Introduction to Mathematical Philosophy by Bertrand Russell

Like reading a glossary for another book

Bertrand Russell won the 1950 Nobel Prize in Literature, though he was a philosopher, mathematician, and public intellectual, not a literary writer. (I suppose any nonfiction, however, could be considered essays.) As near as I can tell, Russell explained his mathematical system of philosophy in three works: In The Principles of Mathematics, published in 1903, he spelled out the fundamentals of his system of thought. He then built upon that foundation to create his magnum opus, together with Alfred North Whitehead, entitled Principia Mathematica, which was published in three volumes from 1910 to 1913. Neither of those books is intended for a general audience. Presumably one would need a PhD in mathematics to understand them. Russell did write many books for general readers, however, and in 1919 he released Introduction to Mathematical Philosophy, a book intended for lay readers (like myself).

Most of us, when we do math, take for granted the fact that 1 + 1 = 2 or 2 x 2 = 4. As a philosopher, however, Russell takes nothing for granted. Like Rene Descartes or Baruch Spinoza, he starts with first principles, assuming nothing, and systematically builds his argument from the ground up. It’s not enough to accept that 1 + 1 = 2 , one must ask WHY 1 + 1 = 2. Indeed, what exactly is addition, or for that matter, what is a number? That is what this book is about. Russell essentially defines the basic terms and functions of mathematics from a foundation of pure logical reasoning. Entire chapters are devoted to defining terms like rational numbers, real numbers, cardinal numbers, or differentiating between finite and infinite series. Reading this Introduction is much like reading an appendix or glossary to some other book, and Russell even admits as much. Introduction to Mathematical Philosophy merely provides the basic Rosetta Stone for understanding more advanced Russell books, like The Principles of Mathematics or the Principia.

You may not need a PhD in mathematics to read this Introduction, but you might very well need a master’s degree. Even if you’re good with numbers, however, that may not help you here. Leaning towards the philosopher rather than the mathematician, Russell writes all the mathematical formulae in paragraph prose, often using confusing, serpentine syntax. In order to express these concepts in textual form, Russell has to give new mathematical definitions to everyday words, which requires you to learn and memorize this new complex vocabulary.

Around chapter 14 (out of 18), however, the book finally turns in the direction of what I expected when I chose to read it; that is, how we use all these mathematical foundations to make logical deductions. From this point onward, the book is really quite interesting and can actually be understood by non-mathematicians. I question, however, whether I really needed to know many of those definitions that Russell spent so much time on. Once you get past chapter 13, many of those terms aren’t even used, and the text reads more like common sense.

What’s the point of all this? I suspect that Russell is a modern version of Pythagoras. He thinks mathematics is not merely a part of reality; mathematics is reality. Or rather, the logical rules that govern mathematics are the same that govern the movements of atoms or the thoughts in our heads. Russell sees no separation between mathematics and logic; they both operate on the same principles, whether the propositions are expressed through number or word. I believe Russell would assert that all human thought is fundamentally mathematical. We collect empirical sensory data, group it together in a complicated system of set theory, and then assess and organize that data with logical principles to create knowledge.

I was lost for much of the first half of this book, but I did find the latter half rewarding. Overall, I don’t think this Introduction is very effective in accomplishing what Russell set out to do, which is to provide the general public with an on-ramp to his school of thought. To get a handle on this subject, you’d be better off reading a Logic 101 textbook for college undergrads.

Icarus; or, The Future of Science by Bertrand Russell

Pessimistic outlook on scientific progress

Bertrand Russell won the 1950 Nobel Prize in Literature, even though he was not a literary writer. He was a philosopher and mathematician who broke through to a wider general audience as a public intellectual. His essay Icarus; or, The Future of Science was published in 1924 as a 72-page book. The London publisher Paul Kegan produced a series of 110 books called To-day and To-morrow, consisting of short volumes containing essays that speculate on the future. The first book in this series was Daedelus; or, Science and the Future by J. B. S. Haldane. Russell’s Icarus, published six months later, is a response to Daedelus. The two authors were not in total disagreement. Both expressed doubts that some recent scientific advances were actually beneficial to mankind, but overall Haldane was the more optimistic of the two. In general, Haldane thought scientific advances would elevate the happiness of the common man, while Russell predicts that only the powerful will reap the benefits of progress.

