There need to be a few things clarified in what we are about
to discuss. First, let me briefly
define what an argument is and what it isn’t. An argument is a
collection of statements – which assert something is or is not the case
– in which one statement (the conclusion) is said to follow from the other
statements (premises). In other words, the premises are meant to provide
support for the conclusion. A statement which asserts/claims something is the
case or is not the case is a proposition. Second, if an argument follows the rules of logic, then it is a valid
argument. To say an argument is valid is to say the conclusion follows from the
premises. An argument being valid has nothing to do with the premises
and the conclusion being true or false. An argument being valid is concerned
with the form or structure of the argument; it is not concerned
with the truth of the premises or the conclusion. By contrast, if the conclusion fails to follow from the
premises that preceded it, then the entire argument is invalid. For an
argument to be a sound argument the conclusion has to follow from
the premises and the premises have to be true. But in this blog post
we will not be discussing the soundness of an argument but its validity.
Rule #1
Modus Ponens
This is a rule, which is very simple and straightforward to understand.
The rule Modus Ponens can be defined as follows: A rule of inference in which a certain truth is automatically implied
by another truth that precedes it: P implies Q. P; Therefore, Q. I will
show a few examples on how this is worked out.
Example #1
-
Since
I am hungry for Italian food right now, I will go to Olive Garden to eat.
-
I
am hungry for Italian food right now.
-
Therefore,
I will go to Olive Garden to eat.
Example #2
-
Anything
that comes into existence has to have a cause
-
The
universe came into existence
-
Therefore,
the universe has to have a cause
Example #3
-
If
it is raining outside, then I will stay inside
-
It
is raining outside
-
Therefore,
I will stay inside
Rule #2
Modus
Tollens
Modus Tollens is similar to Modus Ponens but has a critical difference. In Modus Tollens, the
second half of a premise (the consequent) is denied or negated in the second
premise of an argument:
P > Q (the > sign means implies. Q is implied by P or is a consequence of P)
~Q (the ~ sign means negation or denial. Q is being denied in this case)
~P
Whatever is true of P is also true of
Q and vice versa. There is never a time in which something is true of either P
or Q but false of the other variable. Let’s look at some examples.
Example #1
-
If
God does not exist, then objective moral values do not exist
-
Objective
moral values do exist (Notice that this premise is a *denial* of the second part of the first premise)
-
Therefore,
God exists
Example #2
-
Since
the Pacers have tied the series 2-2 with the Heat, they will win the remaining
games of the Eastern Conference Finals
-
They
will not win the remaining games of the Eastern Conference Finals
-
Therefore,
the Pacers have not tied the series 2-2 with the Heat
Example #3
-
Whatever
comes into the marketplace to be sold must be fresh food
-
Raspberries
are not fresh food
-
Therefore,
raspberries did not come into the marketplace to be sold
In the next blog post pertaining to logic I will talk about a
hypothetical syllogism and a disjunctive syllogism. Stay tuned!
