fundamental
concern is with the relation between reasons and conclusions. We will adopt
the convention of representing this relationship schematically as follows:
When a specific reason is given for a specific
conclusion, we will represent this by writing the reasons and conclusions
inside the boxes with an R under the box containing the reason and a C under
the box containing the conclusion. So, for example, if I tell you that I'm
tired today because I slept badly last night, this can be represented as
follows.
Let's think about this example. Everyone
intuitively sees the connection between R and C above. It is an ordinary
sort of reason to give for that sort of conclusion. But here is a question
you may not be able to answer immediately: What exactly is the connection
between R and C? If you posed C as a question (i.e., Why are you so tired
today, Randy?) and I gave you R as an answer, why would you immediately
recognize R as a comprehensible answer to your question?
It's kind of hard to understand what is
being asked here, so let's put the question in a different way. Suppose
I had said this instead: I'm tired today because the moon was full last
night. Now this would have to be represented as follows:
I assume that in this case the connection
between R and C isn't obvious at all. But why not? What is missing? What
is the important difference between these two examples?
2. The Nature of Principles
The logician's answer to the questions posed
above is this. Whenever we give a reason for a conclusion we implicitly
invoke the authority of a principle. In the first example the reason is
connected to the conclusion because it invokes a familiar principle, viz.,
"People who don't get enough sleep will be tired." In the second
example the reason fails to connect to the conclusion because it invokes
an unfamiliar principle, perhaps something like this "People are tired
the day following a full moon."
To make this answer completely clear we
need to address the following questions.
(1) What, exactly, is a principle?
(2) What does it means to invoke a principle?
(3) How does a principle connect a reason
to a conclusion?
2.1 Principles are Rules
You are familiar with many different
kinds of principles: legal principles, moral principles, scientific
principles, mathematical principles, and all sorts of principles relating
to the attempt to achieve specific goals (e.g., principles of carpentry,
body building, cooking, animal husbandry, personal hygiene, etc.) All
of these are rules that prescribe certain kinds of behavior or describe
certain kinds of relationship. Rules or principles have two defining
characteristics. First, they are general. Second, they are conditional.
2.1a The General Nature of Principles
The general nature of principles can
be appreciated by considering the difference between these two statements.
(a) This ice cream is sweet.
(b) All ice cream is sweet.
Statement (a) is not a principle because
it is not general; it just provides information about some specific
helping of ice cream. But statement (b) is much more general than (a).
It isn't about any particular helping of ice cream, but a general rule
about ice cream itself. Obviously, (b) is quite a bit more powerful
than (a). If all you know is (a) then you really don't know what to
expect from your next bowl of ice cream. But if you know (b) then you
know what to expect, not only from this bowl of ice cream, but from
every bowl of ice cream you will ever get.
Generality is not an absolute property.
It comes in degrees. In the above example (b) is more general than (a)
but the following statement
(c) Everything is sweet.
is more general still. Of course, (c)
is false, but that is not relevant at the moment.
2.1b Conditional Nature of Principles
The conditional nature of principles
can be understood as follows. Statement (b) is equivalent to the following:
(d) If something is ice cream,
then it is sweet.
We call this "if...then" statement
a conditional statement because the "if" clause gives you
a condition that must be fulfilled in order to get the content of the
"then" clause. In logic the "if" clause is called
the antecedent and the "then" clause is called the consequent..
Just about any principle can be rewritten
in a conditional form and it is important to learn how to do it. One
trick that facilitates the conditional representation of principles
is to substitute algebraic variables for pronouns. So, (d) can actually
be rewritten as follows:
(e) If X is ice cream, then X
is sweet.
Introducing variables in this way is
valuable in two respects. First, it makes the principles much less cumbersome
to write. Second, it makes the general nature of the principle very
explicit. This is because the generality of the principle is a function
of the variables themselves.
Here are some examples of principles
rewritten as conditionals. Notice that principles can have more than
one variable.
(f) Professors are pretentious
= If X is a professor, then X is pretentious.
(g) Dogs like to chase cats =
If X is a dog and Y is a cat, then X likes to chase Y.
