Tetralemma: Beyond the Binary Logic

Made from Midjourney

Tetralemma is a philosophical concept that originated in Indian logic and metaphysics. It refers to a logical analysis that categorizes a proposition into four possible truths or negations. The four categories are:

1. The proposition is true and is established (Sāstvānumāna)
2. The proposition is false and is established (Asāstvānumāna)
3. The proposition is true but is not established (Sāstvānāstika)
4. The proposition is false but is not established (Asāstvānāstika)

An example of the tetralemma applied to the proposition “All men are mortal” would be:

Category 1 would refer to the established truth that all men are indeed mortal;

Category 2 would refer to a hypothetical situation in which all men were not mortal;

Category 3 would refer to a situation in which the truth of the proposition is not established, for example, in a culture where belief in immortality is prevalent;

Category 4 would refer to a situation in which the falsity of the proposition is not established, such as in a culture where belief in reincarnation is widespread.

This is different from Aristotelian logic.

Aristotelian logic, also known as syllogistic logic, was developed by the ancient Greek philosopher Aristotle. It is based on the idea of syllogisms, which are arguments that consist of three parts: a major premise, a minor premise, and a conclusion. The premises and conclusion are related to each other in a specific way, and the conclusion is deduced from the premises. Aristotelian logic is based on the principle of non-contradiction, which states that something cannot both be and not be at the same time.

The tetralemma is different from the binary truth table in that it provides a more comprehensive analysis of a proposition by taking into account the truth value of the proposition and its status as an establishment. This difference in truth values allows the tetralemma to address certain issues and philosophical questions not easily addressed by Aristotelian logic, such as the relationship between appearance and reality and the nature of paradoxical statements.

Consider the relationship between appearance and reality:

In many philosophical traditions, there is a debate about the relationship between how things appear and how they truly are. Buddhist and Vedantic philosophy is known as the “two truths doctrine.” In this context, tetralemma can provide a framework for exploring the relationship between the way things appear to us and the way they truly are.

Suppose we are considering the appearance of a mirage in the desert. To an onlooker, the mirage appears to be a pool of water, but in reality, it is an optical illusion caused by the bending of light. Using the tetralemma, we can analyze the relationship between appearance and reality by recognizing four possible truth values for the proposition “the mirage is a pool of water”:

1. True: The mirage appears to be a pool of water, and it truly is a pool of water.
2. False: The mirage appears to be a pool of water, but it is not truly a pool of water.
3. Both true and false: The mirage appears to be a pool of water, and it is both a pool of water and not a pool of water.
4. Neither true nor false: The mirage appears to be a pool of water, but it is neither a pool of water nor not a pool of water in some ultimate sense.

In this example, truth value 2 is the most commonly accepted in Aristotelian logic, but truth values 3 and 4 allow for a more nuanced understanding of the relationship between appearance and reality. They recognize that appearances can be deceiving and that there may be a deeper truth beyond appearances that are not easily grasped through our senses.

Consider another example where the tetralemma provides a more nuanced understanding: paradoxical statements.

A paradoxical statement is a statement that contradicts itself, or that appears to be self-contradictory. For example, the statement “This statement is false” is paradoxical because if the statement is true, it is false, and if it is false, it is true.

Tetralemma can be useful in resolving paradoxical statements by providing four possible truth values for such statements:

1. True: The statement is true and does not contradict itself.
2. False: The statement is false and does not contradict itself.
3. Both true and false: The statement is true and false, which means it contradicts itself.
4. Neither true nor false: The statement is neither true nor false, meaning it cannot be evaluated using traditional binary truth values.

In the case of the paradoxical statement “This statement is false,” truth value 3 (both true and false) captures the self-contradictory nature of the statement. In contrast, truth value 4 (neither true nor false) acknowledges that the statement cannot be evaluated using traditional binary truth values.

Consider the statement, “X is a bachelor.” On the surface, this statement seems to be either true or false (Aristotelian Logic), but it can be neither true nor false in certain situations.

For instance, if X is unmarried, the statement “X is a bachelor” is true. However, if X is married, the statement “X is a bachelor” is false. But what if X is a widower or has been divorced? In these cases, the statement “X is a bachelor” is neither true nor false, as it does not accurately reflect John’s marital status.

In the case of the statement, “X is a bachelor,” truth value 3 (both true and false) acknowledges the ambiguity and complexity of the statement. In contrast, truth value 4 (neither true nor false) captures the idea that the statement cannot be evaluated as true or false under certain circumstances.

One of the limitations of tetralemma is its lack of falsifiability. The tetralemma does not provide a clear criterion for falsifiability, an important aspect of scientific investigation. Falsifiability refers to the ability of a theory or hypothesis to be tested and potentially proven false.

Advances in mathematics allowed us to go beyond ‘fixed value’ logic systems. Fuzzy and probabilistic logical systems are a mathematical framework for representing and processing uncertain or vague information. Fuzzy logic allows values to be assigned to propositions that lie between true and false, providing a more nuanced evaluation of truth values than binary or tetra-truth tables.

All logic systems devised by humans have limitations. Reality is not only complex, but we often have to deal with limited information. Being aware of these limitations fills us with awe over the contributions of our ancient saints.

Ekum Sat