The aim of this course is to determine the mathematical content of theories of logic and the specification of its philosophical significance.
The class covers formal systems, models, the foundations of mathematics, Skolem-Löwenheim theorem, Gödel's incompleteness theorems and the Turing machine.
Vertical Tabs
Course Learning Outcomes
Learning Outcomes Upon the completion of this course a student: |
Program Learning Outcomes |
Teaching Methods |
Assessment Methods |
1) learns fundamental theories of mathematical logic thoroughly. |
1,2,4,10 |
1,2,3,4 |
A,B,C,D,E |
2) acquires knowledge concerning Gödel's incompleteness/completeness theorems. |
1,2,4,10 |
1,2,3,4 |
A,B,C,D,E |
3) grasps the working mechanisms of the Turing Machine. |
1,2,4,10 |
1,2,3,4 |
A,B,C,D,E |
4) acquires knowledge concerning Skolem-Löwenheim theorem. |
1,2,4,10 |
1,2,3,4 |
A,B,C,D,E |
Course Flow
COURSE CONTENT |
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Week |
Topics |
Study Materials |
1 |
Introduction |
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2 |
Kurt Gödel - Russels mathematische Logik, in: Whitehead/Russell, Principia Mathematica, Vorwort, S. V–XXXIV. Suhrkamp 1986 |
|
3 |
Russels mathematische Logik, in: Whitehead/Russell, Principia Mathematica, Vorwort, S. V–XXXIV. Suhrkamp 1986 |
|
4 |
Kurt Gödel, Über die Vollständigkeit des Logikkalküls. Doctoral dissertation. University Of Vienna. The first proof of the completeness theorem. |
|
5 |
Kurt Gödel, Über die Vollständigkeit des Logikkalküls. Doctoral dissertation. University Of Vienna. The first proof of the completeness theorem. |
|
6 |
Kurt Gödel, "Die Vollständigkeit der Axiome des logischen Funktionenkalküls". Monatshefte für Mathematik (in German) |
|
7 |
Kurt Gödel, "Die Vollständigkeit der Axiome des logischen Funktionenkalküls". Monatshefte für Mathematik (in German) |
|
8 |
MIDTERM |
|
9 |
Kurt Gödel (incompleteness theorems) Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme, I. Monatshefte für Mathematik und Physik 38: 173-98. |
|
10 |
Gödel: (incompleteness theorems) Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme, I. Monatshefte für Mathematik und Physik 38: 173-98. |
|
11 |
Gödel : (incompleteness theorems) Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme, I. and On formally undecidable propositions of Principia Mathematica and related systems |
|
12 |
Alan Turing, 1948, "Intelligent Machinery." |
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13 |
Alan Turing, 1948, "Intelligent Machinery." |
|
14 |
Turing, A.M. (1936). "On Computable Numbers, with an Application to the Entscheidungs problem". |
|
15 |
Löwenheim, Leopold (1915), "Über Möglichkeiten im Relativkalkül", Mathematische Annalen 76 (4): 447–470. |
|
16 |
FINAL EXAM |
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Recommended Sources
RECOMMENDED SOURCES |
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Textbook |
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Additional Resources |
Andrews, Peter B. (2002), An Introduction to Mathematical Logic and Type Theory: To Truth Through Proof (2nd ed.), Boston: Kluwer Academic Publishers. Barwise, Jon, ed. (1989), Handbook of Mathematical Logic, Studies in Logic and the Foundations of Mathematics. Hodges, Wilfrid (1997), A shorter model theory, Cambridge: Cambridge University Press. Jech, Thomas (2003), Set Theory: Millennium Edition, Springer Monographs in Mathematics, Berlin, New York: Springer-Verlag. Kurt Godel, 1992. On Formally Undecidable Propositions Of Principia Mathematica And Related Systems, tr. B. Meltzer, with a comprehensive introduction by Richard Braithwaite. Dover reprint of the 1962 Basic Books edition. Gerhard Gentzen, "Neue Fassung des Widerspruchsfreiheitsbeweises für die reine Zahlentheorie". Forschungen zur Logik und zur Grundlegung der exakten Wissenschaften 4: 19–44. 1938. Diskussion zur Grundlegung der Mathematik, Erkenntnis 2. in: Monatshefte für Mathematik und Physik. Akademische Verlagsgesellschaft, Leipzig 39.1931-32, S. 147–148. The Consistency of the Axiom of Choice and of the Generalized Continuum Hypothesis with the Axioms of Set Theory, Annals of Mathematical Studies, Volume 3, Princeton University Press, Princeton, NJ, 1940. Russels mathematische Logik, in: Whitehead/Russell, Principia Mathematica, Vorwort, S. V–XXXIV. Suhrkamp 1986 Kurt Gödel Über die Vollständigkeit des Logikkalküls. Doctoral dissertation. University Of Vienna. Kurt Gödel "Die Vollständigkeit der Axiome des logischen Funktionenkalküls". Monatshefte für Mathematik (in German) 1931, Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme, I. and On formally undecidable propositions of Principia Mathematica and related systems I in Solomon Feferman, ed., 1986. Kurt Gödel Collected works, Vol. I. Oxford University Press: 144-195. The original German with a facing English translation, preceded by a very illuminating introductory note by Kleene. Alan Turing, 1948, "Intelligent Machinery." Reprinted in "Cybernetics: Key Papers." Ed. C.R. Evans and A.D.J. Robertson. Baltimore: University Park Press, 1968. p. 31. Turing, A.M. (1936). "On Computable Numbers, with an Application to the Entscheidungs problem". Proceedings of the London Mathematical Society. 2 42: 230–265. Löwenheim, Leopold (1915), "Über Möglichkeiten im Relativkalkül", Mathematische Annalen 76 (4): 447–470. Löwenheim, Leopold (1977), "On possibilities in the calculus of relatives", From Frege to Gödel: A Source Book in Mathematical Logic, 1879-1931 (3rd ed.), Cambridge, Massachusetts: Harvard University Press, pp. 228–251 |
