Exercise 2: The Concept of Validity
Due Date: Monday, January 24
Proportion of Final Grade: 5%
The evaluation of any argument involves two issues. First, are the premises of the argument plausible - that is, likely to be true? Secondly, do the premises provide satisfactory support for the conclusion of the argument?
Arguments are traditionally divided into two sorts: inductive and deductive. In an inductive argument, where the reasoning is good, the premises make it likely that the conclusion is true. In a deductive argument, on the other hand, the reasoning is good only if the relationship between the premises and the conclusion is such that it is logically impossible for all of the premises to be true, and yet the conclusion false.
Deductive arguments where the reasoning is good are described as valid arguments. A valid argument, accordingly, is one where the truth of the premises suffices to guarantee the truth of the conclusion.
Intuitively, then, what one can do to test whether an argument is valid is to ask oneself if one can imagine a world - which may be very different from the actual world - in which all of the premises of the argument true, and the conclusion false. If one can, then the argument is invalid (or fallacious).
In testing whether an argument is valid, it is important, when trying to imagine a world in which the premises are all true, and yet the conclusion false, not to add on to the premises, unconsciously, extra assumptions that one naturally associates with the premises in question. For adding on such extra assumptions may suffice to guarantee the truth of the conclusion when the original premises themselves would not have not done so.
Arguments can also be tested for validity in more formal ways. One method, which we considered in class, and which is applicable to many arguments involving statements containing words such as "all", "some", none", "always", "never", and so on, is the method of drawing a Venn diagram. If, in some cases, you are not confident about the result when you consider the argument in an intuitive way, you may want to make use of a Venn diagram to confirm your initial conclusion.
For each of the following
arguments, simply indicate whether you think that the argument is valid
or invalid. It is not necessary to justify your answer.
1. All fish can swim.
Some things
that swim live in the ocean.
Therefore, some
fish live in the ocean.
Valid ___ Invalid ___
2. If the Bible is the Word of God,
then everything in the Bible is true.
Everything
in the Bible is true.
Therefore, the
Bible is the Word of God.
Valid ___ Invalid ___
3. Ted Kennedy is a closet, John
Birch Society member.
No one who
is not a Democrat is a closet, John Birch Society member.
Therefore, Ted
Kennedy is a Democrat.
Valid ___ Invalid ___
4. All Nazis were anti-Semitic.
Hitler was
anti-Semitic.
Therefore, Hitler
was a Nazi.
Valid ___ Invalid ___
5. If Jesus did not rise from the
dead, then our faith is in vain.
But Jesus
did rise from the dead.
Therefore, our
faith is not in vain.
Valid ___ Invalid ___
6. Everyone who accepts the one
true faith will go to heaven.
Some women
will go to heaven.
Therefore, some
women accept the one true faith.
Valid ___ Invalid ___
7. Only if the burglars were sophisticated
professionals could
they have successfully
dismantled the alarm system.
The burglars
were unable to dismantle the alarm system.
Therefore, they
were not sophisticated professionals.
Valid ___ Invalid ___
8. All Republicans believe in private
property.
No Communists
are Republicans.
Therefore, no
Communists believe in private property.
Valid ___ Invalid ___
9. Anything placed in a safe container
can be transported.
Some explosives
are not placed in a safe container.
Therefore, some
explosives cannot be transported.
Valid ___ Invalid ___
10. Some vegetarians eat some dairy products.
Cheese is
a dairy product.
Therefore, some
vegetarians eat cheese.
Valid ___ Invalid ___