Distinguishing Valid and Invalid Deductive
Arguments
The following method can’t be used to evaluate every deductive argument,
but it can be used to evaluate many of them.
Let’s start by noticing that there are four very common argument forms that
we tend to encounter in everyday discourse:
Valid
Invalid
If (a) then (b)
If (a) then (b)
If (a) then (b)
If (a) then (b)
(a)
Not-(b)
(b)
Not-(a)
(b)
Not-(a)
(a)
Not-(b)
By translating common sentences like “All dogs are mammals” into a
conditional (if___ then ____) format, we can easily test arguments for
validity. Consider the following example:
“Every human has a heart. Jim is a human, so he must have a heart.”
We can see that the conclusion of this argument is “Jim has a heart”, so we
can set the argument up as follows:
Every human has a heart
Jim is a human
_____________________
Jim has a heart
To test this argument for validity, all we need to do is translate the first
sentence into a conditional form. Here’s a rough guideline for how to do it:
The words “all”, “every”, and “if” generally introduce the antecedent
(the “a” term) of our conditional. The words “only” and “only if”
generally introduce the consequent (the “b” term) of our conditional.
