Logicism and probabilism

Classical epistemology distinguished “rationality” from “empiricism.” Rationality derived new knowledge by deduction from existing knowledge, or from intuition. Empiricism derived new knowledge from sensory experience.

Rationalism and empiricism were opposing theories, and different epistemologists advocated one or the other. By the late 1800s, it became clear that knowledge rests on both reasoning and experience. In common usage, the word “rationality” now covers both.

On the other hand, “intuition,” which tradition considered an indispensable part of “rationality,” proved unreliable. People’s intuitions differ. When deductions differ, they can be made public and checked against each other. Intuitions are inherently private, so there is no way to resolve disagreements.

Part One of The Eggplant considers two particular rationalisms, logicism and probabilism, based on two mathematical systems, predicate logic and probability theory.1 These are modern descendents of the rationalist and empiricist traditions, respectively. There are other contemporary rationalisms, but these two have been the most influential over the past century, and the others face similar problems.

In classical epistemology, logic was the theory of how you could deduce true sentences from other true sentences. From “All ravens are black” and “Huginn is a raven,” you can deduce “Huginn is black.” Classical logic (formalized by Aristotle and mostly unchanged until the 1800s) had numerous well-known bugs. The next several chapters cover various attempts to fix them by adding technical machinery. Some were successful to some degree, but overall the logicist project conclusively failed. Hardly anyone takes logic seriously as epistemology nowadays.

Since formal logic is ancient history, it’s easy to ignore it, and many contemporary rationalists do.2 “Yeah, we don’t care about logic, so this discussion is irrelevant to our rationalism!” But it’s important to understand how and why logicism failed, because all other rationalisms face the same problems it tried to solve, and because there are good reasons to think that no rationalist solutions are possible. Many errors of contemporary rationalism are due to ignorance of these issues.

Empiricism also had serious bugs. One seemed fatal: the “problem of induction.” How can we come to know universal truths starting from specific facts? The problem is that it doesn’t matter how many black ravens you see, you can’t conclude “all ravens are black,” because maybe there’s a white one somewhere you haven’t seen.

Maybe, though, if you see more black ravens, you ought to be more confident they’re all black. Or at least that most are!

Probability theory was invented originally as a tool for winning at gambling. Some epistemologists seized it and developed it as a tool for understanding what “confidence” means. A great advance: theoretically, by emphasizing that you don’t simply believe that statements are true or false; and practically, because probability theory is uniquely effective in certain circumstances. Unfortunately, as an overall theory of belief, it is a non-starter. It has almost all the same problems as logic, plus others of its own… as we shall see.

  • 1. I am using the terms “logicism” and “probabilism” in ways that are reasonably mainstream but somewhat broader than is typical. “Logicism” in one narrower sense refers only to a position in the philosophy of mathematics. It is also used to refer to the logic-based research program in artificial intelligence.
  • 2. Math students may learn some basics for use in proofs. Analytic philosophy students also get a bit because it’s supposed to help you think clearly, and it was important in the founding of their field. However, most universities no longer teach the subject seriously in either the math or philosophy department. It’s extremely cool stuff, even though it doesn’t work! Understanding logic does help you think clearly, although mostly not for the reasons it was supposed to. If a university course is not available, “Teach Yourself Logic” is a valuable guide.

Navigation

This page is in the section Part One: Taking rationalism seriously,
      which is in In the cells of the eggplant,
      which is in ⚒ Fluid understanding: meta-rationality,
      which is in ⚒ Sailing the seas of meaningness,
      which is in Meaningness and Time: past, present, future.

The next page in this section is The Spanish Inquisition.

This page’s topics are History of ideas and Rationalism.

General explanation: Meaningness is a hypertext book (in progress), plus a “metablog” that comments on it. The book begins with an appetizer. Alternatively, you might like to look at its table of contents, or some other starting points. Classification of pages by topics supplements the book and metablog structures. Terms with dotted underlining (example: meaningness) show a definition if you click on them. Pages marked with ⚒ are still under construction. Copyright ©2010–2020 David Chapman. Some links are part of Amazon Affiliate Program.