This song seems to share some common themes and similarities to the book "Fahrenheit 451" by Ray Bradbury and the movie "It's a Wonderful Life".

"Fahrenheit 451" is a book written in the post-WW2 era by Ray Bradbury. It takes place in a bleak future where books are strictly prohibitted and any person with them will be lit on fire with them. Montag is a fireman in this modern society. The job of these future firemen is to start fires and burn down the houses containing books rather than put out fires. Montag is obsessed with fire and completes his job mindlessly until he steals a book and reads it.

"Spark becomes a flame
Flame becomes a fire
Forge a blade to slay the stranger
Take whatever we desire"

This is similar to the firemen's obsession with fire and its "purging/cleaning" qualities. The fire can be used as a "blade", or as a weapon to destroy literature and all those who believe in it. The firemen may "take whatever they desire" because they have an occupation of limitless power. In the story, the human race almost becomes a mechanical machine because they do not think for themselves and do the same boring jobs everyday in their dull world. When I hear the song"Intension", the clicking sounds that begin at 4:44 always have reminded me of a microchip, or another component of a computer working. The connection to the book is that it could represent human society completing the same tasks every day as a machine would; the people are completely controlled by their government which leads a totalitarian reign and controls them all as if they were machines. The "pure" mentioned in the lyrics could represent the final product the government and the firemen want to achieve by burning all literature and it's believers. The books however are what help people think for themselves; what helps us be different than a machine.

The song "Intension" could also be connected with the movie "It's a Wonderful Life". In the song, from 2:43 to 3:00 you can hear a bell ringing. In the movie, according to the protagonists little daughter: "Everytime a bell rings an angel gets their wings". This is a common theme during the movie where bells may ring and the movie concludes with the protagonist guardian angel getting his wings when the bell ornament on the family's Christmas tree randomly rings. The bell ringing in the background may be Maynard trying to give his deceased mother her wings. If you do not understand this listen to the lyrics of "Wings for Marie" (parts 1 & 2). The bell ringing in the background may also connect with the other interpretation above because it reminds me of a bell on a firetruck.

Even if this is not what Tool intended the song to mean it will help clarify the lyrics to you and understand the song and the world around you better.
-THINK FOR YOURSELF-