Bertrand Russell

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Bertrand Russell

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1Aerodynamics
Juin 26, 2007, 11:19 am

I'm currently working my way through Bertrand Russell's The History of Western Philosophy and I keep getting hung up on Russell's prose (or, should I say, his manner of thinking). Particularly troubling is his theory of the philosophy of mathematics, specifically that numbers are 'forms' rather than 'constituents'. I believe I read that for a time, Russell viewed numbers as a set of a sort of Platonic Ideas (i.e. universals), but that after discussion with Wittgenstein he abandoned this view.

Also interesting is the character or tone of his writing; by virtue of his erudition and disdain for thought incompatible with his own unique philosophy he comes across as a something of a parody of intellectualism. I cannot decide if his obfuscation of certain points is intentional, unintentional, or simply imagined on my part.

Despite these concerns (and others) I find him a fascinating read.

2NoLongerAtEase
Juin 29, 2007, 1:57 am

Interesting post!

Russell did believe at one point (around Principles) that arithmetic was synthetic a priori and known via direct access to some kind of Platonic Heaven. This surely conflicts with the idea the mathematics (as logic) is tautologous and analytic, which MIGHT be his view by the late teens/early twenties and does seem, in some sense, to be inherited from Wittgenstein.

At the very end of Introduction to Mathematical Philosophy, Russell introduces the idea of tautology as being somehow related to what logic will ultimately turn out to be. He writes that “…the characteristic of logical propositions we are in search of is the one which was felt, and intended to be defined, by those who said that it consisted in deducibility from the law of contradiction. This characteristic…for the moment, we may call tautology…”

Russell admits in the next several pages that he “does not yet know” how to define the term tautology as it is related to the propositions of logic . He claims that logical/mathematical statements, are, in the end, just expressions of tautologies, yet he himself makes it clear that he not entirely sure what it means to make this sort of claim, or, at least, that he does not yet have a grasp upon the proper way to put his understanding into word. While he asserts that mathematical claims are tautologies, he doesn’t really argue for this claim because he admits rather straightforwardly that he isn’t quite sure what the assertion boils down to.

Similarly, in the Lectures on the Philosophy of Logical Atomism, Russell also seems to assert (without any sort of fleshing out of the claim) that logical/mathematical propositions (boiled down to their underpinnings) are tautologies. He writes “Everything that is a proposition of logic has got to be in some sense or other like a tautology. It has got to be something that has some peculiar quality, which I do not know how to define, that belongs to logical propositions and not to others.”

The term tautology itself, as applied to logical propositions, was borrowed from Wittgenstein, and that Russell doesn’t appear to have fully grasped what it was that Wittgenstein meant by the term.

The question is whether or not Russell at this point fully dropped the synthetic a priori in relation to any of the logical underpinnings of arithmetic.

It's honestly hard to tell. Russell's Platonism, it seems, is born in large part out of his repudiation of Bradley style absolute idealism and I think he worries that if he gives up on Platonism across the board that idealism will be that much harder to refute. Even at the time of Introduction, propositional functions (which classes are reduced to) seem to keep on keepin' on up in Platonic Heaven.

He seems to want to deny the direct-access-Platonism of Principles, but on the other hand he doesn't know what to replace it with, so he seems to take on Wittgenstein's bullshit about tautologies as a promissory note. The idea being that, eventually, when the war is over and things are right with the world the great Wittgenstein will return from the trenches to save us all from the terror of a foundationless mathematics and the grip of muddleheaded thinking.

Unfortunately, like most great prophecies, the latter didn't quite come to fruition.

3Aerodynamics
Juil 2, 2007, 9:28 am

Thanks for the insightful response. I find Russell's dilemma regarding numbers perplexing; it seems clear to me that humans have a perceptual sense of "oneness" in that to focus one's attention on a subject is to "single it out", as it were, and of "twoness" as an extension of symmetry, etc.

As numbers grow larger (or as we move away from integers) the perceptual nature of our understanding gives way to abstraction, but in our system of arithmetic all larger or more complex numbers can be reduced to the perceivable integers and logical functions (i.e. addition, repeated addition (multiplication) etc.).

I get the sense that I'm missing something; I'm rather new at this and I haven't really done my homework on the topic. For the time being, I'll content myself that seeing the phrase "Wittgenstein's bullshit" appear in your post means that I haven't lost my mind completely yet.

4Jesse_wiedinmyer
Juil 2, 2007, 9:00 pm


You may be interested in Lakoff's Where Mathematics Comes From.

5logic
Juil 30, 2007, 6:23 am

today there are things like category theory, which maybe he would have worked on, had it existed. in the early 1900s, there was some emphasis on Hilbert's program -- the idea that you could build mathematics from a small set of axioms. today that idea is largely rejected because of the famous works in the mid 20th century.

6zentimental
Jan 28, 2008, 6:09 am

Could it be that there was no use of a computer to iterate equations leading to fractals? Or I am completely off?

