Toll free :
Support :
 ← Class System Theory Ways of Seeing →

# Custom Propositional Logic essay paper

“IF it is not true that all swans are white, and the president believes that all swans are white, then the president is fallible”

The statement above is a classic conditional statement with three atomic statements and connectivity. Generally, atomic statements are simple statements that contain no connectives,  and actually, within this statement; several atomic statements can be depicted. From the statement, it is important to note that it is sufficient and does not require any form of assistance in order to stand conditional since all necessary conditions to describe the president’s situation have been articulated. That is, there are sufficient conditions to prove that the president is fallible, a situation that has been made more discrete by the insertion of the connective “if not…then”

The following are the atomic statements derived from the above conditional statement:

(i)         All swans are white

(ii)        The president believes that all swans are white

(iii)      The president is fallible

When the statement is broken down into three parts as done above, it then fundamentally give the molecular a more simple and prity look that can be interpreted with much ease as possible. One of the important points that come out clealry is how the antecedent and consequent have been used to satisfy the necessary conditions that qualify a statement to be conditional statement. For instance, the president’s fallacy  which is a consequent, solely rests on the satisfaction of the antecedent proof of whether all swans are white. When looking at the statement critically, it then becomes clear that both the consequent and the antecedent of the statement have ballanced each other completly, hence satisfying the conditions for conditional statement.

The information in the conditional statement can also be represented using a propositional logic symbols in order to give the statement a syntax approach. This can be done in the following format:

(A)  To represent all swans are white

(B)  To represent the president believes that all swans are white

(C)  To represent the president is fallible

After dividing the whole molecular statement into three atomic statements and subsequently negating them into symbols, then the whole statement can be negated to propositional symbols as follows:

~(A&B)=>C

The symbol is a perfect representation of the above conditional statement using syntax proporsitional logic symbols. It satisfies all the syntax rules which logically combines different symbols to form well formed formulas (wff).

Truth table is usually essential in showing the semantic relationships between two or more propositional statements. The same action can be performed on this conditional statement in order to determine the exhaustive category of the statement. The truth table for this conditional statement will therefore appear as follows:

 A B C ~(A&B)=>C 1 T T T T F F 2 T T F T T 3 T F T T T 4 T F F T T 5 F T T T T 6 F T F T T 7 F F T T T 8 F F F T T

From the truth table above, there is sufficient proof that the conditional statement is a contigency statement,meaning sometimely truelly stands while during other times it does not. This fact can be proved through logical reasoning, for instance, it is not necessary that the president will be declared fallible when swans are found not tonbe white. Many people will give him the benefit of doubt because it can be that he has never seen swans in his life time.

The conditional statement in this case can be re-written into several other statements to bring the other consistent side of the statement. The statement can therefore take the following different formats: “If it is not true that all swans are white, and the president believes that all swans are white, then the president is fallible”

(i)     If it is true that all swans are white, and the president does not believe, then he is fallible.

(ii)    If all swans are white, and the president does not believe that all swans are white, then the president is fallible.

The two statements actually mean the same thing in that they are all trying to show the grounds under which the president could be considered fallible. In the first statement, the facts have not been proved as to whether swans are white, but should the facts be proved that swans are white, then because of the large following a president usually enjoys, he is likely to be declared fallible by the people who trusted in him for facts. The same action applies for the second statement except that swans are likely to have been found to be white and the president is refusing.