In my physics lab course, I learned how to determine the atomic structure of crystals by means of x-ray diffraction and how to identify subatomic particles by analyzing bubble-chamber photographs. In my philosophy of science course, on the other hand, I was taught by a world-renowned professor (Paul Feyerabend) that there is no such thing as scientific method and that physicists have no better claim to knowledge than voodoo priests. I knew little about epistemology [the philosophy of knowledge] at the time, but I could not help noticing that it was the physicists, not the voodoo priests, who had made possible the life-promoting technology we enjoy today.

Harriman noticed the enormous gulf between science as it is successfully practiced and science as is it described by post-Kantian philosophers such as Feyerabend, who are totally unable to explain the spectacular achievements of modern science.

Harriman's book Logical Leap: Induction in Physics attempts to bridge this gap between philosophy and science by providing a philosophical explanation of how scientists actually discover things. A physicist and physics teacher by trade, he worked with philosopher Leonard Peikoff to understand the process of induction in physics, and this book is a result of their collaboration.

Induction is one of the two types of logical argument; the other type is deduction. First described by Aristotle, deduction covers arguments like the following: (1) All men are mortal. (2) Socrates is a man. (3) Therefore, Socrates is mortal. Deductive arguments start with generalizations ("All men are mortal.") and apply them to specific instances ("Socrates"). Deductive logic is well understood, but it relies on the truth of the generalizations in order to yield true conclusions.

So how do we make the correct generalizations? This is the subject of the other branch of logicinductionand it is obviously much more difficult than deduction. How can we ever be justified in reasoning from a limited number of observations to a sweeping statement that refers to an unlimited number of objects? In answering this question Harriman presents an original theory of induction, and he shows how it is supported by key developments in the history of physics.

The first chapter presents the philosophical foundations of the theory, which builds directly on the theory of concepts developed by Ayn Rand. Unfortunately for the general reader, Harriman assumes familiarity with Rand's theory of knowledge, including her views of concepts as open-ended, knowledge as hierarchical, certainty as contextual, perceptions as self-evident, and arbitrary ideas as invalid. Those unfamiliar with these ideas may find this section to be confusing. But the good news is that those readers can then proceed to the following chapters, which flesh out the theory and show how it applies to key developments in the history of physics (and the related fields of astronomy and chemistry). These chapters do a wonderful job at bringing together the physics and the philosophy, clarifying both in the process.

Harriman argues that as concepts form a hierarchy, generalizations form a hierarchy as well; more abstract generalizations rest on simpler, more direct ones, relying ultimately on a rock-solid base of "first-level" generalizations which are directly, perceptually obvious, such as the toddler's grasp of the fact that "pushed balls roll." First-level generalizations are formed from our direct experiences, in which the open-ended nature of concepts leads to generalizations. Higher-level generalizations are formed based on lower-level ones, using Mill's Methods of Agreement and Difference to identify causal connections, while taking into account the entirety of one's context of knowledge.

Ayn Rand held that because of the hierarchical nature of our knowledge, it is possible to take any valid idea (no matter how advanced), and identify its hierarchical roots, i.e. the more primitive, lower-level ideas on which it rests, tracing these ideas all the way back to directly observable phenomena. Rand used the word "reduction" to refer to this process. In a particularly interesting discussion, Harriman shows how the process of reduction can be applied to the idea that "light travels in straight lines," identifying such earlier ideas as the concept "shadow" and finally the first-level generalization "walls resist hammering hands."

Harriman's discussion of the experimental method starts with a description of Galileo's experiments with pendulums. Galileo initially noticed that the period of a pendulum's swing seems to be the same for different swing amplitudes, so he decided to accurately measure this time period to see if it is really true. Concluding that the period is indeed constant, he then did further experiments. He selectively varied the weight and material of the pendulum's bob, and the length of the pendulum. This led him to the discovery that a pendulum's length is proportional to the square of its period. Harriman notes the experiments that Galileo did not perform:

He saw no need to vary every known property of the pendulum and look for a possible effect on the period. For example, he did not systematically vary the color, temperature, or smell of the pendulum bob; he did not investigate whether it made a difference if the pendulum arm is made of cotton twine or silk thread. Based on everyday observation, he had a vast prescientific context of knowledge that was sufficient to eliminate such factors as irrelevant. To call such knowledge "prescientific" is not to cast doubt on its objectivity; such lower-level generalizations are acquired by the implicit use of the same methods that the scientist uses deliberately and systematically, and they are equally valid.