The unit of reasoning is called an argument. Another term for an argument is an
inference . There are two types of reasoning: justificatory and explanatory. Justificatory
reasoning is used when we want to prove a conclusion, or show that it is likely to be true.
Explanatory reasoning is used to explain why something is true. In this course we are concerned
more with justificatory reasoning.
Official definition: An argument is a set of statements , some of which are offered in
support of another. The statement one is attempting to support is called the conclusion. The
statement(s) offered in support of the conclusion are called the premise(s). Premises are offered
as reasons or evidence to take the conclusion t o be true.
What is a statement? A statement is a sentence that has a truth value, that is, it is either
true or false. The fact that it has a truth value does not imply that we know what that truth value
is. Not all sentences have truth values. Remem ber the grammatical classification of four types
of sentences – declarative, interrogative, imperative, and exclamatory. Which types do not
typically have truth values?
Normally we make statements in the form of declarative sentences: “God exists.” “The
Earth has one natural satellite.” “2 + 2 = 7.” “It certainly is warm today.” It is possible to
express a statement in other forms of sentence. In particular, we sometimes express statements
in the form of questions, and imperatives can also be reworded as statements. What do we call
questions which are used to make statements?
The point of justificatory reasoning is to demonstrate the truth of a conclusion, by
offering one or more premises in its support. Here is an argument, presented in a standar d
format, with the premises given above the line, and the conclusion below the line:
1. Everything that exists has a cause.
2. The universe exists .
3. Therefore, the universe has a cause.
The above argument has two premises. Not all arguments have two p remises. Here is another
argument, with only one premise:
1. In a recent study, 66% of the people who took medication X had fewer colds.
2. Therefore, over half of the population in general who take medication X will have
fewer colds.
Notice that the definition of an argument says only that one must offer some statement(s) in
support of the conclusion. It does not say how many must be offered. The only restriction is that
the number of statements must be finite.
When one makes a statement without offering any supporting reason, one is not making
an argument. A set of statements in which none are offered to support another therefore do not
constitute an argument. The key to an argument (or inference) is offering at least one statement
(premise) to accept ano ther statement as true.
Now, let’s see how much of this you understood. Answer the following questions:
1. How many statements, at a minimum, must an argument have?
2. How many premises must there be in an argument?
3. Why does the definition say that the premises are “offered” in support of the conclusion,
rather than that the premises in fact support the conclusion?
2 22
Arguments can become very complex. As we shall see, one can reason serially, using a
conclusion as support for a further conclusion. The distinction between premise and conclusion
is a functional distinction: whether a statement is a premise or conclusion in an argument
depends solely on whether it is used to support another statement (thereby becoming a premise)
or whether one is offer ing statements to support it (thereby becoming a conclusion). Thus the
same statement may function as a premise in one argument and a conclusion in another.
Consider this example:
1. Everything that exists has a cause.
2. The universe exists.
3. Therefore, the universe has a cause.
4. The cause of the universe could only be God.
5. Therefore, God exists.
6. Therefore, God must have a cause. (By 1 and 5.)
Question: how many arguments are there here? We identify and individuate arguments
(or infe rences) by the conclusion. Each inference to a conclusion counts as a separate argument.
(We shall see when we evaluate arguments why this is so.) So the answer is that there are three
arguments in the above example, arranged serially. So look at state ments 3 and 5. Are they
conclusions or premises or both? Answer: it depends on which inference you are talking about.
In the first inference, from statements 1 to 3, statements 1 and 2 are the premises, and statement
3 is the conclusion. In the second inference, from statements 3 to 5, statements 3 and 4 are
premises, and statement 5 is the conclusion. Similarly, statements 5 and 1 are premises in the
third inference, where statement 6 is the conclusion. Statements 3 and 5 are also called sub -conclusions, and statement 6 the final conclusion of the argument.
DEDUCTIVE AND INDUCTIVE ARGUMENTS
There are two types of justificatory reasoning: deductive and inductive. They differ in
terms of their evidence and purpose. Deductive arguments are those in which one intends to
guarantee the truth of the conclusion. When one argues deductively, one offers premises or
evidence that one takes to provide sufficient justification to show that a conclusion must be true.
