Talk:Primitive notion

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Mathematics Low‑priority

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Philosophy: Logic High‑importance

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Computers

If notions are not defined, but used, how do computers validate proofs?--83.50.70.49 (talk) 01:13, 2 July 2013 (UTC)[reply]

As stated in the article, relations between primitive notions are restricted by axioms. The real question is what kind of relations don't constitute a definition, which I feel can be very subtle, and I hope will be explained by someone more familiar with mathematical logic than me. --Bbbbbbbbba (talk) 01:56, 26 February 2023 (UTC)[reply]

Not primitive

The following was removed as off-topic:

Instead of attempting to define them,<ref Euclid (300 B.C.) still gave definitions in his Elements, like "A line is breadthless length". /ref> their interplay is ruled (in Hilbert's axiom system) by axioms like "For every two points there exists a line that contains them both".<ref This axiom can be formalized in predicate logic as "∀x₁,x₂[ ∈P → (implies) ∃y∈L ∧ (AND) C(y,x₁) ∧ C(y,x₂)]", where P, L, are predicates having as universe of discourse the set of points, of lines, and C is the diadic predicate letter indicating the "contains" relation, respectively. /ref>

Dialogue on primitive notion takes place here. The removed comments misdirect attention from primitivity. — Rgdboer (talk) 01:30, 24 February 2025 (UTC)[reply]