7Naren559
Mar 19, 2008, 11:49 am

Aerodynamics (3) re Wittgenstein (coprophiliac toro):
The Cambridge Companion to Wittgenstein
Wittgenstein's Vienna
Ludwig Wittgenstein: The Duty of Genius
Wittgenstein: A Life
Wittgenstein
Interpreting Wittgenstein: A Cloud of Philosophy, a Drop of Grammar
Tractatus Logico-Philosophicus by Ludwig Wittgenstein
Wittgenstein's Early Philosophy: Three Sides of the Mirror
Wittgenstein Reads Freud
Philosophical Investigations (3rd Edition) by Ludwig Wittgenstein
Culture and Value by Ludwig Wittgenstein
Pulling Up the Ladder the Metaphysical Roots of Wittgenstein’s
Wittgenstein: An Introduction (S U N Y Series in Logic and Language)
Zettel by Ludwig Wittgenstein
Wittgenstein and Political Philosophy
A Wittgenstein Dictionary (Blackwell Philosopher Dictionaries)
Wittgenstein on words as instruments: Lessons in philosophical psychology
Sorry about authors--copy and paste is such a hassle, however, Amazon might help or even Google

8bookmonk8888
Juin 12, 2010, 2:23 am

5 "- - the idea that you could build mathematics from a small set of axioms - - - is largely rejected" Particularly due to Goedel's bombshell.

9bjza
Juin 12, 2010, 4:17 pm

Aerodynamics > Can you give us a quote where the form/constituent distinction is made? I think I understand, but since I haven't read Russell's History, I don't want to jump to conclusions.

Re #2: "...when the war is over and things are right with the world the great Wittgenstein will return from the trenches to save us all..."
- Great bit of writing there, NoLongerAtEase.

10Naren559
Juin 26, 2010, 8:45 pm

Ludwig Wittgenstein: "Whereof one cannot speak, thereof one must be silent."

11bookmonk8888
Juin 28, 2010, 9:02 pm

Category Theory is great for giving an overview of so many branches of mathematics.

12bookmonk8888
Juin 28, 2010, 9:12 pm

>9 bjza: (biza)

A very long time since I read Russel's and Whitehead's "Principia Mathematica". Though memory is failing me, I remember I was impressed until the Goedel bombshell hit. Interesting that a computer also developed the first 5 of their theorems, some more elegant than R&W's. It is said that Russell was amused when he was informed of this.

13bookmonk8888
Juin 28, 2010, 9:17 pm

>9 bjza: (biza)

Found this using Google:

"The comparison of Russell's views on semantics before 1905 with the theory of Frege allows one to expose the common sources of their interest in semantical problems and the specific character of their examination. During the investigation of the principles of mathematics and elaboration and realization of the program of logicism, questions regarding the logical structure of mathematical and logical propositions as well as the relation of linguistic signs and logical forms arise for both authors. Russell assumes the possibility of two kinds of analysis of the structure of propositions. One of them - by means of propositional functions - is analogous to Frege's analysis. But at first it is not accepted by Russell as fundamental. He prefers another kind of analysis, namely that by means of relations. This preference is conditioned in the first place by the intensional interpretation of propositions and in the second place by his ontological and epistemological views. These are based on the theory of external relations which implies the acceptance of real existence of particulars and of the specific relation of predication, resulting in the consideration of predicates as terms."

14wildbill
Juil 12, 2010, 9:45 pm

I enjoyed Russell's book and found it a useful introduction to Western philosophy. I did keep in mind as I read the book that Russell was an intellectual snob who valued his own opinion above all others.

15bookmonk8888
Juil 13, 2010, 4:53 am

>14 wildbill: (wildbill)

Which Russell book are you referring to. If you're referring to his Principia Mathematica which was co-authored by Whitehead, you're quite a mathematician. I struggled with it (I'm a dabbler in Math -- as in so many other things) but did enjoy it. Goedel later demolished the basis of their ambitious project.

16paradoxosalpha
Juil 13, 2010, 8:32 pm

Logicomix did an interesting job of trying to connect Russell's ideas with his biography.

17Teerabhat.Ruensiri
Sep 6, 2011, 2:16 am

Agreed with #16

18Naren559
Sep 22, 2011, 2:22 pm

#13 - Bookmonk8888:

Russell eventually maintained that Wittgenstein had the "final answer' - This also came via Google:-

Ludwig Josef Johan Wittgenstein (1889–1951) studied with Bertrand Russell and became an influential advocate of analytic and linguistic philosophy. In 1918, Wittgenstein had completed Tractatus Logico-philosophicus, which he called the “final solution” to all problems of philosophy. In later years, however, Wittgenstein rejected his own conclusions in the Tractatus and wrote yet another seminal work of modern philosophy called Philosophical Investigations.

Tractatus
In his Tractatus, Wittgenstein, like Russell, maintained that language was composed of things he called propositions, which could be broken down to less complex propositions until you arrived at some basic truths. Similarly, the world is composed of myriad complex facts that can be broken down again and again until you arrive at an atomic fact.

