In my courses I often required students to analyze something important in the course by using the wheel of reason. (Refer to our Academy section - the “Wheel of Reason.”) I often taught philosophy of natural sciences, philosophy of social sciences, philosophy of arts, and health care ethics. In each of these courses students were required to analyze a discipline by applying the eight elements in the wheel of reason, by “going around the circle.” Over the years, students chose a great variety of disciplines or fields or areas to analyze. A few examples of what they chose will give you an idea of the wide range they could apply the wheel of reason to: astrophysics, biology, meteorology; sociology, clinical psychology, behaviorism, rational emotive therapy; jazz, rap, cubism, sculpture, Shakespearean drama; anatomy, physical therapy, nursing.
So here are three examples of student analyses using the wheel of reason (all are used by permission; none has been edited or corrected by me). Note that the analysis counted as a major part of their final grade, and so some students went into considerable detail.
A suggestion: if you are an instructor, what areas, fields, disciplines, or topics could you ask students to analyze using the wheel of reason?
Logic of Astronomy
1. Purpose : The fundamental purposes of astronomy are to discover what actually exists physically in the universe exterior to the earth, to acquire knowledge and understanding of the characteristic and processes of phenomena in the universe.
2. Assumptions : The most central assumption that underlies all astronomy is that all cosmic bodies, structures, and phenomena behave in accordance with the laws of physics and other lesser natural sciences as we know them on earth. Astronomy assumes that the law of universal gravitation,
F = Gm1m2
holds true among planets, galaxies, planetary nebulae, clusters, neutron stars, and everything else. Although our present physics is probably very inadequate, astronomy asserts that the universe abides by all of the rules of physics that intrinsically exist. Secondly, astronomy claims that activity in the universe can be delineated and investigated through mathematics. For example, ellipses describe the orbits of planets while parabolas and hyperbolas can sketch the paths that some comets take which are only seen from earth once.
Another powerful assumption is the Cosmological Principle. This concept states that the universe is homogeneous and isotropic. In other words, the universe looks basically the same to any observer at any point in all directions. It is believed that the general distribution of galaxies, stars throughout galaxies, and clusters of galaxies is fairly constant; it is not the case that there are any radical deviancies in celestial organization anywhere in the universe.
Implications : the above assumptions yield many implications that seem to be supported by findings in nature. Einstein’s field equations from general relativity allow for three solutions which correspond to three possible futures of the universe. The first is that the universe is open; it will continue to expand in all directions eternally. The second possibility is that the universe is closed, meaning that expansion will eventually halt and begin to collapse back to a single point due to gravitational forces. The last solution predicts that the universe is “flat”. This simply entails that the universe will eventually reach a state of equilibrium where the outward expansion and the gravitational forces from within will balance, and the universe will then remain fixed at that size forever. However, this possibility is the most unlikely of the three.
There are many other implications that can be traced out without using mathematics. If the universe has a common origin and was formed as a whole, then everything is inter-related. One cosmic event has an effect on everything else. Proximity to the event and the nature of the event determine how profound its effects will be. Furthermore, if systems in the universe are formed as a whole, they must be composed of basically the same material though, just in varying quantities.
Information, data, evidence : Almost all astronomy is based on observations from telescopes, observatories, astronauts, satellite findings, and information from space voyagers. In addition, much knowledge is obtained through generalizations made from the structure of the earth and moon. The spectrum of stars allows astronomers to conclude what chemicals are undergoing reactions, and even radio signals received from space provide information. Radio waves received from space have helped us to detect neutron stars. All observations and data are then analyzed with physics and mathematics.
Concepts : Astronomy encompasses a profusion of concepts, but only the most central ones shall be listed here. Specifically some prime examples of concepts in astronomy are light, its speed and all of its forms including gamma rays, X-rays, ultra violet light, visible light, infrared light, and radio waves. Other important concepts are Kepler’s laws which discuss planetary motion, Kirchhoff’s laws which govern spectroscopy, Hubble’s law which concerns the rate at which the universe is expanding and other various concepts such as gravity, fusion, and conservation of angular momentum.
Conclusions : Of the numerous conclusions that astronomy has arrived at, some of the most major are as follows: 1) The universe is composed primarily of hydrogen and helium. 2) The age of the universe is between ten and twenty billion years. (The ten billion year uncertainty is due to the fact that the age was calculated by tracing the universe’s expansion back to its starting point. Since we are not sure if the rate of expansion has always been constant, and Hubble’s constant is only estimated between 50 and 100 km/sec/Mpc there is a wide range of uncertainty.) 3) Celestial systems come into being as a whole, i.e., individual solar systems and galaxies evolve in their totality. It is not the case that each star in the Milky Way was born separately - the millions of stars were probably all formed very slowly together. 4)The universe is constantly changing - as things decline, they give rise to new things. 5) Everything is in perpetual motion. The earth rotates on its axis and orbits the sun while the entire solar system moves as the Milky Way spins through space. 6) The masses, ages, temperatures, sizes, distances and other properties regarding planets, stars, and other phenomena have all been concluded through experimentation and mathematical calculations based on scientific theories, e.g., the distance to stars is measured by the method of stellar parallax.
Point of View : Astronomy does not have a religious view point. Modern astronomy opposes the point of view of Plato and Aristotle. Our solar system is heliocentric, and the earth is not at the center of the universe. Orbits are not perfect circles and objects beyond the moon are not perfect and immutable. Astronomy also discards old conceptions of time and gravity. Time is not an objective dimension that is the same for everyone. Time can run more slowly or quickly (or not at all) depending on one’s speed or one’s experience of gravity (or acceleration). Gravity is not perceived as a force but rather as a field which warps time and space. Likewise, high velocity can also slow time.
