S1308 How to Realize the Limits of Human Ability - Necessary Conditions for Decision-making

In this course, we try to make clear the limit of human ability by introducing two theorems, Arrow's Impossibility Theorem and G?del's Incompleteness Theorem, and one principle, Heisenberg's Uncertainty Principle, all of which indicate us impossibility to reach an ideal situation we are expecting to realize. If you correctly understand them, you have to accept that it is impossible to construct an ideal democratic society from Arrow's Impossibility Theorem and that there exists a case which is true but we cannot prove from G?del's Incompleteness Theorem. The latter indicates that we have to reconsider and reconstruct the structure of present society, though we know it is impossible to realize a perfect society without any logical inconsistency, because it is impossible to prevent the happening of, for example, a perfect crime. Meanwhile, Heisenberg's Uncertainty Principle relates to serious disputes between the Theory of Relativity and the Quantum Theory. Arrow's Impossibility Theorem and the theoretical inconsistency given by the dispute between the Theory of Relativity and the Quantum Theory induce the same conclusion in the sense that aggregation of individual decisions does not becomes the social decision in spite that society consists of the collection of individuals, or, in other words, inevitable logical inconsistency between micro issues and macro issues.
In the class, many recent developments in various scientific fields such as Physics, Computer Science, Evolutionary Biology, Gene Science among others are also introduced because they seem to support the conclusions given in the class. For example, today's Gene Science indicates that a human has two rather independent functions for decision makings, instinct controlled by genes and mind developed by genes pursuing an effective way to make their copies. Meanwhile, how to manage so many decision making issues we have to handle is explained by the recent development in Brain Science saying it is similar to present computer system executed by the combination of time-sharing system and parallel computing. Recent rapid development in many sciences especially in natural and engineering sciences urges us to abandon traditional stereo-type ideas and to adjust ourselves to fit for a new environment which is renovated with confident evidences and proofs. Historically speaking, human minds and society have been changed to fit for the development of natural sciences and new technologies, which is still true even today.
The teaching strategy of the theorems and the principle is managed respectively in the following order: historical overview with examples, explanation and proof, theoretical interpretation and actual meaning of the result, and how to use the result for individual decision makings.
Students are expected to realize it is impossible to understand the world with a single consistent logic, especially in case of social science it is impossible to achieve rational conclusion between individual wills and social will given as a collection of the former in any way, which inevitably leads every individual has to give up some of his/her desires to be realized. The conclusions induced from the analysis in the class obviously indicate various directions not only for individual decision makings but also for social decision makings.

Learning Outcomes
The following steps are in order from basic/fundamental to applied/difficult ones.

First Step
To understand proofs of Arrow's Impossibility Theorem and G?del's Incompleteness Theorem.
Especially, understanding the proof of Arrow's Impossibility Theorem is a must.

Second Step
To understand the meaning of the results of Arrow's Impossibility Theorem and G?del's Incompleteness Theorem.
To understand the dispute between the Theory of Relativity and the Quantum Theory including Heisenberg's Uncertainty Principle and the related discussions.

Third Step
To understand the recent development of Physics, Computer Science, Evolutionary Biology, Gene Science among others which are introduced in the class.
To understand mutual relations among results taught in the class. Especially, consider how they affect on actual human decision makings in what way.

Final Step
To complete an essay in which all results and conclusions taught in the class must be mentioned in a logically consistent context with the student's idea developed by the class.

Teaching and Evaluation Methods
Main stream of teaching, especially in the first half of the classes, is a collection of proofs which are necessary to understand the course contents.
Students are indicated to study topics at home in advance.
Students are required to study hard Mathematical Logic and Set Theory but all necessities for them are taught in the class.
Students are required to submit essays at every class. Submission is normally in a week.
Evaluation ratio is assigned to: 40% for First Step, 20% each for the rest.
Evaluation at each step is combined evaluation of essays and exam.
The weight of evaluation between essay and exam is 70% and 30% respectively.

Required Preliminary Knowledge
None. All necessities are given by handouts.