Russell’s Logic and an Invitation to Tea

It was with a steadily increasing nervousness that I followed the porter’s directions and approached my teatime appointment with the Head of Philosophy. Right from the start I had been anxious, from the moment the invitation had arrived, and now, on the final approach, the grand elegance of the sweeping nineteenth-century staircase and the carpeted hush of the oak-panelled hallways of the School of Philosophy were not making things better.

When first I had written to the professor, a brief note from a layman tentatively making an objection to Bertrand Russell’s symbolic logic, viz. that it is not an improvement on natural language but altogether a waste of time, I had not been confident of a reply, and was mightily surprised to receive an invitation to tea.

I very nearly turned it down. At the time I had read exactly one book on philosophy, a general biography of Bertrand Russell that included some discussion of his ideas, besides the half-read book to which I was now objecting, an introduction to his ‘symbolic logic’ plucked on a whim from a library bookshelf. I had found the details impossible to follow and ended up skipping most of them but from a rough understanding of what Russell was trying to do I concluded that in philosophy his idea would be useless. The details did not seem important.

My conclusion seemed unavoidable but it left me puzzled. I was not confident of having any right to an opinion. Despite my general ignorance I did at least know that Russell was a widely respected philosopher and sometimes cited as one of England’s finest. Accordingly, I had to assume that there was an error somewhere in my calculations. But where? My objections to his project could hardly have been more simple or obvious. I decided to ask a professional where I was going wrong. Not knowing any, I posted my thoughts to the Head of Philosophy at my nearest university for comment, assuming that it would be passed on to a student.

My letter had not explained that I knew nothing about philosophy, could not even define it, nor about mathematics, and had almost no understanding of formal logic, having only just learnt what ‘formal’ meant. Rather, I had tried to disguise these facts. Now my ignorance was about to become perfectly obvious. Once the professor had explained my idiotic misunderstanding of Russell what on earth would we talk about?

Regrettably I have forgotten the name of the professor who kindly put aside the time to talk to me. I owe him a lot for his trouble. He explained that my view of Russell’s logical system was widely shared and that his ideas were more taught than used. I remember feeling relieved not have made a fool of myself, but also a genuine sense of surprise. My library book had made no mention of this. Rather, it had expressed unqualified support for Russell’s idea that translating natural language arguments into formal systems of well-defined arbitrary symbols and then manipulating these symbols rather than the words of the original language would allow us to solve problems that would otherwise defeat us. Yet it seems pretty obvious that we cannot take more out than we put in.

I have since learnt that my surprise was naïve. Where philosophers make mistakes it is usually right at the start, before things get complicated, or right at the end, where they become simple again. These beginnings and endings are usually accessible to the layman even where a theory is too technical to understand in any detail. These are the places most vulnerable to the critical and innocent questioning of the interested amateur or bright child, the points of leverage where even the most complicated theories may be defeated by a simple objection. We would not need to know much about philosophy to conclude that an intractable problem stated in English cannot be solved by translating it into hieroglyphics. Later I was to learn that a similar kind of mistake was to scupper Russell’s ten year attempt to axiomatise set-theory.

It seems entirely plausible that thinking about a problem in a different language may allow a solution where the original language did not. We may be forced to think about it differently. But we will not be forced to think about a problem differently if we merely translate it rigorously from one language to another. The ancient language of Sanskrit is said to be the best of all for expressing the most profound truths about the world since it is structured in such a way as to allow their clearest expression. If it is better than English in this regard, however, then this could only be because it would be impossible to translate directly back and forth between English and Sanskrit.

The main lesson I learnt over tea and buns that day was that in philosophy the importance of an issue may be quite unrelated to its complexity. Later I modified this view and concluded that there is a correlation and it is inversely proportional.

I did not acquire a complete mistrust of academic philosophy from this teatime incident. This took many years and a lot more reading. But there was the beginning of a doubt. My host had opened the conversation by casually agreeing with the simple arguments made in my letter, and I was genuinely taken aback. Up until this this point I had assumed that philosophers like Russell could be trusted to think straight on the basic issues, or at least more reliably than me, even if there might come a point where the growing complexity of the issues overwhelmed their intellect. I came away from this conversation with a strong suspicion that that this is not the case. Rather, they seem to think straight on the details that overwhelm my intellect while finding the simple issues beneath their dignity. At first this view was confined to Russell’s philosophy, but as I began to read more widely it became a fairly general conclusion. These days I even suspect that this is the reason why the complex details arise in the first place.

