'Luki'

I felt there was only one topic for my first post. By request: Wittgenstein.

My interest in philosophy began when I returned to Canada after spending a bit of time off and on living in England. I had heard of this thing called ‘philosophy’ that had ‘all questions and no answers’ and, cocky as I was, I thought ‘how is this possible? Let me at it and I’ll put these issues to bed.” Not knowing where to start, and worrying that a turgid slog through a random philosophical treatise might put me off (books had not really appealed to me much since I had got out of school), I went to the local library and began collecting all of the possible books in the ‘Great Philosophers’ series that I could find. Basically, these were pocketbooks of between 50 and 70 pages giving a quick summary of their major philosophical points. Since I was new to philosophy at the time, I had only heard a few names here and there, and of books I found with names I knew: Plato, Aristotle, Rousseau, I found it a bit difficult to get a good picture of just what was going on. I had not really done much critical thinking or testing of my understanding of the world at the time; it simply was what it was. Two philosophers in the series changed everything for me and put me on the path to having a genuine interest in philosophy and all that it deals with. One of those was Wittgenstein (the other was Schopenhauer, but more on that some other time).

Many historians and ‘Wittgensteinians’ refer to ‘Wittgenstein I’ and ‘Wittgenstein II’. Wittgenstein I was the man who had claimed to have ‘solved all philosophical problems’ in the Tractatus Logico-Philosophicus in which the final and most important point is

‘Whereof one cannot speak, thereof one must remain silent.’

The meaning of which was simply that for Wittgenstein (at that time), there was no such thing as a philosophical ‘problem’. What were actually being debated in philosophical circles were ‘puzzles’ that arose because our use of language and our attempts to understand each other’s meaning are imperfect. And so we disagree about things not because there are ‘realities’ to disagree about, but rather because we are not able to properly define terms and communicate ideas. It is only language and meaning that could properly be debated. After a hiatus that he spent teaching schoolchildren in the mountains somewhere in Scandinavia (if I remember correctly) Wittgenstein II then went back on this rather bold summary of philosophy, and wrote his ‘Philosophical Investigations’, which, in my opinion is both a brilliantly ‘playful’ and a brilliantly profound exploration of language (in contrast to the rigorous formality of the Tractatus). The Investigations is famous for, amongst other things, the ‘private language argument’ (he argued that one cannot have a ‘private’ language, that is, a language limited entirely to oneself).

If anyone reading this is interested, I recommend ‘Wittgenstein’s Poker’ for a brilliantly entertaining synopsis of Wittgenstein the man and Wittgenstein the philosopher based around a ‘legendary’ meeting (and the only one ever) between Wittgenstein and another very ‘self-assured’ (i.e. cocky) philosopher, Karl Popper.

At the time of reading this 60-odd-page intro to Wittgenstein, I knew none of this, and a lot of the finer details were lost on me. What struck me as so radical (and still does today) is that all of a sudden language went from a tool to communicate to a thing that can be analyzed in and of itself (and it is especially radical when it is presented in such a way as to lead one to believe it could possibly be a metaphysical basis of reality). I had never really had a reason to ponder over the fact that we call the white liquid that comes from cows ‘milk’ on no other pretense than that a bunch of people once upon a time agreed that it should be so (of course, etymology enters the picture, but one can apply the same argument to the etymological roots of any word). It is nothing more than custom that we use the term ‘milk’ as opposed to, say, ‘rabagooba’ to denote this item in English.

And this idea can be useful to try to make mathematics less intimidating. Of course, we usually take mathematics as the ‘everyday’ mathematics that is grounded in arithmetic and such, and this is entirely justified. We have utilized both language and mathematics for thousands of years, and it has only been within the past 150 years with Frege and Cantor that each of language and mathematics have been seen as an ‘item’ to be analyzed in and of itself. However, if one looks at mathematics itself, one sees that as opposed to all of the other ‘sciences’, which are based on understanding and interpreting reality to some extent, mathematics is a self-contained axiomatic system. Thus it is, in a sense, a ‘language’ as well (and therefore, from a certain point of view, it is entirely a ‘human invention’ not wholly grounded in reality), though one based on the rules of logic. Gödel’s Incompleteness Proof established that there is no such thing as a logical system that can prove itself. Basically, if one begins with different axioms, one can get an entirely different system of mathematics, so long as the axioms are not, in some way, self-contradictory. Hence, there is no ‘true’ mathematics, like one may say there is a ‘true’ chemistry, physics, or biology that accurately describes the secrets of Mother Nature, just like there is no objective reason why one should call milk ‘milk’ rather than ‘rabagooba’. The only difference is that the ‘rightness’ or ‘wrongness’ of mathematics is based on rules of logic in contrast to language, which is based on custom and the systematization of grammar. That is, in terms of mathematics as a ‘system’; the manner in which mathematics is actually applied and 'done' is based on custom. Once students understand that ‘x’ is simply a 'placeholder' and its use to designate an unknown is based entirely on custom (and ‘ease’, since mathematicians are lazy)—there is nothing to stop one designating said unknown by drawing a map of Indonesia, making a chicken noise, or dancing a jig—they stop making silly mistakes, like using x to designate different unknowns that are not equal. The main problem with the other three options is one’s ability to duplicate it when needed: dancing can get pretty tiring, and making a chicken noise? That's just stupid.

Gauss once called mathematics ‘the queen of the sciences’. I forget his justification for this statement, but I always think that maybe his intention was to say that mathematics is such that although it doesn’t rule, you cannot do anything without it. Maybe this is a somewhat sexist (and, along the same vein, overly ‘biological’) interpretation, but one must remember that it was said about 300 years ago, and the human race and its approach to gender equality and human rights has come a long way since. Supposedly.