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How I Got to Think About Knowledge…
What is knowledge? How do we learn stuff? Can we ever be absolutely certain that we know something? What are the limits of our understanding? How do we learn about ourselves and the world around us? Is science and rational thinking the most reliable path to knowledge? What about intuition? And what about introspection? What is the most effective path to self-knowledge and personal growth? And what does Kurt Gödel, mysticism and magic mushrooms got to do with it?
A few weeks ago I signed up to go to a couple of meetups which will be held later on this month in the city where I live, here in the UK. The title of the meetups is “What is Knowledge?” and the group is called Café Philo, short for Café Philosophique, which was originally founded in France, in 1992. Nowadays, there are 100’s of Café Philos around the world, gatherings of inquisitive minds, groups of individuals meeting in a pub or café discussing philosophical subjects for fun, to socialise and just meet like-minded people I guess. I am really excited cause I have never been to this kind of meetup before and I hope it’s going to be really interesting and rewarding. And… it will get me out of the house, in the evening, which is not easy to do, being a single mum and student, trying to juggle way too many things at the same time. So yeah, I am really excited, very much looking forward to that!
So… in preparation for my meetups, a few weeks ago, I started pondering about the subject, it got me thinking, and thinking, and thinking a little bit more… I read and re-read some bits here and there, from books to articles… I also watched some videos…. I actually even bought some new books…Such as this one! (Gödel, Escher, Bach: An Eternal Golden Braid), which I have wanted to read for such a long time; I have just received it on the post this week, but haven’t had a chance to get past the intro yet so… once I have read a few chapters, I am sure that it will provide food for thought for future videos!
After doing a little research and some thinking, I finally came up with a few ideas which…, me being me, I guess they are a little less conventional, as little bit more edgy than your average Epistemology Youtube video! So we will talk about knowledge, but with a rather unconventional spin on it! And of course, I would like to give credit where it’s due…. Cause a large portion of my inspiration for this particular video came from a few paragraphs in this rather obscure, unknown book, called “Bridging science and spirit” by Norman Friedman. I just love the book, so much food for thought…. And of course, lots of fascinating, fringe ideas in it… You will find all the links in the description box below the video.
And just a quick note to shat that this video will be split into three parts, which I’m going to upload to Youtube separately . Right now, you are watching part 1.
Introduction to Kurt Gödel – The Incompleteness Theorem:
Ok, let’s get started! I’ll begin with a little introduction to Kurt Gödel and his Incompleteness Theorem. I think this man was a genius and I feel it’s a shame that the general population does not know anything about him, because his ideas apply to all areas of life, not just mathematics, science, logic… or some abstract idea of human knowledge in general. In fact, I feel very strongly that the very core of Gödel’s ideas can be applied to everyday life itself, to personal growth, to our curiosity about the nature of reality, the nature of consciousness… they can be applied to our understanding of the personal limitations we encounter as human beings, every day, when we try to make sense of what is happening to us, of our behaviour, of our relationships, or the events happening in the world around us.
In 1931, at the tender age of 25, Austrian mathematician Kurt Gödel published a paper titled “The Incompleteness Theorem” with far-reaching philosophical implications, which apply to all formal systems of knowledge. I think that Gödel’s Theorem of incompleteness is unquestionably among the most important theorems ever formulated… So, without further ado, let’s get to the meat of it.
The theorem states that:
“Within any rigidly logical mathematical system there are propositions (or questions) that cannot be proved or disproved on the basis of the axioms within that system and, therefore, it is uncertain that the basic axioms of arithmetic will not give rise to contradictions.”
Now, this is actually a bit too technical for what I’ve got in mind right now for this video. So, let me re-phrase it as very simple statement, one which still encapsulates the essence of the theorem, while making it easier to understand from a non-mathematical perspective. Here it goes…
“Any system – anything which you can draw a circle around – cannot completely explain itself without referring to something else outside the circle it is surrounded with. This ‘something else’ outside the circle needs to be assumed, but cannot be proven. If the system tries to explain itself from within the confines of the circle, then contradictions or paradoxes may arise, which is an inevitable consequence of the self-referential nature of the system which is trying to explain itself”
Let’s focus on the importance of this for a moment… cause it is basically saying that any formal system of knowledge can only produce truth statements which are not provable within the confines of the system itself.
Think about what this really means. Well, among other things…. it means that mathematics can fail, it means that science cannot prove everything, it means that self-reference and paradox is an intrinsic and inevitable part of life, it means that we can only ever hope to gain partial understandings, it means that our knowledge will always be incomplete. It means that intuition and reason are both equally important. It means that there is no such thing as a closed system explaining itself. It means that there is no closure… It means that anything that is objectified, confined within boundaries, cannot satisfactorily understand itself without transcending these boundaries or at least make assumptions about what might be outside the boundaries. It means that the Universe needs to somehow transcend itself in order to fully understand itself.
It means that you can always draw a bigger circle and that… even then, you will still have to assume there is something else outside that bigger circle. It means that this drawing of bigger circles never ends, because the wider context of a bigger circle is subject to the incompleteness theorem as well, and again, it would need to be viewed from the perspective of a wider circle in order to be fully understood…. And this defines a seemingly infinite spectrum of circles, a spectrum of perspectives or levels in which each level includes and transcends the level below it.
It basically means that there is no completion, that there is no end to growth, understanding, and knowledge… As Terence McKenna said: “No program of formal analysis will ever completely exhaust its subject. There will always be a residuum of mystery!… and we need to come to terms with this!” I think this is so exciting… I mean, think about it… how boring would reality be otherwise!
Gödel’s theorem states that, beyond a certain level of complexity, there are intrinsic limits to the truths that can be established from within a given system. However, if we can somehow transcend the system, that is, view it from a wider perspective, or from the outside as it were, the original system’s statements can be provable; but then again, the new wider perspective can only establish half-baked truths, cause it is also subject to the same restrictions….
