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This article and video were made by Candice 
Soundness and Cogency
This topic is going to bring together all
of the components of argument evaluation we have looked at so far and introduce
concepts to apply to arguments as a whole, rather than just individual parts.
You will remember that when we evaluate arguments, we are essentially asking
two questions;
1. Are the premises true?
2. Do the premises give support to the
conclusion? (Irrespective of their truth)
We have covered these questions
separately in detail in previous articles, and a decent understanding of those concepts
is required to understand the new topics introduced here.
So far we have looked at both orthodox
(used alone in formal logic) and unorthodox (used in informal reasoning)
criteria for answering the above two questions. Today we are going to combine
the principles we have covered in order to introduce terminology to describe an
argument as a whole.
Essentially, the question we are asking
is; What is a good argument?
First we will look at the orthodox
criteria...
In the orthodox criteria (formal logic),
a premise or conclusion is either true or false; the argument is valid or
invalid. This can make the orthodox criteria easy to handle since there are no
intermediate degrees. According to formal logic, one is either right or wrong.
The orthodox criterion for evaluating and argument as a whole is soundness. An
argument is sound when it is deductively
valid and has true premises.
An argument may fail to be sound in one
of two ways; the argument isn’t deductively valid, or at least one of the
premises of the argument is false.
The following bits of information should
help you understand soundness a little better.
An argument being unsound does not make
the argument invalid, but the argument being invalid does make it unsound. This
is because an argument can have false premises and still be valid, but a sound
argument cannot have false premises.
An argument being sound means all of its
premises are true, but if an argument is unsound it does not mean at least one
of its premises is false. This is because arguments may have all true premises
but the argument can still fail to be deductively valid making it unsound.
An example of an argument with true
premises but is invalid therefore unsound;
"God has
not shown himself to us and he has not performed miracles any of us have witnessed
so he does not exist."
An argument being unsound does not mean
the conclusion is false, but if the conclusion is false then the argument is
unsound. This is because the argument's conclusion cannot fail to be true if
the argument is deductively valid and it has all true premises.
An example of a sound argument with true
premises, a true conclusion and deductively valid;
"Violence
towards other human beings is a violation of the non-aggression-principle. The
more vulnerable and helpless human beings who have violence enforced on them
the more the non-aggression-principle is violated. Children are the most vulnerable
and helpless human beings. Therefore, violence towards children is the biggest
violation of the non-aggression-principle."
The following is a sound argument, but is
it a good one?
"God does
not exist therefore the bible is false."
Despite the premise being true and the
inference being valid (if we negated the conclusion and conjoined it to the
premise it would clearly make a contradiction), the argument fails to convince
us of its conclusion because anyone who disagrees with the conclusion is going
to disagree with the premise. So we can see that a sound argument can end up
begging the question, which would be useless if we were attempting to convince
someone else of the conclusion of this argument. It is a common mistake to
assume that a sound argument is a good one, the above is an example of a poor
argument that is still sound.
This example though is probably not very
representative of the sort of argument you will face in your daily lives (even
the most ignorant among us would see that such an argument is useless for
convincing people of its conclusion). Something you may come across more could
be in the following format:
"You
think that all religious people are bad, but some of them are not bad, so not
all of them are bad. Therefore you are wrong to think that all of them are bad."
The argument is deductively valid, and it
has true premises, so what could be the problem? Simply by telling someone that
something they believe isn’t the case probably won't convince them, so this
argument is also poor.
On the other hand, it would be a mistake
to assume that an unsound argument is not a good argument because it is
unsound. Take the following example:
"Jimmy’s
fingerprints were on the gun. Street cameras indicate that he was the only
other person on the street at the time. He ran very fast when the police sirens
could be heard and he even admitted to the murder. Jimmy must be the murderer."