Here is Wittgentsein in brief: The world is made up of facts. We perceive facts through turning them into thoughts, which in essence means creating a mental picture of them. Thoughts are expressed in language in what Wittgenstein called propositions. He envisioned boiling language down to what he called atomic sentences, which would successfully, if not poetically, describe reality as we know it.

A Change of Heart
Because language is an expression of facts, it has no meaning. And a truly logical language would not be able to express subjective notions of Beauty and Love. Wittgenstein decided that the massive volume of the Tractatus had left him with nothing more to say on the subject of philosophy. He remained philosophically silent for ten years, only to come back with another major work that basically denounced his earlier theories.

What is meant by the term “postmodern” philosophy?

Postmodern philosophy is basically the state of philosophy today. It covers a wide range of thought, and most postmodernists would deny that they are part of such a movement. It is a convenient label for contemporary philosophy.
Logical analysis is an exact science, and language and physical reality are not so mathematically precise, Wittgenstein came to believe. He decided that his plan to devise the ultimate logical language was not only impossible but also a bad idea. For years, Wittgenstein wrote nothing–what was the point since it's meaningless anyway?–but his students took copious notes as the philosopher forged a new philosophy.

Eventually, Wittgenstein wrote Philosophical Investigations, in which he broadened his view of language to regard words not as the basis of propositions, but as tools that are designed to perform different tasks in communicating. He also came to see language as a game where its many players develop their own rules. Rather than create a logical (and inevitably sterile) language, Wittgenstein now began to celebrate linguistic diversity.

19donbuch1
Juin 30, 2012, 7:27 pm

According to Wittgenstein, philosophy generally is a "therapeutic activity" used to alleviate the cognitive dissonance that philosophers face when dealing with seemingly intractable problems. Yet I think philosophy is more than this as a foundation to build systems even though the foundation is built on a swamp--as Quine would likely admit. Russell learned a great deal from his "pupil," and although he likely left professional philosophy the first time because of Wittgenstein, Russell did not completely discard work that was criticized. For example, in his 1913 manuscript "Theory of Knowledge," he reworked parts of it after Wittgenstein's criticism to produce separate articles for later publication. (See Eames's Introduction to Volume 7, The Collected Papers of Bertrand Russell.

As a side note, the term "game" has such a negative connotation in this context that it should be clarified that language itself is more a competition to be understood rather than something akin to chess. Granted, Wittgenstein expressed the importance of knowing the rules behind various contexts of language, and thus language itself becomes an exchange of expressions based upon those rules. The rules can be flexible in some instances, which it seems leads to new meanings that cause the lexicon to develop in ways beyond wild imagination.

20Gail.C.Bull
Oct 4, 2012, 8:30 pm

>14 wildbill:, Wildbill Quote: "I did keep in mind as I read the book that Russell was an intellectual snob who valued his own opinion above all others."

This is ultimately why I can't stand reading Russell's work. He seems to believe himself so superior to others that he shouldn't have to explain the path of his reasoning. I tried to follow his train of thought through In Praise of Idleness and Other Essays and all of his arguments seems to follow the same rough shod reasoning: "I want this to be true, and you will just have to live with that."

Hardly well-written or well-reasoned philosophy.

21donbuch1
Nov 4, 2012, 8:53 am

Judging Russell by a single work is not advisable since one can lose the opportunity to gain rich insight from his more stimulating writings. In the rush to feed his extended family and to meet publisher deadlines, he churned out some unsubstantiated dross that can certainly be viewed as intellectually inferior. I would start with his Basic Writings for a greater appreciation of his clarity and ideas.

22Gail.C.Bull
Modifié : Nov 4, 2012, 3:13 pm

>21 donbuch1:: Thanks for the recommendation.

I have to admit, I am rather biased against the whole logical positivism school of philosophy. I took a university-level critical reasoning class that was taught entirely in that school, and it was the most bizarre class I've ever taken. Then entire curriculum was devoted to writing out logical formulae as if being able to scribble academic formulae was more important than being able to reason.

I believe that the logical positivists thought that if they made philosophy more mathematical, they would help philosophy remain relevant to a scientific world, but all it really did was to handicap the contribution philosophy as a whole has to make to society, and caused philosophy to seem less relevant. And if you need proof of just how faulty the concept of "common sense" is, consider this: manufacturers have found it necessary to print "warning: contents may be hot" on the side of disposable cups that are designed for the express purpose of holding hot drinks.

23donbuch1
Déc 10, 2012, 10:08 pm

The logical positivists, if anything, taught philosophers what not to do, or pointed out the cul-de-sacs that may lead to avenues not yet accessible, given the mental applications currently available. I agree that the analytic school was mathematically intoxicated, and failed the sobriety test of common sense. However, the scaffolding seems almost artistic in its process, while dull in other features of logical form.

24carusmm
Mai 19, 2016, 5:09 am

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