Essential Questions

1. To what extent is mathematics a product of human social interaction? What is the role of the mathematical community in determining the validity of a mathematical proof? Why is it that mathematics is considered to be of different value in different cultures?

1. Can mathematics be characterized as a universal language?

2. To what extent is mathematics a product of human social interaction?

3. What is the role of the mathematical community in determining the validity of a mathematical proof?

4. Why is it that mathematics is considered to be of different value in different cultures?

5. How would you account for the following features that seem to belong particularly to mathematics: some people learn it very easily and outperform their peers by years; some people find it almost impossible to learn, however hard they try; most outstanding mathematicians supposedly achieve their best work before they reach the age of 30?

6. What counts as understanding in mathematics? Is it sufficient to get the right answer to a mathematical problem to say that one understands the relevant mathematics?

7. Are there aspects of mathematics that one can choose whether or not to believe?

8. How do we choose the axioms underlying mathematics? Is this an act of faith?

9. Do the terms “beauty” or “elegance” have a role in mathematical thought?

10. Is there a correlation between mathematical ability and intelligence?

11. Is there a clear-cut distinction between being good or bad at mathematics?

12. How have technological innovations, such as developments in computing, affected the nature and practice of mathematics?

2. Can human behavior be usefully classified and categorized? Can it be classified within a culture? Across cultures? Can patterns of behaviour be identified as human behavior? Within a culture? What beliefs or prejudices might be involved in our answers to these questions?

1. Can human behavior be usefully classified and categorized? Can it be classified within a culture? Across cultures? Can patterns of behavior be identified as human behavior? Within a culture?

2. What beliefs or prejudices might be involved in our answers to these questions?

3. In what ways might the beliefs and interests of human scientists influence their conclusions? Do the same considerations apply in other areas of knowledge such as the natural sciences or mathematics?

4. In what ways might social, political, cultural and religious factors affect the types of human science research that are financed and undertaken, or rejected?

5. Is research in the human sciences a viable route to learn about and, in the long run, transform or improve public policy or the common good? Or is human science research intrinsically valuable for the sake of the knowledge that can be gained? Might it rather have a utilitarian or even covert purpose behind it? How, if at all, can we determine when it is which, and if one or another of these purposes predominates?

3. Is science, or ought it to be, value-free? What implications does your answer have for the regulation of science? For example: Who should decide whether particular directions in research are pursued? Who should determine priorities in the funding of research?

1. How does the social context of scientific work affect the methods and findings of science?

2. Is science, or ought it to be, value-free? What implications does your answer have for the regulation of science? For example: Who should decide whether particular directions in research are pursued? Who should determine priorities in the funding of research?

3. Should scientists be held morally responsible for the applications of their discoveries? Is there any area of scientific knowledge the pursuit of which is morally unacceptable or morally required?

4. It has been argued that certain discoveries (such as quantum mechanics, chaos theory, Heisenberg’s uncertainty principle, Einstein's theory of relativity, Darwin's theory of evolution) have had major implications for knowledge outside their immediate field. Why is it that science has the power to inform thinking in other areas of knowledge such as philosophy and religion? To what extent should philosophy and religion take careful note of scientific developments?

4. About whom is history written? Are the lives of some groups of people more historically significant than the lives of others? Why do selected past events appear in books as historically important while others are ignored?

1. About whom is history written? Are the lives of some groups of people more historically significant than the lives of others? Why do selected past events appear in books as historically important while others are ignored? 

2. To what extent is history dependent on who kept or preserved a written record?

3. To what extent is history about those who held power, and to what extent is it about ordinary people?

4. Are value judgments a fault in the writing of history? Should value-laden terms, such as atrocity, regime, hero or freedom, always be avoided, or does exclusion of value judgments deprive history of meaning?

5. To what extent can distinctions be made between factual report, biased interpretation and calculated distortion? Can history be used for propaganda? If so, how?

5. What knowledge of art can be gained by focusing attention on its social, cultural or historical context? To what extent do power relationships determine what art or whose art is valued? Is all art essentially a product of a particular place and time in terms of its subject matter and conventions of expression? Does art become obsolete? Is art understood more fully by emphasizing what all cultures have in common rather than by stressing what is unique to each?

