wCHAP.17

(1/31/03)

(p. xvi) “This book is my statement of the fuzzy world view. At the core is the paradigm shift from the black and white to the gray -- from bivalence to multivalence.”

(p. xv) Kosko tells us: "One day I learned that science was not true....There was a mistake and everyone in science seemed to make it. They said all things were true or false....In fact, [facts, are] matters of degree. All facts [are] matters of degree. The facts [are] always fuzzy or vague or inexact to some degree. Only math [is] black and white and it [is] just an artificial system of rules and symbols. Science [treats] the gray or fuzzy facts as if they [are] the black-white facts of math. Yet no one [has] put forth a single fact about the world that [is] 100% true or 100% false. They just said they all were."

"That was the mistake and with it came a new level of doubt."

(p. 5) “More precision does not take the gray out of things – it pins down the gray.”

(p. 6) “Aristotle’s binary logic came down to one law: A or not-A. Either this or not this. The sky is blue or not blue. It can’t be both blue and not blue. It can’t be A and not-A. Aristotle’s ‘law’ defined what was philosophically correct for over two thousand years.”

“The binary faith has always faced doubt. It has always led to its own critical response, a sort of logical and philosophical underground. The Buddha lived in India five centuries before Jesus and almost two centuries before Aristotle. The first step in his belief system was to break through the black-and-white world of words, pierce the bivalent veil and see the word as it is, see it filled with ‘contradictions,’ with things and not-things, with roses that are both red and not red, with A and not-A.”

RESPONSE: Certainly Buddha has offered much of value to the world. He has prepared those who have been influenced by his teachings to recognize the importance of fuzzy logic. However, for me the key issue here is that Buddhist mathematicians did not “discover” fuzzy logic.

From the perspective of Science of Ethics the Buddha way devalues knowledge of the world and therefore demonstrates Buddhism’s inadequacy. Only those who have expanded their thinking to incorporate Western thinking are following the path toward the light at the end of the tunnel. All others benefit humanity indirectly and miss the opportunity to become an Enlightened Person and help participate directly in producing Enlightened Communities.

(p. 6) “You find this fuzzy or gray theme in Eastern belief systems old and new, from Lao-tze’s Taoism to the modern Zen in Japan. Contradiction versus Either-or. Not-A or A. Not-A versus A. The Buddha versus Aristotle.”

RESPONSE: From the perspective of Science of Ethics both Aristotle and Buddha – as well as every other human being – have passed on beliefs that must be discarded if humanity is to reach the light at the end of the tunnel. They also transmit beliefs that help move humanity toward our goal. Sometimes an individual’s beliefs are extremely destructive and cause much pain. Other times their beliefs produce much pleasure and joy. In either case these persons serve humanity by helping us see more clearly the beliefs that encourage such behavior. It is only in this way that humanity has been able to obtain the feedback to continue its movement toward producing an environment in which each person can become an Enlightened Person and live in an Enlightened Community.

(p. 7) “Logician Bertrand Russell found the Cretan’s liar paradox at the foundations of modern math; i.e. The liar from Crete said that all Cretans are liars and asked if he lied. … He seemed to lie and not lie at the same time.”

“I brooded about grayness too. It led me from philosophy to mathematics to electrical engineering.”

RESPONSE: In my mind thanks are due to Kosko and all others who by their insights have provided humanity tools to move more directly toward achieving our destiny.

(p. 7) “I skimmed Sir A.J. Ayer’s anthology on logical positivism, the dominant philosophy of science in this century. Positivism demands evidence, factual or math evidence…. Logical positivism holds that if you cannot test or mathematically prove what you say, you have said nothing. Positivism works out well for scientists and mathematicians, since it allows only them to speak.”

RESPONSE: But of course it is obvious that the forces of irrationalism have not been stopped or even slowed down by philosopher’s decree that they are saying nothing. In fact it seems to me post-modernism – one of the most irrational positions taken seriously by academics and intellectuals – is primarily a reaction against positivism. Because science has not provided a better way to achieve what the faith healers, quacks, and spokespersons for magical thinking in general promise they continue to be looked to to fill an unmet need. Until something as revolutionary as Science of Ethics is put into action in the world this situation will not be ended.

Obviously logical positivism was way off base and any who have thought seriously about the issue realize this was the case. The fact that some scientists have taken science to be something it is not – a source of certain knowledge – points to an underlying flaw we all are vulnerable to; i.e., believing what we want to believe. Fortunately, science allows this error to be discovered, pointed out, and corrected. In other belief systems this failing is often considered a strength and is thereby almost impossible to correct. Part of the problem of current science is that it suffers from the widely held belief that physics provides the foundation for science instead of realizing that the foundation is actually evolutionary biology.

(p. 8) “Every philosopher you ask will attack logical positivism, either on details or on some general principle, but it remains the working philosophy of modern science, medicine, and engineering. Logical positivism hands the future to scientists. It also hands them much of the present.”

The world of math does not fit the world it describes. The two worlds differ, one artificial and the other real, one neat and the other messy.”

“I called this the mismatch problem: The world is gray but science is black and white. We talk in zeroes and ones but the truth lies in between. Fuzzy world, nonfuzzy description. The statements of formal logic and computer programming are all true or all false, 1 or 0. But statements about the world differ.”

RESPONSE And this in my mind is a core difficulty that humanity must overcome if it is to achieve a state of stability based on memes now that we have lost the stability provided by genes. As indicated I think a fundamental problem here is the fact that scientists didn’t recognized what their actual goal should have been when they started their efforts. As a result the world of physics and math loomed large as the goal. As indicated previously the real goal of science couldn’t be seen until Charles Darwin provided the thinking necessary to recognize that evolutionary biology is the key that unlocks the door and puts all science into the proper perspective.

