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Schaum's Outlines of Logic (2nd Ed.)

Schaum's Outlines of Logic (2nd Ed.)

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Chapter 1

Argument Structure

1.1 WHAT IS AN ARGUMENT?

Logic is the study of arguments. A n argument is a sequence of statements of which one is intended

as a conclusion and the others, the premises, are intended to prove or at least provide some evidence

for the conclusion. Here are two simple examples:

All humans are mortal. Socrates is human. Therefore, Socrates is mortal.

Albert was not at the party, so he cannot have stolen your bag.



In the first argument, the first two statements are premises intended to prove the conclusion that

Socrates is mortal. In the second argument, the premise that Albert was not at the party is offered as

evidence for the conclusion that he cannot have stolen the bag.

The premises and conclusion of an argument are always statements or propositions,' as opposed to

questions, commands, or exclamations. A statement is an assertion that is either true or false (as the

case may be) and is typically expressed by a declarative ~ e n t e n c eHere

. ~ are some more examples:

Dogs do not fly.

Robert Musil wrote The Man Without Qualities.

Brussels is either in Belgium or in Holland.

Snow is red.

My brother is an entomologist.



The first three sentences express statements that are in fact true. The fourth sentence expresses a false

statement. And the last sentence can be used to express different statements in different contexts, and

will be true or false depending on whether or not the brother of the speaker is in fact an entomologist.

By contrast, the following sentences do not express any statements:

Who is the author of The Man Without Qualities?

Please do not call after I lpm.

Come on!



Nonstatements, such as questions, commands, or exclamation:;, are neither true nor false. They may

sometimes suggest premises or conclusions, but they are never themselves premises or conclusions.

SOLVED PROBLEM



1.1 Some of the following are arguments. Ide-ntify their premises and conclusions.



(a)

(6)



He's a Leo, since he was born in the first week of August.

How can the economy be improving? The trade deficit is rising every day.



' ~ h i l o s o ~ h e rsometimes

s

draw a distinction between statements and propositions, but it is not necessary to make that

distinction here.

2The distinction between a statement or proposition and the sentence used to express it is important. A sentence can be

ambiguous or context-dependent, and can therefore express any of two or more statements-even statements that disagree in

their being true or false. (Our fifth example below is a case in point.) However, where there is no danger of confusion we shall

avoid prolixity by suppressing the distinction. For example, we shall often use the term 'argument' to denote sequences of

statements (as in our definition) as well as the sequences of sentences which express them.



ARGUMENT STRUCTURE



[CHAP. 1



I can't go to bed, Mom. The movie's not over yet.

The building was a shabby, soot-covered brownstone in a decaying neighborhood. The scurrying of rats echoed in the empty halls.

Everyone who is as talented as you are should receive a higher education. G o to

college!

We were vastly outnumbered and outgunned by the enemy, and their troops

were constantly being reinforced while our forces were dwindling. Thus a direct

frontal assault would have been suicidal.

He was breathing and therefore alive.

Is there anyone here who understands this document?

Many in the U.S. do not know whether their country supports or opposes an

international ban on the use of land mines.

Triangle ABC is equiangular. Therefore each of its interior angles measures 60

degrees.

Solution

Premise: He was born in the first week of August.

Conclusion: He's a Leo.

Technically this is not an argument, because the first sentence is a question; but the

question is merely rhetorical, suggesting the following argument:

Premise: The trade deficit is rising every day.

Conclusion: The economy cannot be improving.

Premise: The movie's not over yet.

Conclusion: I can't go to bed.

Not an argument; there is no attempt here to provide evidence for a conclusion.



Not an argument; 'Go to college!' expresses a command, not a statement. Yet the

following argument is suggested:

Premise: Everyone who is as talented as you are should receive a higher education.

Conclusion: You should go to college.

Premise: We were vastly outnumbered and outgunned by the enemy.

Premise: Their troops were constantly being reinforced while our forces were dwindling.

Conclusion: A direct frontal assault would have been suicidal.

Though grammatically this is a single sentence, it makes two distinct statements, which

together constitute the following argument:

Premise: He was breathing.

Conclusion: He was alive.

Not an argument.

Not an argument.

Premise: Triangle ABC is equiangular.

Conclusion: Each of its interior angles measures 60 degrees.



Though the premises of an argument must be intended to prove or provide evidence for the

conclusion, they need not actually do so. There are bad arguments as well as good ones. Argument

l.l(c), for example, may be none too convincing; yet still it qualifies as an argument. The purpose of

logic is precisely to develop methods and techniques to tell good arguments from bad ones3

3For evaluative purposes, it may be useful to regard the argument in l.l(c) as incomplete, requiring for its completion the implicit

premise 'I can't go to bed until the movie is over'. (Implicit statements will be discussed in Section 1.6.) Even so, in most contexts

this premise would itself be dubious enough to deprive the argument of any rationally compelling persuasive force.

Since we are concerned in this chapter with argument structure, not argument evaluation, we shall usually not comment on the

quality of arguments used as examples in this chapter. In no case does this lack of comment constitute a tacit endorsement.



CHAP. 11



ARGUMENT STRUCTURE



Notice also that whereas the conclusion occurs at the end of the arguments in our initial examples

and in most of the arguments in Problem 1.1, in argument l.l(c) it occurs at the beginning. The

conclusion may in fact occur anywhere in the argument, but the beginning and end are the most

common positions. For purposes of analysis, however, it is customary to list the premises first, each on

a separate line, and then to give the conclusion. The conclusion is often marked by the symbol ':.',

which means "therefore." This format is called standard form. Thus the standard form of our initial

example is:

All humans are mortal.

Socrates is human.

:. Socrates is mortal.



1.2 IDENTIFYING ARGUMENTS

Argument occurs only when someone intends a set of premises to support or prove a conclusion.

This intention is often expressed by the use of inference indicatovs. Inference indicators are words o r

phrases used to signal the presence of an argument. They are of two kinds: conclusion indicators, which

signal that the sentence which contains them or to which they are prefixed is a conclusion from

previously stated premises, and premise indicators, which signal that the sentence to which they are

prefixed is a premise. Here are some typical examples of each (these lists are by n o means

exhaustive):

Conclusion Indicators

Therefore

Thus

Hence

So

For this reason

Accordingly

Consequently

This being so

It follows that

The moral is

Which proves that

Which means that

From which we can infer that

As a result

In conclusion



Premise Indicators

For

Since

Because

Assuming that

Seeing that

Granted that

This is true because

The reason is that

For the reason that

In view of the fact that

It is a fact that

As shown by the fact that

Given that

Inasmuch as

One cannot doubt that



Premise and conclusion indicators are the main clues in identifying arguments and analyzing their

structure. When placed between two sentences to form a compound sentence, a conclusion indicator

signals that the first expresses a premise and the second a conclus,ion from that premise (possibly along

with others). In the same context, a premise indicator signals just the reverse. Thus, in the compound

sentence

H e is not at home, so he has gone to the movie.



the conclusion indicator 'so' signals that 'He has gone to the movie7 is a conclusion supported by the

premise 'He is not at home7.But in the compound sentence

H e is not at home, since he has gone to the movie.



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