I have self-published the second edition of my book, A Validation of Knowledge: A New, Objective Theory of Axioms, Causality, Meaning, Propositions, Mathematics, and Induction. The second edition is available for sale as a paperback and ebook from Amazon. The first edition is no longer for sale.

I have closed my online bookstore because of limitations of the platform.

Shortly before the publication date of the first edition, my longtime closest friend and colleague Glenn Marcus became ill and was not able to review the final draft. Glenn is well again, and the second edition is the result mainly of my incorporating his feedback on the first edition. This new edition also has a foreword by Glenn.

Aside from the foreword and one new short section, the only changes from the first edition are roughly a hundred line edits for clarity. So that purchasers of the first edition don’t find a need to purchase the second edition too, the foreword is reproduced below. (The foreword also can be seen using the Look Inside feature on the Amazon page.)

I am happy to have finished the second edition before the election (which I will write about in the next day or two) and its unpredictable aftermath.

Foreword to A Validation of Knowledge

I am honored to write the Foreword to Ronald Pisaturo’s A Validation of Knowledge: A New, Objective Theory of Axioms, Causality, Meaning, Propositions, Mathematics, and Induction.

In 1992, I asked Ron to write a treatise on philosophy, in order to validate explicitly how we know the fundamental truths of philosophy. This book is his validation. In my judgment, Ron presents a methodologically-explicit, step-by-step, logical argument—where no logical step is skipped, and all abstractions are firmly tied to their concretes.

Let me give some advice to readers who want to engage seriously with this work. First, you must know some mathematics to do so successfully. The issue of how mathematics relates to philosophy has been an open question for more than two and half millennia. Mathematics is the science of measurement, and, as such, can be applied to any field, helping to make that field’s conclusions more precise. Probability measures the certainty of what we know; therefore, philosophy, especially epistemology, can use mathematics to make its conclusions—the certainty of its inductions—more precise. To measure the level of certainty of our inductive generalizations, Ron explicates here his “n/(n+1)” method. The mathematics necessary to understand fully Ron’s validation consists of about two semesters of calculus and one semester of probability. If you don’t already know these two subjects, learning them is certainly within reach if you put your mind to it.

Second, I want to caution readers about potentially misapplying the cognitive method of integration. (I should know, because it was while reading Ron’s book that I learned not to make this error.) As Ayn Rand (1971, 173) explained, “Integration is the essential part of understanding.” But what kind of integration should an active mind perform when reading, and which integrations are fundamental? In my judgment, before trying to integrate a new logical argument with one’s existing context of knowledge, one should first focus on whether the new argument corresponds to the relevant facts. As Ron has stated (in private correspondence), each reader should put aside his own past thinking, follow the book’s argument, and judge whether it identifies reality. That is, focus first on existence: does the argument correspond to the facts? If so, then—and only then—integrate the now-validated argument with one’s old context, making any needed corrections to ensure that one’s new context remains without contradiction. Put existence first, and consciousness second, honoring what Ayn Rand identified as “the primacy of existence.”

The epistemological issues covered in this book are difficult, because they require identifying steps in reasoning that have always been implicit. To do that takes substantive effort. I should know. I have been studying philosophy for almost fifty years now, and I have studied Ron’s work since he began explaining it to me almost thirty years ago. I try not to think about all the effort I have invested during these decades, and all of the many confusions I have had to fight through. Rather than think about my past effort, I take joy in understanding—to whatever extent I do—what I consider a valid proof that resolves these issues, and in how this understanding has substantively enhanced my life. I wish you—the careful, thoughtful reader—a similar understanding and its resultant joy.

Glenn Marcus
September 2020