Building on evolutionary biology it becomes possible to create a Science of Ethics. When we do that we are able to see that meaning of human life is the basic underlying human motivation and all our behaviors are motivated to achieve that goal. We then have a way to use all the findings of science as well as everything else to do that.

(p. 8) “Statements of fact are not all true or all false…. They are not bivalent but multivalent, gray, fuzzy…. We can never prove 100% true a scientific statement or claim of fact…. Fresh evidence may topple any scientific belief, and objects of belief differ only approximately from their opposites.”

RESPONSE I’m not sure what the foregoing has to say about Science of Ethics. But my basic feeling is that fuzzy logic provides Science of Ethics a tool for finding the rules to help an individual make the choices necessary to become or remain an Enlightened Person.

I don’t have a clue at this point as to how to make the foregoing belief into a testable result. But I think doing so might provide the breakthrough needed to turn my efforts into something considered worth looking into by others.

(p. 8) “Laws of science are not laws at all…. Laws of science state tendencies we have recently observed in our corner of the universe. The best you can say about them is so far, so good. In the next instant every ‘law’ of science may change. Their truth is a matter of degree and is always up for grabs.… (p. 9) Math talk differs in kind from science talk. But scientists talk it anyway.”

RESPONSE And the foregoing analysis fits well with the conclusions of Science of Ethics that human living is in the present and must rely on the best beliefs currently available… Choices must be based on present beliefs not some absolute ethical standard which can never exist. The “laws of science” are one source of these best available beliefs. They may change as our knowledge increases, but their value in improving the quality of the life of the individual is what determines whether they are important or unimportant.

(p. 9) “I thought scientists and philosophers would see the mismatch problem as the central philosophical problem of modern science. But they seemed to ignore it.”

RESPONSE I can identify with Kosko in the above. I thought everyone or at least someone would see the idea of a Science of Ethics as the central problem of modern science and religion since it is the central problem for each individual. But in spite of my current efforts to promote it I have not succeeded in breaking through the barriers allowing everyone to ignore it. And I haven’t been asked to chair any international congresses on the topic either.

(p. 9) “Philosophers assumed the world was black and white, bivalent, just like the words and math they used to describe it. After all these years and all that training they still took orders from Aristotle and did not question them…. They did this for two reasons: First, it was easy. Second, it was habit.”

“The same holds in science. The more math an author throws at a problem, the less their audience understands them and the more the audience respects them. Your skill at logic and math places you in the pecking order of science.”

(p. 10) “Probability did not alter or even challenge the black-white picture of the world. It just showed how to gamble on it and in it. Aristotle’s law of A or not-A always holds in probability. The new physicists saw probability wherever they looked. But Einstein did not feel comfortable with it.”

Einstein displays this discomfort when he says: (p. 3) “So far as the laws of mathematics refer to reality, they are not certain. And so far as they are certain, they do not refer to reality.” Albert Einstein, Geometry and Experience

RESPONSE: My guess is that had Einstein been introduced to fuzzy logic, and accepted its message in his youth, he might have helped physics avoid the pitfalls of the Copenhagen interpretation which has helped to maintain the strength of Aristotle’s thinking. He might have helped to lay a better foundation for quantum mechanics. That might have allowed scientists to more directly recognize that human beings are the ultimate reference system not “reality.” However, let me make clear that Science of Ethics does view reality as the objective reference system. It’s just that our ability to understand reality is limited.

But since that didn’t happen (couldn’t happen because fuzzy logic remained to be developed) he became a somewhat unwilling participant in what happened to physics and the world in general. He couldn’t accept the party line developed by Bohr and Heisenberg in the ‘30s that has remained as mainline physics up to this day. But he wasn’t able to provide an alternative that could move the thinking of physicists into a more constructive direction.

(p. 10) “What is probability? What kind of thing is it? What does it look like? How do you measure it? How do you test a probability claim?…. A probability experiment can go either way and you do not know which way.”

“Probability evaporates with increased information. Information up, probability down…. (p.11) So maybe there is no probability. Maybe there is something else, maybe something fuzzy….”

RESPONSE: Since I have believed that the foregoing is the case long before I discovered fuzzy logic it has been deeply gratifying to find an alternative way to look at the universe. I have great confidence that at some point fuzzy logic will help persons of very divergent views to find a shared way to understand human life and the universe.

(p.11) “Probability did not solve the mismatch problem. It compounded the problem. It piled a new theory on top of the black-white theory of bivalence.”

(p. 12) “Probability has proved a powerful tool for social prediction and control. But I could not see how it softened the mismatch between logic and fact.”

“Up close things are fuzzy.”

(p. xvi) "...the fuzzy world view

(p. 13) The Buddha Law: "Fuzzy logic is reasoning with fuzzy sets."

(p. 15) “Criticism fails without a working alternative. Fuzzy logic provided that alternative. It had the same math flavor that probability had, it worked with percentages between 0% and 100%, but it described events happening to some degree, not whether ‘random’ events happened all or none.”

RESPONSE: And in my mind this working alternative should make all the difference in the world for those of us dissatisfied with the current way science and math are seen by most persons including scientists and mathematicians.

(p. 16) “I looked for fuzziness and found it in a family of new math theorems, all housed in the geometry of a Rubik’s cube… The math was so easy I could not believe someone else, everyone else, had not seen it. But soon I saw why even earlier fuzzy theorists might overlook this species of math or why they might see it as simple error if they looked at it at all. It involved strange notions like the whole contained in the parts, big things stuck inside smaller things.”