(h) Nobody likes complainers =
If X is a complainer, then there is no Y that likes X.
(i) Hungry people eat whatever
food is offered them = If X is a hungry person and edible Y is offered
X, then X eats Y.
(j) Only a mother could love a
face like an aardvark's = If X is a face like an aardvark's and Y
loves X, then Y is a mother.
2.2 The Authority of Principles
A principle can be understood as a kind
of license to move from a reason to a conclusion. Here is an analogy
worth elaborating briefly. If you have a driver's license, you know
that you are supposed to carry it with you whenever you operate a motor
vehicle on a public road. You also know that the only time you ever
actually have to produce your license is when an officer of the law
asks you to, and the only time they are supposed to do this is when
your driving behavior appears to be inconsistent with the law. Any other
time you are driving a car it is just assumed that you are a licensed
driver.
Considered as inference licenses, principles
work in pretty much the same way. If the reason you produce for a certain
conclusion is an ordinary sort of reason for that conclusion, then you
will rarely be asked for the principle of your reasoning. We will just
assume you are using a familiar principle. But if the reason you produce
is not consistent with any known principle, then you will be pulled
over and asked to produce your license. If you have a valid license,
then you have the authority to make the inference. If you don't, then
your reasoning will be arrested and you'll be taken in for further questioning.
So, going back to our original example,
if I tell you that I'm tired today because the moon was full last night
you might say: "What does the full moon have to do with you being
tired?" You've just pulled me over and asked me for my license.
For your question really is: What principle authorizes you to give that
reason for that conclusion?
2.3 The Connecting Function of Principles
The connecting function of principles
is a result of their status as generalized conditional statements. The
arrow we draw between the reason and the conclusion will, from now on,
stand for the principle and we will label it with a P, like this.
We noted above that in this example,
P must be something like: People who don't get enough sleep will be
tired. Conditionalized this would be: "If person X doesn't sleep
well, then person X is tired." You should be able to see that the
reason in this example is a particular instance of the antecedent of
the conditional and the conclusion is a specific instance of the consequent
of the conditional. This can be represented graphically as follows:
It may help here to think in terms of
the "input/output" language of mathematical functions. For
example x2 is a function that, written as a principle, says
(k) If input is x, then output
is x2.
So, input a 2 and output a 4, input
a 3 and output a 9, etc. In the above example the principle works in
the same way. Input "Randy sleeps badly" and output "Randy
is tired;" input "Martha sleeps badly" and you output
"Martha is tired," etc..
Criteria for the Attribution of Principles
Earlier we observed that in ordinary
reasoning contexts people do not state their principles unless they
have been called into question. What makes this possible is that people
who reason together tend to share a very large number of principles.
This is actually what makes any form of cooperation possible. You do
not have to state the rule you are following everytime you stop at a
stop sign, or put a stamp on an evelope, or shake a person's hand when
its extended in your direction. Everyone knows the principles involved
in these actions.
Still, attributing the use of a particular
principle to a particular individual is an intellectual undertaking,
and there are some basic criteria (which are themselves rules) that
must be followed. Most of these can be gleened from the preceding text,
but we will now codify them below.
1. Every principle is a conditional
(If...then) statement in which the antecedent, (the "if"
clause) applies to the reason, and the consequent (the "then"
clause) applies to the conclusion.
2. Every principle is more general
than the reason/conclusion pair to which it applies. This generality
can normally be achieved by the use of algebraic variables (x, y,
z, u, v, w).
3. Every principle must make sense
on its own. Among other things this usually requires that the variables
that appear in the consequent of the principle also appear in the
antecedent, and that they be used in the same way.
4. When more than one principle satisfying
1-3 above can be attributed, the principle that best fits the circumstances
should be be employed.
The importance of the fourth critierion
can be undestood as follws. If your friend says that he's going to see
a movie tonight because he is bored, you might attribute the principle
"If person X is bored, then X goes to see a movie." This satisifies
criteria 1-3, but it may not be the principle involved. A better principle
might be "If person X is bored, then X seeks some form of entertainment."
It would be on the basis of having attributed a principle like this
that you might suggest going to your friend's party instead.
