Inclusive Disjunction in Propositional Logic
A disjunction or disjunctive statement is a compound statement or proposition that is
connected by the words “Either…or” or just “or.”
And the component statements in a disjunction are called “disjuncts.” There are two
types of disjunctive statements used in symbolic logic, namely: inclusive and exclusive
disjunction. In this post, I will only focus on inclusive disjunction.
As I discussed in my other notes titled “Propositions and Symbols Used in Propositional
or Symbolic Logic (see http://philonotes.com/index.php/2018/02/02/symbolic-logic/),
the symbol for the connective “Either…or” is v (wedge).
Inclusive disjunction uses the connective “Either…or, perhaps both.” Consider the
example below.
Either Jake is sleeping or Robert is studying, perhaps both. (J, R)
If we let J stand for “Jake is sleeping” and R for “Robert is studying,” then the statement
“Either Jake is sleeping or Robert is studying, perhaps both”is symbolized as follows:
JvR
Please note that the constants J and R do not just represent Jake and Robert
respectively; rather, they represent the entire statement. Thus, J represents “Jake is
sleeping,” while R represents “Robert is studying.”
It must also be noted that in most cases, the phrase “perhaps both” in an inclusive
disjunction is not written in the statement. Thus, in determining whether the statement
is an inclusive or an exclusive disjunction, we just need to analyze the statement per se.
Let us consider this example:
Either Jake is sleeping or Robert is studying.
As we notice, the statement does not contain the phrase “perhaps both.” But if we
analyze the statement, it is clear that it is an inclusive disjunction because it is possible
for the two component statements, namely, “Jake is sleeping” and “Robert is studying,”
to occur at the same time. (Please note that I will discuss the nature and characteristics
of an exclusive disjunction in my next post.)
A disjunction or disjunctive statement is a compound statement or proposition that is
connected by the words “Either…or” or just “or.”
And the component statements in a disjunction are called “disjuncts.” There are two
types of disjunctive statements used in symbolic logic, namely: inclusive and exclusive
disjunction. In this post, I will only focus on inclusive disjunction.
As I discussed in my other notes titled “Propositions and Symbols Used in Propositional
or Symbolic Logic (see http://philonotes.com/index.php/2018/02/02/symbolic-logic/),
the symbol for the connective “Either…or” is v (wedge).
Inclusive disjunction uses the connective “Either…or, perhaps both.” Consider the
example below.
Either Jake is sleeping or Robert is studying, perhaps both. (J, R)
If we let J stand for “Jake is sleeping” and R for “Robert is studying,” then the statement
“Either Jake is sleeping or Robert is studying, perhaps both”is symbolized as follows:
JvR
Please note that the constants J and R do not just represent Jake and Robert
respectively; rather, they represent the entire statement. Thus, J represents “Jake is
sleeping,” while R represents “Robert is studying.”
It must also be noted that in most cases, the phrase “perhaps both” in an inclusive
disjunction is not written in the statement. Thus, in determining whether the statement
is an inclusive or an exclusive disjunction, we just need to analyze the statement per se.
Let us consider this example:
Either Jake is sleeping or Robert is studying.
As we notice, the statement does not contain the phrase “perhaps both.” But if we
analyze the statement, it is clear that it is an inclusive disjunction because it is possible
for the two component statements, namely, “Jake is sleeping” and “Robert is studying,”
to occur at the same time. (Please note that I will discuss the nature and characteristics
of an exclusive disjunction in my next post.)
