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.

Jacques Derrida (1930-2004) was born into a Sephardic Jewish family in El-Biar, Algeria. He 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 wanted 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 identified binary distinctions, such as dominance and subservience, central and marginalized, and reversals. 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

Theories of Knowledge - Locke and Hume

"If you would be a real seeker after truth, you must at least once in your life doubt, as far as possible, all things."--René Descartes

Alice C. Linsley


Francis Bacon insisted that methodical observation and experimentation (the scientific method) can progressively increase human knowledge and benefit all of humanity. Bacon also demonstrated through his experiments that the senses can be fooled and thus raised doubt about "common sense" ideas. Bacon insisted that true knowledge must begin with doubt. He wrote, "If a man will begin with certainties, he shall end in doubts; but if he will be content to begin with doubts, he shall end in certainties." --Francis Bacon (1605) The Advancement of Learning, Book 1, v.8

Descartes felt it necessary to one reject entirely all beliefs about which there is the slightest doubt. He wanted to build a system of belief based on certainty. Descartes' point of certainty was his own rational existence:  "I am thinking, therefore I am existing." He wrote in Discourse on Method, "But I soon noticed that while I thus wished to think everything false, it was necessarily true that I who thought so was something. Since this truth, I think, therefore I am, was so firm and assured that all the most extravagant suppositions of the sceptics were unable to shake it, I judged that II could safely accept it as the first principle of the philosophy I was seeking." (Part Four on "Proofs of the Existence of God and of the Human Soul)

Descartes develops this as a proof for the existence of God. He continues, "After that I reflected upon the fact that I doubted, and that in consequence, my spirit was not wholly perfect, for I saw clearly that it was a greater perfection to know than to doubt. I decided to ascertain form what source I had learned to think of something more perfect than myself, and it appeared evident that it must have been from some nature which is in fact more perfect... I was not the only being in existence..., and it followed of necessity that there was someone else more perfect upon whom I depended and from whom I had acquired all that I possessed. For if I had been alone and independent of anything else, so that I had bestowed upon myself all that limited quantity of value which I shared with the perfect Being, I would have been able to get from myself, in the same way, all the surplus which I recognize as lacking in me, and so would have been myself infinite, eternal, immutable, omniscient, omnipotent, and, in sum, I would possess all the perfections that I could discover in God."

Here Descartes articulates a form of the argument from design. The reasoning goes like this:  I find imperfection in myself and I recognize it, which means that I have consciousness of something or someone more perfect than myself. That being so, I must have been designed by that greater Perfection. Descartes wrote: "The very principle which I took as a rule to start with, namely, that all those things which we conceived very clearly and very distinctly are true, is known to be true only because God exists and because he is a perfect Being, and because everything in us comes from him. From this it follows that our ideas or notions, being real things which come from God insofar as they are clear and distinct, cannot to that extent fail to be true."

Descartes contributed to the development of new theories of mind and consciousness. He defined thought "to include everything that is within us in such a way that we are immediately aware [conscii] of it. Thus all the operations of the will, the intellect, the imagination and the senses are thoughts."

John Locke (1632-1704)

The British empiricist John Locke believed that experience alone is the basis of all knowledge. He argued this against Descartes's position that the human mind holds innate ideas.

Locke contributed to the development of theories of consciousness. If a thought is something “within us" of which we are conscious, what is the nature of consciousness? Locke insists that the mind is empty at birth, a tabula rasa. All our ideas are shaped by experience; sensations, and reflections.

Locke wrote that "the little and almost insensible impressions on our tender infancies have very important and lasting consequences." He argued that the "associations of ideas" that one makes as a child are very important because they are the foundation of the self. He warned against letting "a foolish maid" convince a child that "goblins and sprites" are associated with the dark of night for "darkness shall ever afterwards bring with it those frightful ideas, and they shall be so joined, that he can no more bear the one than the other." Locke's theory of association influenced educational theory up to the nineteenth century. Educators warned parents not to allow their children to develop negative associations. 

David Hume (1711-1776)

The Scottish philosopher David Hume continues the empiricist trajectory, developing the consequences of Locke's thought. Hume held that in the search for truth, we cannot rely on the common-sense pronouncements, popular notions, or metaphysical speculation. Building on Locke's epistemology, Hume tried to describe how the mind works in acquiring what is called knowledge. He concluded that no theory of reality is possible; there can be no knowledge of anything beyond experience. He wrote, "If we take in our hands any volume; of divinity or school metaphysics, for instance; let us ask, does it contain any abstract reasoning concerning quantity or number? No. Does it contain any experimental reasoning concerning matter of fact and existence? No. Commit it then to the flames: for it can contain nothing but sophistry and illusion." (Enquiry Concerning Human Understanding)

In Hume's view, normal human reasoning is flawed and this raises radical doubt about all claims to know something. When we give the reasons for our beliefs about the world, we find that many of the offered explanations are contradictory. For example, one person asserts that something is true for them, but another denies that it is true in their experience. How can something be said to be true for one person and not for another? After exposing a series of contradictions within the human reasoning process, Hume reaches this conclusion: "The intense view of these manifold contradictions and imperfections in human reason has so wrought upon me, and heated my brain, that I am ready to reject all belief and reasoning, and can look upon no opinion even as more probable or likely than another." (Treatise of Human Nature)

To the epistemological conversation he adds an additional criterion: do not consent to any belief that is not found to be universally true. This is the ultimate test of truth: that it should be demonstrated mathematically as a universal truth or, following Sir Isaac Newton, as a universal physical law.

Hume conceived of philosophy as the inductive, experimental science of human nature. He sought to discover the causes of human belief. For Hume, this is the proper work of philosophy. Book I of the Treatise of Human Nature and all of the first Enquiry represent his attempts to do exactly this. He wrote, "my intention never was to penetrate into the nature of bodies, or explain the secret causes of their operations. For besides that this belongs not to my present purpose, I am afraid, that such an enterprize is beyond the reach of human understanding, and that we can never pretend to know body otherwise than by those external properties, which discover themselves to the senses." (Treatise of Human Nature, Sec. V)

Despite Hume's radical empiricism, he continued to value common sense, and apparently did not take his own skepticism, such as the problem of induction, to the extreme that others did after him. He recognized that the consequences of his radical skepticism clashed with common sense and his concern for enlightenment scholarship.  [Antony G Flew, A Dictionary of Philosophy, rev 2nd edn (New York: St Martin's Press, 1984), p 156].

Related reading: Theories of Knowledge - Part 1; Theories of Knowledge - Part 2; Why You Have to Love David Hume; Why Hume Was Wrong