The Logical Leap
Induction in Physics and Philosophy, a 2002 lecture by Leonard Peikoff, is a good study of the role that inductive reasoning plays in physics and philosophy. The lecture is a precursor to David Harriman’s popular book The Logical Leap, first published in 2010.
The lecture and the book are a result of a collaboration between Peikoff and Harriman.
Peikoff begins his lecture with an identification of the axioms of induction and the method of establishing their objectivity. He explains the Objectivist theory of measurement omission, and goes on to establish the difference between induction and deduction.
He talks about things like—how human beings reach their first inductive generalizations—how these generalizations become the foundation of scientific knowledge—the objective criteria for proof in scientific theory. He investigates the methods of scientists like Galileo, Newton, Faraday, Maxwell and others, and goes on to prove that without experimentation, mathematics and inductive reasoning scientific knowledge is not possible.
Peikoff stresses on the important role that mathematics plays in physics. “Mathematical physics is necessitated by the fact that a conceptual consciousness can know objects only through measurement—only through relating quantities.”
The lecture of approximately 13-hours is divided into 7-episodes. I think the last two episodes are most interesting because in these Peikoff presents interesting arguments for proving that inducting reasoning is critical for the development of rational philosophy.
From Plato to Descartes to Kant to Hegel, rationalist philosophers have attempted to deduce the nature of the world from “a priori” ideas, and their spectacular failure has done much to discredit philosophy in the eyes of physicists. Philosophy does not tell us the specific nature of the world—but it does tell us that there is a world, that it has a nature and must act accordingly, and that we discover that nature by following certain principles of method.
Philosophy is the science that defines the relationship between the volitional consciousness and reality. Thus it is the fundamental science of human life, on which all more specialised disciplines rest. It is the voice telling us how to pursue those disciples while staying in cognitive contract with reality at each point—which is a prerequisite of our successfully achieving rational goals in any field. All other sciences presuppose the essentials of a rational view of the universe, of knowledge, and values.
Philosophy is and has to be an inductive subject in every branch except metaphysics…. The normative ideas of philosophy are not innate; they must be learned by starting with perceptual observation and then proceeding up the necessary hierarchy, just as in physical science. All knowledge of reality must be gained on the basis of observation, including the knowledge of how to gain knowledge. Induction is inescapable in every subject.