Three-valued Logic

Western scientific logic is actually three-valued or ternary logic. Ternary logic is such a great improvement over Aristotelian two-valued logic that it inspired the Enlightenment and enabled tremendous scientific and technological progress in a comparatively short time. Nevertheless, most religious thought and theological debate still uses the axioms of Aristotelian logic, despite its serious shortcomings even in elementary material reasoning.

We propose that spiritual inquiry must be at least on the basis of scientific thought and method; that is, an empirical inquiry based on ternary logic, with great sensitivity to and tolerance of the ambiguity and indeterminacy natural to any subjective phenomena. Aristotelian logic is too simple and deterministic for spiritual reasoning, leading to inaccurate and misleading theological conclusions.

Let us demonstrate the insufficiency of Aristotelian logic by comparing its AND operator with that of ternary logic. We will see that even in the simplest cases, ternary logic provides a much richer and more accurate set of logical results. We will also provide a few examples to illustrate the superior reasoning power of ternary logic.

In Boolean logic, the only possible truth values are false and true. Using the Boolean AND operator, the result of the logical expression P AND Q is true only if both P and Q are true, and false if either P or Q is false. This is illustrated in the following truth table, where the possible values of P and Q are shown in gray, and the result of the operation is shown in yellow:

P AND Q	True	False
True	True	False
False	False	False

For example, the statement “The book is on the table” is true only if there is a book (P = true) and it is indeed on the table (Q = true). It is false if observation shows that there is a glass on the table (P = false), the book is on the floor or on the shelf (Q = false).

Now consider the same AND operator in ternary logic. The possible truth values in this logic are false, true and unknown. Here the result of the ternary logic AND operator is true only if both P and Q are true, false if either P or Q is false, and unknown if either P or Q are unknown or indeterminate:

In this example, the statement “The book is on the table” is true only if there is a book (P) and it is indeed on the table (Q). It is false if observation shows that either term of the expression is false. However, if we do not know or cannot observe the state of the book, the table or both, the logical result is unknown or indeterminate.

The possibility of an indeterminate logical result is of great significance, because it encourages us to expand our knowledge. If we can identify that some logical factors are unknown or indeterminate, this provides an opportunity to design an experiment or perform an observation that will provide the missing knowledge. This small difference between Aristotelian and ternary logic accounts for much of the power and progress of scientific method over previous Aristotelian models of Western thought.

The use of ternary logic values significantly expands the number of situations possible to represent accurately in a logical expression or framework. In real life, the facts are often unknown, uncertain or indeterminate. A logical reasoning process that accommodates this reality will lead us to more accurate and rational conclusions.

Aristotelian logic idealistically requires us to assume that we know the state of all the factors in a logical statement or syllogism. Ternary logic realistically admits that there are some things that we do not or cannot know, at least at the present time. Part of the human condition we experience every day is that many factors remain unknown at any particular time.

Thus using non-Aristotelian ternary logic and scientific empirical reasoning will help us a great deal in our pursuit of the perfection of yoga, because they help us to identify the unknown and indeterminate factors in our reasoning, and reach accurate conclusions based on the real state of our knowledge.

Next: Transcendental Logic