“Most of all fuzziness made machines smarter. It increased the machine IQ of dozens of products in consumer electronics and manufacturing: cameras, camcorders, TVs, microwave ovens, washing machines, vacuum sweepers, transmissions, engine control, subway control. But it increased machine IQ in the land of A and not-A, in the Far East, in Japan, where in the early 1990s fuzzy logic took hold…. But Western scientists and engineers only threw stones and we-could-do-it-toos at news of the fuzzy commercial successes in Japan. Earlier they had attacked fuzzy theory as lacking applications. Now they attacked the applications as lacking theory.”

RESPONSE: I hope at least some of this has changed in the decade since this book was written. I would be saddened to learn that the U.S. has not yet stepped more vigorously into fuzzy logic.

(p. 17) “Fuzzy logic begins where Western logic ends.”

(p. 18) "The fuzzy principle states that everything is a matter of degree."

RESPONSE: And, it is this principle that must be understood if we are to avoid all the erroneous results achieved through Aristotle's law of the excluded middle.

(p. 18) “Some things are not fuzzy no matter how closely you look at them. These things tend to come from the world of math…. But when we move out of the artificial world of math, fuzziness reigns.”

“Fuzziness has a formal name in science: multivalence. The (p. 19) opposite of fuzziness is bivalence or two valuedness….”

(p. 19) “Logicians in the 1920s and 1930s first worked out multivalued logic to deal with Heisenberg’s uncertainly principle in quantum mechanics…. This math principle says that if you measure some things precisely, you cannot measure other things as precisely. The principle suggests that we really deal with three-valued logic: statements that are true, false, or indeterminate. In short order Polish logician Jan Lukasiewicz chopped the middle ‘indeterminate’ ground into multiple pieces and came up with many-valued or multivalued logic…. The term ‘fuzzy’ entered the scientific vocabulary about 30 years later. Until then logicians like Bertrand Russell used the term ‘vagueness’ to describe multivalence. In 1937 quantum philosopher Max Black published a paper on vague sets or what we now call fuzzy sets. The worlds of science and philosophy ignored Black’s paper.”

“In 1965 Lotfi Zadeh, then chair of UC Berkeley’s electrical engineering department… published a paper called ‘Fuzzy Sets.’ The paper applied Lukasiewicz’s multivalued logic to sets or groups of objects. Zadeh put the label ‘fuzzy’ on these vague or multivalued sets…. Zadeh saw (p. 20) scientists throwing ever more math at problems and trying to think and run the business of science with the black-white reasoning that computers and adding machines used. He chose the word ‘fuzzy’ to spit in the eye of modern science.”

(p. 20) “The term ‘fuzzy’ invited the wrath of science and received it.”

“Fuzzy logic did not come of age at universities. It came of age in the commercial market and leapfrogged the philosophical objections of Western scientists.”

“The fuzzy principle has emerged from almost three thousand years of Western culture, from three thousand years of attempts to deny it, ignore it, disprove it, relable it, and axiomatize it out of existence. But fuzziness remains despite our best efforts to get rid of it. Our reasoning remains fuzzy.”

“I freely weave my fuzzy experiences into the discussion of the fuzzy matter at hand.”

(p. 21) “The Information Age rests on bivalence because it rests on the ‘digital revolution’ in signal processing and microprocessor computer chips.”

(p. 23) “Western culture now sees binary precision as part of the scientific method.”

“Aristotle’s logic lies behind our bivalent instincts.”

“Every philosophy or religion has a villain or devil it seeks to avoid or destroy. The villain of bivalence is the logical contradiction: A and not-A.”

“In bivalent logic a contradiction implies everything. It allows you to prove and disprove any statement. Mathematicians scour their axioms to keep them from implying statements that contradict one another. So far no one has proved that the axioms of modern math do not lead to statements that contradict one another. Tomorrow that may change and the framework of modern math may collapse…. Fuzziness begins where contradictions begin, where A and not-A holds to any degree.”

“Eastern mysticism offers the only major belief systems that accept contradictions, systems that work with A and not-A, with yin and yang.”

RESPONSE: From my reading of Eastern mysticism I take it to have conclusions very different from those of fuzzy logic in spite of anything they might share in some of their basic assumptions.

(p. 25) “Early in the twentieth century logician Bertrand Russell… showed that paradoxes plague set theory, the mathematical theory of sets of objects and subsets of objects.”

(p. 26) “Underneath the tug of war between bivalence and multivalence lies an equation. Bivalence says the equation does not exist or does not make logical sense. Multivalence says it exists to some degree. In extreme cases it exists to full degree or not at all…. I will give it a name… the yin-yang equation:

A=not-A

This is a ‘contradiction’ in equation form. Instead of writing ‘A and not-A’ or ‘A is not-A’ the equals sign equates the two propositions with all the rigor and pomp of formal math. In logic this means biconditionality: A implies not-A, and not-A implies A. So the paradoxes of bivalent reasoning reduce to the yin-yang equation: the half-empty cup implies that the cup is half-full and vice versa.”

(p. 28-29) “…black and white are special cases of gray… multivalence reduces to bivalence in extreme cases.”

(p. 29) “While teaching fuzziness in the mid-1980s I looked for a picture that captured the tradeoffs between fuzziness and bivalence. I found that picture in a Rubik’s cube…. A Rubik’s cube looks like a three-dimensional cube – a three-dimensional fuzzy cube. Any one of the six faces of the Rubik’s cube looks like a two-dimensional cube or a solid square – a two-dimensional fuzzy cube. Any one of the twelve edges of the Rubik’s cube looks like a one-dimensional cube or a straight line, the number line [0, 1] (sic) ….

(p. 33) “At the midpoint you cannot tell a thing from its opposite, just as you cannot tell a half-empty glass from a half-full glass.

(p. 34) The fuzzy logic cube: "Aristotle rules at the corners of the fuzzy cube....The Buddha rules to some degree everywhere inside the cube."

(p. 34) “It all comes down to this: Where do we draw the line? That question haunts black-white reasoning in a world of grays.”