The premises here are all true, but the
argument is not deductively valid, the argument is unsound but the premises
give strong support to their conclusion, so we could still reasonably call this
a good argument. It isn’t a deductively valid argument because there may be a
myriad of reasons as to how Jimmy may not end up being the murderer, hence
making it unsound, but from this example we can see an argument does not need
to be sound for it to be convincing.
Obviously soundness is not enough for us
to judge an argument as being good. We will now look at the unorthodox
criteria, which helps to solve the problem of the formal logic being too black
and white, since according to formal logic the above arguments about religion
would be considered good arguments (they are both valid and have true premises)
but it is easy to see these arguments fail to fulfil their purpose of
convincing another of their conclusions.
Unlike formal logic (orthodox criteria) in informal reasoning
(unorthodox criteria) arguments have intermediate degrees; the support between
the premises and the conclusions can vary from weak to strong, and premises
that are not proven to be true can still be acceptable.
An argument is cogent
when the premises are rationally acceptable and the argument offers strong or
complete support for its conclusion.
The religious arguments above could never
be considered cogent because they beg the question, but the third one about
Jimmy being the murderer certainly is despite not being valid. This is because
there is a strong degree of support between the premises and the conclusion and
the premises are rationally acceptable.
So an argument can fail to be cogent in
one or two ways; it may not have premises that are rationally acceptable to the
audience it is being presented to, and/or the premises may not give strong
support to the conclusion.
A valid argument with acceptable premises
is not guaranteed to be sound, but a valid argument with acceptable premises is
guaranteed to be cogent. This is because acceptability of premises does not
mean that they are true, just that they are acceptable to the audience at hand,
and it is a requirement for a sound argument to have true premises. If an
argument is sound then that does not make it cogent, because its premises may
be unacceptable, even if true, to the audience.
Perhaps the biggest problem is that an
argument is cogent sometimes even when the premises aren’t true, for example;
"The
stars and sun move around us, so we are at the centre of the universe."
This would have been quite acceptable a
few centuries ago, but because this argument was so accepted and considered
widely held belief for many years we were prevented from finding out the
truth. What is considered rationally
acceptable and giving strong support to its conclusion may also change over
time.
So the best kind of argument one can
possibly make is cogent and sound; the argument is deductively valid, has all
true premises, strongly supporting the conclusion and the premises are
rationally acceptable to their audience, leading to proof of the conclusion. If
all arguments were this way though, it would sort of make debating a little bit
boring (in fact, debates would probably never even take place to begin with!).
Arguments are usually about establishing
that a claim is true, I would like to examine refutation now- how to establish the falsity of a claim. The two topics
aren’t really different; establishing a claim is false is the same thing as
establishing the denial of that claim is true.
One useful method of refutation of
general claims is by use of counter-examples. Let’s refer back to the argument
made in orthodox criteria that a good argument is sound and always justifies
its conclusion, but it was easy to demonstrate this is not necessarily so by
producing a counter-example which showed a sound argument failed to justify its
conclusion. Counter-examples are very powerful in refutation because one need
only produce an instance where the claim doesn’t hold true and then the claim must
be retracted or modified.
In most cases an actual instance must be
demonstrated in which the claim doesn’t hold true. Here is an example; someone
who lives in Europe, has never travelled to the Southern hemisphere and never
read any books about birds, might say that all swans are white, but someone
from the Southern Hemisphere could pick up a bird book, identify a breed of
swan which is black, show photos etc, then the claim ‘All swans are white,’
would have to be retracted or modified. Pointing out the breed of black swan is
a good counter-example. In the case of a claim being asserted as necessarily
true, it is possible to refute it by using a counter-example which is a mere
possibility.
Another very useful technique for refutation is Reductio ad absurdum which is Latin for 'reduction to absurdity'.
It is done by taking an opponents claim, and perhaps with the aid of some
agreed premises, infer an obviously false conclusion from it. False conclusions
cannot come from true premises in valid arguments, so this shows that their
claim is false. This topic involves more detailed knowledge of conditionals
than we have covered thus far, so we will come back to Reductio in detail later.