3. Arguments and Explanations
Now that we know how reasons connect to
conclusions, we need to ask a deeper question. Why do we connect reasons
to conclusions? What, exactly, are we trying to achieve when we do this?
To begin to answer this question, recall
the general way we characterized the study of logic: it is the study of
how we can reliably increase our knowledge and understanding of the world.
If you were reading this very closely you might have wondered whether knowledge
and understanding were actually different concepts, or whether we were just
saying the same thing in two different ways. The answer is that they are
very different concepts and we will employ them now in articulating the
two different functions of reasoning: argument and explanation.
The basic idea is this: you can know something
without understanding it. For example, you can know that there is a stench
in the air without understanding why there is a stench in the air; you can
know that the sun is hot, without understanding why the sun is hot; you
can know that you don't like someone without knowing why you don't like
someone.
The distinction between knowing something
and understanding it gives rise to different kinds of reasons: evidence
and cause. When we ask "How do you know?" we are asking for evidence.
When we ask "Why is it so?" we are asking for a cause.
Now let's develop this distinction a little
more systematically. In the previous section we developed the following
model of reasoning.
This structure is what, from now on, we
will call a rationale. A rationale is any example of a reason connected
to a conclusion by a principle.
Now we can formalize the distinction between
knowing and understanding as follows. There are two kinds of rationales.
The first we call an argument, the second we call an explanation. An argument
is an attempt to answer the question "How do you know C (the conclusion)
is true?" or "Why should one believe C to be true?" When
we ask a question like this, we are thinking of the conclusion as a person's
opinion and we are looking for a reason to believe that opinion. A reason
to believe something is what we call evidence.
An explanation is an attempt to answer the
question "Why is C so?" or "How did C come to be?" When
we ask a question like this, we are usually convinced that the conclusion
represents a fact, but now we are looking for the reason for its existence.
Reasons of this sort we call causes.
All of what we have just said is represented
in the diagram below:
The distinction between argument and explanation
is absolutely fundamental to the study of logic and it is essential to become
good at seeing the difference between them. In order to develop this ability
you need to realize that any statement that describes the world can be understood
as expressing a fact or as expressing an opinion. It all depends on the
context in which the statement is made. Take, for example, the statement:
(k) This squirrel isn't afraid of
people.
Now, considered as a conclusion of a rationale,
would you be inclined to regard this statement as expressing an opinion
or an accepted fact? Well, the answer, is that you really don't know until
you hear the reason that is given for it. If I had said "The reason
this squirrel isn't afraid of people is that people are always feeding it,"
you would say that (k) expresses an accepted fact, because I have just told
you why (k) is so. On the other hand, If I had said "This squirrel
isn't afraid of people. See, it eats right out of your hand," then
you would say that (k) expresses an opinion, because I have just tried to
convince you of (k) by giving a reason for thinking (k) is true.
The important thing to realize is that the
distinction between explanation and argument is a fundamentally contextual
distinction. Whether we call something an explanation or an argument depends
upon what the person doing the reasoning is trying to accomplish with it.
An ARGUMENT
is a rationale designed to convince us of the truth of the conclusion by
giving reasons which are evidence for the conclusion.
An EXPLANATION
is a rationale designed to understand a certain fact by giving reasons which
are causes of that fact. But even if you have a good grasp of this distinction,
there will be times when it is difficult to determine whether a particular
rationale is an explanation or an argument. So here are a couple of observations
that will aid you in making this determination.
Normative conclusions:
Recommendations and Value Judgments
Many of the
rationales you construct will have normative conclusions. A normative conclusion
is one that expresses some kind of value judgment and an explicit or implicit
recommendation. All of the following are normative conclusions.
(1)
Colin Powell would make a good president.
(2)
The Auburn Dam should not be built.
(3)
There is nothing wrong with prayer in public school.
(4)
Americans are too concerned about making money.
(5)
The San Francisco Giants ought to build a new stadium.
The following
conclusions, however, are not normative, but simply descriptive.
(1')
Colin Powell is not president.
(2')
The Auburn dam is being built.
(3')
Allowing prayer in public school is against the law.
(4')
Americans are concerned about making money.
