A Theory of Knowledge
January 1, 2006
Brief Comparison to Leonard Peikoff’s Theory of Induction
Some readers may wonder how my theory of causality and induction differs from Objectivist philosopher Leonard Peikoff’s as expressed in his 2003 course, "Induction in Physics and Philosophy."
In my judgment, Dr. Peikoff’s course consists of essentially incorrect though intelligent answers to some good questions, which I had already answered essentially correctly in my own writings and lectures on causality, induction, propositions, and mathematics.
The closest Dr. Peikoff comes to being on the right track are in the following two ideas of his:
1. Dr. Peikoff is correct that the basic evidence for causality is in causal relations between oneself and external objects. However, Dr. Peikoff—like many other thinkers—thinks the basic evidence is in instances in which the self is the cause and the action of other objects is the effect. E.g., my pushing the ball makes the ball roll. The reverse is true. In keeping with Ayn Rand’s principle of “the primacy of existence,” the basic evidence of causality is in instances in which external objects are the cause, and one's awareness of the objects is the effect. E.g., the ball makes me feel it.
2. (On this second issue, Dr. Peikoff is closer to a correct track.) Dr. Peikoff is correct that concepts are what he calls a “green light to induction,” and that something is needed to fill the conceptual “file folders” (Ayn Rand’s metaphor) created by the forming of concepts. However, much of what Dr. Peikoff attributes to mathematics in this process is actually more generally attributable to propositions. Specifically, Dr. Peikoff claims that mathematical formulas (e.g., d=16t2) relate qualities to each other by “put[ting] back in”—“in numerical terms” —some of the measurements that were omitted during concept-formation. But it is in virtue of mathematical formulas being propositions that they relate quantities to each other and “put back in” some measurements that were omitted during concept-formation. In Dr. Peikoff’s claim above, it is only the phrase “in numerical terms” that applies specifically to mathematics. Non-mathematical propositions, as in biology and the humanities, also relate qualities and “put back in” omitted measurements, along with performing other important functions of propositions. (For my theory of the nature and cognitive role of propositions, see my essay, A Theory of Propositions.) If one understands the function of propositions, one can reduce Dr. Peikoff’s long argument to: “Mathematical formulas are propositions that use numbers.” His argument reveals unawareness of the cognitive role of propositions, and sheds little light on the cognitive role of mathematics per se.
In his course, Dr. Peikoff spends a good deal of time on the philosophical foundation of mathematics. In my judgment, the treatment of this subject by Glenn Marcus and me in our mathematics articles mentioned above is far more precise, fundamental, and thorough. Nevertheless, Dr. Peikoff’s course did remind me of something that induced me to add two words to the latest revision of our first article.
Dr. Peikoff also spends much time arguing for and applying his claim that mathematics cannot be used in measuring consciousness, and therefore cannot be used in philosophy. A glaring counterexample to Dr. Peikoff’s claim is probability theory, which measures states of knowledge; probability theory quantifies the continuum from possibility to probability to certainty. Indeed, a correct theory of probability is an essential element of a correct theory of induction, but Dr. Peikoff dismisses probability theory out of hand.
In short, my theory of causality and induction addresses much of the same subject matter that Dr. Peikoff’s course addresses, but my conclusions are essentially contrary to Dr. Peikoff’s.