Russell opens Icarus by stating he’s not going to talk much about the biological sciences. That’s not his department, and Haldane already covered that topic sufficiently in Daedelus. Strangely, however, Russell then goes on to talk mostly about biological sciences: genetics, eugenics, birth control, and anthropology. The longest chapter discusses changes brought on by the Industrial Revolution. Russell really doesn’t discuss technology much at all, but rather focuses on how our modern industrial and commercial society has spawned a revolution in organization, both in terms of efficiency and ubiquity. The result is that people now have less control over their lives than they did in, say, the 17th century, since much of our existence is regimented by organizational bureaucracy and government oversight, from our lives at work to the media we consume to the education of our children. Russell goes on to argue that science may very well be the downfall of liberalism and democracy.

Science would increase mankind’s happiness and health, Russell argues, if man were a rational being, rather than an emotional and greedy animal. Rapid scientific progress upsets the comfort zone between man’s desires and living conditions. In addition to the mythical metaphor of Icarus, Russell offers the analogy of how wolves become accustomed to periods of starvation; as a result their evolutionary descendants, domestic dogs, overeat every chance they get. It would be interesting to hear Russell’s take on the current (human) obesity epidemic, something he does not predict here.

I suspect that Icarus may have been delivered as a lecture before it was published in book form. That’s how it reads, anyway. The two books, Daedelus and Icarus, comprise a sort of debate in print, a point/counterpoint. Much of what Russell predicts for the future has already come to pass—declining birth rates, global economy, media empires, the arms race, and a general dumbing down of humanity. He presents some really interesting ideas here, but the obvious fault of the book is its brevity. It would have been a more productive work if Russell had had more room to develop his arguments, but the format of the To-day and To-morrow series confined it to a brief discussion. There aren’t enough pages for him to really convince you of anything. This is a thought-provoking work, but more thoughts are provoked than satisfied. Perhaps Russell delves deeper into these topics in other books, and I have yet to discover them.

Understanding History and Other Essays by Bertrand Russell

Three unrelated articles from the 1940s

British philosopher and mathematician Bertrand Russell won the 1950 Nobel Prize in Literature, back when philosophers used to be considered for that award. Understanding History and Other Essays was originally published in 1957 by the Philosophical Library, whose books have been recently rereleased as ebooks by Open Road Media. This volume consists of three of Russell’s previously published essays: “How to Read and Understand History” (1943), “The Value of Free Thought” (1944), and “Mentalism vs. Materialism” (1945). I believe the first two essays were originally published as Little Blue Books by the Haldeman-Julius publishing company. “Mentalism vs. Materialism” is from The Rationalist Annual of 1945. Although the history essay is the title selection, I was attracted more by the subject matter of the latter two essays.

The essay “How to Read and Understand History” is nothing special, probably because Russell is not a historian. He starts by stating that a study of history is useless to most people’s daily lives, and the only reason to read history is if you simply enjoy doing so. He briefly discusses the works of some notable historians, such as Herodotus, Thucydides, Plutarch, and a few modern scholars. Russell criticizes philosophers like Hegel and Marx who attempt to come up with a unified theory of history, characterizing them as “mythologizers,” and offers some thoughts on how he thinks history should be written and taught.

In “The Value of Free Thought,” Russell begins by defining what exactly is “free thought.” The term is not synonymous with atheism or agnosticism, as some might think, but rather with scepticism. A freethinker can believe whatever he chooses to believe, but to be a freethinker, that choice must be based on evidence and rational inquiry. The antithesis of free thought, as Russell asserts, would be William James’s argument: Why not believe in religion when believing is more convenient, comfortable, and who’s to say you’re wrong? Russell goes on to critique religion because of its denial of rational inquiry. Like many atheist writers (Richard Dawkins, Christopher Hitchens), Russell sometimes lapses into smugness. I agree with the message, but not always the tone. Also, if you’re already a free thinker, then this primer on free thought tells you much of what you already know. Overall, however, “The Value of Free Thought” is a good concise manifesto of sorts for the modern freethinker.

“Mentalism vs. Materialism” is exactly what it sounds, contrasting dualism (matter and mind or spirit) with monism (just matter). Russell, as one might expect, is on the side of the materialists, or “physicalists,” the label he prefers. He starts with an explanation of physics that is forgivably outdated and unforgivably confusing. Once he gets into the epistemology of consciousness, however, his argument is well-stated. This essay is very brief, only about half the length of either of the other two selections.

I bought this ebook as a Kindle Daily Deal. Whenever possible, I look over the table of contents before I purchase an ebook. In this case, the table of contents makes it look like there are 18 essays in this ebook. In fact, however, there are only three, the longest of which is maybe a 45-minute read. The remaining 15 lines of the table of contents are just subheads within the last essay. Open Road could have done a better job formatting that. Had I paid more than a couple bucks for this ebook, I would have been a little disgruntled by the discrepancy between what I thought I was buying and what I actually got. Given that these writings are not in the public domain, a few bucks for a few essays is reasonable. These are not earth-shatteringly revolutionary essays, but those sympathetic to Russell’s atheist, materialist, and skeptical views will appreciate his eloquent and intelligently reasoned discourses.

