How we cite our quotes: All quotations are from Star Trek III: The Search for Spock.
Quote #4
MORROW: Now wait a minute. This business about Spock and McCoy, honestly, I never understood Vulcan mysticism.
KIRK: You don't have to believe, I'm not even sure that I believe, but if there's even a chance that Spock has an eternal soul, then it's my responsibility.
This scene clues us in to how immaterial the katra is. If it were a material thing, then you can bet that the Federation scientists would have studied it and measured it with beakers and Bunsen burners and other science-y things. That it has to be "believed" in suggests the katra is a matter of faith and spirituality.
Quote #5
MCCOY: Rapid aging. All genetic functions highly accelerated.
KIRK: What about his mind?
MCCOY: His mind's a void. It seems, Admiral, that I've got all his marbles.
A materialist would see the individual as resulting from combination of nature (read: genetics and other innate qualities we are born with) and nurture (read: our experiences within our environment).
But in this scene, The Search for Spock says that's not the case. Spock's body, which has had several experiences on Genesis, still hasn't developed a self because it lacks the proper katra. Without it, there can be no "I."
Quote #6
T'LAR: Sarek, child of Skon, child of Solkar, the body of your son breathes still. What is your wish?
SAREK: I ask for fal-tor-pan, the refusion.
T'LAR: What you seek has not been done since ages past, and then, only in legend. Your request is not logical.
SAREK: Forgive me, T'Lar. My logic is uncertain where my son is concerned.
The film doubles-down on the value of religious or spiritual beliefs even in the light of scientific inquiry. Logic takes a backseat to mysticism in this scene even for the Vulcans—a race, we'll remind you, who built an entire culture around logic.
Side note: The Vulcans should really invest in some katra cloud technology for some on-demand access. Just sayin'.