Although astronomy welcomes the possibility of life elsewhere in space, astronomers deny the existence of UFO’s. It is asserted that it would be too difficult to construct a spacecraft for traveling several light years. Even if a space craft traveled 50,000 m.p.h., if it came from the neighborhood of Alpha Centauri, it would take 500 million years to reach earth. That’s quite a long time even if the travelers went under some type of suspended hibernation, not to mention that such a trip would require an unbelievable amount of fuel. But even if some ingenious fuel system was devised that would allow velocities near the speed of light, the g-forces would be so strong they would crush the travelers as well as the ship. The ship would have to accelerated very slowly up to an incredibly high speed, so the problem of having a multi-million year ride is almost unavoidable.
But let’s assume that some alien race has intelligence and technology that compares to ours the way our intelligence and technology compares to that of flatworms. It is very unlikely that such beings would come here, fly through the sky, and just leave without making any contact. Moreover, if these beings, as advanced as they are, did not want to be seen, they would probably have the technology to go undetected by our primitive resources.
Aside from UFO’s, astronomy’s most fundamental view point is that events in the universe occur as a necessary consequence of the forces of nature which science tries to explain.
Question at issue :
There is intense research being conducted to discover the best approximation of Hubble’s constant. Hubble’s constant is used to represent the rate of recession of galaxies from us and in effect, the rate of expansion of the universe. A very recent consensus has defined Hubble’s constant as 55 km per second per mega parsec but a new distance determination for a number of galaxies has implied a value near 90 km/sec/Mpc. The more accurate the value that is derived, the more accurate the estimation of the age of the universe will be, and the better a prediction will be concerning whether the universe is closed, open, or flat.
A last interesting question is that of black holes. The best way of detecting one is to search for certain effects caused by an invisible object whose mass is comparable to that of a star. An excellent place to look is in a mass-transfer binary where a star loses mass to a companion which can be a white dwarf, a neutron star, or possibly a black hole. When a black hole finds matter to pull into itself, the matter being spiraled in forms an accretion disk whose temperature becomes so high, X-rays are emitted. In short, if an unseen companion in a mass-transfer binary system has a considerably high mass and exhibits a spectrum containing X-rays, ultraviolet light, and visible light, it may very well be a black hole.
AN ANALYSIS OF THE LOGIC OF PHYSICS
There are several purposes of physics, and one of the most important is to understand the fundamental laws that govern the interaction of matter and energy.
Some of the assumptions of physics are that rigorous scientific explanations of natural phenomena are superior to other explanations offered by non‑scientific areas. The world physics studies is the actual world and not a fictitious creation, and it exists independent of humans. Complex systems can be analyzed and understood in terms of simpler systems, and therefore ultimately all phenomena can be explained by physics. Physics uses mathematics as its language and assumes physical systems can have math applied to them and that the axioms of math are correct....
Some of the implications and consequences of physics are that understanding natural phenomena is not restricted to the gifted few, but to all humans; and that every human can act on the world by using the concepts of physics. Useful technologies can be constructed by using natural phenomena.
The information, data and evidence that physics uses come from all physical actions and interactions. For example, planetary motion, electron tunneling, refraction, etc. It uses this data to create general predictive models and consistent theories. These theories, as long as they continue to work, provide evidence for physics by predicting and explaining various phenomena. The theories also provide information about how energy and matter behave in certain situations.
Some of the concepts of physics include the existence and conservation of energy, matter, momentum, and charge; the use of fields to describe forces at a distance, and the concepts underlying quantum mechanics and relativity.
The conclusions physics draws: experiments are about the behavior of matter such as the nature of light, the speed of light as the maximum speed of a signal, heat as a measure of energy. In its natural state an object has no acceleration. Magnetic poles exist only in pairs.
Some of the questions physics is trying to answer are: What is the ultimate building block of matter? What kinds of cosmological objects exist? What is the nature and fate of the universe, and how did it begin? Can all the elementary forces of nature be united and explained by one theory? Physics is also interested in answering more practical problems such as how to get cleaner and more efficient energy sources, and how to use energy most efficiently.
From the point of view of physics, it is the basic experimental science that all other sciences must reduce to because it studies the most basic elementary processes, objects, and interactions....
LOGIC OF A LITERATURE COURSE
purpose: to think the way a literary reader thinks about his or her life
q at i: How can I think in deep literary terms about stories and about my life in terms of those stories?
assumptions: • that I can learn about life by reading stories deeply.
• that I will connect more deeply to stories by seeing them in terms of character, conflict, change.
• that a story can be like an old friend–in which I can always find new and worthwhile things.
implications & consequences: • that my reading of stories will become deeper during the course.
• that I will apply stories to my life in a richer way at the end of the course than at the beginning.
concepts: • character • plot • theme
• the concept of story itself ➞ What makes something a story?
information: • the actual stories we will read in the course.
• sometimes, information about the author, or the context in which the story was written.
conclusions: • conclusions about specific stories (e.g., how Holden Caulfield has changed);
• conclusions I will draw about my life, on the basis of the stories
interpretations: see items in my life in a different way: the way when you read a book (Shirley Jackson) or see a movie, and you can see the world in terms of the story.
point of view: • the points of view of various characters: What does the story look like from their point of view? (E.g., the kid that Holden Caulfield can’t stand) • also: developing empathy with alien pts of v.