Exemplary Answer

1. Explain why "Wayne hopes that" is an operator.

An operator determines the truth value of a whole statement.  By placing "Wayne hopes that" in front of any simple sentence, it changes what we analyze to be true or false from the simple sentence (or simple proposition) to the whole statement.  So, instead of looking at a simple proposition like, "there will be ice cream," which may be either true or false, we look at the entire statement: "Wayne hopes that there will be ice cream." This statement could always be true, or false- but is dependent on the function of the operator.

 

An operator has the power to change an entire statement's meaning-- In the same way any operator like "&" can change or alter the parts' values.
 
A: Bob takes a walk.
B: Sue takes a nap.
 
A&B: Bob takes a walk and Sue takes a npa.
 
Both simple propositions are true, when this whole statement is true.
So, if one or both is not true, then the entire statement is false.
 
This shows that the use of an operator creates a new statement whose truth value may or may not differ from the truth values of the parts.
 

2. Explain why "Wayne hopes that" is not a truth-functional operator.
 

 
"Wayne hopes that" is not a truth-functional operator because when given the same type of input, the entire truth value of the statement may vary.

 

I.e. when given T as input, the output may be either T or F, dependent on that operator.
 
"Wayne hopes that he will receive a present"
     This statement is True.
However, "Wayne will receive a present." is False
 
But when another False Statement:
"Wayne will go to school on Saturday" is operated on, it comes out False.
"Wayne hopes that he will go to school on Saturday.
 
The idea that an operator is truth functional shows that when given certain input, the output will always be the same.  But because two different False statements came up with two different values (when in the whole)-- we see this is not true:
 
Therefore, "Wayne hopes that" is not truth functional.

This exemplary answer is the work of Cognitive Science major Jessica Mamey.