George Boole's Laws of Thought

Everyone who knows computing knows the Boolean operators AND, NAND, OR, XOR, and NOT.  They allow us to construct conditional statements, and programmatic branching.  Electrical engineers learn the rules of Boolean Algebra with two values OFF and ON; and with three operators,  PARALLEL, SERIES, and a simple switch for NOT.   0 and 1 are OFF and ON. The three operators  of Boolean algebra are + X and ~ corresponding to OR, AND, and NOT. They are the same as PARALLEL, SERIES, and SWITCH.  George Boole had a different view entirely.  His 1853 book, An Investigation of the Laws of Thought on Which are Founded the Mathematical Theories of Logic and Probabilities, is a treatise on epistemology.  

We learn that correct thinking by logic is a reduction by syllogism.  All men are mortal. Socrates is a man. Therefore, Socrates is mortal.  If A =B and B = C, then A = C. The middle or the mean term is factored out. Boole granted that syllogism is one kind of valid method. However, rather than reducing statements, Boole argued by expansion for a deeper and extended understanding of seemingly simple truths.  His algebra is deceptively similar to – but different from – the forms we learned in high school; and so the learner here must pay close attention to these laws of thought. 

If x is “red” then xx means “red red” which is nonetheless still “red.”  If the essential attribute under consideration is “red” then red red things with their redness removed do not exist: xx – x = 0. Taking from Leibniz, Boole lets 0 be non-existence and 1 be the universe.   If x is our subject, then (1-x) is everything else in the universe except x. Boole rewrites xx-x as x(1-x) = 0 to give Aristotle’s Law of Contradiction: A thing cannot both have and not have the same attribute in the same way at the same time.  Boole calls this “duality.”  Also following Leibniz, Ayn Rand delivered that as  “A or non-A.”  

In 400 pages, Boole carefully applies the essential truths he discovered. He extracts more meaning – and more exacting meanings – from common statements.  However, his insistence on closely laying every step of this long journey, couched, as it was, and, indeed, of necessity, both historical and personal, must have been, in Victorian prose, renders this important work so Germanic as to be nearly unreadable.  It is well worth the effort.

“Wealth consists of things transferable, limited in supply, and either productive of pleasure or preventive of pain.” 

w = wealth

s = limited in supply

t = transferable

p = productive of pleasure

r = preventive of pain

Boole specially defines 0/0 to mean the undefined.  He includes this to stand for the indefinite class: those things not included in the present statement but which exist nonetheless.

Given that this book is 400 pages and Ayn Rand’s Introduction to the Objectivist Epistemology is 164, Boole boldly goes beyond the orbit of concept formation.  He nonetheless is in the same material space: he identifies reality; and ties concepts to objects. Boole explores the relationships between the processes of thought and perception and the expression of them through language. 

Boole even applies his method to statements about God.  His goal is not to address God’s existence but to expand and analyze statements about God asserted by Baruch (“Benedict”) Spinoza and Samuel Clarke.  (“… considered the major figure in British philosophy between John Locke and George Berkeley.” – Wikipedia here.)  From there, he examines Aristotle’s logic and Fermat’s probabilities.   The last third of the book is about the logic of probability theory.

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The Validity of the Senses

On the “Galt’s Gulch” discussion board for fans of the movie Atlas Shrugged, username Maphedus asked an old question: “How do we know whether our senses are being deceived or not?”  The easy answer is the that the primacy of reality means tautologically that reality is the primary experience: you know because you know; it is irreducible.

On a different tack, I would ask why the senses of bees, birds, and beavers are reliable for them, but ours are specially cursed?  Like them all, we, too, evolved on Earth and adapted to its changing environments. Our senses are in and of the world.  Moreover, we invent and construct transducers – telescopes, microscopes, electroscopes, spectroscopes – that extend and enhance our senses. Would you suggest that the rings of Saturn and the nucleus of a paramecium are not real?

The Outer Limits: "The Brain of Col. Barham"
is housed in a vat. Nonetheless, he adapts.