In this way, as human beings, we can only ever hope to gain a partial understanding of our Universe. At least from the perspective of science, currently we can only attempt to explain it from within.
We are not only connected to what we are measuring, but we are part of what we are measuring. From a wider perspective, I would say that what we are measuring is part of us. We inevitably find ourselves trapped in what is apparently true, in paradoxes within paradoxes. Certainty, proof and absolute knowledge are forever out of our grasp.
I love how beautifully Mark Arka expressed these same thoughts in a recent comment on Cracking the Nutshell’s FB page. He wrote…
“It seems to me that there is and always will be mystery at the edges of our knowledge and perception. We are encapsulated in a mystery within a riddle within a conundrum. That is the nature of the universe, for us humans at least… it is a myth… a story. Whichever form of enquiry you take, it seems you will eventually find the mystery, the unfathomable and unknowable. It is at this point that the universal story seems to be telling the inquirer to change his eyes, his vision, his way of thinking…”
Transcending Stuff to Know Stuff:
A really cool video by Carl Sagan has come to my mind now, where he explains the idea of Flatland, a 2-dimensional land designed and named by Edwin Abbott. In the video, you can see Carl Sagan using an apple, as a way to illustrate the impossibility of gaining complete knowledge of a 3-dimensional world from the limited perspective of a 2-dimentional being. I will put a link in the description box; it’s such a lovely video, a classic not to be missed…. For now, here is a lovely passage taken from Flatland, the actual book itself, which beautifully illustrates the idea of this 2-dimensional geometrical being suddenly finding itself transcending to a new sphere of existence, experiencing a 3-dimensional world for the first time, seeing Flatland from a perspective no other flat being had seen before, therefore gaining knowledge which was previously completely inaccessible to him. Here it goes…
“An unspeakable horror seized me. There was a darkness; then a dizzying sensation of sight that was not like seeing; I saw… Space that was not Space: I was myself, and not myself… I shrieked…, “Either this is madness or it is Hell.” “It is neither,” replied the voice of the sphere, “it is Knowledge; it is Three Dimensions: open your eye once again and try to look steadily.”
I looked, and, behold, a new world! “
~ Edwin A. Abbott, Flatland
It’s such a wonderful little passage, isn’t it? It illustrates wonderfully the idea of gaining new knowledge through transcendence.
Self-Knowledge and Transcendence:
Now… and this is where I am heading with the rest of this video, particularly in parts 2 and 3… Think of the idea of the self, the age-old question we all ask ourselves at some point or another. “Who am I?” Have you ever wondered… Could we be like Mr Square in Flatland…? Is it possible that we are actually a lot more than we thought we were? Is this physical reality all there is? Or is there another larger reality which includes it and transcends it – something analogous to Flatland’s mystical dimension called “Up” or “Down”? Something we can’t even fathom from our current limited perspective? What are we – who are we – from the perspective of a higher dimensional sphere of existence? And if there are higher dimensional spheres of existence… is it possible for us to gain knowledge about them?
Well, I say, why not start with self-knowledge… Think about it. How is it obtained? One can argue that subjective experience, self-exploration, is the most important tool; that it is at the root of it all! If you think about it, it is in fact the only tool we have to gain knowledge! The only way for us to attain new levels of understanding. And the reality is that, as Gödel very elegantly pointed out, we can only ever find partial truths, paradoxical understandings which we may be able to refine with self-growth, which is nothing but the continuous expansion of the idea of who we really are, an expansion of our identity, an expansion of the boundaries we surround ourselves with.
In other words, we need to learn how to transcend ourselves in order to gain a better understanding of ourselves. And this process of transcendence is a never ending process. The beauty of it is that it goes ad-infinitum. And don’t forget, our understanding of the self is intimately interconnected with our understanding of what we define as the outside world, that is, what we conceive as being outside ourselves, the not-Self. Where we draw the boundary between self and not-self will determine the type of knowledge we gain about ourselves and the Universe.
And of course, here is where mysticism comes in. I do feel that rational thinking is overrated, I think there are many valid paths to knowledge… All useful in some way or another, in our quest to find truth. Or shall we say partial truths… Which leads me to Wittgenstein. He had the idea that philosophy should not be about finding truth, but finding statements which are true enough. As Gödel pointed out, true enough is as close to the truth we can ever get, that is, if there is anything such as absolute truth. And this of course applies not only to philosophy, maths, or science, but most importantly, it applies to life, our experience, our desire to understand, our self-growth and our spiritual paths.
As physicist Paul Davies once said, while referring to the implications of Gödel’s theorem: "We are barred from ultimate knowledge, from ultimate explanation, by the very rules of reasoning that prompt us to seek such an explanation in the first place. If we wish to progress beyond, we have to embrace a different concept of 'understanding' from that of rational explanation. Possibly the mystical path is a way to such understanding. Maybe [mystical insights] provide the only route beyond the limits to which science and philosophy can take us, the only possible path to the Ultimate." (Paul Davies 1992).
Makes you think, doesn’t it ? So… what are mystical insights then?
To be continued…
Books that inspired me:
“Bridging Science and Spirit: Common Elements in David Bohm's Physics, the Perennial Philosophy and Seth”, by Norman Friedman:
“No Boundary : Eastern and Western Approaches to Personal Growth“, by Ken Wilber:
Other recommended books :
“Flatland : A Romance of Many Dimensions“, by Edwin A. Abbott:
“Gödel, Escher, Bach: An Eternal Golden Braid”, by Douglas R. Hofstadter:
Carl Sagan video from “Cosmos – Episode 10 : The Edge of Forever“: