Final answer:
President Wilson's philosophy that the security of nations would be achieved through collective security within an international organization like the League of Nations is a key component of his Fourteen Points.
Step-by-step explanation:
The theory that suggests that the security of nations would be achieved through membership in an international organization dedicated to maintaining order and cooperation is known as collective security. This was indeed the lynchpin of President Woodrow Wilson's philosophy, detailed in his Fourteen Points speech, which outlined his vision for a post-World War I world. Central to this vision was the creation of the League of Nations, an organization that was intended to provide a forum for countries to resolve their issues peacefully, with the idea that an attack on one member would be met with a unified response from all members, thus deterring aggression and maintaining international stability.