Lexicon of Arguments

 

I 176
Loewenheim/Hacking: it is a paradox: that statements about an area where they, for example, state the lack of clear assignability (e.g. subsets of natural numbers cannot be assigned unambiguously to the natural numbers), also apply to a countable area: then it would follow that the natural numbers cannot be unambiguously represented in the natural numbers (unintended model). Today that is no longer considered to be a paradox.
>Unintended models.
I 178
Loewenheim/HackingVsPutnam: Putnam's criticism only applies to the correspondence theory or the representation theory.
>Correspondence theory.
I 180 ff
HackingVsLoewenheim/HackingVsPutnam:
1) Physics does not fit into 1st order logic.
2) Everyday language always has indicators.
3) VsWittgenstein: Wittgenstein does not prove that our use is essentially unreliable.
4) The Loewenheim 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 Loewenheim proposition is not constructive! I.e. there is no method for producing an unintended model.
8) Affixes such as "sour" to cherry and "Persian" to cat do not work like the adjective "sweet." You do not pickle Vistula cats and do not eat heart cats as fresh fruit.
Cf. >Loewenheim/Putnam.