Thinking And Moral Problems/2. Solving Problems/Endnotes

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1. Steven Pinker, How the Mind Works (New York: W. W. Norton and Company, 1997), 21.

2. And perhaps by the same formula—something like: the universe’s underlying causality enforces its rational behaviour, while mathematics underlying rationality enforces its causal interrelationships.

3. Of course, mathematics must describe the real world because each of its many terms has been precisely defined using language, a language that has itself been constructed from our knowledge of the real world (as section six of Chapter One and the previous paragraph pointed out).

4. See “The Conservation Laws,” a postscript to Chapter Seven.

5. A light-year is the distance that light travels through space in one year, about 9.5 x 10¹² kilometres, or 5.9 x 10¹² miles.

6. There are many important branches of theoretical science, where specialists work with pen and paper (or, more often these days, with computers) and do not work in laboratories or the field, but their work will always have its links to the real world. If it didn’t, colleagues would probably start calling them mathematicians.

7. W. E. K. Middleton, The Scientific Revolution (Toronto: C.B.C. Publications, 1963), 12.

8. This is because the universe’s various substructures (e.g., quarks, electrons, atoms, etc.) are very small.

9. They both probably knew that Aristarchus of Samos had discussed the idea of a sun-centred solar system in the third century BCE. (And was promptly accused of impiety for doing so.)

10. When individuals judge people (or more accurately but perhaps less frequently, people’s behaviour) to be “good” or “bad,” they most commonly use criteria valued by their own society. (Note that these values always mirror those espoused by the nation’s dominant religion; this is because religions gain their prominence by both guiding the state’s evolution and by being reciprocally supported by the state as it grows.) Society and its intertwined institutions (families, schools, churches, governing bodies, powers-elite, laws, etc.) collectively, over time, determine what is considered “good” or “bad” within that society. And society’s criteria provide adequate guidance for many, probably the majority, of us, for we often look no further when making a moral decision.

11. These criteria reflect Kohlberg’s six stages of moral judgement: from Self-Interest (Punishment and Reward) through Social Approval (Interpersonal Relations and Social Order) to Abstract Ideals (Social Contract and Universal Rights). See Lawrence Kohlberg, The Meaning and Measurement of Moral Development (Massachusetts: Clark University, 1981). Or see Lawrence Kohlberg, Essays on Moral Development. Volume I. The Philosophy of Moral Development: Moral Stages and the Idea of Justice (San Francisco: Harper & Row, 1981), 409-412. Kohlberg, and others, have found that children generally operate at the first two stages (Punishment and Reward)—as do many in prison; that most adults work at stage four (Social Order); and very few are at stage five (Social Contract). No one has yet been found at stage six (Universal Rights).

12. Social mores, of course, are necessarily trivial standards in this book’s frame of reference because they are local and temporal. The criteria used to determine correct social behaviour vary from society to society and are constantly changing. (They can even be observed changing from moment to moment during emergencies.)