Logical and Critical Reasoning
and Munson and Black,
The Elements of Reasoning
were used as sources for the above information.
The Basics of Arguments III
NECESSARY AND SUFFICIENT CONDITIONS
is a condition which
be present in order for a given result to follow.
example, there are a number of necessary conditions that govern whether or not our car will start moving
when we press the accelerator.
There must be gas in the car, the car must be turned on, the engine must
be working, etc.
A necessary condition is
to bringing about a result, but does not guarantee that
is one which, whenever it is present,
produces a given result. If my Saturn SL2
lacks an engine, this is a sufficient condition for knowing that it will not work properly.
condition is just that
, it is all that is needed, to bring about a certain result.
These terms can be applied to some of the statement forms we
ve looked at so far.
For example, in the
, we know that if P is true then Q must also be true.
Therefore, P is sufficient to
guarantee Q; in other words, P is a sufficient condition for Q.
On the other hand, Q is a necessary condition
for P: Q must be true, in order for P to be true.
Q is necessary for P.
In evaluating arguments symbolically, we must use the following rules establishing equivalent (and
therefore substitutable) argument forms.
An equivalent form is another way of stating the same thing.
Many of these will look like common sense, but it is necessary to know them in their standard forms.
Double Negation (DN)
This is certainly common sense: a thing is the opposite of its opposite; P is not the opposite of P; P
is not not-P.
This allows us to switch the two terms of a conjunction:
P and Q
is the same as
Q and P
applies to disjunctions,
We can switch their terms because the order of
(On the other hand, this is not true in
the case of implication:
If Q then P
the same as
If P then Q.
Albert has a pet lizard and a pet monkey.
is equivalent to
Albert has a pet monkey and a pet lizard.
(P v Q)
↔ (Q v P
Either James will win the game or Marie will.
is equivalent to
Either Marie will win the game or James will.