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As someone who took a few university courses on analytic philosophy covering Russell, I've never heard anyone suggest he "sold out". Maybe that's just people who aren't really familiar with Russell or his personal life that say that?
If you're going to argue that he wrote sellout books, then he did that long before he gave up on logicism. See for example Introduction to Mathematical Philosophy, which is aimed at people who know nothing above regular public school math.
I think the ability to recognize that he had basically hit a dead end with logicism was probably his greatest success, instead of falling prey to a sunk-cost fallacy. The guy wrote one of the most influential papers in philosophy of the 20th century ("On Denoting"), as well as being one of the central figures in the founding of an entire field of study, but he knew when to call it quits, and I doubt he regretted it at all. His social and political writings and activism are a treasure trove of wisdom IMHO.
Edit: if I'm being fair though, it is pretty common for people to say History of Western Philosophy was a bit of a poor work that he did just because it would sell well. That is just one book out of hundreds of works though, and honestly it's not that bad if you balance it with more neutral sources on some of the material.
I don't think History of Western Philosophy is bad but it is opinionated. If someone were expecting either a dispassionate overview or heartfelt enthusiasm for all philosophers past I can see how they'd come away disappointed. Especially when he's particularly dismissive.
If you go in expecting Russell's view of Western philosophy through the ages then you'll get just that.
I thought Russell's History of Western Philosophy was interesting precisely because it gave Russell's personal view on all the philosophers. (This is just like Kenneth Clark's Civilisation.) There are already dozens of dry textbooks out there, whereas Russell was uniquely positioned to write an entertaining opinion piece on the topic.
Not to mention he is good at writing and it is a very interesting read
Read it main years ago and found it both enlightening and a good read. There were parts whre he was clearly struggling to understand the work of particular philosophers, but he had no secret of the fact in the book. It was interesting to a great mind grappling to understand the work of another. Parts made me chuckle, too.
History is a terrific book. Whatever its flaws, it's a great read, and often very witty.
Wasn't it based on lectures?
As a side note since this discussion is related to Russell and his brilliant contributions, I think a similar discussion can be had regarding Russell's contemporary and co-author Alfred North Whitehead (mentioned breifly in the article).
If Russell can be charged with "selling out" or directing his work toward a more general audience, Whitehead can be accused of the opposite, or perhaps even worse. If you read into his works post Principia (which he co-authored with Russell) you find a brilliant logician and philosopher begin to deviate from commonly held assumptions of Western thought and attempt to articulate a philosophy often at odds with "objective" ways of thinking. His works are interesting yet difficult because he is often so at odds with 20th century science and philosophy that he has to create his own terms to describe phenomena, which he builds upon with increasingly unfamiliar terminology until most readers feel completely alienated and give up.
Imo both Russell and Whitehead were great minds and deserve their fair share of consideration and contemplation, pre- and post- Principia.
Apropos AN Whitehead, I listened to an interesting talk the other week [1] about "process philosophy", specifically in phil of biology. The speaker (John Dupré) thought that he was working along the same lines as Whitehead, but that he was a poor writer so no-one can really be sure if they understood him.
If you're interested in Russell, or mathematics in general, I can't recommend the graphic novel Logicomix highly enough. It's about Russell and the Principia Mathematica
As a former mathematician, I totally disagree.
Logicomix has nearly no mathematical content. The most technical part is a quick description of Hilbert's Hotel, but I thought it was very shallow, since there was no explanation. It did not even try to define infinity, or suggest how to distinguish several kinds of infinity. And, at least in the French edition, the Barber Paradox is wrongly stated!
Logicomix is mostly about people, especially Russell, with the postulate that everyone that worked on the foundations of logic was insane. But if you scrutinize the story, many details are wrong (IIRC, the young years of Russel, Frege's aggressive bursts, the last years of Cantor, …). They bent the reality to obtain the cliché that most people expected: genius mathematicians are mad.
I agree, the graphic novel was entertaining, but not an accurate portrayal of their lives.
If you're looking for something more factual, then Russell's own autobiography is a good place to start. Also "The Cambridge Companion to Bertrand Russell" (edited by Nicholas Griffin) is a source I can vouch for.
https://www.amazon.com/Cambridge-Companion-Bertrand-Companio...
I think there is an issue of mismatched expectations. Logicomix is just a divulgative effort that briefly surveys Russell’s life. As somebody with little knowledge of post-Enlightenment philosophy, I honestly did not come away from it thinking philosophers were mad, but simply that his gallant effort in logicism reached the end of the line once Gödel entered the scene - which is what happened, by all accounts. He looked extremely reasonable, particularly considering how his whole prestige and career depended on the methods Gödel wiped away.
If i remember correctly (been a while since I read it), Logicomix really failed to explain how Russell went on to become relevant in public discourse at large, basically assuming that philosophers are interesting by default... I bought it mostly to find that out (he was very influential on my parents’ generation, as one of the classic intellectuals mentioned in ‘68 movements) and was somehow disappointed to just get the story of a logician instead. Still, it was a coherent story with great reverence for its subject, IMHO. Had it been trying even harder to delve into logic, as you expected, I would have probably thrown it out of the window.
It has little mathematical content and as anaphor pointed out in a sibling comment is is not even an accurate portrayal of Russel's and his contemporaries lives.
I think trained mathematicians and the philosophically educated are probably just not the right target audience for the book.
I still found it an interesting and entertaining read. Just a few days ago I gave it to my eight year old and she came up with a lot of good questions while reading it. It is not a children's comic though and it is definitely a book that needs guidance, especially because of the artistic liberty it takes in many respects. For example, the first thing I had to set straight is that Russel's brother was nothing like he was portrayed in the book.
I don't think teaching math was the goal of Logicomix at all.
Also his autobiography is pretty readable and worth reading if you want to know more about his personal life.
Christos Papadimitriou is one of the two authors.
>Arguably Russell saw the limitations of “technical philosophy” more clearly than those who thought of themselves as following in his footsteps. The analytic tradition has produced some great work but too many of its practitioners have conflated rigour with technical argument. I would wager that there is not a single major work of political or moral philosophy which depends on a formal logical proof. What endures of Russell’s logic is of interest only in logic. If Russell wanted to address the problems of real life, he had to leave behind the symbols and numbers that had so captivated him in his youth.
What are the shortcomings of logic? Just incompleteness, or is there more?
For a fun logical proof that proves why you can't use logical proofs for philosophical questions, see the "Tractatus Logico-Philosophicus" by Ludwig Wittgenstein.
https://www.gutenberg.org/files/5740/5740-pdf.pdf Introduction by Bertrand Russell
Spoiler: logic is inherently limited by language. To quote Russell, "In order to understand Mr Wittgenstein’s book, it is necessary to realize what is the problem with which he is concerned. In the part of his theory which deals with Symbolism he is concerned with the conditions which would have to be fulfilled by a logically perfect language. There are various problems as regards language. First, there is the problem what actually occurs in our minds when we use language with the intention of meaning something by it; this problem belongs to psychology. Secondly, there is the problem as to what is the relation subsisting between thoughts, words, or sentences, and that which they refer to or mean; this problem belongs to epistemology. Thirdly, there is the problem of using sentences so as to convey truth rather than falsehood; this belongs to the special sciences dealing with the subject-matter of the sentences in question. Fourthly, there is the question: what relation must one fact(such as a sentence) have to another in order to be capable of being a symbol for that other? This last is a logical question, and is the one with which Mr Wittgenstein is concerned. He is concerned with the conditions for accurate Symbolism, i.e. for Symbolism in which a sentence “means” something quite definite. In practice, language is always more or less vague, so that what we assert is never quite precise."
I'd say the major shortcoming of logic is its inability to express uncertainty.
It's well-suited for mathematical proof as practiced, where axioms and definitions are precisely defined, and there is no reliance on empirical observation with potentially noisy data.
However, most of real-life is not as clear-cut. Deriving the truth of a statement may depend on multiple potentially faulty pieces of evidence which must be taken into account together. For this, one needs to assign probabilities.
This is useful even when applied back to mathematics. In practice, mathematicians form conjectures "likely to be true" long before they are formally proven. Additionally, they must narrow the search space in their minds in order to try the most likely avenues of proof, a process we refer to as "creativity".
Even using probability is only one more step towards solving the question of formally codifying general reasoning. We must also consider factors such as use of language and forming concepts (what precisely IS a "chair", after all?), and further aspects which form a basis for human action and which cannot be logically derived, namely our morality and base goals. Not to mention the entire plethora of such questions with which the field of philosophy concerns itself.
(These are the types of questions to which we will need to find some answer if we are ever to construct a useful generally reasoning AI)
Much as classical Newtonian mechanics is a useful approximation of physics at large scales and low speeds, formal logic is a useful approximation of reasoning at high certainty and low flexibility of interpretation.
> I'd say the major shortcoming of logic is its inability to express uncertainty.
There are formal logics that incorporate uncertainty, non-crisp truth values, or both.
Handling uncertainty is difficult regardless; attaching probabilities to judgements did not ensure the social sciences avoided the replication crisis.
I'm not sure what you mean by "low flexibility of interpretation": purely logical proofs are supposed to assume nothing about interpretation.
> However, most of real-life is not as clear-cut. Deriving the truth of a statement may depend on multiple potentially faulty pieces of evidence which must be taken into account together. For this, one needs to assign probabilities.
This what the fuzzy people want you to believe. The logicians have a better answer. For this you need more context. E.g in programming you would add types, pre- and post conditions. And not this statement will be 85% true. As the current AI hype is pretending.
Might be horrible books with good theory see John Rawls Theory of Justice
Minor correction: Gödel's incompleteness theorem dates to 1931, not 1944.
That said, I agree that the later Russell's more popular writing has been given short shrift, and stands the test of time in many ways better than the earlier Russell's logicism.
That is true, Gödel's incompleteness theorem dates to 1931.
In 1944 Gödel published his first philosophical paper, entitled "On Russell's Mathematical Logic".
The mistake was probably made because the author Julian Baggini is a philosopher and so he is mostly aware of Gödel's philosophical works and not so much of his mathematical accomplishments.
The Principia Mathematica was surely one of the most useful wrong-turns in history.
I highly recommend The History of Western Philosphy precisely because it’s highly opinionated. It’s got many things to like, including being frank about not knowing the answers, and treating figures such as Augustine and Aquinas as philosophers in their historical context. A very engaging book.
If you are looking for a proper introduction to western philosophy and a history of ideas, I recommend instead Antony Kenny's A New History of Western Philosophy, which academics think is an excellent introduction.
No applied logic is useful, but you need computers because the proof is big. https://en.wikipedia.org/wiki/Automath gets started just around the time he dies, so Russel still made the right call, but lets not sacrifice a good idea "cause Gödel" for all eternity to prop him back up.
I was halfway through the third or fourth paragraph and thoroughly confused which Russel is the author talking about. I don’t understand why the author mentions the first Russel if the article isn’t (mainly) about a comparison between the two.
It confused me so I’ll ask the obvious question: this article is about the second Russel who wrote Why I am not a Christian, right?
I don't know if this is what you are actually asking but it reads like that.
There are no two Russells, it's the same person, just different kind of works in different periods of his life.
> There are no two Russells
What? Okay, I really didn’t realize that it’s just one Russel.
I mean if you read the first paragraph and don’t have background in philosophy you would assume there were two persons named Russel after reading the first paragraph! I mean author says the first Russell was short lived and gives yearX-yearY. So yeah, I thought the first Russell died in yearY!!
I feel stupid now :-/
I never thought that Godel incompleteness of a logical system was particularly damaging; the ability to make self-referential statements is useful, the ability to resolve self-referential paradoxes less so.
Same for the halting problem in CS, which is typically resolved by (sleep 9999; kill -9 $pid). QED. ;-)
Russell's hope was to establish that one could find proof of all true mathematical statements, so that one needed a fixed-for-all-time set of axioms and nothing more. Incompleteness obviously destroys that hope.
There is an interesting, if quite technical, answer here about Goodstein's Theorem which is a very reasonable number theory theorem which cannot be proven in first order logic.
So questions around statements which are true but not provable in certain logical systems do have concrete examples and are interesting imo.
https://math.stackexchange.com/questions/625223/do-we-know-i...
Goodstein's Theorem cannot be proved in Peano axiomatization of natural numbers in first order logic. You can have stronger axiomatization of natural numbers in first order logic that allows to prove Goodstein's Theorem - such axiomatization would contain subset of set theory and transfinite induction up to ordinal e_0. But it is still axiomatixation in first order logic.
As mentioned in that answer, these "natural independence phenomena" do seem much more interesting than Gödel's incompleteness results.
Something like a Turing machine, with its finite states, deterministic transitions, and simple tape seems so mechanical, so physical. So predictable.
Sure, there's the halting problem, but that relies on a paradox.
Surely something as artifical as self-referential statements would seem a bit pointless.
And yet, with the help of that principle, it turns out we can write simple, mechanical programs where if the input is < N we can calculate the answer, and if the input is > N we can't figure out what the program will do (using standard mathematical thinking).