Mephesdus framed his question in some detail: "How do we know what reality is? Through our senses? If that's all it takes, then how do we know whether our senses are being deceived or not? Doesn't the existence of hallucinogenic drugs prove that our senses are not always reliable? What about optical illusions? And then there are aspects of reality which are imperceptible to our senses – how do we deal with that?"  And further, in our private discussion, he amplified his concerns: “There’s a philosophical thought experiment called "Brain in a Vat" which I think is very intriguing, and relates directly to the idea that our senses are supposedly reliable. … A variation on the "Brain in a Vat" thought experiment is presented in the sci-fi movie The Matrix, where the entire world is really just a computer program.  …  I also seem to recall an excerpt from Barbara Branden's biography of Ayn Rand, titled The Passion of Ayn Rand, in which Ayn Rand was in a hospital after surgery, heavily medicated, and a street lamp outside was casting a shadow across the window, and Ayn Rand thought it was a tree. When Barbara Branden corrected Ayn Rand, telling her that it was a street lamp and not a tree, Ayn Rand became extremely irritated at Barbara for daring to suggest that her senses could not always be trusted.”

As far as I know from second-hand reports, hallucinogenic drugs do not alter perception to the point of invention.  No one has reported something that was not “there” only that what they reported was distorted or otherwise processed into something else.  Teenage friends of mine said that the front grills of automobiles looked like animals.  They did not claim that animals seemed to exist where no animals were found.  This supports the facts that we evolved to perceive. While various roots, shoots, herbs, and berries variously prepared can affectively change our mental processes, the facts of reality are not alterable.  That is why they are reality, and not the products of our (altered) consciousness.

 

Paramecium: real or artifact of misperception?

The “Brain in a Vat” paradox is another sophistry.  We could also ask: “How do we know that we are not really angels and rather than just corporeal husks in which the consciousness of angels have been entrapped?”  In order to answer either question, you would have to be “outside” the question, able to see the vats, the Matrix, or the entrapped angels.  Moreover, in the movies of the Matrix triology, very many unresolved paradoxes would plague any inhabitant.  Agents can take over any entity, as when Smith became a helicopter pilot.  Did the pilot never go home to his wife? Will she and the kids and the air traffic controllers and the commanding officer and their bunkmates all not wonder what happened?  We do not have such problems with reality because reality is real.

“Ayn Rand on drugs” is compelling to contemplate.  In truth, she was on Benzadrine.  But certainly in the hospital scene, the question was not the validity of her senses per se but of her mental processes.  The shadows were whatever they were, but it was her interpretation of them that defined them.  From Plato’s Cave to Freud’s Interpretation of Dreams, the “stuff” is unarguable; what we make of it is highly debatable.

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Is Physics a Science?

In sociology, students at all levels are presented with some discussion about whether and how sociology is a science. Physics – especially Newtonian physics – is taken as a kind of standard against which sociology is measured. Actually, a scientific investigation of college textbooks revealed that physics education is deficient in presenting students with the methods and limits of experiment and theory. 

Since the Renaissance, the term experiment has been used in diverse ways to describe a variety of procedures such as a trial, a diagnosis, or a dissection … To examine changes in the textbook construction of experimental method, introductory texts in psychology, sociology, biology, and physics were surveyed during three time periods: 1930-1939, 1950-59, and 1970-79. […] … the percentage of texts with discussions of research methods increased from 50%-90% in psychology, from 25%-70% in sociology, from 20%-45% in biology, and from 16%-30% in physics. Even in the 1970s, such discussions were absent from the majority of biology and physics texts.
"What Counts as an Experiment?: A Transdisciplinary Analysis of Textbooks, 1930-1970," Andrew S. Winston and Daniel J. Blais. The American Journal of Psychology, Vol. 109, No. 4 (Winter, 1996), pp. 599-616.

Visiting the University of Texas Kuehne Library for Physics, Mathematics and Astronomy, I found that this is still true.

Another concept is missing, paradigm. Kuhn’s Structure of Scientific Revolutions was published in 1962. (See Necessary Facts here.) I was assigned it in a philosophy class at Lansing Community College in 1975. My last undergraduate class in physics was in 1982. Paradigm and experiment were never explicitly discussed.
  

At the UT Kuehne Library (honoring John Matthias Kuehne, 1872-1960), I checked nine recent physics textbooks, both for freshmen and for classes in modern physics, typically the second year for majors, seeking index entries for experiment and paradigm. The results were disappointing. Neither term appeared in these:

• Bernstein, Fishbone, Gasiorowicz, Modern Physics (2000).
• Benson University Physics, (1996)
• Giancoli, Physics for Scientists and Engineers (2000)
• Halliday, Resnick, Walker, Fundamentals of Physics (2005)
• Hech, Physics: Calculus (2000)
• Learner, Physics for Scientists and Engineers (1996)
• Tipler, Physics for Scientists and Engineers (1991)
• Young and Freedman, Sears and Zemansky’s University Physics (2004). 