(5')
The San Francisco Giants are building a new stadium.
It should
be fairly obvious that normative statements can be the conclusions of arguments,
for we often try to convince people to accept conclusions of this sort.
But can they also be the conclusions of explanations? At first glance you
might think so. We often say things like "Let me explain why Colin
Powell should not be president." But in our way of thinking, a person
who "explains" why Colin Powell should not be president is really
trying to convince us of this. In fact, it is difficult to give any sense
to the idea of explaining a value judgment, for value judgments do not express
facts of the sort that can be caused. To see this, compare each normative
statement in the first list above with its corresponding non-normative statement
in the second list. The entries in the second list are all capable of entering
into causal relations. Something might cause Patrick Buchanan not to become
president; something might cause the Auburn dam to be built, but nothing
really causes these outcomes to be good or bad.
Having said
this, it is important to understand that value terms like "good"
and "bad" are often used in a way that do not really express a
recommendation, but which are really more or less synonymous with statements
about the world. For example,
(6)
Red wine is good for the heart.
(7)
Forest fires are bad for the environment.
Statements
like these may express vague recommendations, but their content is primarily
empirical. The "goodness" here is identical to certain physical
effects on arteries or ecosystems. So it can make just as much sense to
talk about causes of (6) and (7) as evidence for them.
All this boils
down to the following principle of analysis: If the conclusion of a rationale
is a value judgment, expressing an explicit or implicit recommendation then
the rationale itself should be understood as an argument.
Now, here
is a tricky question: Is the following statement a value judgment?
(8)
René believes that Colin Powell would make a good president.
The answer
is no. Even though what René believes is a value judgment, statement
(8) is not itself a value judgment. (8) just tells us what René believes,
and it makes as much sense to talk about causes of (8) as it does to talk
about evidence for it. Hence, depending on the context, a rationale for
which (8) is the conclusion might be either an argument or an explanation.
This leads us to our next topic: conclusions that express a person's psychological
states.
Psychological Conclusions
and Linguistic Behavior
Any statement
we make about the world is the sort of thing that a person can come to accept
or reject. The acceptance or rejection of this statement can be expressed
in another statement that actually contains the first statement. Example:
(6)
Red wine is good for the heart.
(6')
Sheila believes that red wine is good for the heart.
(6")
Sheila doubts that red wine is good for the heart.
(6"')
Sheila said that red wine is good for the heart.
A conclusion
about what a person believes, thinks, feels, or says is not the same as
a conclusion about the content of the belief itself. So even though (6')
- (6"') make explicit use of (6), they are actually very different
statements. (6) is a statement about red wine, (6') - (6"') are statements
about what Sheila believes and says about red wine. It is extremely important
not to confuse these types of statements. All of them are the sort that
may be either argued for or explained. That is, it makes as much sense to
talk about arguing that red wine is good for your heart and explaining why
red wine is good for your heart, as it does to talk about arguing that Sheila
believes (or says ) red wine is good for your heart and explaining why Sheila
believes (or says) red wine is good for your heart. But arguments and explanations
for statements of type (6) will look very different from arguments and explanations
for statements of types (6') and (6'').
Consider each
of the following:
(8)
Red wine is good for your health. Researchers have found that people who
drink red wine regularly are less prone to heart attacks.
(9)
The reason red wine can be good for your health is that it prevents the
build up of cholesterol in the arteries of the heart.
(10)
Sheila must believe that red wine is good for your health. She is very
health conscious, and she drinks it with every meal.
(11)
Sheila believes that red wine is good for your health because her doctor
told her so.
Now, how are
each of these to be understood? The answers are as follows. (8) is an argument
that red wine is good for your health. (9) is an explanation why red wine
is good for your health. (10) is an argument that Sheila believes that red
wine is good for your health. (11) is an explanation why Sheila believes
that red wine is good for your health.
It is extremely
important to develop the ability to see the differences between these types
of rationales. Those who can not, will often misconstrue the rationales
of (10) and (11) by assuming that because (10) and (11) express Sheila's
opinions they must be arguments purporting to establish that red wine is
good for your heart. As we have seen, this would be a faulty analysis for
both of these statements.
