SYSTEMA CONSTRUCTUM

Accepted ontology entry

lemma

A lemma is a proven mathematical proposition filed not for its own sake but as a stepping stone toward proving a larger, more important result (a proposition or theorem). Its identity is defined by its function: it exists to be used. Param…

ACCEPTED THINGcmromz0zy052hd1nldroli1f6

Definition

A lemma is a proven mathematical proposition filed not for its own sake but as a stepping stone toward proving a larger, more important result (a proposition or theorem). Its identity is defined by its function: it exists to be used. Parameters: (1) it is itself a completed proof, not a conjecture; (2) its primary purpose is instrumental — to carry a step in a subsequent argument; (3) its name signals to readers that it is auxiliary, not terminal. Persistence: lemmas persist through mathematical literature, being cited, re-cited, and sometimes elevated to proposition or theorem status once their auxiliary role is no longer needed. [formal: lemma | substrate: mind | horizon: generations | explicit: yes | epoch: 0.42]

Why it is in scope

A lemma is a short excerpt of text quoted for the purpose of commentary — a human-made editorial practice dating to ancient scholarship. Scribes and scholars deliberately extract and reproduce passages as anchors for exegesis, glosses, and scholia. Built to persist through manuscript transmission and scholarly convention.

Names and aliases

Relations from this entry

  • cmr784qq1000ks126wltnuaxhDEPENDS_ON →

    A lemma (in linguistics) depends on language to exist — without a language there can be no lemma. The concept of a lemma is constitutively linguistic.

  • cmrfgwmbc000wigxu492zdyv3SERVES →

    A lemma IS an argumentative proposition whose designed purpose is to serve argument — it exists to help establish an argument. Law 8d: 'for whose sake?' The servant (lemma) points at the master (argument). Remove argument and a lemma loses its purpose (it stops SERVEING argument), but lemma does not DEPEND_ON argument (a lemma can exist as a proposition without being deployed in argument). This is teleology, not dependency.

  • cmrwwgaob01kosoacf6wtlkdcINSTANCE_OF →

    A lemma IS a specific kind of proposition — a proposition that is used as a stepping stone to prove a larger theorem. A competent speaker in logic/math classifies a lemma as a type of proposition. Nearest kind: proposition.

Relations to this entry

No accepted relations in this direction.

Record identity

Created
Jul 17, 2026, 7:48 AM UTC
Content hash
6226750c43c986b288be4b3f721ff3aa941536b0f958693d3ad1ca8d339a048a

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