(p. 36) “Fuzzy theory draws a curve between opposites, between A and not-A. More information, more ‘facts,’ help us draw the curve. If we have enough information, we can turn our vague notions of OLD and YOUNG into fuzzy-set curves.”

“Legal decisions are also fuzzy and relative.”

(p. 37) “Legal concepts vary among cultures and within them.”

(p. 36) "Beauty is both fuzzy and relative. It depends on the speaker and the culture....Beauty lies not only in the eye of the beholder, it lies there to some degree."

(p. 38) “Fuzzy engineers design software and chips to make computers reason more as people do…. the adaptive fuzzy systems we discuss in a later chapter, learn from experience and program themselves.”

RESPONSE: That sounds like a fantastic tool for putting Science of Ethics into practice for individuals. Properly programmed this might form the core of an individual support system; i.e., a Computer Tutor, Recorder, and Expert System (CTRES).

(p. 38) “Fuzzy knowledge comes down to fuzzy rules. A fuzzy rule relates fuzzy concepts in the form of a conditional statement: If X is A, then Y is B. If the traffic is HEAVY, then keep the traffic light green LONGER. Just common sense.”

“Fuzzy systems store dozens or hundreds or thousands of these common-sense fuzzy rules. Each new piece of data activates all the fuzzy rules to some degree (most to zero degree). The fuzzy system then blends together the outputs and produces a final output or answer. On a fuzzy chip this ‘parallel’ reasoning takes place thousands or millions of times per second. We count the reasoning in FLIPS or fuzzy logical inferences per second.”

“High-speed fuzzy systems are smart. Today in Japan they control subways and stabilize helicopters better than humans can. (p. 39) The fuzziness in their rules leads to smooth control.”

(p. 39) “Sensor technology speeds the fuzzy revolution.”

“In older fuzzy systems an expert gives the common-sense rules. A fuzzy engineer may sit down with an expert and ask them how they focus a lens or make a left turn or steady a helicopter. In adaptive fuzzy systems a ‘brainlike’ neural network, a computer system that mimics how brains learn and recognize patterns, generates the fuzzy rules from training data. They learn from experience. DIRO: data in, rules out.”

RESPONSE: This sounds like a giant step forward in developing expert systems. This tool could provide an essential way to help individuals become Enlightened Persons and develop an Enlightened Community.

(p. 39) “Adaptive fuzzy systems ‘suck the brains’ of experts. Experts do not have to tell the system what makes them experts. They (p. 40) just have to act as experts. That gives the data that the neural nets use to find and tune the rules.”

RESPONSE: Fantastic!

(p. 40) "Career science, like career politics, depends as much on career maneuvering, posturing, and politics as it depends on research and the pursuit of truth."

"The hardest things I learned in my fuzzy quest were that modern science does not welcome a truly new idea. And it makes mistakes even at the 'self-evident' level of logic and math."

(p. 41) “Everyone pursues fame and power to some degree. Scientists are unique in their pursuit for at least two reasons. First, their product is reputation. Second, they answer to no higher authority.”

RESPONSE: In my mind this grossly misses how a scientist fits into any society. Certainly a creative scientist like any creative person has the potential to create a niche where they can pursue their goals and follow their bliss. However, if they desire to achieve fame and power they can only do that with the support of others. And usually this support has strings and guidelines attached. Those unable, or unwilling to be so controlled are very unlikely to achieve such fame or their ideas much power at least during their lifetime.

But the science model does provide them great opportunity to look beyond the current paradigm and sometimes produce a paradigm shift. Or, at least provide the data that is necessary for others to use in making such a shift.

(p. 41) “Last century John Stuart Mill said that new ideas pass through three phases of denial. First, they are wrong. Second, they are against religion. Third, they are old news, trivial, common sense, and we all would have thought of them if we had had the time, money, and interest. Fuzzy logic, tied to society’s rapid rate of change of information, is passing from phase one to phase three.”

(p. 43) "...[and] if scientists can err at the 'self-evident' level of logic and math, they can err at anything."

(p. 40) "...science prefers small steps to large creative leaps."

"...science differs from scientists. The product of science is knowledge. The product of scientists is reputation."

(p. 42) "At root fuzzy logic or multivalence is a world view or ideology. Bivalence is an ideology too, and that is where the conflict lies."

RESPONSE: Generally speaking bivalence is the ideology or world view of traditional religion, and enmeshment in tradition in general. These are the persons least able to change and most likely to deny the need for change. To open such a person up to a new approach is not easy. Probably the most successful process requires being available when some part of their world view crumbles. At this point one must be ready to provide a more useful answer that helps them cope with life while at the same time opening their mind to the potential of other approaches.

(p. 222) “A fuzzy cognitive map or FCM draws a causal picture. It ties facts and things and processes to values and policies and objectives. And it lets you predict how complex events interact and play out.”

(p. 224) “…the FCM predicts outcomes and we can compare these with data to test them. The outcome of large FCMs may surprise you. The best most of us can do is argue about single arrows [of cause and effect]. We do less well when we try to reason with a large set of connected concepts. FCMs help us (p.225) see the big picture and do something with it. Best of all behind the FCM lies a pure math scheme that computers can use and we need not worry about.”

RESPONSE: I am greatly impressed by FCMs. It seems to me they might provide a way to utilize, test, and improve the ideas of Science of Ethics. Since I have long believed that an essential component of becoming an Enlightened Person is help in making individual choices FCMs sound like a useful tool for accomplishing this. For me one of the most important uses of computers will be to make this possible.

(p. 224) “I came up with FCMs in 1983 to solve a problem. Cognitive maps of one type or another had been around for ten years in psychology and political science…. The old cognitive maps did not let you have fuzzy nodes and fuzzy arrows or rules. And they did not let you have feedback. The arrows could not form a closed loop as they do in the real world.”

