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Löwenheim/Hacking: Paradox: that statements about an area where they E.g. state the lack of clear assignability (E.g. subsets of natural numbers are cannot be assigned unambiguously to the natural numbers) then also apply to a countable area: then it would followed that the natural numbers cannot be unambiguously represented in the natural numbers (unintended model). - Today that is no longer considered to be a paradox.
Löwenheim/HackingVsPutnam: his criticism only applies to the correspondence theory or the representation theory.
I 180 ff
HackingVsLöwenheim/HackingVsPutnam: 1) Physics does not fit into 1st order logic - 3) everyday language always has indicators - 4) VsWittgenstein: does not prove that our use is essentially unreliable - 4) The Löwenheim proposition refers to numbers, not words - 5) I do not need a theory of reference to refer - 6) There are photographs in books about myons 7) The Löwenheim proposition is not constructive! - I.e. there is no method for producing an unintended model - 8) affixes such as sour cherry and Persian do not work like the adjective "sweet." - You do not pickle Vistula cats and do not eat heart cats as fresh fruit.
Einführung in die Philosophie der Naturwissenschaften Stuttgart 1996