Here are some common forms of deductive reasoning:
1. All humans are mortal. 1. If Jill owns a Porsche, then she owns a car.
2. Socrates is human. 2. Jill owns a Porsche.
3. Therefore, Socrates is mortal. 3. Therefore, Jill owns a car.
In inductive reasoning one offers premises or evide nce to provide some support for the
conclusion. The best one can do in inductive reasoning is to demonstrate that a conclusion is
probable or likely to be true . This is because the premises offer empirical evidence , or evidence
derived from experience or observations. In inductive arguments, the premises make claims
about observed cases, and draw conclusions about unobserved cases, as in the following:
1. All swans observed so far are white. 1. In the past, the sun has risen every day.
2. Therefore, all swan s are white. 2. In the future, the sun will rise every day.
Because deductive and inductive arguments have different purposes (related to the different
types of evidence they offer), there are different methods for evaluating them. Put briefly,
deducti ve arguments can be evaluated for validity and soundness. By contrast, inductive
arguments are evaluated in terms of their degree of strength. Because most philosophical
arguments are deductive, we shall focus on the concepts of validity and soundness.
3 33
IDENTIFYING ARGUMENTS: INFERENCE INDICATORS
Inference indicators are words or phrases used to indicate that someone is making an inference
(an argument). Because inferences have two parts – premises and conclusions – there are two
types of indicators. In both cases the indicator precedes the statement it indicates as a premise or
a conclusion. For example, this sentence has two statements, and one inference indicator:
“Because the final counts for 30% of your grade, you should study carefully for it.”
The indicator here is the word ‘Because’, which is a premise indicator. This word indicates that
the first statement ‘the final counts for 30% of your grade’ is used as a premise to support the
statement ‘you should study carefully for it.’ The followin g sentence makes the same argument,
but uses a conclusion indicator instead of a premise indicator:
“The final counts for 30% of your grade, so you should study carefully for it.”
The same statement functions as a premise supporting the same conclusion.
Here are some common premise indicators:
Because… since…(time exception) for…(preposition exception)
as shown by… as indicated by… follows from…
assuming that… for the reasons that… in view of the fact that…
may be inferred /derived from…
Here ar e the most common conclusion Indicators:
Consequently… Therefore… So…
I conclude that… proves that… hence…
Which shows that… must… (some exceptions) implies that…
Entails that… accordingly… allows us to infer that…
Thus… (exceptions) demonstrates that… it follows that…
These are not the only ways to indicate premises and conclusions, but these are the most
common. You need to think about the meaning of the phrases preceding statements that might
be construed as reasons or conclusions.
Another point to keep in mind when identifying arguments is that premises and
conclusions can be stated in any order. The brief argument given above can also be stated with
the conclusion given before the premise: “You should study carefully for the final, si nce it
counts for 30% of your grade.” So when you are reading for arguments, you have to identify the
premises and conclusions in terms of which statements offer support, and which statements are
being supported.
Some reasoning contains NO inference i ndicators, e.g.: “It’s going to rain. You should
take an umbrella.” To decide whether discourse contains reasoning, we go through this
procedure:
1) we look for inference indicators. If we find them, we must analyze the reasoning
following the infere nce indicators (even if it is not good reasoning).
2) if there are no inference indicators, we follow the Principle of Charity. The
Principle of Charity says that you must interpret the passage so as to make it the strongest
reasoning possible . This means: If a passage has no inference indicators and there is no way to
interpret it as containing good reasoning, we must call it nonreasoning. If the passage has
inference indicators but there is more than one possible interpretation, we must choose the
i nterpretation that results in the strongest reasoning. Now why do we do this?
Remember: the argument is in the speaker’s or writer’s intention. If someone is offering
premises to support a conclusion, we must call it an argument, even if the reasoning is bad
reasoning. Once you understand this point, you will be on the way to understanding the
nature of argument.
4 44
Argument identification exercises
Decide which of the following passages contain arguments. Be able to defend your
position. For those that do, use inference indicators to determine which statements are premises
(reasons) and which are conclusions. In some cases you may need to insert inference indicators
where they are reasonable. You also may need to supply an implicit conclusion (one that is
logically implied but not actually stated). Do your best.
1. John would help us move, but he has a bad back. So we are going to need to find someone
else.
2. Men are better at lifting heavy furniture than women.
3. She must have money. Just look at the clothes she’s wearing.
4. The nicotine in tobacco is addictive like heroin. Therefore, tobacco should be treated as a
drug.
5. Using threats of foreign trade sanctions as a device to punish nations that violate human
rights is a bad poli cy, for it does not change the behavior of the violators and only hurts our jobs
and trade.
6. If Jones were the thief, he would have skipped town. But he stayed around. Can you see
what that says?
7. Everybody has needs. You don’t fill mine. So I’ m splittin’.
8. Don’t chew ice. You may crack a tooth.
9. She’s been married since last June.
10. Heat the oil in a frying pan with a cover. When hot, add the onion, ginger, garlic, and salt
and pepper to taste, and stir fry for 1 minute. Add the cauliflower and turn the pieces in the oil
in a gentle stir fry for 2 minutes. Add vegetable broth, butter, and milk, and continue to stir fry
gently for 2 minutes, until the butter has melted and the liquid has coated the vegetable and is
boiling vigorously.