“FCMs thrive on feedback. That was the key. I was trying to work with FCMs as experts in artificial intelligence work with computer programs, with long chains of if-then rules. The new FCM idea was to drop that and view the FCM as a neural net. Make it a dynamical system. Let it swirl and reverberate like a Bidirectional Associative Memory. It will converge.”

RESPONSE: This model appears to be well grounded from my perspective.

(p. 226) “Feedback loops grow as you add more nodes to the FCM.”

“You look for hidden patterns in the FCM edges. You turn the (p. 227) FCM net on and let it swirl. You let the dynamical system converge to an equilibrium. Events blink on and off or fire to some degree. One concept or event swirls into others… And round and round it all swirls as the hidden pattern emerges.”

“What is a hidden pattern? It is where the swirl stops. It is an equilibrium…. A hidden pattern is what ends up at the bottom of the energy well…. The well is an attractor basin. That is what dynamical systems theorists call it. The point of rest at the bottom is the attractor. It ‘attracts’ the system ball to it…. That means the attractor is a fixed point…. in other dynamical systems the ball may not stop rolling. The ball may just spin round and round in the well. That means the attractor is a limit cycle. In the most complex case the ball moves round in the well with no pattern or period. That is ‘chaos’ and the attractor is a chaoticattractor.”

“FCM balls stop or else they roll round and round in a limit cycle…. FCMs cool down to limit cycles very fast. That’s a theorem. They may take a few steps to get there but you can prove they will always get there and stay there until you change the FCM.”

(p. 229) “FCMs can’t prove… [that the results they get are correct]. They can help show how the whole of your beliefs behave. They show global patterns. As the FCM grows more complex the hidden patterns become harder to see. You need a math method to find them. And they may surprise or offend you.”

“I like the fact that FCMs can offend and can paint causal pictures of hot topics. They lay bare your beliefs and biases and (p. 230) your grasp of the world. They help most in the value clashes that mix head and heart. I have found that students draw their best FCMs when they try to model a clash of governments or the spread of AIDS or any topic that deals with power or sex.”

RESPONSE: Laying bare beliefs and biases and our grasp of the world is just the tool Science of Ethics needs to improve itself, and to help individuals to recognize their need to improve.

(p. 233) “Neural nets give a shortcut to tuning an FCM. The trick is to let the fuzzy causal edges change as if they were synapses in a neural net. They cannot change with the same math laws because FCM edges stand for causal effect not signal flow. We bombard the FCM nodes with real data. The data state which nodes are on or off and to which degree at each moment in time. Then the edges grow among the nodes. When I first tried this in 1985 I let the edges grow as synapses grow. Synapses correlate neural firings. But in an FCM that leads to spurious causal links. Two concepts do not affect each other just because they are both on at the same time.”

“So I once again turned to my ‘worthless’ philosophy degree to look for ideas. Philosophers have said a lot about cause and effect. Until David Hume most believed in it. After David Hume in about 1800 they no longer believed in it. Hume said cause was an illusion, a ‘sentiment’ the mind imposed on the flow of events, a pattern of correlation, a ‘constant conjunction of events.’ You could replace ‘Fire causes heat’ with ‘If fire, then heat.’ I did not like this use of correlation. It was too static. Causality deals with changes.”

RESPONSE: In my mind Hume and other philosophers who take this approach missed the point in understanding cause and effect. Because they have tended to take a “God’s eye view” of the universe, rather than recognizing that human beings are the ultimate reference system they wanted to think of cause and effect divorced from the observer and the intent of the observation. As a result they failed to take into account that in an important sense humans do impose cause and effect on the universe. We select which causes and which effects we want to examine and how we want to tie them together so as to understand them in a way relevant to our concern.

(p. 233) "I turned to John Stuart Mill, the heir to Hume, and his view of causality. In his SYSTEMS OF LOGIC Mill said causality is 'concomitant variation.' We infer or feel or make up a causal connection between A and B if they vary or change together. A and B have to move in the same way. In neural nets the Hume or correlation view means that you multiply A by B to find the synaptic value between them. They call that Hebbian learning after neuroscientist Donald Hebb, who first wrote about it in 1949. I wanted to multiply how A changes by how B changes. In calculus the derivative measures change in a thing or process.... So in 1985 I multiplied the derivative of A by (p. 234) the derivative of B and called it differential Hebbian learning [DHL]. I put forth DHL as a way for FCMs [Fuzzy Cognitive Maps] to learn from data. But I also thought it might apply to real synapses in brains and some researchers have since suggested that it does. Right now I want to stick with FCMs to show how DHL works."

(p. 234) “Let A and B be FCM nodes. A or B can be a social policy or the strength of a government…. Suppose A goes up a little. The difference between the new and the old A is positive…. Now say B goes up a little too. So the change of B is positive too. Then plus times plus equals plus…. The friend of my friend is my friend. So you add a little number to the edge from A to B. Now say A falls. Then the change is negative. Say B falls too. So the B change is negative too. Then if you multiply the two changes you get a positive value… The enemy of my enemy is my friend. So again you add a small number to the edge. So if A and B change together, we guess a causal link between them.”

“The reverse happens if they move in opposite directions. Say A goes up and then B goes down. Then multiply a positive by a negative to get a negative… The friend of my enemy is my enemy. The same happens if A goes down and B goes up. The enemy of my friend is my enemy. In both cases you subtract a small number from the edge and it tends to move to a negative link. If neither A nor B changes, you get zero and add zero to the edge. This gives you a small hint of what a computer can do when it runs DHL or some other learning law to create and tune large FCMs as data pour in.”

