T1.3: 3 of 8
So, frequently we need to give arguments even when our evidence only
makes a conclusion likely, but not inescapable. Here's another
example of this "inductive" thinking:
I have surveyed hundreds of students here at ITU and found
that less than 10% say they are happy with the new course fees. My sample
was selected at random. So, I conclude with confidence that the vast majority
of ITU students do not find the course fees acceptable.
Here, the argument's author is clearly claiming that the evidence cited
makes the conclusion likely to be true but not a certainty (surveys sometimes
do go badly awry, for instance when the participants have some reason
to lie.) So, this argument is a clear case of an inductive argument.
To Reiterate : An argument is inductive
if and only if its premises are intended to lead to its conclusion
with high probability.
We do not say that an inductive argument is valid when it succeeds
at supporting its premises as intended. Rather, an inductive argument
who's premises do support its conclusion as intended (i.e., they make
the conclusion likely) is called "inductively strong":
An argument is inductively strong if and only if its conclusion is highly probable to be true given its premises.
Inductive strength is a counterpart to validity: by definition, deductive
arguments are intended to be valid, inductive arguments are intended to
be inductively strong. Of course, people often give arguments falling
short of what was intended. That's why we have logic classes! But the
point is that the concepts of validity and of inductive strength play
similar roles for deductive and inductive arguments respectively: such
arguments support their conclusions as intended.
Finally, we need to define a counterpart to "sound" for inductive
arguments. Remember, that an argument is sound if and only if it's both
valid and has all and only true premises. For an inductive argument, just
substitute "inductively strong" for "valid" to get
the notion of cogency:
An argument is cogent if and only
if it is both inductively strong and all its premises are true.
Why do we study deductive logic rather than inductive
logic? Doesn't it seem that most arguments are inductive anyway? These
are good questions and their answers are not easy to give completely in
just a few sentences. But to begin:
 We are interested in studying logical possibility and meaning. This
is a core of logic. It's deductive logic.
 Even within the more common inductive thinking, deductive argumentation
is often an important part. (For example, if I try to convince you that
deductive logic is important — that's this page! — I'll be
arguing inductively. But in so doing, I'll sometimes utilize steps that
are themselves deductive. For example, 1 applies the definition of "deductive
logic".)
 Deductive logic, unlike inductive thinking, is formalizable. This
allows us to treat deductive logic in a simpler, more systematic way.
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