[Lecture Seven] Induction in Physics and Philosophy
by Dr. Leonard Peikoff
Total Time: 2 hours, 9 minutes
Course summary: This course features Dr. Peikoff’s presentation of his solution to the problem of induction. He discusses the axioms of induction and the role of measurement omission and relates them to the process of forming generalizations. By comparing these features to the process of concept formation, Peikoff indicates the parallels in logic that give rise to new insights about the relationship between induction and deduction. Special attention is given to the similarities between physics and philosophy. Read more »
In this lecture: This lecture concludes the discussion of induction by showing how the principles of induction apply to all fields of human knowledge. It indicates the crucial role that induction plays in validating knowledge in any field.
Study Guide
This material is designed to help you digest the lecture content. You can also download below a PDF study guide for the entire course.
| What is the proper understanding of the claim that philosophy is not mathematical? |
| How do quantitative relationships arise in philosophy? |
| Why does the integrating faculty of human consciousness not allow for the selection of a unit to serve as its standard of measure? |
| Why do the concepts of concept formation not reduce to units in the way that matter does? |
| How does the numeration of degrees become inapplicable in ethical arguments about principles? |
| Why do states of consciousness have intensity but not discrete numerical units? |
| Why does grasping the quantity of physical things become essential to grasping the quality of things? |
| How have two crucial errors in philosophy made mathematics in physics incomprehensible? |
| What is the proper understanding of mathematics in understanding physics? |
| Why is it not a black mark against philosophy that it is not mathematical in its inductions? |
| What is the essential guidance of philosophy on all levels? |
| How is it proper to say that philosophy is as scientific as physics? |
Q&A Guide
Below is a list of questions from the audience taken from this lecture, along with (approximate) time stamps.
| 1:37:32 | I’d like to hear David Harriman’s explanation of integers and exponents. |
| 1:41:39 | Doesn’t what you’re saying here with regard to the unique human capacity to identify a unit and measure on its base show that the people who are trying to say that animals conceptualize are, in a sense, barking up the wrong tree? Does the crow really have a crow? |
| 1:44:12 | Are these two aspects of consciousness—the analog/continuous process you mentioned and the digital matter of whether consciousness exists—two separable things packaged together? |
| 1:46:45 | Would you say that knowledge of numbers and counting is necessary for our survival and, if so, wouldn’t a theory of number formation have to be a part of general epistemology? |
| 1:50:44 | What’s the relationship between the two uses of “proof” and does one subsume the other? |
| 1:52:19 | Can you say anything about Ayn Rand’s interest in higher mathematics as relating to epistemology? |
| 1:54:38 | Your comment that the great physicist immediately jumps to the generalizations once he grasps the pattern brought to mind Ayn Rand’s description of how she came to her theory of concept formation. In other words, although she knew she had other items to check, she “had it” when she “got it.” Could you comment? |
| 1:58:33 | You said something like that there are two forms of measurement, preconceptual or conceptual, and it seems to me that that implies that philosophy is approximate… |
| 2:00:21 | In experimentation, what is the relationship between an equation that happens to fit the data and a causal explanation? |
| 2:01:28 | You talked about how axioms and first-level generalizations are starting points. And when I first learned about axioms and their self-refuting nature I was very impressed polemically. Is there a similar thing with first-level generalizations in physics? |
| 2:03:10 | I think you said “we grasp the quality of things by grasping their quantity.” I was wondering if you could elaborate on that. |
| 2:05:52 | I heard once that one of Ayn Rand’s achievements was to see that logic pertains not only to the process of deduction, but to the entire process of reasoning. Can you talk about how logic pertains to induction? |
| 2:06:45 | Given what you’ve studied and shown that philosophy and its inductions are not necessarily quantitative or disqualified on that count, have you given any thought to other non-quantitative fields, say, in the humanities, for example history? |