Jonathon D. Jones
Where Russell Went Wrong
In this paper I will show various inaccuracies in Bertrand Russell’s introduction to Ludwig Wittgenstein’s Tractatus Logico-Philosophicus. The introduction is not completely wrong, and indeed even helps to elucidate some of Wittgenstein’s more confusing logical symbolism. However, on points where Wittgenstein ventures too far away from Russell’s own ideas, difficulties arise, and it is upon these that I will focus.
The first mistake Russell makes is also one of his biggest. He writes on page ix of the introduction, “In the part of his theory which deals with Symbolism he is concerned with conditions which would have to be fulfilled by a logically perfect language.” Some passages do, indeed, sound as if Wittgenstein is interested in creating a “logically perfect language”. For instance, 3.325 states, “In order to avoid such errors we must make use of a sign-language that excludes them by not using the same sign for different symbols and by not using in a superficially similar way signs that have different modes of signification: that is to say, a sign-language that is governed by logical grammar – by logical syntax.” He notes that “the conceptual notation of Frege and Russell” (3.325) is the type of sign-language to which he refers. What he is pointing out, however, seems to have more to do with problems in our own language than conditions for a “logically perfect language”. In fact, the rules he points out seem to be applicable to any language, not just some mystical perfect language. For instance, in 3.343 he writes, “Definitions are rules for translating from one language to another. Any correct sign-language must be translatable into any other in accordance with such rules: it is this that they all have in common.” Here, he’s not making a new rule for a perfect language – he’s saying that if a language doesn’t translate, it isn’t a language. German can translate to English, but a dog’s bark cannot. Therefore German is a language and barking is not.
The point is, then, that Wittgenstein is concerned with showing the limits of language and of logic, not with creating a new, “logically perfect language”. Russell thinks that he is because Rusell is concerned with creating such a language. He assumes that Wittgenstein is continuing his work in that area.
The second thing that Russell misconstrues is Wittgenstein’s ideas about philosophy. Russell writes, “The best that we can hope to achieve by philosophical discussion is to lead people to see that philosophical discussion is a mistake” (ix). This isn’t Wittgenstein’s true view, however. Philosophy isn’t just one big mistake. He writes in 4.112, “Without philosophy thoughts are, as it were, cloudy and indistinct: its task is to make them clear and to give them sharp boundaries”. He seems to think that philosophy has a bit more work to do than simply showing people that “philosophical discussion is a mistake.” Instead, he seems to delegate to philosophy the important task of delineating the boundaries of language, of showing what cannot be said. The only way Russell could really defend his analysis is to define “philosophical discussion” as “things that cannot be said, but only shown”. But of course, this is a silly view to take – not everything that is nonsense is philosophy. For instance, “time stepped upon the negative square root of yellow and proceeded across infinity” is not philosophy, but is clearly nonsense. Wittgenstein believes that philosophical discussion would show that phrases such as mine above are nonsense and say nothing. Russell’s analysis either assumes my phrase is part of “philosophical discussion”, or denies that philosophical discussion would show us that it is meaningless, both of which are hard to assert and, at the very least, are not supported by Wittgenstein. Thus, I think he misconstrues Wittgenstein’s point.
Russell probably makes the analysis he does because of his own view of philosophy. For Russell, philosophy should be more like science, and any discussion outside of the scientific realm is essentially a waste of time, or at least meaningless. I think, then, that Russell probably saw Wittgenstein as supporting his assertion that non-scientific philosophical discussion was a mistake.
Russell is also critical of a number of things that Wittgenstein proposes. On page xxiii he writes, “There are some respects, in which, as it seems to me, Mr. Wittgenstein’s theory stands in need of greater technical development. This applies in particular to his theory of numbers (6.02) which, as it stands, is only capable of dealing with finite numbers. No logic can be considered adequate until it has been shown to be capable of dealing with transfinite numbers. I do not think there is anything in Mr. Wittgenstein’s system to make it impossible for him to fill this lacuna.” In other words, because the theory cannot account for things like infinity, it is weak. Wittgenstein would not see this as a weakness in his theory of numbers, however. Two quotes from him can help to show this. 4.1272 says, “…It is nonsensical to speak of the total number of objects…” 4.116 says, “Everything that can be thought at all can be thought clearly. Everything that can be put into words can be put clearly.” The “total number of objects” seems to be a lot like infinity. Infinity would actually go beyond this total, having no limit. If speaking of a smaller number of things, like the total number of objects, is nonsensical, it seems like speaking of an infinite amount of things would be at least as nonsensical.
