Theology of George Boole

2nd November 2015 will be celebrated internationally to mark the bicentenary of the birth of a remarkable Unitarian, George Boole, who in the opinion of many scientists is in the same rank as Darwin and Einstein. The address below was delivered at the Cork Unitarian Church earlier this year and we are indebted to Des MacHale for allowing us to cite his definitive biography.
          Most of my remarks today are drawn from the research of Des MacHale and contained in his book The Life and Work of George Boole – a Prelude to the Digital Age.
          George Boole was a professor of mathematics at University College Cork in the middle of the 19th century and is regarded by many as the founder of pure mathematics. He developed a system of symbolic logic that sought to “investigate the fundamental laws of operations of the mind by which reasoning is performed;...” He was born 200 years ago and there have been a number of events throughout the city and indeed the world to commemorate that anniversary. What is all the fuss about?

Most of you will be familiar with the syllogism attributed to Aristotle:
1. All men are mortal.
2. Socrates is a man.
3. Therefore, Socrates is mortal.

This can be compared to the following argument
All crows are black.
My dog is black
Therefore my dog is a crow

Most will intuitively grasp that second conclusion is incorrect. Explaining why is more difficult, particularly when the premises and conclusions of such arguments become more complex. Boole developed his system of symbolic logic that produced its output in binary form, that is to say: just two outcomes, e.g. yes/no, on/off. In Boole’s system, the valid conclusion is expressed in what is called “Truth Table.” Based on the premises given, the results are either 1 or zero. That is to say, True = One; False = 0. A nice Unitarian ring to it.
          His system of computational logic to produce these results is based on just 3 “operators”: AND, OR and NOT.
          Information Technology today is based on “Boolean searching”, an algebraic system of logic formulated by George Boole. In a Boolean search, keywords are combined by the operators AND, OR and NOT to narrow or broaden data searches. An example of this use is in ‘search’ on all computers but used extensively by all search engines on the World Wide Web.
          However in his day there was no known practical application for his work and he was therefore regarded by many - including Bertrand Russell - as the founder of pure mathematics. Boole was a practical man. His tradesman father had a profound interest in astronomy, which young Boole followed intently. Although he became a mathematician, Boole saw the scientific method and its advances as a way to improve our human condition. He was a committed educator and was socially involved. It is significant that for an abstract mathematician he regarded “induction... as the highest exercise of our intellectual powers.” The importance of empiricism or observations deserves mention. Today we regard empirical evidence as integral to the scientific method. And science has had such large part in shaping our lives. Yet, when Aristotle posited that a heavy object falls faster that a lighter object, he based it entirely on his sense of logic and deductive reasoning and the idea was never rigorously tested. It was not in the ancient mindset to test the hypothesis under experimental conditions. It is only in the modern era that the scientific method with its combination of inductive and deductive reasoning became the norm. 2000 years after Aristotle, Galileo challenged that falling objects hypothesis atop the Tower of Pisa. Forty four years ago, the point was definitely settled by Apollo 15 astronauts on the 2nd August 1971 while standing on the moon.
          Moreover, when Boole was in his early 30’s the planet Neptune was discovered, an event that is instructive to understanding the history of science. To explain, there are seven heavenly bodies visible with the naked eye. The planet Uranus is not normally or easily visible. It was only discovered in the 18th century with the assistance of a new technology in the form of the telescope. The orbit of the next planet out, Neptune, however was plotted mathematically before it was seen. The calculations made it possible for astronomers to eventually observe the planet through a telescope. This triumph of deductive reasoning was rightly lauded by Boole in an address he delivered in 1847. I sense in this an intersection in Boole’s mind between science / mathematics - on one hand – and religion, that is to say, a belief in unseen things.
          Similarly, Boole revered Isaac Newton and admired his work with light and optics. Again Boole - the abstract mathematician - emphasised the importance of observation as the basis of all scientific reckoning. In Lincoln where he grew up, Boole was deeply involved with the Mechanics Institute, with its worthy Victorian social objectives of education and advancement. In 1831 he was selected by them to deliver a lecture entitled “The Genius and Discoveries of Isaac Newton” at the age of just 16. Boole shared Newton’s Unitarian outlook and Boole would certainly have related to the famous quotation attributed to Newton toward the end of his life:
          ‘I don't know what I may seem to the world, but as to myself, I seem to have been only like a boy playing on the sea-shore and diverting myself in now and then finding a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me.’
          Des McHale in his book expresses a view that there was a “strong undercurrent of religious awe in Boole observations on Newton’s work.” “Boole believed that delving into the mysteries of nature and mathematics were principally, in Milton’s famous words, ‘to justify the ways of God to Man”.
          George Boole’s father, John Boole was a shoemaker. He was a polymath but a poor businessman. He had many interests including astronomy, cameras, microscopes and telescopes. To broaden his knowledge young George - with his father’s encouragement - received tuition in Latin and Greek so he could read the works of the ancients in their original language. One wonders how John Boole’s life might have evolved had he had the educational and material opportunities. We are reminded of the words of Thomas Grays poem ‘Elegy Written in a Country Churchyard’
          Full many a flow'r is born to blush unseen,
          And waste its sweetness on the desert air.
          Among John Boole’s proudest possessions was a large telescope which he made himself. In his shop window he displayed a sign that said “Anyone who wishes to observe the works of God in a spirit of reverence is invited to come and look at my telescope.” This convergence of science and religion was certainly passed on to his son.
          His son George mastered Latin by the age of 12, and went on to teach himself Greek. He was particularly adept at translation and at age 14, his proud father submitted his translation of Ode to Spring, an ancient Greek poem, to the editor of the town’s newspaper. This triggered in a local controversy about whether the young George Boole was actually the author.
          He added to his linguistic range by teaching himself French, German and Italian. Because of his humble circumstances, a university education was out of the question. It is remarkable that a life so full of accomplishment was completed without a university degree.
          Following the breakdown of his father’s health he became responsible for the support of his family and at just 16 years commenced his career as a teacher at which he excelled.
          Boole had Unitarian outlook regarding social activism. In addition to being involved in the aforementioned Mechanics Institute he was a member and later President of the Cuvierian Society in Cork at which he would have met and conversed with well-known Cork Unitarians, Francis Jennings and Richard Dowden
          The Cuvierian Society for the Cultivation of the Sciences had been founded in Cork in 1835 with the aim of providing popular education in the sciences, fine arts and literature. In many ways it was regarded as a successor organisation to the Royal Cork Institute, founded by Unitarian lay minister, Thomas Dix Hincks. [In another example of his social activism, before he came to Cork, Boole was the founder of a charitable society with the wonderfully Victorian name of the Lincoln Female Penitents’ Home.]
          I am struck by the fact that these involvements are quite specific and reveal an abhorrence of social injustice. And although he was present in Ireland during the later stages of the Great Famine and was deeply moved by what he saw, there is nothing I have read to suggest any interest any “big-picture” ideas about the 19th century social structure or politics: neither the gloominess of Malthus who died when Boole was still a young man nor the revolutionary fervour of Karl Marx whose Communist Manifesto was published the year before Boole came to UCC.
          UCC or Queens College as it was known was officially opened on 7th November 1849. There were Queens Colleges also in Galway and Belfast. These were the brainchild of Sir Robert Peel, Prime Minister and primarily intended for Catholic laity who otherwise would not have educational opportunities at Trinity College. It was a daring innovation in its day. Boole was appointed to be its first professor of Mathematics.
          The prevailing RC Church reacted with suspicion to the establishment of the Queens Colleges. Catholic clerics were forbidden to take any part in the work of the Colleges. The Catholic laity, while not forbidden from attendance, were warned against it. The religious sensitivities in Ireland were a source of tension in Boole’s day and later. The Queens Colleges were non-denominational. The only religious dimension was that each had Deans of Residence for spiritual needs. The NSPCI has one such chaplain in Belfast now: Rev.C.Hudson MBE is assigned to Queen College Belfast.
