§2: SOME BASIC FORMS OF GOOD REASONING AND THEIR FALLACIOUS COUNTERPARTS
¡ì2: SOME BASIC FORMS OF GOOD REASONING, AND THEIR FALLACIOUS
COUNTERPARTS
Chapter 2:
The basic requirements of good argument
Ben Bayer
Drafted January 24, 2010
Revised July 19, 2010
The science¡ªand art¡ªof logic, and its products
At the end of the last chapter, we defined logic as the science of the method
of non-contradictory inference. As we discussed, we need such a science
because we begin our cognitive lives with limited information¡ªhence the
need to draw inferences from what we begin with. We can make mistakes
when we make inferences, so we need a method to guide us. We need to be
reminded to rely on this method, because we can fail to be completely
conscientious in the way we think. And we need to be conscientious,
because the world isn¡¯t going to change itself to make up for our mistakes: it
is what it is, and not another thing.
The definition we have used so far treats logic as a kind of science,
but we can also think of it as an art. It is not an art in the sense that painting
and music are (it is not a fine art), but it is in the sense that we speak of ¡°the
art of cooking¡±: it gives us a ¡°recipe¡± for
producing a special kind of product, a product we
need to achieve important goals. In just the same
way that the art of cooking instructs us in the
production of soups, cakes, and souffl¨¦s, which
we need if we want to eat and enjoy ourselves, the
art of logic instructs us in the production of
conceptual knowledge, which we need if we want
to grasp reality and live successfully in it.
How does the logician decide on the recipe
needed to produce this knowledge? Of course
cookies can¡¯t be made in just any way. A mixture
of tofu, Worcestershire sauce, and deer venison
wouldn¡¯t do the job. A good cook observes which
ingredients actually go together to produce a tasty Picture credit 1:
and nutritious meal. He may experiment, by
e:Crisco_Cookbook_1912.jpg
adding or subtracting ingredients to see which best perfect the dish. The
same is true of the art of logic. The logician doesn¡¯t just decide in advance
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which thinking processes are best, but observes the actual methods of
reasoning people use, and which ones of them lead to real knowledge and
practical success.
A model logician in this regard was one of the first: Aristotle. In his
treatise, the Prior Analytics, Aristotle surveyed every possible form of
deductive, syllogistic reasoning (which we will study in more detail in
chapter 18): he observed which forms yielded false conclusions when
supplied with known premises as inputs, and discarded these as invalid. The
rest that avoided contradiction were classified as valid.
Most logic textbooks will not focus on every ingredient of knowledge,
only on one of the most crucial, the argument. An argument is a connected
series of propositions (premises) intended to establish another proposition
(a conclusion) as known. Here is an example of an argument of the kind that
logicians study:
The Earth always casts a circular shadow on the moon during an
eclipse.
Circular shadows are cast by flat circles, cones, cylinders, and
spheres.
Flat circles, cones, and cylinders cast shadows other than circular
shadows from different perspectives.
Only a sphere always casts a circular shadow.
Therefore, the earth is spherical.
This argument should look familiar, because it¡¯s one of the examples we
considered in the last chapter of evidence that needs to be assembled and
interpreted methodically to derive
even the most commonplace piece of
knowledge, such as that of the shape
of the planet on which we live. Notice
that this time, the evidence is
structured in a more formal way. The
premises are written neatly at the top,
like the separate addends in an
addition problem, while the
Picture credit 2:
conclusion is under a line drawn
beneath the premises, like the sum in
an addition problem. In this argument, we need each of these premises to
systematically consider all of the possible explanations for the shape of the
Earth¡¯s shadow, and then rule out all of those that we have other evidence
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against. By this methodical use of the ¡°process of elimination,¡± logic helps
us see how premises ¡°add up to¡± a conclusion.
At their best, logicians study the widest range of cognitive processes
over which people exercise control that is relevant to acquiring knowledge.
A good cook wouldn¡¯t just pay attention to which combination of
ingredients adds up to the best souffl¨¦. He¡¯ll search the world for the best
ingredients. Not just any old cream, but the finest cream from the finest
dairy, for instance. A good logician will do the same. What makes for a good
argument is not just a matter of the way the premises add up to the
conclusion, but a matter of premises and the components of those premises.
In this chapter, we will spend at least a little time talking about what makes
for a good premise, i.e. what makes it contain knowledge which can add up
to more knowledge in the form of a conclusion. In other chapters, we will go
even further than that. A premise is only as good as the concepts which
make it up.