“Every time you change an FCM you learn in some way since learning is change. I worked out a scheme that lets you add one FCM to another (and you can weight the relative importance of each FCM). You can add up all FCMs. Plus edges can cancel negative edges. Or a lot of plus edges add up to a strong positive link and likewise for a lot of negative edges. It turns out you can write down an FCM for every book or article ever written and every speech ever given and add them all up into one giant FCM. That just starts the process. There are now many ways you can let the FCM learn for itself as a true adaptive fuzzy system.”

“Imagine this giant FCM cloud with all known human knowledge, (p. 235) with the good and the bad and the stupid. It might lie among a thousand linked computers. Or it might fit as a tiny chip in the back of tomorrow’s laptop or in the base of you brain. News events fire its nodes. The latest learning laws turn the node firings into new causal links. The whole thing swirls and cools down to the latest prediction. Some FCM nodes fire entire sub-FCMs. Fuzzy-rule systems fire some nodes or sub-FCMs. Some nodes fire fuzzy-rule systems. Sub-FCMs break off and contradict the big FCM…. It gives a new way to represent knowledge.”

(p. 235) “The fuzzy future will have many new tools in it…. Fuzzy logic will change our world views in small ways and in deep ways. It will bring us closer to machines and bring them closer to us. And fuzzy logic will poke holes in moral absolutes. It will help solve some problems and will muddy up others.”

(p. 233) "I turned to John Stuart Mill, the heir to Hume, and his view of causality. In his SYSTEMS OF LOGIC Mill said causality is 'concomitant variation.' We infer or feel or make up a causal connection between A and B if they vary or change together. A and B have to move in the same way. In neural nets the Hume or correlation view means that you multiply A by B to find the synaptic value between them. They call that Hebbian learning after neuroscientist Donald Hebb, who first wrote about it in 1949. I wanted to multiply how A changes by how B changes. In calculus the derivative measures change in a thing or process....So in 1985 I multiplied the derivative of A by the derivative of B and called it differential Hebbian learning [DHL]. I put forth DHL as a way for FCMs [Fuzzy Cognitive Maps] to learn from data."

(p. 15) "I learned how to manipulate probability but did not believe it existed."

(p. 44) "What is probability? What is randomness? Can you define one without the other? What is chance?"

(p. 45) "The probability view commits to a property hard to find....Where is the 'randomness'?"

"Total information leaves little room for probability."

(p. 47) "Where is the probability? Everywhere. Where is the randomness? Everywhere....[But] We never catch probability in the act."

(p. 50) Where does probability come from? "The math comes from thin air and we apply it everywhere. Probability math comes from naked assumptions and not from some more general theory....So far it has had no logical roots. We can deny the axioms as easily as we accept them."

(p. 44) "One night in a hot tub I found an answer: the whole in the part. That answer comes at the end of a long hunt for probability. It also lays the foundation of fuzzy logic."

(p. 61) Subsethood as probability: "I could feel the answer in me as you feel a tip-of-the tongue name come to you after a question....A solution has a way of bubbling up out of your subconscious if you brood about a problem long enough."

(p. 59) "The whole in the part is probability. It is the probability of the part. What is the probability of success? The degree to which all trials are successful, the degree to which the set of successful trials contain the set of all trials."

(p. 80) "Science seeks truth." "Fuzzy logic says all scientific truths are gray. Bivalent science says....the truths of science are not gray but tentative.... Fuzzy logic agrees that scientific truths are tentative but still says they are gray."

RESPONSE: As Kosko indicates tentative and gray are not mutually exclusive descriptions of truth. For many areas of science as we learn, our knowledge makes certain understandings less tentative. Scientific truths may always be gray, but our greater knowledge improves our ability to predict or better understand the limits of our ability to predict. More knowledge allows us to improve the quality of human living.

(p. 80) "What does truth refer to? What sorts of things are true or false?....Truth refers to statements we make, to what we utter or write or nod and point at."

"The focus on statements has reduced the analysis of truth to a study of language."

(p. 82) "Philosophers distinguish logical truth from factual truth....Logical truth comes from symbols and their formal relationship. It does not depend on how the world is or is not."

(p. 83) "Aristotle called...factual truth contingency and called logical truth necessity. Logical truths are true in all cases....Contingent or factual truths...are sometimes true and sometimes false."

(p. 85) "Fuzzy logic views truth as accuracy. And accuracy is clearly a matter of degree."

(p. 86) "If [a statement] describes the world, you can't prove it. You can prove only math things or logic things, coherent things in an arbitrary formal system of made-up rules. That means emptiness. You can prove only tautologies or logical truisms like 'Rain is rain' [It is raining?] or 'A is A' but nothing at all about the real world that science describes. Proof techniques cannot touch the real world."

"Factual statements are partially accurate or partially inaccurate."

(p. 87) "Scientists....seek accuracy....But they achieve only inaccuracy."

"Scientists try to find the math that best fits the world or the world that best fits the math."

(p. 88) The True Mismatch: Hemingway's Challenge -- produce one true factual statement.

(p. 92) "All traditional logic habitually assumes that precise symbols are being employed. It is therefore not applicable to this terrestrial life, but only to an imagined celestial one. The law of excluded middle [A or not-A] is true when precise symbols are employed but it is not true when symbols are vague [fuzzy], as, in fact, all symbols are." Bertrand Russell, "Vagueness," AUSTRALIAN JOURNAL OF PHILOSOPHY, Volume I, 1923

(p. 93) "In the early 1920s Russell laid the logical foundation for fuzzy (vague) logic but never pursued the subject."

"Heisenberg's quantum uncertainty principle ended, or at least dented, our blind faith in the certainty of science and factual truths."

"Up close it [science] could provide only partial truths, uncertain truths, fuzzy truths."

(p. 96) "We pay in certainty points for each inference we make. Reasoning is not a free good. The more steps in our argument, the fuzzier our argument." Except in mathematics. "A two-line proof is no tighter than a million-line proof."

