Talk:Primitive notion

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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]

By not defined it is meant that it is just assumed as truth, not formulated using already known terms (but these also at some point would lead to axioms, as you need to start with some assumptions as math is based purely on formal logic) ~SpectralFlux 01:37, 2 September 2025 (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]