§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, <

>.

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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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