"Bivalence: 1 x 1 x 1 x ... x 1 = 1. Multivalence: 1 x .99 x .98 x .97 ... x .00001 = a number very close to zero. The fuzzy product 'goes to zero' as the number of uncertainty factors increases to infinity."

(p. 97) "Paradoxes of self-reference [both asserts and denies themselves; e.g., the Cretan who says all Cretans are liars]have the same form. They both assert and deny themselves. They have the logical form of a contradiction, A and not-A...."

(p. 98) "Russell found a set where things were in it and not in it. He found the set of all sets that are not members of themselves."

(p. 99) "Russell's paradox was not a paradox but a contradiction. That meant you could prove any claim you please since a contradiction implies everything. And there goes certainty. Russell put math in its first crisis."

(p. 99) "The first response [to Russell's paradox] was denial....That attitude continues to this day. Few mathematicians lose sleep over Russell's paradox even though the paradox affects every branch of math because every branch builds on set theory. The set or collection or class is the fundamental structure in math."

"The next response was to define the paradox out of existence."

(p. 100) "The new axioms either threw out too much of math or led to new paradoxes."

(p. 101) "Russell seems to have been the first to suggest the fuzzy response. He did not pursue it but he made it. Why not drop the law of excluded middle? To hell with Aristotle. Who says A or not-A must hold for every statement A? But that seemed too radical. No one wanted to give up proof-by-contradiction."

(p. 102) "Paradoxes generalize to sets as well as logic. Remember that the number line from zero to one defines a hypercube of one dimension. A unity square defines a hypercube or fuzzy cube of two dimensions (with four black-and-white combinations or sets of two objects). A solid cube like an ice cube or a Rubik's cube defines a fuzzy cube of three dimensions (with eight black-and-white combinations of three objects). In each case the corners define the only black-white Aristotelian outcomes where A or not-A holds. The cube midpoint defines the unique Buddhist outcome where A equals not-A, where the yin-yang equation holds 100%: A = not-A. The midpoint is the only point in the cube that is equally far, and equally close, to every corner. You cannot round off the midpoint to any one corner just as you cannot find a unique direction south when you stand at the north pole of a planet."

(p. 103) "The bivalent fear of logical contradiction ends in contradiction."

"Heisenberg showed that even in physics the truth of statements is a matter of degree. He made the world face multivalued logic, statements true or false or indeterminate to some degree. He did not work out the math of fuzzy logic....Heisenberg made doubt scientific. At the time probability theory was the only way known to put this doubt in math form. So rather than shift us from black-white truth to gray truth, the uncertainty principle had the effect of shifting to the probability of all-or-none bivalent truth. In time fuzzy math and fuzzy quantum mechanics may fix that."

(p. 108) "So it is a good bet that someday quantum mechanics will fall because it is linear to its core."

(p. 109) "Heisenberg's uncertainty principle is part of the linear model. A nonlinear quantum mechanics may not lead to an uncertainty principle."

(p. 109) "Where you have linear theories you will have uncertainty relations."

(p. 106) "Many scientists believed, as many still do, that uncertainty relations were unique to quantum mechanics. But uncertainty relations arose from a math quirk....It all has to do with right triangles."

(p. 110) "The Pythagorean Theorem on right triangles is the most important theorem in mathematics...Today it lies at the heart of what we call Hilbert space, which in turn lies at the heart of quantum physics and modern engineering."

(p. 107) Quantum mechanics "is not 'strange' at all. Quantum mechanics is linear. It's as linear a theory as we have. It's so linear and the world is so nonlinear that many of us have little faith in quantum mechanics except as a rough first cut at all the nonlinear reality that swirls around us and in us. Werner Heisenberg does not win the Hemingway prize for producing the first 100% true factual statement. The uncertainty principle is only an approximation."

(p. 108) "System complexity exceeds subsystem complexity."

"We know a great deal about linear math. In comparison we know almost nothing about nonlinear math -- except that almost all math is nonlinear....The sea of math is infinitely vast. And no matter how much we explore it, even if we work at it for an eternity, we will never know more than an infinitesimal point in the sea of nonlinear math."

(p. 89) "[My philosophy] professor said [Rudolf] Carnap and friends had gotten rid of God, mind, ethics, and metaphysics and reduced philosophy to (binary) symbolic logic and the study of how we use words."

(p. 121) What is a chair? What does any word represent?

"Think of arm chairs and reading chairs and dining-room chairs, and kitchen chairs, chairs that pass into benches, chairs that cross the boundary and become settees, dentist's chairs, thrones, opera stalls, seats of all sorts, those miraculous fungoid growths that cumber the floor of the arts and crafts exhibitions, and you will see what a lax bundle in fact is this simple straightforward term. I would undertake to defeat any definition of chair or chairishness that you gave me." Charles Pierce, DICTIONARY OF PHILOSOPHY AND PSYCHOLOGY, Volume 2, 1902

(p. 122) "We all speak and write the same words but we do not think the same words. Words are public but the sets we learn are private. And we think in sets."

(p. 155) "Words stand for sets of things. These sets are fuzzy."

(p. 145) Principle of Incompatibility: "...as the system [gets] more complex precise statements [have] less meaning."

(p. 148) "...precision increases fuzziness." "The closer one looks at a real-world problem, the fuzzier becomes its solution."

(p. 148-151) Criticisms of fuzzy logic started early and fell into three areas:

1). What good is it?

2). Fuzziness is just randomness in disguise. (Probabilists)

3). It conflicted with bivalence, i.e., Aristotle.

(p. 154) "Philosophers of science, like [William Van Orman] Quine, speak for science and tell us what is science and what is error or pseudo-science....bivalence is one of the deepest key ideas of science."

