PHIL433 INFINITY
| Course Code: | 2410433 |
| METU Credit (Theoretical-Laboratory hours/week): | 3 (3.00 - 0.00) |
| ECTS Credit: | 5.0 |
| Department: | Philosophy |
| Language of Instruction: | English |
| Level of Study: | Undergraduate |
| Course Coordinator: | Prof.Dr. MUTLU MURAT BAÇ |
| Offered Semester: | Fall Semesters. |
Course Objectives
David Hilbert, a 20th century logician, famously said: “The infinite! No other question has ever moved so profoundly the spirit of man; no other idea has so fruitfully stimulated his intellect; yet no other concept stands in greater need of clarification….” As pointed out by Hilbert, the concept of infinity has been an important topic in philosophy since the time of early Greek philosophers. In addition to its philosophical importance, it also has significant mathematical aspects. For example, the concept forms the basis of some counter-intuitive mathematical results, such as being able to paint an infinite surface with a finite amount of paint. Thus, a thorough investigation of the concept of infinity will need to have both a philosophical dimension and a mathematical/logical dimension. This proposed course aims to provide such an investigation. The investigation will be carried out in three overlapping dimensions: historical, metaphysical, and mathematical. In the first dimension, the development of the concept of infinity will be traversed, starting from early Greek thought and ending with 20th century views on infinity. The main focus of the metaphysical dimension of the course will be the distinction between potential infinity and actual infinity. The arguments for and against the existence of actual infinity will be thoroughly examined. In addition to these arguments, the metaphysical dimension of the course will also include an analysis of human finitude and the possibility of infinite beings. The mathematical dimension will cover early paradoxes of motion and time, Galileo’s “paradox”, Torricelli’s trumpet, Cantor’s transfinite mathematics, and some theorems relevant to the discussion of infinity.
Course Content
For course details, see https://catalog2.metu.edu.tr.Course Learning Outcomes
At the end of the course, the student is expected to have acquired:
- Mastery of paradoxes of infinity
- A good grasp of the historical development of the concept of infinity
- Mastery of the distinction between potential infinity and actual infinity
- Mastery of the arguments for/against the existence of actual infinity
- A good grasp of metaphysical underpinnings of the concept of infinity
- A good grasp of different degrees of infinity
- A conceptual understanding of transfinite mathematics
- A conceptual understanding of the Löwenheim-Skolem theorem and Gödel’s first incompleteness theorem
Program Outcomes Matrix
| Level of Contribution | |||||
| # | Program Outcomes | 0 | 1 | 2 | 3 |
| 1 | Have the knowledge and skills of research method which is a requirement in order to be successful in academic studies. | ✔ | |||
| 2 | Have the capacity for applying philosophical knowledge to scientific and social issues. | ✔ | |||
| 3 | Examine and analyze a subject matter and make philosophical interpretations on it. | ✔ | |||
| 4 | Have the skills of critical thinking, analytical approach, problem solving, multi-dimensional view, making inferences and interpretations regarding to philosophical texts and scientific facts. | ✔ | |||
| 5 | Identify the basic concepts and issues in philosophy. | ✔ | |||
| 6 | Evaluate and understand the underlying philosophical assumptions of fundamental and social sciences. | ✔ | |||
| 7 | Have capacity to make interdisciplinary readings and analysis. | ✔ | |||
| 8 | Have verbal and written presentation and effective communication skills, be open to team work and do interdisciplinary study. | ✔ | |||
| 9 | Make connections between contemporary ethical, social, cultural, esthetic and politic issues. | ✔ | |||
| 10 | Interpret the historical development of scientific and philosophical questions. | ✔ | |||
| 11 | Have knowledge about contemporary philosophical issues and their relations to other disciplines. | ✔ | |||
| 12 | Use modern information tools in order to make research in philosophy. | ✔ | |||
| 13 | Improve their professional and personal skills lifelong. | ✔ | |||
| 14 | Use information technologies effectively in domain applications in philosophy. | ✔ | |||
| 15 | Have self-confidence and develop original ideas regarding to philosophy. | ✔ | |||
| 16 | Have social and ethical responsibility regarding to contemporary issues. | ✔ | |||
| 17 | Have good knowledge of English, research method and computer skills and use these skills effectively. | ✔ | |||
| 18 | Comprehend the basic theories and issues in sub-disciplines of philosophy. | ✔ | |||
| 19 | Have an advanced knowledge in certain specific fields such as environment, technology, culture, art etc. | ✔ | |||
0: No Contribution 1: Little Contribution 2: Partial Contribution 3: Full Contribution