There are nine major tenets of the Linux philosophy outlined in the document: small modular programs, storing data in text files, combining programs together through inputs and outputs, avoiding captive user interfaces, and making every program a filter. The Unix philosophy at the core of Linux emphasizes small, single-purpose programs and flexibility for users to chain programs together to perform complex tasks. It treats all hardware and software as regular files that can be accessed and manipulated in the same way for consistency.