Philosophy 103: Introduction to Logic
The Structure of Arguments
Abstract: The concept of an
argument is discussed together with the related concepts of premiss, conclusion,
inference, entailment, proposition, and statement.
I. We have seen that one main branch of philosophy is epistemology and one main branch of
epistemology is logic.
A. What is epistemology?
B. What is logic? Simply put, the purpose of
logic is to sort out the good arguments from the poor ones.
II. So the chief concern of logic is the structure of an
argument.
A. Every argument in logic has a structure, and
every argument can be described in terms of this structure.
1. Argument: any group of propositions of
which one is claimed to follow logically from the others.
a. In logic, the normal sense of
"argument," such as my neighbor yelling to me about my trashcans is not termed
"an argument" in logic.
b. By "argument," we mean a
demonstration or a proof of some statement, not emotional language. E.g.,
"That bird is a crow; therefore, it's black."
2. The central parts of an argument include ...
a. Premiss: (more usually spelled
"premise") a proposition which gives reasons, grounds, or evidence for accepting
some other proposition, called the conclusion.
b. Conclusion: a proposition, which is
purported to be established on the basis of other propositions.
B. Consider the following example of an argument
paraphrased from an argument given by Fritz Perls in In and Out of the Garbage Pail.
If we set our ideals too High, then we
will Not meet those ideals.
If we do Not meet those ideals, then we
are Less than we could be.
If we are Less than we could be, then
we Feel inferior.
If we set ideals too High, then we Feel
inferior.
1. By convention, the reasons or premisses are
set above a line that separates the premisses from the conclusion. The line is sometimes
thought of as symbolizing the word "therefore" in ordinary language.
2. As you read the passage and come to understand
it, you are undergoing a psychological process called "making the
inference."
a. An inference is the reasoning process
by which a logical relation is understood.
b. The logical relation is considered valid
(good) or not valid (not good) even if we do not understand the inference right away. In
other words, it is convenient to consider the logical relation as not being dependant for
its validity on the psychological process of an inference.
c. In this manner, logic is not considered as
"the science of reasoning." It is prescriptive, as discussed in a previous
class.
3. So, this logical relation between the
premisses and conclusion of Perl's argument holds regardless of whether we pay attention
or not.
a. In Perls' argument in the boxed text above,
we can symbolize the argument by using the bold letters in the text, as follows:
H ⊃ N
N ⊃ L L ⊃ I
H ⊃ I
b. This kind of logical relation is called an entailment.
An entailment is a logical relation between or among propositions such that the
truth of one proposition is determined by the truth of another proposition or other
propositions, and this determination is a function solely of the meaning and syntax of the
propositions concerned.
c. Another way to remember the difference between an
inference and an entailment is to note that people infer something, and
propositions entail something.
d. The argument structure is the sum and substance of logic.
All that remain in this course is to sketch out a bit of what this means. (Note that
Perls', argument has a good structure, so if the conclusion is false, one of the premisses
has to be false.)
III. We have spoken earlier of the relation between or among
propositions. What is a proposition or statement (we will use these words
interchangeably)?
A. Proposition
or Statement : a verbal expression that can
be regarded as true or false (but not both). Hence, a proposition or a statement is a
sentence with a truth-value. Note that a sentence is considered to be a statement even if the
truth-value of the statement is not known so long as it is known that the sentence has a
truth value. E.g. “Tomorrow it will rain” is a proposition or statement
even though its truth value is not known today.
B. Hence logic is just concerned with those
statements that have truth-values. (There is very much of life that is irrelevant to
logic.)
Consider the confusion that would result if we
considered the following sentences as statements:
1. "Good morning." (What's so good
about it?)
2. "You are looking good today." (Well,
I just saw my doctor and ...)
3. "What is so rare as a day in June? Then,
if ever, come perfect days..." (Well, I don't know about that.)
4. To a waiter: "I'd like a cup of
coffee." (Yeah, but I think bigger, I'd like a BMW.)
Thus, phatic communication, greetings, commands,
requests, and poetry, among other uses of language, are not mean to be taken as
statements.
C. Which of the following sentences are
statements?
1. There is iron ore on the other side of Pluto.
2. Tomorrow, it will rain.
3. Open the door, please.
4. Whales are reptiles.
5. "Yond' Cassius has a lean and hungry
look."
6. Pegasus has wings.
7. You should vote in all important elections.
IV. More distinctions with regard to statements are worth
suggesting.
A. Consider whether there are two statements in
the box:
A Republican is President (of the U.S.).
A
Republican is President (of the U.S.).
1. Aside from the ambiguity of when the
statements are uttered, of which President is being spoken, and so on, we would say that
there is one statement and two sentences in the box. Sometimes logicians make a
distinction between a sentence token (the ink, chalk marks, or pixels) and a sentence type
(the meaning of the marks).
2. Every statement comes with an implicit time,
place, and reference.
B. Summary of the distinction between a sentence
and a statement assumes that adequate synonymy of expression and translation between
languages is possible.
1. One statement can be expressed by two
different sentences. E.g., the sentence …
2. A sentence can express different statements at
different times. E.g., the sentence …
“A Democrat is the U.S. President”
as expressed in 1962 and 2002 is two different statements since a Democrat was
President in 1962 and a Republican was President in 2002.
3. A statement is independent of the language in
which it is asserted, but a sentence is specific to the language in which it is expressed.
E.g., the sentences *…
“Das ist aber viel!” and “But that is a lot”
express the same statement, ceteris paribus.
4. A sentence can express an argument composed of
several statements. E.g., the sentence …
“The graphical method of solving a
system of equations is an approximation, since reading the point of intersection depends
on the accuracy with which the lines are drawn and on the ability to interpret the
coordinates of the point”
can be interpreted as two or three different statements — depending on how we
choose to analyze it. Normally, the sentence would be considered as being composed of
two premises and a conclusion. Thus, this sentence would be composed of three statements.
