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Leopold Löwenheim: Leopold Löwenheim (1878-1957) was a German mathematician who worked on mathematical logic. He is best known for the Löwenheim-Skolem theorem, which states that every first-order theory with an infinite model also has a countable model. See also Models, Model theory, Satisfaction, Satisfiability, Infinity, Countability, Real numbers, Numbers, Word meaning, Reference, Ambiguity.
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Annotation: The above characterizations of concepts are neither definitions nor exhausting presentations of problems related to them. Instead, they are intended to give a short introduction to the contributions below. – Lexicon of Arguments.

 
Author Concept Summary/Quotes Sources

Ian Hacking on Loewenheim - Dictionary 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.

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Explanation of symbols: Roman numerals indicate the source, arabic numerals indicate the page number. The corresponding books are indicated on the right hand side. ((s)…): Comment by the sender of the contribution. Translations: Dictionary of Arguments
The note [Concept/Author], [Author1]Vs[Author2] or [Author]Vs[term] resp. "problem:"/"solution:", "old:"/"new:" and "thesis:" is an addition from the Dictionary of Arguments. If a German edition is specified, the page numbers refer to this edition.

Hacking I
I. Hacking
Representing and Intervening. Introductory Topics in the Philosophy of Natural Science, Cambridge/New York/Oakleigh 1983
German Edition:
Einführung in die Philosophie der Naturwissenschaften Stuttgart 1996


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