Here are some hints and suggestions for better understanding the readings from Thomas Kuhn's The Structure of Scientific Revolutions.

Chapter VI

Summary:  "Anomalies" disrupt "normal science" and therefore lead (sometimes) to the rejection of the dominant "paradigm" in favor a new one.  When we examine this process historically, we see that there is no way to sharply distinguish between observable facts and the theory that interprets them.

Both "normal science" and "paradigms" have been discussed in previous chapters. (Kuhn is, in fact, responsible for making the word "paradigm" such a common term in contemporary English.) But Kuhn actually gives his clearest exposition of what he means by a scientific paradigm in the Postscript to the book, p. 175. There, he says that he uses "paradigm" primarily to mean two things: (1) the complete WORLDVIEW of a particular community, and (2) an AUTHORITATIVE EXAMPLE of how to do science.

"Normal science" is science conducted by a community which has an accepted paradigm (in both senses). So normal science is science conducted when scientists agree, in broad outlines, about the way the world is and agree about what good examples of proper scientific research are. Normal science is contrasted with science during periods of scientific revolution, when there is disagreement about both the way the world is and what successful examples of research are. For example, we are currently in a period of "normal science" in astronomy, but the period of Galileo's life was a period of revolution, when the Aristotelian-Ptolemaic paradigm was collapsing, and the Copernican-Galilean paradigm was gaining adherents.

"Anomalies" are things that, at the least, are not explained by the contemporary paradigm, and may even seem to be inconsistent with the contemporary paradigm.  To illustrate "anomalies" that may lead to disruptions in "normal science," Kuhn gives three examples: the "discovery" of oxygen, X-rays and the Leyden jar.

I assume you all know that the current theory of combustion (burning) is that it is oxygen bonding with carbon and releasing energy.  Kuhn refers to "phlogiston" in connection with the discovery of oxygen.  At one time, scientists believed that combustion was a process by which the substance phlogiston was released by burning objects.  The ashes left after combustion were the pure, or "dephlogisticated" matter.

A Leyden jar is a glass jar with a narrow neck, the inside and outside of which have been lined with conducting metal foil.  An insulated stopper is put in the opening, with a conducting rod inserted through it that reaches down to the conducting foil inside the jar.  If you expose the conducting rod to a charge, the Leyden jar will store the charge, so long as the inner and outer foil (separated by the glass of the jar) are not connected by a conducting material (like metal or a human body).  Scientists were led to construct Leyden jars because of the belief that electricity is some sort of fluid.  (They reasoned:  if electricit is a fluid, maybe we can store it in a glass jar.)  Early Leyden jars had water inside them, in the hope that the electric fluid would collect in the water, but it was soon discovered that the water was unnecessary.  Current scientists would say that a Leyden jar is a crude "capacitor" or "condenser," which is formed whenever two conducting materials are separated by a nonconducting material.

Go here for a picture of someone charging a Leyden jar from a generator.

Here is a more elaborate explanation of Leyden jars, with several images and pictures.

There is a very natural, but very mistaken, way to understand the point that Kuhn is making in this chapter.  Prior to Kuhn, many people would say that anomalies are essentially observations that violate the dominant scientific theory. The proper scientific response to anomalies is to develop a new theory that explains all the old observations, along with the new observations.  This new theory is superior because it keeps all the same observations and theoretical truths of the old theory, plus handles some additional observations.  (On this old view, science is like building a pyramid:  the original "building blocks" [observations] are kept, but new ones are added.)  But Kuhn is arguing AGAINST this way of understanding science!  The most important sentence in this chapter is the following:  "That distinction between discovery and invention or between fact and theory will, however, immediately prove to be exceedingly artificial" (52).  In order to understand this chapter, you must understand WHY Kuhn rejects the "pyramid building" model of science.

Chapter VII

Summary:  When a paradigm encounters anomalies, it can ALWAYS be modified to account for them.  However, the repeated failure of a paradigm to account for a large number of anomalies leads to a crisis, which is only resolved when a new paradigm is adopted.

Kuhn discusses three examples of major theoretical upheavals to demonstrate his point:  the crisis of Ptolemaic-Aristotelian astronomy (also called the "Geocentric," meaning earth-centered, vew), which was replaced by Copernican-Galilean astronomy (also called the "heliocentric," or sun-centered, view), the phlogiston theory of heat, which was replaced by the oxidation theory, and the replacement of the "luminous ether" theory of light (which fit in with the Newtonian paradigm) with the Einsteinian theory.

Aristotle presented a plausible paradigm, in which the earth was the center of the universe, and the Moon, Sun, planets and "fixed stars" revolve around it.  Ptolemy (the initial "p" is silent) was a later astronomy who gave a precise mathematical formulation to Aristotle's view, that allowed people to predict astronomical events with a high degree of accuracy. Here is an image of the universe as envisioned by Aristotle and Ptolemy.  Copernicus revived the view of the ancient Greek Aristarchus, that the Sun was the center of the universe.  Copernicus presented a mathematical model for predicting astronomical events using this model.  Later, Galileo presented arguments for why it was physically plausible that the earth both rotated on its axis and revolved around the Sun.  Here is an image of the universe as envisioned by Copernicus and Galileo.

As Kuhn observes, the difficulty of the Ptolemaic view in dealing with an increasing number of anomalous observations led to its downfall.  New observations were accomodated by modifications of the Ptolemaic view such as adding epicycles upon epicycles.  (See the link above on the Copernican-Galilean universe.)  These changes made the Ptolemaic theory more and more complicated, to the point that it began to seem increasinbly implausible.  (Why would God have designed the universe in such a complicated, inelegant way?)  This was clearly a key problem.  However, there is a common, but mistaken,view of why the Copernican-Galilean view replaced it.  The mistaken view is that the Copernican-Galilean view was simpler and did a better job of predicting astronomical events than did the Aristotelian-Ptolemaic view.  However, one of Kuhn's achievements was to demonstrate (in his book The Copernican Revolution) that  the Copernican-Galilean view was neither mathematically simpler nor better at prediction than the Aristotelian-Ptolemaic system!So why did people switch to it?  "Ptolemaic astronomy had failed to solve its problems; the time had come to give a competitor a chance" (Kuhn, Structure, 76).  (The preceding is an important sentence and should be read carefully!  If you find that sentence unsurprising, you probably do not understand it.)  In other words, it was not that the Copernican system already was an elegant and accurate model of the universe.  It was just that the Ptolemaic system was becoming more complex with every new observation, and did not show signs of getting any better.  So the decision to opt for the Copernican system may have been rational, but it cannot be explained using the "pyramid model" (see notes on Chapter VI).
 

Chapter X

Summary:  Scientists observe different things when guided by different paradigms, and so competing scientific paradigms are "incommensurable."

Kuhn discusses the term "incommensurability" in more detail in chapter XII (especially pp. 148-150) and the Postscript (especially pp. 198-204).  Primarily, to say that two paradigms are incommensurable is to say that there is no way to prove definitively that one paradigm is superior, because the two paradigms result in different observations (i.e., advocates of the different paradigms see different things) and they disagree over what the criteria for evaluating paradigms are.

Kuhn is criticizing a view that is extremely common (even today):   "Many readers will surely want to say that what changes with a paradigm is only the scientist's interpretation of observations that themselves are fixed once and for all by the nature of the environment and of the perceptual apparatus" (120).  In other words, science is a process of getting more accurate and more comprehensive explanations of observations, where observations are theory-independent, objective, and "given."  If this were true, it would give an objective basis for choosing between paradigms.  But Kuhn presents a variety of arguments for why this cannot be the case.

