Single Idea 17748

[catalogued under 5. Theory of Logic / J. Model Theory in Logic / 3. L÷wenheim-Skolem Theorems]

Full Idea

The L-S Theorem is ...a shocking result, since it implies that any consistent formal theory of everything - even about biology, physics, sets or the real numbers - can just as well be understood as being about natural numbers. It says nothing more.

Gist of Idea

The L-S Theorem says no theory (even of reals) says more than a natural number theory


Michal Walicki (Introduction to Mathematical Logic [2012], History E.2)

Book Reference

Walicki,Michal: 'Introduction to Mathematical Logic' [World Scientific 2012], p.34

A Reaction

Illuminating. Particularly the point that no theory about the real numbers can say anything more than a theory about the natural numbers. So the natural numbers contain all the truths we can ever express? Eh?????