The aim of this course is to enable the students to question philosophical foundations of mathematics.
The nature of mathematical knowledge since Plato. The comparison of the nature of mathematical knowledge with the philosophical knowledge. The discussion of the problems about the foundation on which mathematical knowledge rests; the question whether mathematics is discovered or invented; the origin of the first principles and axioms of mathematics. A critical examination of the three views about the foundation of mathematics (Logicism, Intuitionism, Formalism).
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Course Learning Outcomes
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Learning Outcomes Upon the completion of this course a student: |
Program Learning Outcomes |
Teaching Methods |
Assessment Methods |
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1) acquires critical approach to the nature of mathematical knowledge. |
1,2,3,6,8,11,12 |
1,2,3,4 |
A,B,C,D,E |
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2) discusses the problems about the foundation on which mathematical knowledge rests. |
1,2,3,6,11,12 |
1,2,3,4 |
A,B,C,D,E |
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3) relates to epistemological concepts in a historical and critical way. |
1,2,3,6,7,11,12 |
1,2,3,4 |
A,B,C,D,E |
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4) grasps the historical significance of mathematical knowledge. |
1,2,3,6,7,11,12 |
1,2,3,4 |
A,B,C,D,E |
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5) distinguishes the importance of the question whether mathematics is discovered or invented. |
1,2,3,6,7,8,11,12 |
1,2,3,4 |
A,B,C,D,E |
Course Flow
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COURSE CONTENT |
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Week |
Topics |
Study Materials |
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1 |
Infinitistic theorems in XVIIth century mathematics. |
17th century mathematics |
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2 |
The foundations of the Leibnizian differential calculus and Berkeley's Analyst. |
Leibniz |
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3 |
Kant on pure intuition in arithmetic and geometry. |
Kant |
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4 |
The arithmetization of analysis: Bolzano's proof of the intermediate value theorem |
Brentano |
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5 |
Dedekind's theory of irrational and natural numbers. |
Dedekind |
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6 |
Frege's Begriffsschrift. |
Frege |
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7 |
Frege's The Foundations of Arithmetic. |
Frege |
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8 |
Frege's The Foundations of Arithmetic. |
Frege |
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9 |
Frege's The Foundations of Arithmetic. |
Frege |
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10 |
Review |
- |
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11 |
The emergence of Cantorian set theory and the mathematical theory of the infinite; Zermelo's axiom of choice and his axiomatization of set theory; semi-intuitionism. |
Set Theory |
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12 |
Hilbert's program I (axiomatization). |
Hilbert |
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13 |
Russell's type theory |
Russell |
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14 |
Hilbert's program II (proof theory); Gödel's results |
Hilbert |
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15 |
General Assessment |
- |
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16 |
Final Exam |
- |
Recommended Sources
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RECOMMENDED SOURCES |
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Textbook |
Course Reader prepared by the instructor. |
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Additional Resources |
Frege, The Foundations of Arithmetic, Northwestern University Press. Dedekind, Essays on the Theory of Numbers, Dover. P. Mancosu, ed., From Brouwer to Hilbert: The debate on foundations of mathematics in the 1920s, Oxford University Press, 1998.
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Material Sharing
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MATERIAL SHARING |
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Documents |
- |
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Assignments |
- |
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Exams |
- |
Assessment
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ASSESSMENT |
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IN-TERM STUDIES |
NUMBER |
PERCENTAGE |
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Attendance |
15 |
10 |
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Midterm |
- |
- |
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Participation in seminar discussions |
15 |
10 |
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Assignments |
1 |
10 |
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Presentation |
1 |
10 |
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Critical reading notes |
10 |
10 |
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Final examination |
1 |
10 |
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Final Paper |
1 |
40 |
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Total |
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100 |
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CONTRIBUTION OF FINAL PAPER TO OVERALL GRADE |
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40 |
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CONTRIBUTION OF IN-TERM STUDIES TO OVERALL GRADE |
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60 |
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Total |
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100 |
Course’s Contribution to Program
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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. |
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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. |
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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.
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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.
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X |
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5 |
develops a consciousness of professional and social ethics. |
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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 .
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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.
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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 analyse issues that might arise when conducting discussions concerning history of philosophy in the Turkish language. |
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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.
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X |
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11 |
uses his/her philosophical knowledge to establish interactions at national and international level.
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X |
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12 |
produces work of the quality of a contribution in national and international peer-reviewed journals in philosophy.
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X |
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13 |
holds the necessary knowledge of classical languages, a modern language in addition to English and history of philosophy to conduct an advanced philosophical study particularly in history of philosophy. |
X |
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ECTS
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ECTS ALLOCATED BASED ON STUDENT WORKLOAD BY THE COURSE DESCRIPTION |
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Activities |
Quantity |
Duration |
Total |
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Course Duration (Including the exam week: 16 x Total course hours) |
16 |
10 |
160 |
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Hours for off-the-classroom study (Pre-study, practice) |
15 |
10 |
150 |
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Midterms |
- |
- |
- |
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Assignments |
1 |
40 |
40 |
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Presentation |
1 |
30 |
30 |
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Critical reading notes |
10 |
4 |
40 |
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Final examination |
1 |
40 |
40 |
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Final Paper |
1 |
40 |
40 |
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Total Work Load |
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500 |
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Total Work Load / 25 (h) |
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20 |
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ECTS Credit of the Course |
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20 |