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Zorns Lemma is named after mathematician Max Zorn's "lemma," an axiom which states that given a set of sets, there must be a further set containing a representative item from each individual set. The film is constructed in three parts, each of which is meant to represent a phase of intellectual development. The short first part, which mimics the intellectual and moral education of young children, consists of a blank screen and a voice reading from The Bay State Primer, an early American grammar textbook that teaches the letters of the alphabet by using them in sentences derived from the Bible. The 47-minute second section is much more complex and alludes more specifically to the mathematical axiom from which the film takes its title. It begins with a presentation of a 24-letter version of the Roman alphabet (dropping two letters corresponds to earlier versions of the alphabet and the 24 frames-per-second rate at which film runs through a projector). The letters are presented against a black background and each is shown for one second -- a rhythm that continues throughout the section. Further sets follow which present alphabetically arranged words filmed in the environs of New York. During each run-through of the alphabet, the letters are replaced, one by one, by successive one-second shots of continuing actions (waves breaking, a man changing a tire, etc.), until all of them have been replaced. Hollis Frampton intended this section to imitate the way cognitive and linguistic skills develop a fuller understanding of the world. The contemplative final section of the film depicts the philosophical serenity that comes with intellectual fulfillment. A man, a woman, and a dog cross a snowy field and enter a woods in a mostly continuous wide shot of the landscape, while on the soundtrack different voices, alternating one word at a time, read from an 11th century metaphysical text, On Light, or the Ingression of Forms, by Robert Grosseteste. Zorns Lemma established Frampton's importance as an experimental filmmaker. Its commitment to knowledge as the path to enlightenment stood in deliberate opposition to fellow avant-garde filmmaker Stan Brakhage's then-dominant belief that experimental film should strive to attain a pure state of pre-verbal, childlike vision uncorrupted by education.