Propositions and Symbols Used in Propositional Logic
Just as in traditional or Aristotelian logic, our main goal in propositional logic (or
symbolic logic) is to determine the validity of arguments. But because arguments are
composed of propositions, and because we need to symbolize the argument first before
we can determine its validity using a specific rule, we need therefore to discuss the
types of proposition and symbols used in symbolic logic.
Please note that symbolic logic uses only declarative statements or propositions
because any other types of proposition are not truth-functional, that is, they cannot be
either true or false. For example, the interrogative proposition “What is your name?” is
not truth-functional because we cannot assign any truth-value to it, that is, it cannot be
either true or false.
In similar manner, the exclamatory proposition “What an exciting journey!” cannot be
used in symbolic logic because, again, we cannot assign a truth-value to it. Hence, again,
we can only employ declarative propositions in symbolic logic because they are the only
types of proposition that can either be true or false. Think, for example, of the
proposition “Donald Trump is a racist president.” Depending on the context, we may say
“Yes, it is true that Donald Trump is a racist president,” or we may say “It is false that
Donald Trump is a racist president.”
There are two types of declarative proposition used in symbolic logic, namely, simple
and compound proposition.
On the one hand, a simple proposition is one that is composed of only one proposition.
For example, “Donald Trump is the president of the United States.” As we can see, this
proposition has only one component.
On the other hand, a compound proposition is composed of two or more propositions,
such as:
1) Jack is singing, while Jill is dancing.
2) If the road is wet, then either it rains today or the fire truck spills water on the
road.
As you notice, the first example is made up of two propositions, namely:
Just as in traditional or Aristotelian logic, our main goal in propositional logic (or
symbolic logic) is to determine the validity of arguments. But because arguments are
composed of propositions, and because we need to symbolize the argument first before
we can determine its validity using a specific rule, we need therefore to discuss the
types of proposition and symbols used in symbolic logic.
Please note that symbolic logic uses only declarative statements or propositions
because any other types of proposition are not truth-functional, that is, they cannot be
either true or false. For example, the interrogative proposition “What is your name?” is
not truth-functional because we cannot assign any truth-value to it, that is, it cannot be
either true or false.
In similar manner, the exclamatory proposition “What an exciting journey!” cannot be
used in symbolic logic because, again, we cannot assign a truth-value to it. Hence, again,
we can only employ declarative propositions in symbolic logic because they are the only
types of proposition that can either be true or false. Think, for example, of the
proposition “Donald Trump is a racist president.” Depending on the context, we may say
“Yes, it is true that Donald Trump is a racist president,” or we may say “It is false that
Donald Trump is a racist president.”
There are two types of declarative proposition used in symbolic logic, namely, simple
and compound proposition.
On the one hand, a simple proposition is one that is composed of only one proposition.
For example, “Donald Trump is the president of the United States.” As we can see, this
proposition has only one component.
On the other hand, a compound proposition is composed of two or more propositions,
such as:
1) Jack is singing, while Jill is dancing.
2) If the road is wet, then either it rains today or the fire truck spills water on the
road.
As you notice, the first example is made up of two propositions, namely:
