This morning I talked about hierarchies of thought...the system. Now I want to talk about methods of finding one's way through these hierarchies...logic.

Two kinds of logic are used, inductive and deductive. Inductive inferences start with observations of the machine and arrive at general conclusions. For example, if the cycle goes over a bump and the engine misfires, and then goes over another bump and the engine misfires, and then goes over another bump and the engine misfires, and then goes over a long smooth stretch of road and there is no misfiring, and then goes over a fourth bump and the engine misfires again, one can logically conclude that the misfiring is caused by the bumps. That is induction: reasoning from particular experiences to general truths.

Deductive inferences do the reverse. They start with general knowledge and predict a specific observation. For example, if, from reading the hierarchy of facts about the machine, the mechanic knows the horn of the cycle is powered exclusively by electricity from the battery, then he can logically infer that if the battery is dead the horn will not work. That is deduction.

Actually I've never seen a cycle-maintenance problem complex enough really to require full-scale formal scientific method. [...] For this you keep a lab notebook. Everything gets written down, formally, so that you know at all times where you are, where you've been, where you're going and where you want to get. In scientific work and electronics technology this is necessary because otherwise the problems get so complex you get lost in them and confused and forget what you know and what you don't know and have to give up.
[...]
The logical statements entered into the notebook are broken down into six categories: (1) statement of the problem, (2) hypotheses as to the cause of
the problem, (3) experiments designed to test each hypothesis, (4) predicted results of the experiments, (5) observed results of the experiments and (6) conclusions from the results of the experiments.

In the temple of science are many mansions -- and various indeed are they that dwell therein and the motives that have led them there.

Many take to science out of a joyful sense of superior intellectual power; science is their own special sport to which they look for vivid experience and the satisfaction of ambition; many others are to be found in the temple who have offered the products of their brains on this altar for purely utilitarian purposes. Were an angel of the Lord to come and drive all the people belonging to these two categories out of the temple, it would be noticeably emptier but there would still be some men of both present and past times left inside -- . If the types we have just expelled were the only types there were, the temple would never have existed any more than one can have a wood consisting of nothing but creepers -- those who have found favor with the angel -- are somewhat odd, uncommunicative, solitary fellows, really less like each other than the hosts of the rejected.

What has brought them to the temple -- no single answer will cover -- escape from everyday life, with its painful crudity and hopeless dreariness, from the fetters of one's own shifting desires. A finely tempered nature longs to escape from his noisy cramped surroundings into the silence of the high mountains where the eye ranges freely through the still pure air and fondly traces out the restful contours apparently built for eternity.

I talked about Phædrus' lateral drift, which ended with entry into the discipline of philosophy. He saw philosophy as the highest echelon of the entire hierarchy of knowledge. Among philosophers this is so widely believed it's almost a platitude, but for him it's a revelation. He discovered that the science he'd once thought of as the whole world of knowledge is only a branch of philosophy, which is far broader and far more general. The questions he had asked about infinite hypotheses hadn't been of interest to science because they weren't scientific questions. Science cannot study scientific method without getting into a bootstrap problem that destroys the validity of its answers. The questions he'd asked were at a higher level than science goes. And so Phædrus found in philosophy a natural continuation of the question that brought him to science in the first place, What does it all
mean? What's the purpose of all this?

Phaedrus's (author's) path through philosophy.

Suppose a child is born devoid of all senses; he has no sight, no hearing, no touch, no smell, no taste...nothing. There's no way whatsoever for him to receive any sensations from the outside world. And suppose this child is fed intravenously and otherwise attended to and kept alive for eighteen years in this state of existence. The question is then asked: Does this eighteen-year-old person have a thought in his head? If so, where does it come from? How does he get it?

Unless we apply the concepts of space and time
to the impressions we receive, the world is unintelligible, just a kaleidoscopic jumble of colors and patterns and noises and smells and pain and tastes without meaning. We sense objects in a certain way because of our application of a priori intuitions such as space and time, but we do not create these objects out of our imagination, as pure philosophical idealists would maintain. The forms of space and time are applied to data as they are received from the object producing them. The a priori concepts have their origins in human nature so that they're neither caused by the sensed object nor bring it into being, but provide a kind of screening function for what sense data we will accept.

Kant called his thesis that our a priori thoughts are independent of sense data and screen what we see a ``Copernican revolution.'' By this he referred
to Copernicus' statement that the earth moves around the sun. Nothing changed as a result of this revolution, and yet everything changed. Or, to put it in Kantian terms, the objective world producing our sense data did not change, but our a priori concept of it was turned inside out. The effect was overwhelming. It was the acceptance of the Copernican revolution that distinguishes modern man from his medieval predecessors.

What Copernicus did was take the existing a priori concept of the world, the notion that it was flat and fixed in space, and pose an alternative a priori
concept of the world, that it's spherical and moves around the sun; and showed that both of the a priori concepts fitted the existing sensory data.

He became aware that the doctrinal differences among Hinduism and Buddhism and Taoism are not anywhere near as important as doctrinal differences among Christianity and Islam and Judaism. Holy wars are not fought over them because verbalized statements about reality are never presumed to be reality itself.

