DEDUCTIVE AND INDUCTIVE
ARGUMENTS
Deductively valid arguments are arguments in which the
premises guarantee the truth of the conclusion. If the premises the
true, the conclusion must also be true. Deductive arguments have a
formal structure, which can be put into symbolic form. Deductive
arguments are either valid or invalid based on their structure or
form, so they are sometimes called formal arguments. We looked at
some basic deductively valid argument forms: modus ponens, modus
tollens, disjunctive syllogism and dilemma. We also looked at
two formal fallacies; denying the antecedent and asserting the
consequent.
You can put any set of premises and any conclusion into a valid
deductive argument and know that the conclusion is true if the
premises are. If Socrates is human and hemlock is fatal to all human
beings, it follows as a matter of logic that Socrates will die after
drinking the hemlock. If Socrates drinks the hemlock and seems no
the worse for wear, then one of our premises must be false. Either
he's not really a human being - maybe he's a god in human disguise
or an alien - or it's not true that hemlock is fatal to all human
beings. Maybe he didn't really drink the hemlock. Maybe some human
beings have an immunity to hemlock. Whatever the case, we know that
one of our premises must be false, because if the premises were
true, the conclusion would have to be. If the premises are not true,
nothing can be deduced about the truth of the conclusion.
Inductively strong arguments only guarantee the truth of the
conclusion with a certain degree of probability. If the premises are
true, then the conclusion is probably true, perhaps with
99.999999999% certainty, but there is a logical possibility
that it's false. Why not just go with deductive arguments then? Take
the following example: "If the defendant had the means, motive and
opportunity to commit the crime, then he is guilty. He had the
means, motive and opportunity to commit the crime, therefore he is
guilty." That's modus ponens and a deductively valid
argument. But how do you know the second premise is true? The
prosecutor gains nothing by casting his argument in deductive form,
because what matters is the strength of inductive evidence, not the
formal structure of his argument. It's more natural to argue, "The
defendant had the means, motive and opportunity to commit the crime,
therefore he is guilty to a reasonable doubt. Most arguments
are inductive in nature and attempting to stuff them into a formal
deductive structure is counter-productive.
Logicians reserve the terms valid and invalid for deductive
arguments but refer to inductive arguments as strong or weak.
Like deductive arguments, they can go wrong in two ways: weak
premises or faulty logic. If one of the premises is
false or doubtful, then the conclusion doesn't logically follow. Or,
all of the premises may be true and well grounded in evidence, but
they still don't support the conclusion. Suppose someone argues,
"The rich hardly pay any taxes, therefore any tax reform plan should
exclude them. This might be a good argument if the premise was true,
but it's not. For example, the top 20% pay 95% of all Federal income
taxes, whereas the bottom 40% pay nothing or get money back. The
flaw in this argument is a faulty premise. On the other hand,
suppose someone argues, "Margaret Sanger, the founder of Planned
Parenthood, was a white supremacist and promoted abortion as a means
of keeping keeping the 'less desirable' races from breeding.
Abortion is a eugenics project." The premise is actually true in
this case, but doesn't support the conclusion. Just because Planned
Parenthood was founded on eugenicist principles doesn't mean it
operates on those principles today. To conclude something about a
thing based on its origin is called the genetic fallacy.