(p. 79) "Let us grant, then, that the deviant can coherently challenge our classical true-false dichotomy. But why should they want to? Reasons over the years have ranged from bad to worse. The worst one is that things are not just black and white; there are gradations. It is hard to believe that this would be seen as counting against classical negation; but irresponsible literature to this effect can be cited." Willard Van Orman Quine, PHILOSOPHY OF LOGIC

(p. 158) "A fuzzy system is just a big bunch of fuzzy if-then rules...."

(p. 167) "FAT (Fuzzy Approximation Theorem) says you can always cover a curve with a finite number of fuzzy patches."

(p. 168) "A system is anything that maps inputs to outputs....causes to effects. A nonlinear system has a curve that wiggles. A continuous system has a curve with no gaps or tears in it. The FAT says a fuzzy system can approximate a continuous system...as closely as you please. This includes all systems studied in calculus. It also includes almost all systems studied in science."

(p. 170) "The FAT....says you can get rid of all the books on physics and chemistry and biology and economics and replace them with new books that have fuzzy systems where equations used to be."

"You can use fuzzy systems anyplace we today use brains. And you can use them in places where even brains don't work."

(p. 171) "Knowledge is rules." (Fuzzy logic does rules best!)

(p. 171) "In fuzzy systems all rules fire all the time. They fire in parallel. And all rules fire to some degree. Most fire to zero degree."

(p. 171) "In the U.S. or Europe theorists like me do not build things. We write papers and prove theorems and argue math. We look down on those who dirty their hands with simulations or, worse, who build and test real systems."

GENERAL REMARKS: There are many fuzzy concepts that probe different areas and provide tools for dealing with those areas. Below are some of these concepts:

(p. 203) "DIRO: Data in, rules [come] out. Numbers in, knowledge [comes] out. Experience in, common sense [comes] out. Examples in, expertise [comes] out. A neural network can fill the DIRO black box."

(p. 172) FLIPS = fuzzy logical inferences per second. Used in association with fuzzy chips. Dealing with inputs and outputs.

RR. (p. 24) fits = fuzzy units just as “bits” contracts “binary units.” A fit value is a degree or number between zero and one. A bit value is a zero or a one.

(p. 175) FAM = fuzzy associative memory. Used to explain how a fuzzy system works.

(p. 218) AVQ = Adaptive Vector Quantizers. Relates to rules governing neural nets.

(p. 222) FCM = Fuzzy Cognitive Maps. Fuzzy nets that differ from FAT [Fuzzy Approximation Theorem: you can replace any system with a fuzzy system] systems.

(p. 234) DHL = Differential Hebbian Learning. Provides a way for FCMs to learn from data.

(p. 203) "An adaptive or neural fuzzy system changes or tunes its rules as it samples new data. Just as every pattern we see or hear or taste or feel changes slightly our world view...."

(p. 205-206) What is learning?

"To learn is to change. And to change is to learn. You can learn well or badly. But you cannot learn without changing or change without learning."

"But what does learning change? Your...muscles change...your brain changes...your world view changes....your behavior changes...."

(p. 254) "Human beings are the measure of all things." Protagoras

(p. 276) "Why is there something rather than nothing? One answer is that if nothing then you have math trouble....But so what? Why should the world care if some symbols foul up and no longer cohere?"

"The reason is the world seems to obey math."

"Science tracks math. Induction tracks deduction."

(p. 87) "Scientists try to find the math that best fits the world or the world that best fits the math."

(p. 169) "Scientists often respect math more than truth and they do not mention that a math guess is no less a guess than a guess in everyday language....A math guess has more dignity the less math you know."

(p. 277-278) "So where is God in all this? We see deeper and deeper into nature and we find no sign of Him. No evidence. No God in math. No God in fact. We have not seen or measured Him with microscope or telescope. He does not seem to be in the observable universe. And He seems to have left no footprints. We find only the smooth flow of events according to physical law. A flows into not-A and not-A flows into something else. What we can explain with God we can explain without Him."

(p. 278) "...there seems no evidence for a God. The more we find out the more the ground seems to drop out from under us....It all seems to lead to nihilism."

"And it may end in nihilism. There may be no meaning or purpose to the world at least in a sense that we can grasp."

The challenge of a Science of Ethics is to produce the environment and ideas which can not only allow persons to achieve a FLIHM (a Feeling that their LIfe Has Meaning), but a SFLIHM ( a Sustainable FLIHM). This is the key need of humanity.

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1. "FUZZY THINKING: The New Science of Fuzzy Logic," Bart Kosko, Hyperion, New York, 1993.

2. Bell’s Inequality: Bell’s proposed “proof” that entangled particles affect each other instantaneously over vast distances; i.e., that hidden variables do not account for these effects.

See: "ENTANGLEMENT: The Greatest Mystery in Physics," Amir D. Aczel, Four Walls Eight Windows, New York, 2001.

My take is that it is in Bell’s assumptions (i.e., the assumptions of the Copenhagen interpretation of quantum mechanics) that instantaneous effects over vast distances are buried. Nothing I read on this issue convinces me that it has been proved. All that has been proved to my satisfaction is that the quantum world is indeed currently beyond our understanding. Quantum mechanics has been a marvelous creation that has allowed vital things to be accomplished – experiments, technology, etc. But all without advancing our understanding of what lies beneath our current understanding.

I believe the primary reason for the foregoing is that the Copenhagen interpretation essentially barred developing theories that would permit efforts to look more deeply into the mystery of the quantum world. As a result it created false mysteries (dual nature of particle/waves, superposition of states, observation as a cause, random as a causal explanation, instantaneous effects over vast distances, etc.)

3. There is something independent of human beings that makes human life meaningful.

4. Human beings are themselves the source of meaning and value.

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