1. What knowledge of art can be gained by focusing attention on the artist? Can or should artists’ intentions, and the creative process itself, be understood through observing artists or knowing something of their lives? Is the creative process as important as the final product, even though it cannot be observed directly? Are an artist’s intentions relevant to assessing the work? Can a work of art contain or convey a meaning to which the artist is oblivious?

2. What knowledge of art can be gained by focusing attention solely on the work itself, in isolation from the artist or the social context? Can or should technical virtuosity in itself, a skilled mastery of the medium, be enough to distinguish a work of art? Are certain compositions, ways of structuring sounds or shapes, inherently more pleasing than others? Can a work be judged primarily by the harmony of form and content, the way in which structure and style work effectively to create or support the subject matter?

3. What knowledge of art can be gained by focusing on the reader or audience’s response? Can it be plausibly argued that art is brought into being only in the response of the audience, that a work is created anew each time it is viewed, heard or read? What is the role of the critic in the judgment of the worth of art? Are any of the following sufficient indicators of the value of a work: its popularity, its commercial value in the market, its universality in its appeal beyond its cultural boundaries, and/or its longevity?

4. What knowledge of art can be gained by focusing attention on its social, cultural or historical context? To what extent do power relationships determine what art or whose art is valued? Is all art essentially a product of a particular place and time in terms of its subject matter and conventions of expression? Is art best seen as anthropological or historical documentation, bringing to life a remote society or era, but understood esoterically, only with independent knowledge of that remote life? Does art become obsolete? Is art understood more fully by emphasizing what all cultures have in common rather than by stressing what is unique to each?

6. How may moral dilemmas arise? Is it possible for an individual to act in a morally justifiable way within a context of restricted choice, oppression, or corruption? To what extent may the circumstances of people’s lives excuse actions that might be condemned by society’s moral principles? Can respect for a culture, in harmony with principles of tolerance and openness, be reconciled with a condemnation of specific practices within that culture, on the basis of other principles?

1. To what extent does the state of a person’s knowledge play a part in deciding whether an act is right or wrong? Under what conditions would it be legitimate for a person to plead ignorance? Are people responsible for finding out as much relevant information as possible?

2. What knowledge of morality can be gained by focusing attention on the individual making moral judgments? Is freedom of choice a necessary condition for making moral judgments? Should the person’s intentions be the criterion for deciding whether an action is right or wrong? Are people always aware of their real intentions or motives?

3. What knowledge of morality can be gained by focusing attention on the features of the moral
   judgment or act itself? Are some thoughts or actions intrinsically right or wrong, independent of circumstances? Is it possible to establish firm principles to determine moral action? If so, on what basis? On the basis of reason? Divine revelation? Is it possible to rank principles in order of importance? What are “human rights” and on what basis do they rest?

4. What knowledge of morality can be gained by focusing attention on the consequences of the
   thoughts or actions? Which matters more, the consequences for individuals or the consequences for the group? Can consequences be quantified or weighed scientifically?

5. What knowledge of morality can be gained by focusing attention on the social, cultural or historical context of the moral judgment? Is a shared moral code a necessity for a harmonious society? To what extent can acceptance of dissent be a feature of a shared moral code? To what extent do moral values differ, depending on the society or the historical time? For example, can a practice such as slavery be right in one era or region and wrong in another? Can the practices of one society be judged with any validity by applying the values of another generation or another culture? Do some values seem to be universal, or nearly so?

6. How may moral dilemmas arise? Is it possible for an individual to act in a morally justifiable way within a context of restricted choice, oppression, or corruption? To what extent may the circumstances of people’s lives excuse actions that might be condemned by society’s moral principles? Can respect for a culture, in harmony with principles of tolerance and openness, be reconciled with a condemnation of specific practices within that culture, on the basis of other principles?

7. When confronted by an unjust situation, is a person obliged to act? If the unjust situation is in the context of friendship or family, does this make a difference? Should this make a difference? Are there ethical constraints on the actions that a person should take to “right a wrong”?