Critical Dharma for Thinking Minds
The following post is explores Buddhist cosmology using fuzzy logic, of which I am only just becoming familiar. Fuzzy logic is a fairly new branch of mathematics that creates sets (categories) out of continuous variables (among other things). In the West, it began to be explored in the 1920s. Professor Lofti Zadeh designed fuzzy logic set theory at the University of California in 1965. In 1983, Maria Zemenkova, a scientist at the National Science Foundation, designed the first fuzzy relational database. Today, fuzzy logic is used for computer-based artificial intelligence.
Bart Kosko’s fuzzy logic (he is one of its originators and leading thinkers) takes its inspiration from the Buddha and the love of contradictions that typifies Eastern mysticism.
From Andrew Olendzi’s course, “Deepening Wisdom”:
“3.9b Investigation A. The teaching of interdependent origination invites us to investigate the nature of relationship. This is not seeing how things are connected, for connection points to the attachment of parts. In Buddhist thought attachment is not a healthy thing, and independent parts are an illusion. Rather, this is an exploration of the relationship between processes that are happening, looking to see how events are influenced by other events.”
In terms of connection/impermanence, I am able to see beyond an either/or situation, both/and or neither/nor, all of which are discrete yes/no is/is not categories, toward a range or spectrum of existence. At the smallest level, particles are popping in an out of existence all the time, but in a pattern that has sufficient continuity that it gives rise to higher forms, which is ’emergence.’ At larger scales, energy/matter slows down and solidifies. Matter appears to emerge (arise) in a complex systemic pattern, continue holding that pattern, and dissipate (cease), with varying degrees and rates of change and impermanence. So there’s a range or spectrum of arising/ceasing that differs with scale, with complexity, with types of energy/matter. To me, that sounds more like what the Buddha meant when he refused to answer the question as to whether objects exist or not.
I can see a mountain existing for millions of years, and I can also see the subatomic particles that make up the mountain arising and vanishing in an instant. “Mountain” and “subatomic particles” are the two poles or extremes, which is a “both/and” logic. Between these two poles, however, there are an infinite number of gradations, a spectrum of existence/solidity/rate of change. Between the subatomic particle and the mountain, there is an infinite range of scales of existence, at different levels of complexity.
The point is that all the categories of Nagarjuna: is/is not; both/and, neither/nor are questions framed in terms of discrete logic. All of them require a “yes or no” answer. Buddhist cosmology cannot be understood that way, and I believe that’s why the Buddha refused to answer questions framed that way. If you ask a question about Buddhist cosmology such that it requires a “yes or no” answer, “is/is not”, you are asking the wrong question, or you are asking it the wrong way. Instead of using discrete logic, use fuzzy logic.
Fuzzy logic is an innovation in mathematics that began to be explored in the 1920s, along with quantum physics. (Heisenberg’s uncertainty principle is a kind of fuzzy logic.) Fuzzy logic looks at continuous variables, a “range” or “spectrum” of values. Between the points “0” and “1” on the number scale, there are an infinite number of values. (0 is the subatomic particle, 1 is the mountain). That infinite gradation of values is the subject of fuzzy logic. So it’s not a matter of whether something “is” or “is not” a 0 or a 1, but where it is on the spectrum. Questions that require fuzzy logic would have answers like “it depends” or “it’s more complex than that.” Fuzzy logic allows for complexity. The boundaries between objects are permeable; we can’t tell exactly where the boundary of once object ends and another begins. However, wee can put things into categories using fuzzy set theory. In fuzzy set theory, something tends to be “more” a member of a set than “less”, but it is not exactly “in” or “out” of the set.
Fuzzy logic is an approach to computing based on “degrees of truth” rather than the usual “true or false” (1 or 0) Boolean logic on which the modern computer is based.
The idea of fuzzy logic was first advanced by Dr. Lotfi Zadeh of the University of California at Berkeley in the 1960s. Dr. Zadeh was working on the problem of computer understanding of natural language. Natural language (like most other activities in life and indeed the universe) is not easily translated into the absolute terms of 0 and 1.
Fuzzy logic includes 0 and 1 as extreme cases of truth (or “the state of matters” or “fact”) but also includes the various states of truth in between so that, for example, the result of a comparison between two things could be not “tall” or “short” but “.38 of tallness.”
Fuzzy logic seems closer to the way our brains work. We aggregate data and form a number of partial truths which we aggregate further into higher truths which in turn, when certain thresholds are exceeded, cause certain further results such as motor reaction. A similar kind of process is used in artificial computer neural network and expert systems.
