I was just sitting in my studio reading Gödel’s Theorem: an incomplete guide to its uses and abuses,
which I stumbled upon in a used bookstore recently,
I have over a dozen books about Gödel: How do I know when I understand this?
How much more do I have to read to understand Gödel? His work?
To understand Incompleteness? Their History?
To appreciate their consequences?
How deep do I go?
Should I be able to teach a class about this subject matter? … Or,
just feel comfortable explaining the bare essentials
to another person over a coffee?
What is gained by either?
What about different frameworks of analysis? Do I understand Gödel and his work through the framework of pure mathematics?
What about a historical framework or is it more important to see this breakthrough in Logic as a sociological phenomenon
that has crafted our knowledge and advancement ever since?
How about through the Philosophy of Mind or
Philosophy of Logic? Or, something else? Is there any way to understand the Incompleteness Theorems without a framework …
At what point can I say: “this is knowledge that I have and I can communicate it to you …”
And: Why can’t I just take all of this for granted
and finish reading the book,
write my sentences,
speak my words,
walk my walk and move on to something else? Ay, there’s the rub:
This ungraspable unknowingness – both in the sense that a sufficiently complex formal system is never both complete and consistent, as Gödel has shown, and in the sense that I find it difficult to know when I know fully, whether it is what Gödel was doing with his mathematics or his life and the relationship between the two, or another subject matter entirely – is similar to the tension that drove me into my art process and what I have always moved towards and sought to understand with my artistic research. This has been the case for a long time if not since before I knew artist was a career choice. I, also, have struggled with whether I am guilty of misinterpreting not only Gödel’s work, but any reference material I’ve used.
This may sound strange coming from a contemporary artist, given that the theoretical dominance in contemporary art is to combine and combine again … and to not worry about it … because, in fact, that’s the point. It is to recombine systems and representations, reassociate them and reappropriate more and more and more – all for new uses and new meanings, which is, as the thinking goes, the only way something new can come about anyway. OK: so, I suspect my motivation is entirely different than what is mostly happening around me – so be it. I am still fascinated with Gödel and driven to discover my own work: whether I continue to link them or am able to be consistent in my explanation and use of both/either is another issue.
Around the time I called myself an artist and when wondering deeply and continually about these questions seemed circular, I eventually wandered outside and started to break stones… and have been doing so for quite a while, using it as an art form. With learning about Gödel, I am able to say that I am intrigued by what we call Incompleteness and Inconsistency and that these are strong currents in my artistic motivation.
Rebecca Goldstein said it best:
(Kurt Gödel’s incompleteness theorems) are at once mathematical and metamathematical. They have all the rigor of something that is a priori proved, and yet they establish a metaconclusion. It is as if someone has painted a picture that manages to answer the basic questions of aesthetics; a landscape or portrait that represents the general nature of beauty and perhaps even explains why it moves us the way it does.
– Incompleteness, Goldstein, p. 28
Without realizing it as I transitioned into practicing my art and stating as such (almost 20 years ago), I wanted to “paint” that picture, or rather “sculpt” that sculpture – not to understand aesthetics, but rather the creative pulse, the thought instinct, the neurological throbbing. I wanted to capture this self-referential tension: understand it; know it; use it or maybe, just, be free from it. There is tension in the possibility of performing/claiming your own action – in that, by definition, it is contingent on nothing else but you and you alone – in asserting your own agency. There is tension in the enormity of knowing all the contingencies that make you what you are at this moment – in claiming your own history, owning your context and seeing their consequences – in that claiming such a terminal may be hubris (or strategem) because the line of causality just continues. And, there is tension in devising strategies to deal with all this and, even, a tension in relying upon strategies that you simply use because of education or evolution: is the strategy ultimately yours and fully accountable to you and complete? Or, is it better to ask: helpful, workable, viable? What is the bias within the strategy – How does it limit perception, and harness and, thereby, determine process? Furthermore: How do you know you are not being used by another strategy in devising your own?
I’ve been propelled into art by this desire to understand metathinking. Finding Gödel’s Theorem: an incomplete guide to its uses and abuses was a welcome reminder of this. I’ve discovered many pitfalls, run into some big blocking patterns and tripped over more than a few intellectual coppices as I’ve investigated this tension within Incompleteness, Inconsistency, Paradox, Strategy and Art and Knowledge. I’ve shown some of this in my art. There is more …
to be continued …