Log in

19 August 2005 @ 12:48 pm
A terminal case of physics envy  
I have spent the last year (on & off) trying to work my mind around Wittgenstein's Tractatus Logico-Philosophicus. I have been drawn to this work because I disagree with it strongly, without being able to fully understand why or how to put that disagreement into words. Also, I have the deepest respect for what W attempts; that most audacious of all philosophical endeavors, to build a complete system from first principles.

I think I can begin to articulate my main problem with this work, at least in broad strokes. Wittgenstein's building block of simple objects forms the basis for the system in the Tractatus (2.021), and simple objects are appealing on many counts. Atomistic theory has a long history in natural philosophy. It answers the question of "what is this stuff made of?" Atomic theory in the modern sense was making leaping progress at the time Wittgenstein was writing the Tractatus. There was a feeling in the air that real, scientific understanding comes from breaking the thing being studied down into it's smallest constituent parts and examining those parts.

This form of reductionism was being applied by several eminent philosophers of the time to mathematical systems, including set theory and number theory. Wittgenstein's mentor Russell and his associate Whitehead were attempting to build a complete system of mathematics that was based only logic, and which eliminated all paradoxes. In order to exorcise the possibility a paradox being a well-formed statement in their system, Russell and Whitehead created a strict hierarchy, at the base of which were irreducible simples. Above that level there were sets of simples. Above that level were sets of lower-level sets, and so on. This rigid system prevented any set from being a member of itself, which kept out paradoxes like "the set of all sets that do not contain themselves."

Wittgenstein imported this clumsy apparatus from Russell & Whitehead's Principia Mathematica; from formal mathematical systems to subset of natural language that is philosophical discourse. He cannot give any worthwhile example of a simple object in even an idealized language, much less the actual language that we use to communicate. Their existence is simply a necessary aspect of his formal system, and he takes them for given. Simple objects combine to form states of affairs (2.01), facts consist of structures of states of affairs (2.03), thoughts are pictures of facts (3), propositions are well-formed projections of thoughts (3.13). This is an obvious isomorphism with the system of the Principia Mathematica.

Having imported this system into the domain of philosophy, Wittgenstein asserts that only well-formed propositions have sense, and it is impossible for propositions about most areas of philosophy to be well-formed. Propositions cannot express anything higher than the level below themselves, ie states of affairs. One cannot make a well formed proposition about the metaphysical subject (the self), about other propositions, about ethics or aesthetics (6.421). It is literally senseless to talk about anything which does not conform to the rules of the Tractatus, and that includes most of the enduring questions of philosophy. Therefore Wittgenstein has solved those enduring questions, by showing that they are the result of cloudy thinking. "What we cannot speak of we must pass over in silence" (7).

Now, before Godel arrives and proves that no system of mechanical reason (no formal axiomatic system like logic) is capable of representing all truths, there is still something extremely unsatisfying about Wittgenstein's conclusions. First, it is completely solipsistic (5.63). The entire system of the Tractatus is a lovely exploration of Wittgenstein's philosophical process, but he could have spent just as much time dissecting the process of eating a tomato and it would have conveyed largely the same information; information idiosyncratic to Wittgenstein's particular genius and experience, not a system that can be usefully embraced by others.

Second, Wittgenstein rejects the possibility of a priori reasoning (2.225), for in order for a proposition to make sense it must be composed of structures of states of affairs, which in turn are combinations of simple objects. Simple objects are strictly empirical phenomena (even though they completely evade direct observation), therefore a priori reasoning doesn't exist.

Wittgenstein's rejection of a priori reasoning goes to the core of my disagreement with him. It is logically consistent for him to discount a priori reasoning, because the whole apparatus that Wittgenstein imports from the Principia is designed to prevent self-referrential statements. The whole class of self referencing propositions is thrown out because there are more than a few of them that misbehave. Wittgenstein cuts off such intuitively true statements like "I think" because they don't refer to any simple objects.

My whole conception of humanity is built around an idea of reflexively self cognitive agents. In other words, people think about themselves and their thinking habits and modify their behaviors accordingly. Wittgenstein says that my conception of what it means to be human is meaningless, but he doesn't offer any replacement.

It would be remiss to talk about the problems with Wittgenstein's and Russell's systems without bringing up Godel's contribution, but I am not sufficiently versed in his mathematical reasoning to do it justice. The most significant aspect that I take from Godel (as it applies to W & Russell) is the realization that "provability is a weaker notion than truth" (Hoftstadter 19). There will always be things that are true which defy mechanical processes of reasoning, and these things may prove to be of some interest to philosophers, who are after all more intelligent and flexible than any axiomatic formal system.

To wrap this up, I think of early Wittgenstein as a brilliant and ambitious student who sees potential new applications in his advisor's work and expands that work into new realms. The Tractatus is a beautiful and challenging piece of philosophy, but it is based on a system that has been proven to be critically incomplete. Wittgenstein's most creative stroke in the Tractatus is recognizing that incompleteness and attempting to turn it into the great strength of his system.

(crossposted around)