Reasoning About the
Future
We often give
reasons in support of conclusions about the future. For example,
(12)
Tomorrow the moon will be full.
(13)
Mr. Pheeper is going to die someday.
(14)
An asteroid will wipe out life on earth in the year 2947.
It is fairly
obvious that conclusions such as these may be argued for; the question is
whether they can also be explained. You might think not, because, like value
judgments, claims about what is going to happen in the future seem to be
essentially a matter of opinion. But this is really not true. Consider (12)
above. It is perfectly natural to say that right now it is either a fact
or not a fact that the moon will be full tomorrow. When you think about
how accurately we can predict such matters it makes perfect sense for someone
to accept it as a fact that on a certain date the moon will be full and
then go on to ask for an explanation of this fact. There is actually no
good reason to define a fact as something that has already occurred. Indeed,
claims about the remote past or even what is happening presently in a remote
location can be much more a matter of opinion than claims about the future.
So the only
way to determine whether conclusions about the future are being argued for
or explained is just to pay very close attention to the context. And the
truth is that sometimes it is just impossible to tell. In (13) it is reasonable
to assume that a person knows that she is going to die at some point in
the future. On the other hand, (14) is such a bold prediction, that one
would normally expect to get an argument in support of such a claim. However,
if the year were 2946 this claim might have been regarded as common knowledge
for centuries so that anything given in support of it would be understood
as an explanation rather than an argument.
Until now we have been speaking as
if any given passage of reasoning can be identified as either an argument
or an explanation. This is a defensible idealization,
but
it's not correct. Sometimes it is just not clear whether someone is arguing
or explaining. (After all, lots of people don't even know the difference.)
Sometimes,
for example, people will clearly be trying to convince us of something, but
will give reasons that are causes rather than evidence. We'll see examples
of this
later.
But it is not always incompetence or lack of clarity that gets arguments
and explanations tangled up. We often see this because arguments tend to
give rise
to explanations, and vice versa. For example, if someone argues compellingly
that the war in Iraq was a colossal mistake; this naturally raises the explanatory
question: Why did we do it? If someone were to claim that the reason we did
it was to secure U.S. oil interests in that region, a curious person would
naturally
ask: How do you know that? Authors constantly anticipate questions like these,
and consequently you will see arguments and explanations occurring together
even in very short passages of reasoning. Consider the following examples.
1. Men simply
have no business becoming gynecologists or obstetricians. There are plenty
of competent women trying to get into the field, and most women patients
prefer their ob-gyn’s to be women. But most are still men and that’s
just one more example of the insensitivity of the medical establishment to
the needs of women.
2. It is ridiculous that Ichiro Suzuki was voted the American
League Rookie of
the year for 2001. He wasn’t a rookie. He had 10 years of experience
in Japan before coming here. Why do you think he was so good his first year
here?
Duh!
3. We can’t blame the activities of Islamic extremists on the culture or
teachings of Islam. Islam doesn’t condone or promote terrorism. People
just want to think otherwise because it satisfies their own racist impulses
and their desire to escape responsibility for the havoc we have caused in
Middle
Eastern countries during the last century.
4. A recent study shows that mammograms
are not more effective in preventing breast cancer than manual methods. Previous
studies indicated otherwise because
they failed to correct for certain variables, like the fact that women who
have mammograms are more likely to have annual exams.
5. The reason we recognize intellectual
property rights at all is to provide economic incentives to inventors and
entrepreneurs. But patents and copyrights
can’t last forever, because that allows corporations to monopolize entire
industries and it interferes with the free exchange of ideas. That’s why
it’s regrettable that the U.S. Congress keeps extending the period
of copyrights. They will keep doing it, too, since money from these corporations
is what keeps
our politicians in office.