Sometimes philosophers speak as if we should take our concepts for
granted and leave it to psychologists to account for them. But concepts are
of philosophical and especially logical
interest if human beings have some control
over them: specifically, over their
formation and their definition.1 Consider
just one example from the argument above:
the concept of ¡°eclipse.¡± Forming that
concept is a cognitive achievement: early
astronomers had to carefully distinguish the
surprising temporary darkness that appears Picture credit 3:
the moon on a single given evening
_Lunar_Eclipse_%28by%29.jpg
from the more regular darkness that waxes
and wanes across the moon over the course of the month, the kind that
accounts for the phases of the moon (new,
half, full, crescent, etc.). Astronomers also
had to notice the similarities between the
temporary blotting out of the moon and the
temporary blotting out of the sun, and realize
how both had a common cause: the
positioning of one heavenly body between
the sun and another, so as to blot out light.
1
Picture credit 4:
For more reasons on why this author considers this
on.jpg
approach to be a mistake, see ¡°A Role for
Abstractionism in a Direct Realist Foundationalism,¡± Synthese, forthcoming, 2010, <
>.
3
Noticing these differences and similarities required effortful attention, and
the result of these choices¡ªthe concept of ¡°eclipse¡±¡ªadds something useful
to human thinking. Like the selection of ingredients of a souffl¨¦, then, it is
something that can be done well or poorly, and
part of the subject matter of the art and science
of logic. Since the formation of a concept or
definition is not exactly an inference¡ªit is
more like a condensation of many past
observations¡ªthe definition of logic is
actually broader than we originally suggested.
It is not only the science of the method of noncontradictory inference, but of any kind of
non-contradictory identification.
Picture credit 5:
al_solar_eclipse_1999.jpg
Exercises
1. Above we compared the art of logic to the art of cooking. Can you
name some other practical activities that involve a kind of ¡°art,¡±
and what products they produce?
2. Can you think of other parallels between the art of logic and the art
of cooking? Consider the argument concerning the earth¡¯s shape. Is
it well-prepared or only half-baked? Is the conclusion something
that sustains us?
3. Can you identify other concepts in the argument about the earth
which could have been formed only by careful attention to various
differences and similarities?
The crucial ingredient of inferential knowledge: logical argument
We will devote a separate chapter (12) just to the logic of concepts
and their definitions. But the bulk of this book will follow the tradition and
deal with the logic of arguments, the formal statements that illustrate the
structure of inferential knowledge. For
this reason it is important to get really
clear on what arguments are and what
they are not. To begin with, an argument
in logic is not merely a ¡°heated
exchange,¡± the kind of argument that
two lovers may have during a fight.
There¡¯s a famous sketch from Monty
Python¡¯s Flying Circus in which one
Picture credit 6:
ver_a_Card_Game.jpg
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character patronizes an ¡°Argument Clinic,¡± looking for a good argument. He
first enters the wrong room, and is met with a torrent of expletives and
name-calling. It turns out that he has entered the room for abuse, not
argument. Too often people who engage in arguments, conventionally
understood, are just heaping abuse on one another, not engaging in any
intellectual process.
In the next room, the Python character says he¡¯s looking for an
argument, and the attendant says no, he isn¡¯t. The patron insists that he is,
and the attendant continues to deny it. They go back and forth affirming and
denying this proposition for a while, at which point it becomes obvious to
the patron that this is not an argument, but simply ¡°contradiction.¡± ¡°An
argument is a connected series of statements intended to establish a
proposition,¡± he says. ¡°Argument is an intellectual process. Contradiction is
just the automatic gainsaying of any statement the other person makes.¡±
Even if this exchange is not as heated as what we found in the room for
¡°abuse,¡± it is still clear that there is no intellectual process here, just
mindless affirming and denying. (One is reminded of the old commercials
for Budweiser: one crowd yells ¡°Tastes great!¡± The other responds, ¡°Less
filling!¡± They go on and on.) Remember: the reason that we need logical
arguments is that they formalize the process of methodically collecting
evidence needed to draw inferential conclusions. Just saying that something
is or isn¡¯t so is not a methodical collection of evidence.
The fact that logical arguments involve the methodical organization of
propositions does not mean that every methodical organization of
propositions is an argument. The purpose of assembling them is important,
too. There are at least two methodical ways of assembling propositions from
which arguments should be distinguished, because they involve a different
purpose.
One notable example is the explanation. Here¡¯s an example of a good
explanation:
The earth is spherical in shape, because eons ago, nebulae
collapsed into disks of gas and dust, forming stars and clouds of
dust, which collected together due to gravitational attraction.
Eventually the collections become large enough that they
melted and formed globular structures.
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