Logic

"Logic is the cement of our civilization with which we ascend from chaos using reason as our guide."
 * - T'Plana-Hath, Matron of Vulcan Philosophy

Logic is the study of the principles of reasoning. As a form of science, logic is used to solve various problems through the application of deductive reasoning.

History
Vulcans have adopted logic as their way of life. Surak introduced a strict logic regime to his people in the hope of stopping the destructive wars which plagued Vulcan. His hope was that with the help of logic the Vulcans could control their violent emotions and in doing so might lead a life of order and control.

Although the Vulcan majority lives by logic, there are some who try to balance their emotions and logic; they are better known as V'tosh ka'tur, Vulcans without logic. There have also been Vulcans, like Sybok, who rejected logic outright and embraced emotion. 

Other Vulcans may choose instead to further develop their mental discipline through the Kolinahr ritual to the point of purging all vestigial emotions and live solely by pure logic. This process can involve years of intense study and meditation. 

Several machine-based lifeforms strictly followed logic as well:
 * One notable individual, Data, was an android and as such was governed by the rules of logic. Later in life, Data gained the ability to experience emotions, though these were still simulated by a computer which relied on logic to operate.
 * The huge living machine V'Ger exhibited thought patterns of pure logic, as Spock observed. That may have changed, however, when V'Ger united with Captain Willard Decker.
 * The behavior of the Andromedan androids on planet Mudd was guided by logic. The android Norman was even damaged when confronted with the Liar Paradox..

References to logic

 * "You cannot succeed, Commodore. Your only logical alternative is to return to the ship."
 * - Spock, to Commodore Matthew Decker
 * "You cannot succeed, Commodore. Your only logical alternative is to return to the ship."
 * - Spock, to Commodore Matthew Decker


 * "I saw you crying."
 * "I did not cry"
 * "I was there, I saw the tears."
 * "You exaggerate, captain. I recall only one tear."
 * "So you were emotionally affected by the music."
 * "That is not possible."
 * "You still haven't answered my question, Sarek. Is it logical for a Vulcan to cry?"
 * - Picard and Sarek
 * '"It is illogical for a Vulcan to show anger! Illogical! Illogical! Illogical! Illogical!"''
 * - Sarek, raging against Picard's arguments
 * "I will not read this or any other statement."
 * "If you do not, you will die; all of you will die."
 * "Since it is logical to conclude that you will kill us in any event, I choose not to cooperate."
 * (enraged) "...I hate Vulcans!"
 * Spock and Sela
 * "We have all suffered losses at the hands of the Alliance. Nonetheless, logic dictates caution in the face of a superior enemy".
 * "The question of Commander Worf's motive is relevant. I will allow you to explore this issue but only as far as logic permits".
 * - T'Lara
 * "One could say that you were both the doubter and the doubted. I do not envy the paradox of logic that you were faced with in that situation."
 * - Tuvok
 * "You can use logic to justify almost anything. That's its power, and its flaw."
 * - Kathryn Janeway
 * "Structure, logic, foundation, control. A structure cannot stand without a foundation. Logic is the foundation of function. Function is the essence of control. I am in control. I am in control."
 * - Tuvok, attempting to build a keethara
 * Movies
 * "Logic clearly dictates that the needs of the many outweigh the needs of the few"
 * - Spock
 * "Or the one"
 * - Kirk
 * "Logic is the beginning of all wisdom, not the end."
 * - Spock
 * "Even logic must give way to physics."
 * - Spock to Valeris
 * "Structure, logic, foundation, control. A structure cannot stand without a foundation. Logic is the foundation of function. Function is the essence of control. I am in control. I am in control."
 * - Tuvok, attempting to build a keethara
 * Movies
 * "Logic clearly dictates that the needs of the many outweigh the needs of the few"
 * - Spock
 * "Or the one"
 * - Kirk
 * "Logic is the beginning of all wisdom, not the end."
 * - Spock
 * "Even logic must give way to physics."
 * - Spock to Valeris
 * - Spock
 * "Even logic must give way to physics."
 * - Spock to Valeris