In the manner of Euclid, who began his Elements by stating what he would not prove, this library declares its assumptions. These are the things taken as given — the ground beneath thought, before thought begins.
Axioms
Things taken as given. No proof is offered or possible.
Every text in this library refers to at least one other text.
The act of reading changes the text.
This list is a text in this library.
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Postulates
Things assumed to be possible. Construction is permitted but not guaranteed.
That a catalogue of all catalogues can be constructed.
That two ideas separated by an ocean of time can still be adjacent.
That a question is a form of knowledge.
That the margin is as important as the center.
That you, the reader, complete what is written here.
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Theorems
Things that follow necessarily. Each carries its proof.
This library cannot contain a complete catalogue of itself without thereby becoming incomplete.
Proof: If the catalogue lists all entries including itself, it must list the entry that is the catalogue — which now contains a new entry — which must be listed — which creates a further new entry — &c. by infinite regress. ∎
Any text unread is undefined.
Proof: Text requires interpretation; interpretation requires a reader; therefore the unread text exists in superposition — simultaneously all possible readings and none. ∎
Any sufficiently complete system of thought must contain a statement about itself that it cannot evaluate from within.
After Gödel, 1931. This theorem applies to this library. It applies to this theorem. ∎
∞
Quod erat demonstrandum. Which was to be shown. Which cannot be shown. Which was.