7 ideas
17813 | Löwenheim-Skolem says any theory with a true interpretation has a model in the natural numbers [White,NP] |
13472 | Hilbert aimed to eliminate number from geometry [Hilbert, by Hart,WD] |
17812 | Finite cardinalities don't need numbers as objects; numerical quantifiers will do [White,NP] |
9546 | Euclid axioms concerns possibilities of construction, but Hilbert's assert the existence of objects [Hilbert, by Chihara] |
18742 | Hilbert's formalisation revealed implicit congruence axioms in Euclid [Hilbert, by Horsten/Pettigrew] |
18217 | Hilbert's geometry is interesting because it captures Euclid without using real numbers [Hilbert, by Field,H] |
19347 | Substance needs independence, unity, and stability (for individuation); also it is a subject, for predicates [Perkins] |