How we cite our quotes: All quotations are from Star Trek III: The Search for Spock.
Quote #1
KIRK: U.S.S. Enterprise, Captain's personal log. With most of our battle damage repaired, we're almost home, yet I feel uneasy and I wonder why. Perhaps it is the emptiness of this vessel. Most of our trainee crew have been reassigned. Lieutenant Saavik and my son David are exploring the Genesis planet, which he helped create, and Enterprise feels like a house with all the children gone.
At the end of The Wrath of Khan, Kirk looks at the Genesis planet with a sense of hope and new life. But Kirk's view on life has become one of loneliness and lost purpose.
Quote #2
KIRK [on recording]: To fully understand the events on which I report, it is necessary to review the theoretical data on the Genesis device, as developed by Doctors Carol and David Marcus. Genesis, simply put, is life from lifelessness. It was the intention to introduce the Genesis device into a preselected area of a lifeless space body, a moon or other dead form. The device, when delivered, would instantaneously cause the Genesis effect. Instead of a dead moon, a living, breathing planet now exists, capable of sustaining whatever life forms we see fit to deposit on it.
Genesis returns in The Search for Spock, but like Kirk's joie de vivre, the script has been flipped on this life-granting symbol. In the Wrath of Khan, the device provided hope and new life. As we'll learn later, Genesis is unstable and serves as a symbol for how the truth of life and existence will forever be beyond the grasp of science.
Quote #3
SAREK: Because he asked you to. He entrusted you with his very essence, with everything that was not of the body. He asked you to bring him to us and to bring that which he gave you, his katra, his living spirit.
KIRK: Sir, your son meant more to me that you can know. I'd have given my life if it would have saved his. Believe me when I tell you, he made no request of me.
SAREK: He would not have spoken of it openly.
The katra is the Vulcan equivalent of the mind, soul, or essence. It is completely separate from the material world, and Spock's contains everything that is essentially Spock. It can also, apparently, be uploaded from on body to another.
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'.
Quote #7
SPOCK [Remembering]: I have been…and ever shall be, your friend.
KIRK: Yes. Yes, Spock.
SPOCK: The ship. Out of danger?
KIRK: You saved the ship. You saved us all. Don't you remember?
SPOCK: Jim. Your name is Jim.
KIRK: Yes.
The film ends with the ultimate success of spirituality over science. Genesis may have resurrected Spock's body, but much like the planet, it was an empty shell. Only through believing in the katra and a world beyond the material was Spock truly able to be rescued.