Two Types of Binary Reasoning

 

Dr. Alice C. Linsley

Recently, I read an article critical of people who were "binary" thinkers, by which the author meant people who tend to classify information in one of two categories: true or false, black or white. He called this binary thinking. Though not the only definition of binary thinking, his is the most common and generally accepted definition.

If one does an internet search using the phrase "binary reasoning" this comes up on Goggle: 

Binary reasoning is a system of logic where information is categorized into only two, mutually exclusive states—typically TRUE (1) or FALSE (0). Used in computer logic and analytical reasoning, it simplifies complex problems by allowing only two, non-overlapping possibilities (e.g., truth-tellers vs. liars). 

According to this definition, binary reasoning has an either-or framework that does not allow for contradiction (only one can be true) or hierarchy (both are true but one has higher authority).

The Goggle definition reflects the Aristotelian logic that dominates Western philosophy. It does not recognize the much older and more complex binary reasoning of the early Hebrew (4000-2000 BCE). Were we to investigate the Hebrew binary reasoning we would discover that it breaks out of the either-or framework by recognizing hierarchy rather than non-contradiction. Binary reasoning is the way humans make sense of features in Nature that signal something beyond. The Semitic way of thinking allows for both-and. It opens an avenue for the exploration of the "and".

Western philosophy recognizes the logic of non-contradiction. However, the original arguments made by Aristotle are not that simple. Aristotle presented three versions of the principle of non-contradiction: an ontological, a doxastic (opinion), and a semantic version. The first version concerns things that exist in the world, the second is about what we believe, and the third relates to assertions about truth.

The binary reasoning that pertains to the ontological are the most significant. These are observations of binary sets in Nature. Here we find hierarchy, that is to say, things exist even when they exist as a trace, to borrow Derrida's term.

It is fascinating that both the Structuralist Claude Lévi-Strauss and the Deconstructionist Jacques Derrida began with binary reasoning.

Lévi-Strauss (1908–2009) founded structural anthropology, proposing that universal mental structures or patterns shape human culture. He argued that human thought operates through binary oppositions (e.g., raw/cooked, nature/culture). On the basis of his anthropological research, he argued that the "primitive" mind has the same structures as the "civilized" mind. He believed that myths, kinship, and customs can be decoded to reveal these mental structures. He came to these conclusions based on his 1930s fieldwork among the Bororo and Nambikwara peoples of the Amazon and Matto Grosso. His experiences and structuralist theories were documented in his 1955 memoir, Tristes Tropiques.

The French Algerian Jacques Derrida (1930-2004) sought to uncover the underbelly of meaning in myths and texts. He enjoyed making fun of traditional interpretations, yet as he developed his "ontotheology" he concluded that there was something fixed at the metaphysical center. He developed this in his lectures at Villanova University.

Deconstruction reveals a “presence” that has been called by different names throughout history: logos, nous, arche, God, the metaphysical center, etc. However, for Derrida the fixed presence is not a being, but rather a necessary function by which we are able to discover meaning. 

Derrida’s deconstruction reveals great complexity of meaning in written texts, ideas, myths and human customs. He explored the “metaphysics of presence.” He wants to know what dominates and blocks what seems not to be present. He ascribes to subordinate objects a more substantial existence than the shadow they cast, or their “trace.” Derrida wrote: "Deconstruction cannot limit itself or proceed immediately to neutralization: it must, by means of a double gesture, a double science, a double writing, practice an overturning of the classical opposition, and a general displacement of the system. It is on that condition alone that deconstruction will provide the means of intervening in the field of oppositions it criticizes" (Metaphysics).

Derrida was a master when it came to identifying binary distinctions, such as dominance and subservience, and reversals. In the case of binary oppositions, each component of the binary set means something, and the relationship of the oppositions means something, and the hierarchy exhibited by the set means something. The reversal of the oppositions also means something. The reversal of the subordinated term of an opposition is a significant aspect of Derrida's strategy. In examining a binary opposition and reversals, deconstruction brings to light traces of meaning that cannot be said to be present, but which have metaphysical presence.

Derrida explores the hidden presence. In so doing, deeper and/or unfamiliar meanings emerge. His method involves neutralizing the shouting voice in order to hear resonances of underlying voices. He looks for Plato behind Aristotle, for mystery behind logic, and for the metaphysical behind the physical. His reversals are a strategic intervention to free western philosophy from the constraints of materialism, and the deductive and linear reasoning in ancient Greece. In a true sense, Derrida lifted up a Semitic way of reasoning. (See Jeff Benner on Greek Linear Logic vs. Hebrew Step Logic.)

In summary, there are two distinct types of binary reasoning. The West is heir to both, but the earlier binary reasoning of the biblical Hebrew has been largely ignored and forgotten.

Binary Reasoning of the Biblical Hebrew

The binary reasoning of the early Hebrew involves binary sets of two closely related entities which, when observed empirically, reveal that one of the entities is greater than its partner. Genesis 1:16 speaks of the sun and the moon as a binary set and notes that the sun is the greater of the two. Likewise, in the male-female set, it is universally true that the human male is anatomically larger and stronger than the female.

Not all pairs of opposites are binary sets. Consider that talented-untalented does not represent a binary set because this involves subjective judgement. Tall-short is not a binary set because this is relative to the observer. For example, the tall-short contrast is relative to the observer. I am 5 feet 5 inches tall. Standing beside a Watusi warrior, I would appear to be short. However, were I to stand beside a Pygmy, I would appear to be tall.

The binary reasoning of the Bible is based on the early Hebrew priests' acute observation of patterns in Nature. It prevents the biblical worldview from slipping into dualism, a view in which the two entities of a set are equal in every way.

 

Related reading: Binary Sets in the Ancient World; "Binary" is a Bad Word These Days; Theories of Knowledge Among Archaic Humans; Theories of Knowledge - Bacon and Descartes; Theories of Knowledge - Locke and Hume; Remarks on Bertrand Russell's Theory of Knowledge by Albert Einstein; A Christian Anthropologist Considers Gender in the Bible; Orthodoxy Requires Binary Reasoning