Thoughts on Logical Leap by David Harriman
What is the Full Context of Knowledge?
This essay represents my notes on the intricacies of Induction as a method of scientific inquiry. It is not necessarily a critique of Harriman’s (or Peikoff’s) ideas presented in the book. I appreciate Dr. Travis Norsen’s review of the book found here. His thoughtful critique helped me read Harriman’s book with greater intensity. And as a result, I believe I got more out of Harriman’s material.
Inductive reasoning has been defined as the development of generalizations derived from a limited number of observed instances. These generalizations are said to apply universally, meaning they are true for all times in the past, present and future. They are true across all locations in space. While this is the accepted definition. No philosopher has managed to define a satisfactory method of induction. Consequently, the subject has suffered from a lack of attention in the philosophy of science.
Some have claimed that induction is a modified form of deductive reasoning. Others have asserted induction is simply a matter of probabilities and/or enumeration. Philosopher David Hume dismissed induction entirely saying it relied on circular reasoning and was inherently uncertain. With no defined process to follow, scientists have looked elsewhere for guidance, to their detriment.
Leonard Peikoff’s 2002 lecture series titled Induction in Physics (Part I can be viewed on YouTube, along with the full series) has, fortunately, provided a new look at the process of induction. David Harriman, with Peikoff’s assistance, extends that work in the book Logical Leap: Induction in Physics. Logical Leap builds on the lecture series by adding more detailed descriptions of historical scientific discoveries. These examples outline a method for inducing the laws of nature. I would encourage the reader to pick up a copy of the book and explore his ideas on their own.
The examples Harriman gives range from simple investigations of light (Newton) and kinematics (Galileo) to more complex theories like Newton’s laws of motion and the multi-disciplinary investigations that led to the discovery of the atom. Each story is dissected to emphasize and define particular aspects of the inductive method. I do not wish to rehash his method here. Rather, I would like to focus on a point Travis Norsen makes in his review of the book - How do you define the “full context of knowledge” when practicing induction in physics.
A proper inductive method requires that the scientist apply all the available and applicable scientific knowledge when crafting an experiment or exploring the cause of some phenomenon. Harriman/Peikoff refer to this as “the full context of knowledge”. When discussing specific scientific investigations, Harriman is clear about what constitutes ‘full context’ for that situation. The history of Newton’s theory of gravity serves as a good example.
Newton’s theory subsumes motion in all it’s forms. As such, it has a very large context. But rather than dive into the deep end of the pool, let us look at Galileo’s investigation of motion - his pendulum and inclined plane experiments. Galileo’s findings form one pillar of Newton’s theory. And both the pendulum and inclined plane experiments are simple, isolated systems that will allow the reader to see full context easily. Both have very few variables - length of the string, angle of incline, weight of the bob/ball, speed of a rolling ball and the time it takes for the bob to travel back and forth (the period).
But that wasn’t enough to integrate Galileo’s observations with knowledge of the wider world. He needed to survey his knowledge of motion across multiple disciplines and sources. He had to focus on those aspects of motion that may affect his experiments while ignoring others that clearly had no bearing.
Galileo settled on two additional ideas that he felt would apply to his experiments. His experience moving objects taught him that friction retarded motion. He designed his experiments so as to eliminate or reduce friction from sliding objects (inclined plane) and from air resistance (pendulum).
He also knew the scientific consensus of the time described motion using the concept of impetus. Impetus was thought to be similar to a invisible fluid contained within an object in motion. When thrown, a person imparts some impetus into an object, say a ball. As the ball travels, it loses impetus as if this invisible fluid were draining out of it. Once all the impetus was expended, the object would fall straight down. Galileo rejected this notion based on his observations in the inclined plane experiments. Instead he treated the horizontal and vertical motions as independent of each other when analyzing his results.
Having included and accounted for all of this, Harriman claims that Galileo had included the full context of knowledge in his experiments. Travis Norsen points out that this isn’t entirely true, but I will get to that later.
The popular myth is that Newton discovered gravity when an apple dropped on his head. But the truth is much more complex because the full context had expanded greatly since Galileo’s time. Galileo’s kinematics became part of Newton’s full context. Galileo had demonstrated vertical motion on earth occurs under constant acceleration and horizontal motion occurred at constant velocity. Newton would have to incorporate this into his laws of motion. But Newton also knew of Kepler’s three laws of planetary motion. This got Newton thinking, could kinematics developed for motion on earth be applied to the motion of celestial objects? Then there was Newton’s own independent studies. He had run calculations for an object swung in a circle at the end of a rope. These experiments convinced him that terrestrial and celestial motion might be related. Further, Newton had demonstrated that the ocean tides were somehow related to the orbit of the moon and the position of the sun. This vast array of knowledge led him to develop the new concepts of Velocity, Acceleration, Mass and Force.
Given this vast context and valid new concepts, Newton was able to develop his three laws of motion and his famous theory of gravity. He was able to prove that pendulums, apples and planets all follow the same rules. Harriman uses Newton’s discovery as a textbook case of the Inductive Method. And it is difficult to argue with Harriman’s claim that Newton had included the full context of knowledge when deriving his three laws of motion and the theory of gravity.
Travis Norsen, however, brings up some interesting points in his review of Logical Leap that paint a slightly murkier picture. He does not see this as a flaw in the book’s thesis, per se. But he does wish Harriman had gone further. Norsen views treatment as much as a missed opportunity to better define “full context of knowledge”. In this essay, I simply wanted to present Harriman’s concept of full context. I will go over Norsen’s thoughts in my next essay.