Material Sharing
MATERIAL SHARING |
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Documents |
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Assignments |
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Exams |
Assessment
ASSESSMENT |
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IN-TERM STUDIES |
NUMBER |
PERCENTAGE |
Midterm |
1 |
20 |
Presentation |
1 |
20 |
Final examination |
1 |
30 |
Final Paper |
1 |
30 |
Total |
|
100 |
CONTRIBUTION OF FINAL PAPER TO OVERALL GRADE |
|
30 |
CONTRIBUTION OF IN-TERM STUDIES TO OVERALL GRADE |
|
70 |
Total |
|
100 |
Course’s Contribution to Program
COURSE’S CONTRIBUTION TO THE PROGRAM |
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No |
Program Learning Outcomes |
Contribution |
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1 |
2 |
3 |
4 |
5 |
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1 |
acquires fundamental conceptual and methodological knowledge to use productively and creatively in academic studies. |
X |
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2 |
improves a versatile critical and analytical approach, problem-solving, interpretative and argumentative skills in relation to advanced philosophical investigations. |
X |
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3 |
proves to be a philosopher with principles, who communicates effectively, is specifically successful in written and oral presentation, has proper capacities for teamwork and interdisciplinary studies, takes the initiative, has developed a sense of responsibility, and contributes original ideas to the field of philosophy. |
X |
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4 |
applies life-long learning attitude to various ways of acquiring knowledge in order to maintain a professional and personal development. |
X |
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5 |
develops a consciousness of professional and social ethics. |
X |
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6 |
acquires the necessary skill of choosing and developing actual means and using computing technologies effectively for a philosophical study. |
X |
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7 |
conducts an advanced study in history of philosophy which requires expertise, independently by using original texts. |
X |
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8 |
applies philosophical knowledge to questions concerning contemporary, socio-cultural and political problematics. |
X |
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9 |
considers universal values and concepts of philosophy as a basis for [furthering] philosophical studies in Turkey; and is able to develop an approach to study and analyze issues that might arise when conducting discussions concerning history of philosophy in the Turkish language. |
X |
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10 |
acquires the skill and background for making contributions to the field of history of philosophy, in national and international terms. |
X |
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11 |
uses his/her philosophical knowledge to establish interactions at national and international level. |
X |
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12 |
produces work of the quality of a contribution in national and international peer-reviewed journals in philosophy. |
X |
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13 |
holds the necessary knowledge of classical languages and history of philosophy to conduct a philosophical study, particularly in history of philosophy. |
X |
ECTS
ECTS ALLOCATED BASED ON STUDENT WORKLOAD BY THE COURSE DESCRIPTION |
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Activities |
Quantity |
Duration |
Total |
Course Duration (Including the exam week: 16 x Total course hours) |
16 |
3 |
48 |
Hours for off-the-classroom study (Pre-study, practice) |
10 |
7 |
70 |
Midterms |
1 |
22 |
22 |
Presentation |
1 |
15 |
15 |
Final examination |
1 |
20 |
20 |
Final Paper |
1 |
25 |
25 |
Total Work Load |
|
|
200 |
Total Work Load / 25 (h) |
|
|
8 |
ECTS Credit of the Course |
|
|
8 |