          George Boole married very late in life. Mary Everest was the niece of John Ryall, Vice-President and Professor of Greek at Queen's College Cork; her paternal uncle Sir George Everest was Surveyor-General of India, and gave his name to the world's highest mountain. They were closely united and their marriage was a happy one, producing five children, all of which were girls. In the mid-1840s, Boole made a major conceptual leap by combining algebra with logic. This prompted his first book A Mathematical Analysis of Logic, published in 1847.
          His 1854 book An Investigation of the Laws of Thought was described by the philosopher and mathematician Bertrand Russell as ‘the work in which pure mathematics was discovered’.
          Boole laid the foundations of the information age. His pivotal advances in mathematics, logic and probability provided the essential groundwork for modern mathematics, microelectronic engineering and computer science. His influence is such that he has been called - as MacHale suggests - the “father of the digital age.”
          After he died in 1864, this work was of interest only to academics with no practical use. Some 70 years later, engineers at MIT in the United States were attempting to build an electronic calculating engine harnessing the advances in transistor technology. A common feature of electronic components is that they have two easily distinguished states: on/ off, high/low, positive negative, clockwise / anti-clockwise, open / closed. This suggests that - if we are to use such components to store and reason about information - the information should be represented using a scheme that uses only two symbols. By contrast our numerical system has 10 numbers and our English alphabet uses 26 symbols. What the electronic engineers needed was a logic and representational system to suit their binary world. In 1938 Claude Shannon of MIT wrote a landmark paper saying the Boole system of algebraic logic developed decades previous was perfectly suited to the age of the transistor. From that the Computer Age began.
          Des MacHale said: “Boole is a pivotal figure who can be described as the ‘father of the information age’. His invention of Boolean algebra and symbolic logic pioneered a new mathematics. His legacy surrounds us everywhere, in the computers, information storage and retrieval, electronic circuits and controls that support life, learning and communications in the 21st century.”
          Boole’s theology was Unitarian, Boole certainly was a student of the Bible and believed it to be the word of God. Although I would sense that he would understand it as a revelation of divine truth rather than as an instruction manual. His conception of God was rather Victorian and he saw God as a kind of task-master. He rejected Trinitarian doctrine and did not accept the divinity of Christ on the same level of God and the Holy Spirit.
          Accordingly to MacHale, he felt “no really scientific man could be an atheist.” In his 1854 book Laws of Thought, Boole quoted Xenophanes, "referring to the whole world, said the One was God”. He cites the “equally intimate alliance” between his fundamental equation: x(1-x) = 0 and “those forms of philosophical speculation know under the name of dualism.”
          After his death his wife wrote about him: “The hope in his heart had been to work in the cause of true religion. Mathematics had never been more that a secondary interest for him; and even logic [was] a means of clearing the ground of doctrines imagined to be proved, by showing that the evidence on which they were supposed to rest [did not] to prove them. [Instead he wanted] to give a more active and positive help ... to the cause of pure religion.”
          This is in sharp contrast to the aggressive atheism of some in today’s scientific community. We spoke earlier of the discovery of the planet Neptune by entirely mathematical, deductive means. And Boole - no doubt - was influenced by the developments in the science of microscopic organisms that were emerging in his time. Said Boole, “men... are reluctant to admit the reality of [what] they do not see with their eyes, That and teaching of science are sometimes alike... [This is not unlike] the moral scene. ... Life lived by principals of rectitude is the most favourable to public and private happiness. This requires that men should in some instances do what contrary to their personal interest as is judged by the common standard... It demands... trust in unseen principals.” Thus was the faith of this brilliant, self-educated, curious man who followed unseen principals to develop the Boolean logic that bears his name and which had no practical application in the century in which he lived. Only, it was resurrected many years after his death in the use of technologies unimaginable in his world in such way that has revolutionised ours. For this we are grateful.

F. Spengeman                     August, 2015
Unitarian Church Cork