The second quote is even more relevant. It reflects his view that anything that we can say, we can think, and we can say and think it clearly. Infinity, however, doesn’t seem to be the least bit clear. It doesn’t have any relevance to the world, and cannot be imagined. It is a mathematical fiction, as are all “transfinite” numbers – there is not an infinite amount of anything. As such, it seems to be precisely the type of thing that he would not want us to speak about. If we cannot imagine it, if we cannot think it, how could we possibly say anything about it? Wittgenstein would say that we can’t. Thus, he would see his theory of numbers as being perfectly fine without allowing for any “transfinite” numbers.
On page xxiii, Russell points out the seeming contradiction in the fact that Wittgenstein even wrote the book, saying “Mr. Wittgenstein manages to say a good deal about what cannot be said, thus suggesting to the skeptical reader that possibly there may be some loophole through a hierarchy of languages, or by some other exit…His defense would be that what he calls the mystical can be shown, although it cannot be said.” I’m not sure Wittgenstein would actually respond as Russell pretends he would. In 6.54, Wittgenstein writes, “My propositions serve as elucidations in the following way: anyone who understands me eventually recognizes them as nonsensical, when he has used them – as steps – to climb up beyond them. (He must, so to speak, throw away the ladder after he has climbed up it.) He must transcend these propositions, and then he will see the world aright.” In other words, Wittgenstein recognizes that his own work is nonsense, but it is meaningful nonsense, in that it can help to guide the reader in such a way as to come to understand what he cannot say. Russell’s explanation of his defense makes it sound more like a cop-out.
The final concern I had with Russell’s introduction is an objection he makes on xxiv, writing, “These difficulties suggest to my mind some such possibility as this: that every language has, as Mr. Wittgenstein says, a structure concerning which, in the language, nothing can be said, but that there may be another language dealing with the structure of the first language, and having itself a new structure, and that to this hierarchy of languages there may be no limit. Mr. Wittgenstein would of course reply that his whole theory is applicable unchanged to the totality of languages. The only retort would be to deny that there is any such totality.” Russell seems to be saying the following: that if there were some meta-language that dealt with our language, Wittgenstein would believe his theory to apply. In fact, even if there were a meta-meta-meta-meta language, Wittgenstein would still believe his theory to apply, and so on for the “totality of languages”. Russell believes a possible retort is that there is no totality, presumably that for any language there would be a meta-language to describe it. His objection seems to be, then, that if there is some sort of infinite amount of meta-languages, Wittgenstein’s theory might prove false.
This objection doesn’t work, however, for the simple reason that it doesn’t matter how many languages there are, let alone if there is an infinite amount of them (which is nonsense anyway). Wittgenstein’s theory applies to any language, because without the rules as he lays out, it wouldn’t be a language. The following analogy might help: suppose my theory is that the following applies to anything we might call an apple: that it is a fruit. If someone came along and said “ah ha, but what about this! This is a vegetable apple. Therefore your theory is wrong” I would calmly reply, “No, it isn’t. For part of the definition of apple is that it is a fruit, and that is precisely what my theory asserts.” That is, anything not a fruit is not a vegetable, and all my theory would be doing would be to assert that fact.
Wittgenstein’s theory is similar. His theory is such that, were a supposed “language” to not follow his rules, it would not be, in fact, a language. It doesn’t matter how many meta-languages are examined, we would know before examining that they follow his theory because otherwise they cannot be languages. This is hard to explain precisely because such discussion is attempting to say what can only be shown.
These things are what I feel Russell misunderstood. The mistakes seem mostly to be a function of the fact that some of Wittgenstein’s theories differ from Russell’s own, and that Russell seemed not to understand that. Russell’s objections to the Tractatus I have shown to be without merit. The rest of the introduction I leave to the reader.