Zeitraum: 03.09.2018 09:00 Uhr - 07.09.2018 18:00 Uhr
Ort: Johannisstraße 13, 07743 Jena, Auditorium Zur Rosen
The Löwenheim-Skolem theorem was proven approximately 100 years ago, namely 1915 by Löwenheim and in a more general form 1920 by Skolem.
It is not only the first theorem of model theory that was proven, but also the first theorem of metalogic. In the summer school we will read the original proofs from Löwenheim and Skolem, as well as papers from Gödel and Herbrand, which rely on Löwenheim's and Skolem's work: Gödel's completeness proof has astonishing overlaps with Skolem's proofs of the Löwenheim-Skolem theorem.
Herbrand criticizes the proofs of Löwenheim and Skolem in his Dissertation harshly from a finitistic perspective and his fundamental theorem (now known as "Herbrand's theorem") could, as van Heijenoort pointed out, be viewed as a "reinterpretation, from the point of view of Hilbert's program, from the result of Löwenheim and Skolem".
We will dig into the proofs and recognize these points.
We will discuss several questions regarding the history and philosophy of logic, such as:
- What does the so called Skolem-Paradox mean for foundational issues?
- Does the Skolem-Paradox has consequences for the philosophy of language, as Putnam supposes?
- How should one evaluate Herbrand's critic?
- How is Herbrand's fundamental theorem (historically and systematically) linked to the Löwenheim-Skolem theorem?