To illustrate the alternative view that he favors, Kuhn makes reference to "gestalt" psychology and "ducks" and "rabbits."  He has in mind certain classic images, in particular the "duck-rabbit," made famous by philosopher Ludwig Wittgenstein in his Philosophical Investigations. (Here is an image of the  "duck-rabbit." Notice that you can look at it either as a duck or as a rabbit.) The Gestalt school of psychology used similar examples to show that we see things as a whole. They were famous for the phrase that "the whole is more than the sum of its parts," which they took to be true both of human psychological faculties, and about how we perceive things: we do not merely see a set of lines, we see them as a duck (or as a rabbit).  As Kuhn notes later in the chapter, this suggests that "two men with the same retinal impressions can see different things" (127).

Kuhn applies this to science with the case of Herschel and the discovery of Uranus.  One of the reasons this is so important is that Uranus was the first new planet discovered. The other six planets are the earth plus the five planets that are visible to the naked eye (i.e., without a telescope), which were known to many (perhaps all) pre-modern civilizations.  Many astronomers saw a celestial object in the sky where we now believe Uranus to be.  However, they did not see it as a planet.  Even Herschel saw it as a comet before he became convinced that it was a new planet.  Soon after this disovery, astronomers (using equipment that had been available before) suddenly started seeing asteroids!  Kuhn is suggesting that the recognition that there was at least one more planet than we realized enabled astronomers to see the same sky in a different way.

Kuhn uses Galileo's theories on the motion of pendulums as an illustration at several points. A typical pendulum is a mass hanging from a string. Galileo said that the "period" of a pendulum (how long it takes it to go from one end of its arc to the other) depends on the length of the pendulum, but is totally independent of the "amplitude" of the pendulum (the angle it starts its arc at). It turns out that this is basically true where the initial amplitude is less than 20 degrees, but become only an approximation as the amplitude becomes greater than 20 degrees. (Cf. Kuhn, p. 124.) However, Galileo did not see this. A further illustration of Kuhn's point is the famous story of how Galileo dropped two canon balls from the leaning Tower of Pisa. This experiment is supposed to demonstrate that, contrary to what Aristotle said, the rate of fall of objects is independent of their weight. (Heavy and light objects accelerate at the same speed, 32 feet per second, unless air resistance affects one more than another.) However, Galileo never performed this experiment. The story is a myth. Galileo just theorized that it was true and left it at that.

Kuhn also wants to make the point that Galileo was influenced by a variety of schools of thought (including a revival of Platonic thought and the medieval "impetus theorists") so that he had a slightly different paradigm from Aristotle.  This allowed him to see pendular motion differently from the way an Aristotelian did:  "To the Aristotelians, who believed that a heavy body is moved by its own nature from a higher position to a state of natural rest at a lower one, the swinging body was simply falling with difficulty. ... Galileo, on the other hand, looking at the swinging body, saw a pendulum, a body that almost succeeded in repeating the same motion over and over again ad infinitum" (118-119).  (Actually, as Kuhn knows, it was only with Galileo that the motion of pendulums became a paradigmatic kind of motion in modern physics.  For Aristotelians, there's nothing even particularly interesting about pendulums.  Aristotle probably never even mentions pendulums.  This, in itself, shows the importance of paradigms.)

So it seems that, in a fairly immediate and intuitive sense, people see different things under the influence of different paradigms.  However, some philosophers have tried to argue that there is a more fundamental level of experience that is fixed and objective.  The philosophical doctrine that all real knowledge is grounded in sensory experience is called "empiricism."  Scottish philosopher David Hume (who published A Treatise of Human Nature in 1739-1740) is one of the great classical empiricist thinkers.  In the early twentieth century, the empiricist tradition was carried on by the "Logical Positivists."  The Logical Positivists attempted to reduce all of science to a combination of statements that were pure reports of sensory experience (like "red, here, now") plus some purely formal manipulations of these sentences by logic and mathematics.  Although the Logical Empiricist program led to some very interesting philosophical results, it was ultimately a failure.  It turns out that some of the greatest minds of the 20th century were unable to explain how to reduce even basic science to pure sensory reports.  This is what Kuhn means when he says that "No current attempt to achieve that end [i.e., a pure observation-language] has yet come close to a generally applicable language of pure percepts" (127).