In all of the Oriental religions great value is placed on the Sanskrit doctrine of Tat tvam asi, ``Thou art that,'' which asserts that everything you think you are and everything you think you perceive are undivided. To realize fully this lack of division is to become enlightened.

Logic presumes a separation of subject from object; therefore logic is not final wisdom. The illusion of separation of subject from object is best
removed by the elimination of physical activity, mental activity and emotional activity. There are many disciplines for this. One of the most important is the Sanskrit dhy_na, mispronounced in Chinese as ``Chan'' and again mispronounced in Japanese as ``Zen.''

Pursuit of the ghost of reason.

The real University, he said, has no specific location. It owns no property, pays no salaries and receives no material dues. The real University is a state of mind. It is that great heritage of rational thought that has been brought down to us through the centuries and which does not exist at any specific location. It's a state of mind which is regenerated throughout the centuries by a body of people who traditionally carry the title of professor, but even that title is not part of the real University. The real University is nothing less
than the continuing body of reason itself.

You are never dedicated to something you have complete confidence in.

Assembly of Japanese bicycle require great peace of mind.

[...] Sir Isaac Newton had when he wanted to solve problems of instantaneous rates of change. It was unreasonable in his time to think of anything
changing within a zero amount of time. Yet it's almost necessary mathematically to work with other zero quantities, such as points in space
and time that no one thought were unreasonable at all, although there was no real difference. So what Newton did was say, in effect, `We're going to presume there's such a thing as instantaneous change, and see if we can find ways of determining what it is in various applications.' The result of this presumption is the branch of mathematics known as the calculus, which
every engineer uses today. Newton invented a new form of reason.

It's the sides (science) of the mountain that sustain life not the top (philosophy).

(Un)definition of quality.

Removal of quality.

Quality is not the result of collision between subject and object. Rather subject/object are deduced due to quality.

In his Foundations of Science Poincaré explained that the antecedents of the crisis in the foundations of science were very old. It had long been sought in vain, he said, to demonstrate the axiom known as Euclid's fifth postulate and this search was the start of the crisis. Euclid's postulate of parallels, which states that through a given point there's not more than one parallel line to a given straight line, we usually learn in tenth-grade geometry. It is one of the basic building blocks out of which the entire mathematics of geometry is constructed.

All the other axioms seemed so obvious as to be unquestionable, but this one did not. Yet you couldn't get rid of it without destroying huge portions of the mathematics, and no one seemed able to reduce it to anything more elementary. What vast effort had been wasted in that chimeric hope was truly unimaginable, Poincaré said.

Finally, in the first quarter of the nineteenth century, and almost at the same time, a Hungarian and a Russian...Bolyai and Lobachevski...established irrefutably that a proof of Euclid's fifth postulate is impossible. They did this by reasoning that if there were any way to reduce Euclid's postulate to other, surer axioms, another effect would also be noticeable: a reversal of Euclid's postulate would create logical contradictions in the geometry. So they reversed Euclid's postulate.

Lobachevski assumes at the start that through a given point can be drawn two parallels to a given straight. And he retains besides all Euclid's other
axioms. From these hypotheses he deduces a series of theorems among which it's impossible to find any contradiction, and he constructs a geometry
whose faultless logic is inferior in nothing to that of the Euclidian geometry.

Thus by his failure to find any contradictions he proves that the fifth postulate is irreducible to simpler axioms. It wasn't the proof that was alarming. It was its rational byproduct that soon
overshadowed it and almost everything else in the field of mathematics.

Mathematics, the cornerstone of scientific certainty, was suddenly uncertain. We now had two contradictory visions of unshakable scientific truth, true for all men of all ages, regardless of their individual preferences.

This was the basis of the profound crisis that shattered the scientific complacency of the Gilded Age. How do we know which one of these geometries is right? If there is no basis for distinguishing between them, then you have a total mathematics which admits logical contradictions. But a mathematics that admits internal logical contradictions is no mathematics at all. The ultimate effect of the non-Euclidian geometries becomes nothing more than a magician's mumbo jumbo in which belief is sustained purely by faith!

And of course once that door was opened one could hardly expect the number of contradictory systems of unshakable scientific truth to be limited
to two. A German named Riemann appeared with another unshakable system of geometry which throws overboard not only Euclid's postulate, but
also the first axiom, which states that only one straight line can pass through two points. Again there is no internal contradiction, only an inconsistency with both Lobachevskian and Euclidian geometries.

According to the Theory of Relativity, Riemann geometry best describes the world we live in.

The trap consists of a hollowed-out coconut chained to a stake. The coconut has some rice inside which can be grabbed through a small hole. The hole is big enough so that the monkey's hand can go in, but too small for his fist with rice in it to come out. The monkey reaches in and is suddenly trapped...by nothing more than his own value rigidity. He can't revalue the rice. He cannot see that freedom without rice is more valuable than capture with it.

Japanese "mu" -- neither yes nor no.

Mythos-over-logos argument.

Euclid's horizon straight line.