Essays in this collection

How to Read and Understand History

The Value of Free Thought

Mentalism vs. Materialism

Proposed Roads to Freedom by Bertrand Russell

Socialism, Anarchism, and Syndicalism demystified

Bertrand Russell

In Proposed Roads to Freedom, Nobel Prize-winning philosopher, mathematician, and essayist Bertrand Russell thoroughly and thoughtfully explains the political and economic systems of three potentially viable alternatives to capitalism: Socialism, Anarchism, and Syndicalism. The book was published in 1918, when these movements were likely at their height on the world political stage and in the public’s collective consciousness. At that time, all three were ambitiously active in Europe and America, but it is hard to imagine the average reader having a minute understanding of their doctrines, which is where Russell comes in, as an eloquent interpreter of political economy for the masses. Today, in the age of Bernie Sanders and Alexandria Ocasio-Cortez, when the term Socialism inspires knee-jerk anger, Anarchism inspires fear, and Syndicalism inspires a head-scratching “Huh?”, we could use a book like this now more than ever.

Russell begins by devoting a chapter to each of the movements, defining their basic premises and providing historical background for each. He then goes into exploring specific issues of government and society by comparing and contrasting the three systems, examining such questions as how many hours workers should work and how they would be paid under each system, how would a nation operating under one of these philosophies conduct itself in international relations and war, and to what degree would art and science flourish or stagnate in a Socialist, Anarchist, or Syndicalist society. Russell states honestly that he does not think capitalism is the ideal economic system under which mankind should conduct itself, and that we should be working towards an alternative system. What’s refreshing about this book, however, is that Russell is no utopian optimist. Rather, he admits that any of the three systems in question are likely to fail in the face of mankind’s inherent greed and propensity to violence. Russell doesn’t advocate any of the three as his personal preference, but rather proposes a fourth alternative, a British form of Syndicalism known as Guild Socialism, which combines some of the better elements of all three. In the final chapter he outlines what his perfect world under Guild Socialism might look like, but again he states his case in a tone more hopeful than dogmatic.

As one would expect, Russell uses the writings of Karl Marx as the basis for his explanation of Socialism. For Anarchism, his main source is Peter Kropotkin. With Syndicalism, no one sage rises to the top, so Russell draws from a variety of texts, mostly of French origin. If Russell commits one error in his writing of this book it is that he quotes too extensively from the original doctrinal texts. I’m reading this book because I don’t want to read Marx’s Das Kapital, so I prefer it when Russell explains these ideas in his own words. Those wishing to read deeper can draw a very good bibliography from his 61 footnotes. Because the book was published a century ago, it contains a few unfortunately antiquated comments on race, such as when Russell expresses concern over “the exploitation of inferior races” where we today would use the term “developing countries.”

Russell doesn’t claim to have all the answers in Proposed Roads to Freedom, but he sure does provide the reader with an in-depth education on the subjects at hand. If more philosophers could write like Russell, using clear and accessible language without insulting the reader’s intelligence, perhaps philosophy wouldn’t be so frightening to the typical nonacademic reader (in America, at least). Russell’s body of work is a treasure trove for the rationalist and freethinking reader, and I look forward to digging deeper into his extensive catalog of writings.
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The Philosophy of Bertrand Russell by George Santayana

More about Santayana’s thought than Russell’s
Having previously read a couple works by George Santayana and Bertrand Russell, I was interested in learning more about these two philosophers, so when I discovered that the former had written a book about the latter my interest was piqued. The content of The Philosophy of Bertrand Russell was first published as part of a 1913 book by Santayana entitled Winds of Doctrine: Studies in Contemporary Opinion. At some later date another publisher extracted these essays on Russell and published them as a separate book. This book should not be confused with a 1944 book of the same title edited by Paul Arthur Schlipp with contributions from various authors.

Santayana’s The Philosophy of Bertrand Russell is comprised of four chapters. The first of these chapters, “A New Scholasticism,” is little more than a brief introduction. Santayana writes from the perspective of a senior scholar commenting on an up-and-comer, even though Russell had published close to ten books by this time. Santayana encouragingly intimates that he admires what Russell has accomplished so far but disagrees with him on a number of matters. The overall tone of Santayana’s writing is one of a mentor offering his mentee a mixture of faint praise and mildly reproachful but constructive criticism.

