Do you understand?

(There is an earlier dutch version of this post)

What are the results of your math homework?” the teacher asked my grandson. He showed his sheet with the results. “How did you solve them?” “I don’t know, sir,” he replied. The man frowned. They were all perfect, but how did the boy reach the results? “Explain me how you calculated them”. “Well, just”, said my grandson. “I looked at the problem and then wrote down the result“. The teacher was dissatisfied. He had explained a method for solving the exercises and wanted his pupils to use it. “If you can’t explain to me how you arrived at the results, you haven’t understood. Do you understand?” “No sir, I just understood what the answers should be.”

Is it possible to express understanding in words? Can we explain something in such a way that someone else will understand it? The teacher thinks so. My grandson should be able to understand what he had explained. And he expects him to be able to reproduce it, or at least to phrase in words what he has understood himself. From the concept, a truth or a reality penetrates our consciousness. But is that always easy to put into words? Or is it possible that words fail us, but that we understood anyway. Phrases like: “How will I explain that to you?” we may hear every now and then and these indicate the latter.

What language can do, what language is, how language is constructed are subjects that philosophers have often studied. Their detailed explanations and discussions already indicate that this is not a simple matter. How can we understand each other otherwise than through language?

I read a book [1] about the insights of Wittgenstein (1989-1951). It discusses the famous Tractatus Logico-Philosophicus, [2] written in his early years, and his insights in his middle age and beyond. In between was a period in which he had apparently retired from philosophy and worked as a school teacher. The book‘s author, Grayling, clearly believes that Wittgenstein’s influence on philosophy is much less than his fame would suggest. He clearly explains how the Tractatus and the post-Tractatus work differ essentially. Wittgenstein himself has also clearly distanced himself from his own early work. It dawned on me how the reality-language problem was approached from completely different worldviews in these two periods.

Wittgenstein was strongly influenced by the philosopher/mathematician Bertrand Russell who wrote a basic work on the foundations of mathematics [3], strongly based on set theory and logic. The tight schedule of propositions and rules introduced by Russell appealed to Wittgenstein. Mathematics itself does not describe reality, but can be used as a picture of it. By inverting the image after applying the rules, truths can then be found from the observations.

In the Tractatus, a far-reaching attempt is made to consider language in a similar way as a picture of reality given as “facts” and a “state of affairs”, through propositions of rules resulting in a verbalized picture of a conclusion.

In this approach, language relates to a reality outside itself. Just as mathematics is not part of the phenomena being described, language is outside the world being depicted. This is thereby a dualistic approach. Reality is described from the outside. The origin and change of language in that reality is not taken into account. One of the consequences is that the observed and described reality is mainly one of objects, their names and their properties. People and their inner life are much more difficult to grasp in this way.

Wittgenstein ends the Tractatus with the now famous statement: “Whereof one cannot speak, thereof one must be silent.”. This indicates that things can live in man for which no words can be found. This ties in with the above experience that we can understand something that cannot be phrased in words. Our understanding is broader than language. After a period of silence during which he worked, among other things, as a village schoolteacher, Wittgenstein went to Cambridge where he worked with Russell. Eventually he became a professor. In his lectures he rejected much of what he had previously written. He came to the insight that language and understanding coincide only partially. Sometimes thinking is indescribable. The language is sometimes incomprehensible and can only be logically analyzed under strict conditions.

This has been discussed in detail by Georg Kühlewind in “Der Sprechende Mensch” [4]. He explicitly mentions the stages of thoughts and ideas before we can find and speak the words.

  1. Grayling, Anthony C. Wittgenstein: A very short introduction. OUP Oxford, 2001.
  2. Wittgenstein, Ludwig. Tractatus logico-philosophicus (trans. Pears and McGuinness), 1961.
  3. Whitehead, Alfred North, and Bertrand Russell. Principia mathematica to* 56. Vol. 2. Cambridge University Press, 1997.
  4. Kühlewind, Georg, Der Sprechende mensch, Klostermann, 1991.
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