Before you keep reading...
Runestone Academy can only continue if we get support from individuals like you. As a student you are well aware of the high cost of textbooks. Our mission is to provide great books to you for free, but we ask that you consider a $10 donation, more if you can or less if $10 is a burden.
Before you keep reading...
Making great stuff takes time and $$. If you appreciate the book you are reading now and want to keep quality materials free for other students please consider a donation to Runestone Academy. We ask that you consider a $10 donation, but if you can give more thats great, if $10 is too much for your budget we would be happy with whatever you can afford as a show of support.
2.6. Complexity Thinking¶
We are getting farther afield now, but the shifts we are postulating in the criteria of scientific modeling are related to 20th century developments in logic and epistemology.
Aristotelian logic → many-valued logic
In traditional logic, any proposition is either true or false. This system lends itself to math-like proofs, but fails (in dramatic ways) for many real-world applications. Alternatives include many-valued logic, fuzzy logic, and other systems designed to handle indeterminacy, vagueness, and uncertainty. Bart Kosko discusses some of these systems in Fuzzy Thinking.
Frequentist probability → Bayesianism
Bayesian probability has been around for centuries, but was not widely used until recently, facilitated by the availability of cheap computation and the reluctant acceptance of subjectivity in probabilistic claims. Sharon Bertsch McGrayne presents this history in The Theory That Would Not Die.
Objective → subjective
The Enlightenment, and philosophic modernism, are based on belief in objective truth, that is, truths that are independent of the people that hold them. 20th century developments including quantum mechanics, Godel’s Incompleteness Theorem, and Kuhn’s study of the history of science called attention to seemingly unavoidable subjectivity in even “hard sciences” and mathematics. Rebecca Goldstein presents the historical context of Godel’s proof in Incompleteness.
Physical law → theory → model
Some people distinguish between laws, theories, and models. Calling something a “law” implies that it is objectively true and immutable; “theory” suggests that it is subject to revision; and “model” concedes that it is a subjective choice based on simplifications and approximations.
But it is not clear that they are very different. Some concepts that are called laws are really definitions; others are, in effect, the assertion that a certain model predicts or explains the behavior of a system particularly well. We come back to the nature of physical laws in Section 6.9, Section 7.9, and Section 10.9
Determinism → indeterminism
Determinism is the view that all events are caused, inevitably, by prior events. Forms of indeterminism include randomness, probabilistic causation, and fundamental uncertainty. We will come back to this topic in Section 7.6 and Section 12.7
This chapter is an overview of the themes coming up in the book, but not all of it will make sense before you see the examples. When you get to the end of the book, you might find it helpful to read this chapter again.