In the second chapter, “The Study of Essence,” Santayana begins by explaining how philosophers since Plato have made a distinction between the ideal world and the world that man is capable of perceiving with his senses. Santayana describes Russell’s contribution to this continuum as a sort of oxymoronic logical idealism in which mathematics is seen as the underlying truth of the universe. The elder scholar then goes on to critique what he sees as the fallacies in this line of reasoning.

At some point prior to the writing of this book, Russell must have published some essay criticizing the philosophy of pragmatism, because chapter 3, “The Critique of Pragmatism,” reads like a response to such a statement. Santayana, who studied under William James, is closer to a pragmatist than Russell, but that doesn’t stop him from finding fault in pragmatic doctrine. In fact, this chapter is really about Santayana’s views on pragmatism and yields little insight into the philosophy of Russell, who’s name is only mentioned a few times in the entire chapter.

The final chapter, “Hypostatic Ethics,” is a more pointed critique of Russell, focusing on his conception of ethics. Santayana chides the absolutism of Russell’s ethical philosophy, seeing it as prescribing right and wrong in terms as rigid as mathematical equations. Santayana advocates a more relativistic ethics, not as relativist as the pragmatists, perhaps, but at least a happy middle ground.

If you are looking for an introductory or blanket overview of Russell’s philosophy, this is not that book. Despite what its title indicates, this book really reveals more about Santayana’s thought than Russell’s. A very brief book as far as philosophy texts go, it won’t take up too much of your time, and Santayana’s prose is more accessible and less cryptic here than in The Life of Reason, though he still has a tendency to say with a hundred words what he could have said in ten. Those interested in Russell will likely be disappointed by this book. Those interested in Santayana, however, might find it a satisfying read.
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The Problems of Philosophy by Bertrand Russell

An excellent epistemological primer
Philosophers usually direct their writings towards their fellow philosophers rather than to the general reader, thus making the pursuit of philosophy a difficult and frustrating task for anyone falling into the latter category. Most philosophical works expect the reader to know the entire history of Western thought leading up to the work in question. Every once in a while, however, some benevolent philosopher will come along and write an accessible text that serves as an inviting entryway into the discipline. Bertrand Russell’s 1912 book The Problems of Philosophy is one of the better examples of a philosophical primer. Rather than the usual chronological approach to such books, Russell proceeds thematically, addressing a series of philosophical questions, with each topic building upon the knowledge acquired in the previous chapter. Though Russell references other philosophers like Plato, Descartes, Kant, and Hegel, the reader is not required to have prior familiarity with any of their works in order to comprehend the philosophical concepts being discussed.

That’s not to say the book is an easy read. Russell doesn’t dumb down any of his ideas in order to pander to an audience of philosophical novices. He does, however, express philosophical concepts in a plain and simple vocabulary that general readers can understand. No knowledge of disciplinary jargon is required; Russell defines all the terms necessary for understanding his argument. His prose can get convoluted at times when the complex subject matter requires it, but there’s nothing that precludes a diligent reader from fully appreciating the text. Throughout the book he uses examples and analogies from everyday life that are easily comprehensible.

As a title, The Problems of Philosophy is a little misleading, or at least too broad. A more fitting title (though less inviting) would have been The Problems of Epistemology because Russell is almost exclusively concerned here with the particular branch of philosophy that deals with the theory of knowledge—how we perceive the reality around us and form beliefs as to what is true or false. This book only touches on metaphysics and doesn’t cover ethics at all. Russell does delve rather deeply into the territory of logic, which is essentially the application of mathematical principles to language or ideas in order to differentiate between truth and falsehood. He begins by questioning the difference between appearance and reality. To what extent can we be certain that the information we gather through our senses reflects the true nature of reality? From there he proceeds to discuss the existence and nature of matter. Subsequent chapters go on to explain how we acquire knowledge from sense data and inductive reasoning, how we form a priori judgements, and why we sometimes harbor erroneous beliefs. Although the book primarily advances Russell’s own ideas on these subjects, he does give due consideration to theories and philosophies that oppose his own, so the reader gets a well rounded perspective on each topic.

I’ve often wondered why Russell was awarded the Nobel Prize in Literature even though he is a mathematician, logician, and philosopher. After reading this book, one sees how the elegant quality of his prose serves to enlighten readers and expand their perspective. Russell was a master of language as well as mathematics. His concluding chapter on the value of philosophy is positively inspiring. This excellent book not only provides stimulating insight into the processes of human thought; it also opens your mind to new ways of thinking about reality.
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