There is a sequel to this story involving a conversation with the remarkable George Spencer Brown, who for a while was a colleague of Russell and who solved his famous philosophical and mathematical paradox in the 1960’s in a book called Laws of Form, and who is still the most terrifying person I have ever had a conversation with, but that will have to be episode two.

Episode II – https://theworldknot.wordpress.com/2013/12/06/the-logic-of-spencer-brown-and-an-unlikely-phone-call/

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7 Responses to Russell’s Logic and an Invitation to Tea

  1. While I agree that simply translating terms is no guarantee of a solution, I think the power of a more rigorous system is that translating into it requires that one clarify terms and be precise, while language allows a fair amount of ambiguity. In short, the translation process forces one to think more clearly and precisely about the problems.

    Of course that could simply shift the problem to an endless debate about the meanings of the terms 🙂

    • guymax says:

      Yes, a fair point, but I don’t think it changes anything. .I didn’t discuss it because it seems to me that in order to translate a term we would have to clarify it, and once we have clarified it the translation becomes unnecessary. If we cannot clarify it then we cannot translate it, and if we can clarify it then we don’t need to translate it. So either way the translation does not help. The translation may help us communicate a problem more clearly (or not – sometime the ambiguity of natural language is useful) but it isn’t going to make it any easier to solve.

      • Fair enough, but two things come to mind.

        First, the need for clarity may only become apparent upon an attempt at translation. Yes, in theory we can be specific about our terms in natural language, but it’s easy to miss the ambiguities until we try moving to another system. Natural language hides as well as reveals.

        Second, after translation, using a suitable notation may make the relations among the terms clearer and thus reveal patterns that were not apparent with language. To appreciate this, try solving even a moderately complex equation in plain English. I think very few would argue that mathematical notation (including the Hindu/Arabic numerals we use) had a huge impact on the mathematical developments that followed. Wouldn’t this notational boost possibly help?

  2. guymax says:

    I agree with your first paragraph, and the second as well up to a point. I’d hate to have to score a game of darts in natural language, so I think I can agree with you wherever we have to deal with large numbers of easily quantifiable quantities. But philosophical problems are not like this. If they could be translated into a mathematical language they wouldn’t become any easier to solve. On the other hand, it has just occurred to me that a technical language may be a lot less emotive than natural language, and that this might lead to a more dispassionate approach to the issues. Score one for Russell.

    I admire George Spencer Brown for solving Russell’s mathematics and creating a calculus capable of modelling the emergence of form from formlessness, thereby showing that the use of a mathematical language can be useful in philosophy, allowing us to look at a problem from a different angle. But his system of symbols could hardly be more simple, for the problem it models is difficult but not complex, and his translation does not make the solution any more or less difficult to understand,.

    Perhaps my complaint is not against the idea of translating to a mathematical language when it’s convenient and helpful, but the idea that this would require any more than a few integers and couple of rules. .

  3. Pingback: The Logic of Spencer Brown and an Unlikely Phone Call | The World Knot

  4. jabowery says:

    You wrote: “He explained that my view of Russell’s logical system was widely shared and that his ideas were more taught than used. I remember feeling relieved not have made a fool of myself, but also a genuine sense of surprise.”

    For insight into how far The Theory of Types has been taken by modern computer scientists and mathematicians, see:

    http://www.math.lmu.de/~ptc14/Palmgren.pdf

    It’s really quite disturbing to that Russell claimed Laws of Form obviates The Theory of Types, yet over the intervening decades, what has happened is that The Theory of Types has been taken from what was once thought to be a dead end in mathematical logic, and expanded to be the primary focus of computer-aided mathematics!

    • PeterJ says:

      Hi jabowery. Good to meet someone interested in these things.

      It was R’s symbolic logic rather than his Theory of Types about which the professor was speaking. I’m sure your right about the usefulness of this theory or method but Brown showed that it it is not necessary in metaphysics. On whether he showed it is not necessary on set-theory I can only rely on Russell himself, not being a mathematician. Such a theory is bound to be useful in a binary system, probably necessary, but Brown shows that we have to go beyond such systems for a fundamental approach to metaphysics.and mathematics, beyond the forms and distinctions on which they rely.

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