000000 Knowledge Across Cultures and Languages (Wimmer)
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Words for knowledge exist, and are widely used, in all known natural languages. But do people across the world think of knowledge the same way or are there important differences? The aim of this course is to look at how diverse cultural and linguistic communities think of knowledge. This will allow us to appreciate how different in some ways, but also similar in others, their conceptions are. The seminar will begin by covering work in experimental philosophy that highlights cultural similarities and differences in when humans intuitively say of others that they know. We then draw on anthropological work to learn about knowledge in the Ifa religious system (in West Africa) and amongst speakers of Ende (in Eastern Indonesia). Turning to differences in how words for knowledge are realized in the world's languages, we will compare English and German to a number of other languages, including, among others, Turkish and Korean. This part of the course will also involve a guest lecture by a linguist from Sweden, who is a world-leading expert on how human languages represent knowledge.
The seminar will be held in English. However, exams and questions may also be in German. In addition to the content-related learning goals, the seminar will also be about practising reading and discussing in English. Students who find their English to be somewhat ‘rusty’ are very welcome. The course will be based on individual articles and book chapters by a number of authors. All texts will be accessible via moodle.
030094 Gödel: The Unprovability of the Consistency of Arithmetic (Kürbis, Skurt)
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Gödel’s first incompleteness theorem proved that if arithmetic is (omega) consistent, then it is not negation complete, that is, there is a sentence such that neither it nor its negation is provable in arithmetic. Gödel established this result by exhibiting a sentence of arithmetic, the so-called Gödel sentence, that is equivalent to the statement of its own unprovability in arithmetic. The second incompleteness theorem showed that if arithmetic is consistent, then it cannot prove the statement that expresses the consistency of arithmetic.
This course is an introduction to all formal aspects of Gödel’s incompleteness theorems. We will begin with a recapitulation of fundamental results about first order logic, such as its completeness and the Löwenheim Skolem Theorem, and proceed to first order theories, in particular a fragment of number theory. Gödel’s method of the arithmetisation of syntax and its application to the formalisation of proofs in arithmetic will be presented in detail. We will then be ready to prove Gödel’s first incompleteness theorem. Afterwards we will consider the resources needed to prove the second incompleteness theorem. There will also be time to discuss the philosophical importance of Gödel’s results.
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Literature:
George Boolos: The Logic of Provability (Cambridge University Press 1993)
Herbert B. Enderton: A Mathematical Introduction to Logic, 2nd edition (San Diego: Harcourt 2001)
Eliot Mendelson: An Introduction to Mathematical Logic, 6th edition (Boca Raton: CRC Press 2015)
030120 Colloquium: Philosophy of Language, Logic, and Information (Liefke, Rami)
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This colloquium serves the discussion of current topics at the semantic interface of logic, the philosophy of language, and the philosophy of information. The colloquium will combine talks by international experts with presentations of local researchers and (PhD/MA) students. Students will be given the opportunity to present their (ongoing) work in English. A detailed schedule will be available by end-March at https://www.ruhr-uni-bochum.de/phil-inf/colloquium/index.html.en.
030128 EXTRA Research Colloquium “Metaphilosophy, Experimental Philosophy, and Argumentation Theory” (Horvath)
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In this colloquium in seminar-style, we will discuss current topics from argumentation theory, epistemology, experimental philosophy, and metaphilosophy, broadly construed. The colloquium will also host a number of talks by external guests, many of which are leading experts in their field. Students at the advanced bachelor, master, or doctoral level are especially welcome in the colloquium, and they can also acquire the normal range of credit points. Moreover, student participants will have the option of presenting their own work, e.g., related to their thesis, in English.