It may help to see fuzzy logic as the way reasoning really works and binary or Boolean logic is simply a special case of it.
Fuzzy logic is a form of many-valued logic in which the truth values of variables may be any real number between 0 and 1, considered to be “fuzzy”. By contrast, in Boolean logic, the truth values of variables may only be 0 or 1, often called “crisp” values. Fuzzy logic has been employed to handle the concept of partial truth, where the truth value may range between completely true and completely false. Furthermore, when linguistic variables are used, these degrees may be managed by specific (membership) functions.
Fuzzy logic is logic with continuous variables, rather than discrete values. Between the numbers ‘0’ and ‘1’ on the number line, there are an infinite number of values. Fuzzy logic is a way of deciding whether a measurement is somewhere between ‘0’ and ‘1’, and the degree of it’s closeness to one or the other. These are called degrees of truth.
Is the glass empty or full?
Both degrees of truth and probabilities range between 0 and 1 and hence may seem similar at first. For example, let a 100 ml glass contain 30 ml of water. Then we may consider two concepts: empty and full. The meaning of each of them can be represented by a certain fuzzy set.one might define the glass as being 0.7 empty and 0.3 full. Note that the concept of emptiness would be subjective and thus would depend on the observer or designer. Another designer might, equally well, design a set membership function where the glass would be considered full for all values down to 50 ml. It is essential to realize that fuzzy logic uses degrees of truth as a mathematical model of vagueness, while probability is a mathematical model of ignorance.
In general use, ecorithms are algorithms that learn from their more complex environments (hence eco-) to generalize, approximate and simplify solution logic. Like fuzzy logic, they are methods used to overcome continuous variables or systems too complex to completely enumerate or understand discretely or exactly. 
Fuzzy Logic Distinct from Probability
Fuzzy logic and probability address different forms of uncertainty. While both fuzzy logic and probability theory can represent degrees of certain kinds of subjective belief, fuzzy set theory uses the concept of fuzzy set membership, i.e., how much a variable is in a set (there is not necessarily any uncertainty about this degree), and probability theory uses the concept of subjective probability, i.e., how probable is it that a variable is in a set (it either entirely is or entirely is not in the set in reality, but there is uncertainty around whether it is or is not).
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On Bart Kosko’s book, Fuzzy Thinking:
Fuzzy Thinking is about a whole new kind of logic, a radically different way of structuring our thoughts and experience. It is the kind of logic required to understand the new science and – Kosko asserts – the kind of logic needed to make the technological spin-offs of that science ‘intelligent’, but it challenges the very substance of what the West has meant by logic for 2,000 years.
Western logic began with Aristotle, and is modelled on the precise thinking and categories of mathematics. Two plus two equals four, never four and a half or five. A is either A or not-A, it is never both A and not-A. This is an all-or-nothing logic that admits neither contradictions nor shades of grey. It is the basis for the either/or thinking of classical physics (and of many aspects of our daily lives and decision-making), and has been enshrined as the emblem of the digital computer with its high-speed, black and white binary strings of 0s and 1s.
It is a both/and logic that stresses matters of degree and all those shades of grey in between black and white. It’s about the possibilities that exist between 0 and 1, and how a new breed of ‘parallel’ computers can be programmed to respond to them with something almost touching on creativity. Kosko illustrates his fuzzy principle with a piece of fruit.
Suppose we consider an apple. An Aristotlean would say that it either is or is not an apple. But, Kosko asks, what happens when we take a bite out of the apple. Is it still an apple? Perhaps we take another bite, and so on until there is nothing left. ‘The apple changes from thing to non-thing to nothing. But where does the apple cross the line from apple to non-apple? The half apple fails all- or-none descriptions.’ The half apple is a ‘fuzzy’ apple
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Editor’s note: The fruit example above is a perfect example of Buddhist Abbhidharma analysis. What makes a tree a tree? When you strip off the leaves and the bark, cut off the limbs and grind down the stump, is it still a tree? When does it stop being a tree? It’s like the Seven-fold Reasoning of the Chariot. What makes it a chariot? One could say that the whole thrust of Buddha’s teaching was to get people to understand the universe through fuzzy logic.
So—is there a self or not? Well, it depends. It’s more complicated than that. The self is socially constructed from lots of things that aren’t “self”, from genetic ancestry, developmental history, and from a moment to moment response to environmental conditions that provoke”self” as a response. Furthermore, it’s constantly changing. So some of what constitutes your self is always new and changing, while there is also some continuity with prior constitutions of self. That’s non-self as fuzzy logic.