260 Unit 7 Critical reasoning: Advanced Level
not support the conclusion. Even if we later
find out that the conclusion was in fact true,
and the ring did contain a genuine diamond,
the argument would still remain a fraud!Deductive standards – and limitations
The arguments examined in this chapter –
even the more natural ones – have been
deductive in character. The standard of
validity required for a deductive argument is
very strict and unbending. Deductive
arguments are intended to draw conclusions
with absolute certainty. The kind of proofs
that logicians and mathematicians use depend
on rigid deductive arguments, and nothing
less will do. But some quite ordinary reasoning
can also be interpreted as deduction, as we
have seen in several of the examples.
Partly because deductive arguments are so
watertight, they can be rather limited, too. For
a conclusion to follow validly from its premises,
the premises have to be stronger than the
conclusion. To use the more technical term, the
premises must entail the conclusion. It is often
said that if we know the premises of a deductive
argument, the conclusion itself tells us nothing
we did not know already. There is something in
this. Certainly if we know that all true fish do
have gills, and that whales have no gills, then
we really do not need to add that whales are not
fish. In a way, deductive arguments are more
like proofs explaining why something is true,
than means to discovering new facts or
supporting new hypotheses.
By no means all argument is deductive.
Moreover, not all reasoning requires the same
level of certainty from the conclusion. Often it
is sufficient to be able to say that the truth of a
claim that is supported by an argument is
beyond reasonable doubt, or even that it is
more likely than not to be true – i.e. true on
the balance of probabilities.
In the next chapter we turn our attention to
certain kinds of non-deductive reasoning, and
arguments which fall short of deductive
validity, but still have powerful persuasive force.Activity
Read the following carefully and decide if you
think it is sound or unsound.
[13] No ring with a diamond that size
would sell for less than $20,000.
Miranda Marchi’s ring fetched
$50,000 in an auction, so the stone
in it has got to be a diamond.Commentary
This time we are not told whether the reasons
are true or not, but let’s suppose they are, for
the sake of argument. Therefore we accept that
the stone in the ring is big enough to be worth
at least $20,000, if it’s a diamond; and we
accept that the ring really did fetch well over
that figure in an auction. Could these two
premises be true and still lead to a false
conclusion?
Yes, they could. There are all kinds of
circumstances under which the ring could
have sold for a very high price without being a
diamond. The buyer could have been a fool.
Alternatively Miranda Marchi could have been
a celebrated film star, who had worn the ring
(with a fake diamond in it) in her best-known
film. No one had ever pretended it was real; it
fetched a high price as a collector’s item.
There are many plausible scenarios under
which the premises could be true and the
conclusion false. So the argument is not
reliable. Unlike the ring that featured in the
previous example, which could not have been
a real diamond and have a value of $20, this
stone could have been a fake and still sell for
thousands. That possibility makes the
argument invalid – along with all arguments
that follow the same pattern.
A fair assessment of this argument would
therefore be: we don’t know if the premises are
true or not, but we can say that the argument
is unsound anyway, because the reasons do