For some N we can get creative, but for a yet bigger N, we may well find ourselves unable to be creative enough to work out if we could ever work out the the answer.
https://en.wikipedia.org/wiki/Busy_beaver#Non-computability
"In 2016, Adam Yedidia and Scott Aaronson obtained the first (explicit) upper bound on the minimum n for which Σ(n) is unprovable in ZFC. To do so they constructed a 7910-state[2] Turing machine whose behavior cannot be proven based on the usual axioms of set theory (Zermelo–Fraenkel set theory with the axiom of choice), under reasonable consistency hypotheses (stationary Ramsey property).[3][4] This was later reduced to 1919 states, with the dependency on the stationary Ramsey property eliminated.[5][6]"
My thoughts exactly. Goedel is just basically "set of all sets that don't contain themselves ... does it contain itself or not?" applied to 'provability'.
It gives you no more profound insight than "you can eff yourself with recursion if you aren't super careful" which is obvious for any beginner programmer who encounters recursion and tries to write whatever he likes in recursive function.
I guess this might have been surprise for mathematicians who always thought they have all infinites at their disposal and thus are completely unrestricted and brushed self-referential paradoxes under the rug as curiosities until Godel showed they can be constructed about things mathematicians care about like provability.
I believe you can make a consistent fully provable axiomatic system by excluding statements that are not provable from your system, as meaningless.
You don't consider whether "number 5 contains itself" is true because it's nonsensical. "This statement is unprovable" can be considered similarily nonsensical not because it wrongly combines math concepts but because it's a self-referential paradox and we choose to not allow that.
> I believe you can make a consistent fully provable axiomatic system by excluding statements that are not provable from your system, as meaningless.
The problem is not how to exclude the unprovable statements. The problem is that the unprovable statements will include statements that are true, but that the system can't prove. Some of those statements are probably not ones you care about, like "this statement is unprovable". But you have no way of knowing that all of the unprovable true statements are like that. Some of them might be ones you do care about.
Thus, the real import of Goedel's theorem is not "you need to exclude unprovable statements"; it is "the intuitively attractive ideal of having a system in which every true statement you care about can be proved is not achievable".
> I believe you can make a consistent fully provable axiomatic system by excluding statements that are not provable from your system, as meaningless.
That's what ZFC does.
While `effing yourself with recursion is a takeaway from his finding, to me at least, it's a striking limitation of formal methods of 'sufficient ability'. There exists a completely understandable query that has no well defined answer. Back when it was felt that mathematics could somehow prove itself, this must have been a crushing blow.
But imagine what we could do if we didn't have incompleteness or the halting problem
The trope of self-referential paradoxes as the foundation for grander proofs has always bugged me. My gut always says "sure, but what if we just banned self-referential paradoxes?"
That's not a thing. The problem isn't self referential statements. The problem is much larger, and self referential statements are the easiest way to construct a counterexample. Self referential statements are a symptom, not a cause.
Trying to construct a mathematical system of axioms is like trying to construct the most powerful system of computation possible that isn't subject to the halting problem.
You want to prove stuff, so you want a powerful system. Eventually, you end up with a system of axioms that is so powerful it can prove contradictory results, or you end up with a language where you cannot prove it halts or does not halt.
You want to not be able to prove untrue true, and you want true things to be unable to be proven false, so you weaken your tools. Either you fail to weaken your tools enough, or you eventually end up unable to prove true statements are true.
In programming, the fact that it's unprovable that a program halts isn't actually a big deal. Most of the normal problems we deal with don't need algorithms which probe the boundaries of halting, and QA picks up the stuff we miss. (usually, and if not, it's the customer's problem, not mine) That doesn't work in math. In math, if you want to publish a paper that proves x, you want to be sure that nobody's going to publish a paper proving !x anytime soon. So you need a restricted language, unlike programmers.
It turns out banning self referential statements makes it really, really hard to prove stuff.
Well, and that is the essence of Gödel's first theorem: you can't, any sufficiently powerful system can generate an infinite number of them.
Options include not letting this bother you (my favourite) and just ignoring it and hoping it doesn't come up, as indeed, it often doesn't.
I think those are called type theories. IIRC that was at least the idea behind the original type theories, before they got co-opted by the CS rabble. :)
> But although it is true that Russell’s political writings were often
> naive and simplistic, ...
Say what? Of all the books on politics I've read in my youth Russell's were some of best. Not simplistic but written in a clear language. Not naive but stemming from the rich classical liberal and socialist tradition of the likes of Wilhelm von Humboldt and John Stuart Mill. A tradition that has been completely erased from the history books in the last decades (which ought to make his political works all the more interesting).
(I fully accept the possibility that I am in fact naive and simple-minded, of course. :D)