Each of these examples presents at least one argument
and one explanation. In the first example, the author argues that men shouldn’t
be ob-gyns and explains the fact that they continue to predominate in terms of
the establishment’s insensitivity to the needs of women patients. In the
second example the author argues that Ichiro shouldn’t have been picked
as the NL Rookie of the Year and explains the player’s prowess in terms
of the fact that he was already an experienced player. The third example
argues that terrorism should not be blamed on Islam and explains the tendency
to do
so in terms of racism and the desire to escape blame. The fourth example
argues that mammograms are not more effective in preventing breast cancer
and explains
the prior belief that they are in terms of flawed studies. Finally, the fifth
example explains why we have intellectual property rights, argues that Congress
should not keep extending their period of duration, and explains why we will
carry on doing so.
Obviously if you don’t understand the difference between
argument and explanation
you don’t have a prayer of analyzing reasoning like this correctly. But
even if you do it can be pretty difficult. In the middle of analyzing a complicated
piece of reasoning it’s easy to forget that you are working on an explanation
and start tacking on pieces of evidence.
The more you pay attention to this distinction,
the more you’ll see that
the majority of articles that advance and defend a particular point of view
are not simply arguments or explanations, but a combination of both types
of rationale
in which the author both argues for a particular claim and explains away
contradictory claims and phenomena. For example, an argument for
legalizing marijuana is supported
by an explanation of why people oppose legalization and/or how marijuana
came to be criminalized; an argument for developing alternative energy resources
is
supported by an explanation of why there is so little public interest in
it; an argument that a study published in a leading scientific journal is
fraudulent
is supported by an explanation of how it managed to pass peer review. But you
will also start to notice the pervasiveness of a certain kind of confusion,
of which the following is an example.
6. Increasing the minimum wage harms the very people it is intended
to help. In
order to regain their profit margin employers simply terminate
a certain percentage of their lowest paid employees and require those
who remain to be more productive.
The inevitable result: higher unemployment and poorer working conditions
than before.
Is this an argument or an explanation? The answer is that, while
it has the "feel" of
an argument against raising the minimum wage, it is actually an explanation
why increasing the minimum wage hurts those it is intended to help. I call
this a
convincing explanation, not simply in the sense that it is a fairly plausible
sounding causal account of the phenomenon at issue, but rather in the sense
that, having read it, we are now more convinced than before that the phenomenon
being
explained actually occurs; this, in spite of the fact, that not a shred of
evidence for it has actually been given.
Our vocabulary makes it easy to characterize
this sort of error, which consists simply in attributing argumentative
force to an explanation. (This occurs in
various fallacies, including circumstantial ad hominem and the genetic
fallacy, both of which rely on substituting explanatory for argumentative
reasoning).
A modified version of the error -somewhat more difficult to detect-
occurs
when rationales that begin as genuine arguments are illegitimately supplemented
with
explanatory reasons. For example:
7. People with persistent, incapacitating lower back pain should consider
spinal fusion surgery. The surgery is increasingly recommended
and performed by both
orthopedic surgeons and neurosurgeons. Last year alone surgeons
performed approximately a hundred and fifty thousand lower-lumbar spinal
fusions. The
operation works
by removing lumbar disks and mechanically bracing the vertebrae.
This significantly reduces spinal instability, which causes lower back
pain.
Notice that
the argument does give some evidence for the value of spinal fusion surgery,
namely that it is widely performed and increasingly recommended
by experts.
However, no statistical evidence supports the most significant claim, viz.,
that the procedure actually works. Instead we are given an explanation
of how it works.
The effect here is the same as in the first example. If we fail to analyze
this as two distinct rationales, an argument for considering spinal fusion
therapy
and an explanation how it works, the argument becomes speciously convincing.
It is difficult to overstate our susceptibility to convincing explanations. Bad science obviously prospers a great deal from offering convincing
explanations of non-existent facts. For example, repressed memory therapists
offer a
plausible explanation of their ability to help patients recall forgotten
events, just
little
independent evidence that these events actually occurred. But mainstream
science employs convincing explanations with equal facility. For example,
it offers compelling
descriptions of the causal mechanism behind the benefits of mammography,
arthroscopic knee surgery, estrogen replacement therapy, full body
scanning, and low fat diets.
What it cannot give us, as good scientists themselves will remind us,
is compelling evidence that these benefits actually occur. Hence, a clear
grasp of the relation
between argument and explanation provides the thinking layperson with
a
powerful tool for evaluating scientific reasoning.