Valid and Invalid Logic
A valid argument can be considered as an argument that provides sufficient grounds for
accepting a conclusion as true if the stated premises of the argument are also true.
Valid arguments fall into two categories: deductive and inductive. In the first part of the
course we will examine deductive logic. In the latter part, inductive logic.
Deductive logic is a form of reasoning that assures us that if we start with true premises,
apply the rules of valid deductive logic, then our conclusions will also be true. In other
words, we will not come to false conclusions derived from the truth if we use deductive
logic. There are logical forms that when used will allow us to derive only truths if we
start with truths. These are called valid logical forms. If a false conclusion can derive
from true premises, then the logical form is said to be invalid.
Valid Logical Forms
Rule of Detachment -- RD
The first valid logical form we will use is called the Rule of Detachment.
The RD (Rule of Detachment) basically reaffirms the implication.
Recall the implication states that if proposition P is true then it follows that proposition Q
must also be true.
Implication: If P is true then Q is true.
Example:
Premise: All dogs have hair. (Implication)
Premise: Astro is a dog.
Conclusion: Astro has hair.
If both premises are true, we are guaranteed that the conclusion is true.
In symbolic form:
P Q
P
Q
Example:
Joe is an athlete.
Athletes have athlete’s foot fungis.
 Joe has athlete’s foot fungis.
In symbolic form:
P
P Q
Q
Note: The order of the premises is not important.
A list of premises followed by a conclusion is called a logical argument.
Note: There are many logical arguments. RD is a valid logical argument form.
Many other logical argument forms are not valid.