11. Smoking endangers nonsmokers too. It should be banned from buildings open to the public.
12. The houses were covered with vines bearing bell-shaped flowers playing coloraturas. The
guitars inside of the houses or on the doorsteps took up the color chromatics and emitted sounds
which evoked the flavor of guava, papaya, cactus figs, anise, saffron, and red pepper.
13. Neutron: a neutral uncharged particle of atomic weight approximately unity…. Closely
packed neutrons and protons compose the nuclei of all atoms. The neutron is slightly heavier
than the proton; in the free state it decays, yielding a proton, with a half life of about 12
minutes. It has some magnetic properties.
5 55
EVALUATING DEDUCTIVE ARGUMENTS: VALIDITY AND SOUNDNESS
When we evaluate DEDUCTIVE arguments, we are trying to determine whether the
premises succeed in proving the truth of the conclusion. (For inductive arguments, the premises
can supply weak to strong support, but cannot conclusively prove a conclusion.) A succ essful
deductive argument is called a sound argument . To be sound, a deductive argument must pass
two tests: the validity test and the truth test. These tests are independent of each other: an
argument can pass both, or fail both, or pass one but not th e other.
1. Deductive Validity: has to do with the logical correctness or form of the argument,
with the degree of support the premises give the conclusion. In testing for validity, we have to
decide whether the conclusion follows logically from the premises.
2. Truth: has to do with the actual truth value of the premises (NOTE: only the
premises, not the conclusion). In particular, we must decide whether all the premises of the
argument are in fact true (to the best of our ability).
If an ar gument flunks either test, then it is UNSOUND:
SOUNDNESS = DEDUCTIVE VALIDITY + TRUTH (of all the premises)
Terminology: An argument is not true or false; it is valid or invalid. Individual statements in
the argument (premises and conclusion) are true or false, but they are not valid or invalid. The
statements are not sound or unsound, only a complete argument is sound or unsound.
Validity: A deductively valid argument is one in which, if the premises were true, the
conclusion must be true. ( Note that this does not say that the premises are in fact true.) In
other words, if in evaluating an argument, we decide that even if the premises were true the
conclusion could still be false, then we have decided that the argument is invalid.
Here is a deductively valid argument: 1. If Sadie is a cat, then Sadie is a mammal.
2. Sadie is a cat.
3. Therefore, Sadie is a mammal.
Now does the validity of the argument depend on whether premises 1 and 2 are both true? What
do you need to kno w to decide whether the argument is valid? Sound?
What about this argument? Is it valid? Is it sound? Defend your answers by reference to the
definitions. 1. All elected politicians are liars.
2. Clarence Thomas is an elected politician .
3. The refore, Clarence Thomas is a liar.
What about this argument: is it valid? is it sound?
1. Some roses are red.
2. Some violets are blue .
3. Therefore, interest rates will not rise this year.
In reading philosophy, when you encounter an argume nt, you should ask these questions:
Is it a valid argument; that is, if the premises were true, would the conclusion have
to be true?
Are the premises in fact true (to the best of my knowledge)? If I think the conclusion is
false, can I sa y which of the premises are false or explain why the argument is invalid? Can I
defend my evaluation?
6 66
Homework
Evaluate the following deductive arguments according to the validity and truth tests. Say
whether they are valid or invalid, and sound or unsound . Defend your answers. If you cannot
decide on soundness, explain why .
Argument 1:
1. Anyone who is in San Bernardino is in California.
2. I (the student now doing this homework) am currently in California.
3. Therefore, I (the student now doing this homework) am currently in San Bernardino.
Argument 2:
1. All CSUSB professors are under the age of 29.
2. Dr. Nist is a CSUSB professor.
3. Therefore, Dr. Nist is under the age of 29.
Argument 3:
1. Barack Obama is currently President of the United States.
2. Therefore, water is composed of two molecules of hydrogen and one molecule of oxygen.
Argument 4:
1. All trout are cats.
2. All cats are fish.
3. Therefore, all trout are fish.
Argument 5:
1. If I own a Boeing 747, then I own an airplane.
2. I don’t own a Boeing 747.
3. Therefore, I don’t own an airplane.
Argument 6:
1. If I own a Boeing 747, then I own an airplane.
2. I don’t own an airplane.
3. Therefore, I don’t own a Boeing 747.
PLACE THIS ORDER OR A SIMILAR ORDER WITH US TODAY AND GET AN AMAZING DISCOUNT 🙂