Of those, the last was most disappointing being the 11^th edition of the standard textbook that served the first post-war generation in the 1950s and 1960s. Tipler was one of the books we had at Lansing Community College because it was newly written in 1976 and because Paul Tipler taught at the University of Michigan. He, too, ignored Kuhn.

M31: Andromeda Galaxy, at first a "cloud"
then a spiral within our galaxy,
then an "island universe" like our
own Milky Way.

Better treatment appeared in Lea and Burke, Physics: the Nature of Things (1997). And this speaks to the validity of critical sociology: It is Susan M. Lea who made the effort to present students with discussions of experiment, including the nature of experiment, thought experiment (first Galileo, then Einstein: pp 11, 132, 445), and experiment and theory. As a woman in a man’s world, Dr. Lea easily adopted the sociological perspective of considering the accepted from a different point of view.

However, even Lea and Burke fall into positivist fallacies that plague science with “the problem of induction.”  (See Necessary Facts on David Harriman’s Logical Leap here and here.)  

They say (page 12): “Physics is an experimental science that prides itself in getting close to reality through laboratory testing of theory. … How can we be certain that the experimental process of dissecting nature into component part is ultimately correct? We can’t! Belief in experimental science depends on one’s worldview.” Again (page 14): “Consistency with experiment and usefulness in understanding nature are the properties of a good physical theory. The word truth is conspicuously absent. Aristotle… Kepler and Galileo… Newtonian physics, thought absolutely true for 250 years. In the twentieth century, we have learned that Newtonian physics is not exact but stands as an excellent approximation. Absolute truth is elusive. We continue to seek greater depth in our understanding, greater elegance in our theories, and greater precision in our experiments. Whether truth can be achieved in some approximate sense by this process is unanswerable. We believe in physics because we know we can organize our knowledge and employ it to describe the behavior of nature with greater accuracy using only a small number of fundamental ideas.”

 The objectivist answer is that rational-empiricism works. The physicists who are not sure about reality never think twice about getting into an elevator and expecting it to operate. And if it fails – despite the failsafe which was designed by the same laws – then some cause must be and can be found. In a lecture on “The Primacy of Existence,” Objectivist philosopher David Kelley notes that these doubters do not drive their cars according to the theory that we can never know anything for certain.

(Note the two words, lower case o-objectivist, and upper case. The first is the general rational-empirical method, the scientific method. Capital-O Objectivism derives explicitly from the published works of Ayn Rand and is a modern school of thought based on the objectivism of pre-Kantian Enlightenment )

Also, Lea and Burke gloss over the key problem with doubt: “Physics is an experimental science that prides itself in getting close to reality through laboratory testing of theory.”  What is this reality to which we can get close, but never discover?

To know that we are closer, not farther, requires some test. That test is reality.

In the history of science, few inventions came from engineering applications of scientific principles. Rather, engineering achievements provided data for theoretical explanation. The telegraphs of the world transmitted our ideas across continents, each click creating a magnetic field that collapsed, inductively broadcasting evidence of our existence into the Galaxy, all a generation before Maxwell.

The best sociology discovers facts, creates theories, identifies causes, and tests hypotheses. As passive description, ethnography is not highly regarded, though it is passionately defended. Passive description is good science – and good description is not passive. We bring our expectations to our observations. A scientist knows to be ware of preconceived notions and to be open to new perceptions. At the same time, the scientific observer often has good reason to seek exactly the phenomenon under investigation. It is not really passive. If only implicitly, certain factors are held constant, while others change. Aristotle’s description of the chick embryo is a paradigmatic example cited as one of the greatest scientific experiments in history. (See Necessary Facts here.)  

But sociology knows these facts. Sir Anthony Giddens’s international standard undergraduate textbook, Sociology, has an entire chapter (number 20) on Research Methods with three explicit discussions of experiment. It begins with two discussions of sociology as a science (pp 7-8; and 12-14).

Moreover, in sociology, we enjoy some self-criticism in examining the historical development of our field, from Comte (I prefer Spencer), Weber, Durkheim, and Marx, through to Parsons, Merton, and your choice of pop stars of the current generation. Physics students do not understand their science as a historical development. As Kuhn pointed out fifty years ago, physics is presented whole and complete, without development. No wonder they are surprised by a new explanation of a previously unperceived fact.

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