Contributions to the Fields of Mathematics and Logic

Today, I set forth my ultimate contribution to the fields of Mathematics and Logic.  I can sternly assure you that the impact of my dissertation will be equivalent to that of Sir Isaac Newton's Principia.

In the following Tenets, I provide a clear and logical method for one to view and understand the world as we know it, using the sociological phenomena of the Meme as a medium.  These Tenets, I believe, also explain a plethora of human psychological functions and disorders, such as paranoia and trust.  

As such, I formally present to you 

"The Logical Theory of Visible and Invisible Social and Psychological Stabilty Concerning the presence of Dangerous Objects"




============Tenet I===============


Let P = Admiral Ackbar;
Let Q = the Presence of a Trap

Statement: "If Admiral Ackbar is present, it's a trap."  
                                       P => Q 


As we know, Admiral Ackbar always indicates a present trap.  The logical value of this statement is true.
                                       L(P => Q) = True


This implies that
                  "If a trap is present, Admiral Ackbar is there." 
                                              Q => P


As we know, this is not always true.  Traps exist in nature independently of Admiral Ackbar's presence.
                                        L(Q => P) = False


The presence of a Trap does not necessarily imply the presence of Admiral Ackbar.  Traps can (and do)
exist without his physical presence.

============Tenet II================

In the case of
Let R = Jigsaw,


Statement: "If Jigsaw is present, it's a trap." 
                                      R => Q

Indeed, the presence of Jigsaw indicates the presence of a trap.  The logical value of this is True.
                                      L(R => Q) = True


This implies that 
                  "If a trap is present, Jigsaw is there."   
                                     Q => R


As we know, traps exist in nature independently of Jigsaw's presence, such as in the presence or absence of Admiral Ackbar.  The logical value of this statement is False. 
                                     L(Q => R) = False

============Tenet III================

Statement:  "Admiral Ackbar and Jigsaw both indicate the presence of traps." 

                                    (P => Q) ^ (R => Q)

Indeed, both Admiral Ackbar and Jigsaw indicate the presence of traps.  The logical value of this statement is True. 

                L(

(P => Q) ^ (R => Q) ) = True

However, this does not imply that

               "Since Admiral Ackbar and Jigsaw both indicate the presence of traps, Admiral Ackbar and Jigsaw are one in the same." 

               (

(P => Q) ^ (R => Q) ) => ( (P => R) ^ (R => P) )

It has been proven that, although Admiral Ackbar and Jigsaw both indicate the presence of traps, Admiral Ackbar and Jigsaw are versed in different species of traps.  Therefore, Admiral Ackbar and Jigsaw are, in fact, not one in the same.  

=============Tenet IV================

Statement:  "Since Admiral Ackbar and Jigsaw both indicate the presence of traps, if a trap is present, Admiral Ackbar or Jigsaw is there." 

                                    Q => (P V R)

However, we have already proven that traps exist without the presence of Admiral Ackbar or Jigsaw, though they are always present when Admiral Ackbar or Jigsaw is present.  Therefore, the logical value of the previous statement is False. 
                                     L (Q => (P V R) ) = False

=============Tenet V================

Statement:  "The absence of both or either Admiral Ackbar and Jigsaw indicates an absence of traps."

                                     ~(P V R) => ~Q

We have already proven that traps exist in nature without the presence of both or either Admiral Ackbar or Jigsaw.  The logical value of the previous statement is false. 

                                     L ( ~(P V R) => ~Q) = False

=============Tenet VI================

Therefore, 

Let S = ( L (Tenet I) + L (Tenet II) + L (Tenet III) + L (Tenet IV) + L (Tenet V) ) 

As we have proven, the logical values of Tenets I-V are true. The logical value of S is, therefore, also true.  

                                   L ( S ) = True

This implies that 

                    "Tenets I-V are true, therefore, a trap is present." 

                                   S => Q

Because the Variable S is the sum of the logical values of Tenets I-V, and the logical values of Tenets I-V are true, the logical value of the previous implication is true.

                                   L (S => Q) = True

=============Conclusion================

Based on the truths set forth by Tenets I-VI, we can imply only one thing:

                                 Q

As we have defined previously, Q indicates the presence of a trap.  If traps exist in nature independently of the presence of either or both Admiral Ackbar or Jigsaw, we can reach only one logical conclusion:

                                IT'S A TRAP!!!!