Rationality Part 2- A Leap of Faith

The previous dialogue highlights the limitations of rationality. It focuses on its most basic part- logic. The Tortoise twists a simple logical sequence of a geometric proof into a nightmare that has no end and is composed of an infinite amount of steps. How does he do it? He forces Achilles to use logic to prove and justify the use of it. I would like to explain further what this means.

Systems and Boundaries

When I was a young child I would force my grandmother to make awards for me. Awards saying that I was “the strongest”, “the bravest”, “the smartest" and etc... A few years ago we remembered the awards she used to give me and laughed. My grandmother even joked that now she wants to give me an award saying that the awards I received were the most well deserved awards she had ever given anybody. But wait a second! How do I know that the last award is legitimate? My grandmother better convince me that this last award she is giving me is true. Maybe she should give me another award to reeaally convince me. But even after a million more awards I will still remain unconvinced. That is because every system has a boundary. If the system that we are talking about is awards than the last award that she gives me (which is about the previous award which is about the previous award etc…) is something that I simply must accept with no reason. If she were to give me a reason totally independent of the awards I would still be forced to accept this new reason without a reason. The same is true for rationality. It too, will always have its boundaries and assumptions that are not explained for (rational).
This is exactly what is going on in the dialogue. I got this idea (and the dialogue) from the book Gödel Escher Bach, written by Douglas Hofstadter. He explains:

“The dialogue shows the difficulty of trying to use logic and reasoning to defend themselves. At some point you reach rock and bottom and there is no defense except loudly shouting, “I know I’m right!” You can’t go on defending your patterns of reasoning forever. There comes a point where faith takes over.
A system of reasoning can be compared to an egg. An egg has a shell which protects its insides. If you want to ship an egg somewhere, though, you don’t rely on the shell. You pack the egg in some sort of container, chosen according to how rough you expect the egg’s voyage to be. To be extra careful, you may put the egg inside several nested boxes. However, no matter how many layers of boxes you can pack your egg in, you can imagine some cataclysm which could break the egg. But that doesn’t mean that you’ll never risk transporting your egg. Similarly, one can never give an ultimate, absolute proof that a proof in some system is correct. Of course, one can give a proof of a proof, or a proof of a proof of a proof- but the validity of the outermost system always remains an unproven assumption, accepted on faith” (Hofstadter 193.)

Rationality As A Leap of Faith

I have found that the best way for thinking about this idea is to imagine a two dimensional plane in which the only tool that lets me get from point a to point b is rationality. So I begin thinking and I try to make my first step forward. But just when I start moving forwards I feel that I begin to sink. After all, any possible argument or statement that I could make must be built on an assumption. This level is lower because it is the assumption that structurally supports the step I am trying to make. An idea can be only be true if the ideas that it is premised on are also true. When I continue to try and make another step forward once again I feel myself sinking even deeper. And so I continue to think about point a and whether the ideas that lead from point a to point b make sense. But I never get anywhere and always continue to sink infinitely deeper because there will always remain some assumption or belief that underlies my whole investigation, and that I have yet to consider.

The only way to get anywhere is to jump. Intuitively, we think of rational thinking as a continuous path on our path from point a to point b. Every step makes sense. However this is not the case. The path of rationality is a path of small jumps, or as I like to call it, a path of tiny leaps of faith.
As the idea shows, rationality is not enough. It will not not be sufficient for you to be able to attain the truth. You will also need to make small jumps and accept certain premises based on "what makes sense", a standard that by definition cannot be coded for rationally.

For me, this is a very powerful idea and I have yet to grasp all of its implications. For even if it does not make much of a difference in our daily lives it in poetic terms, does to the world of thinking as quantum mechanics did to the physical. One idea that emerged in quantum mechanics was that time is not a flowing experience but rather is composed of tiny distinct jumps. It turns out that rationality is the same way.

Further Implications
There is one area that I think this idea plays a huge role and that is the proof of Har Sinai. In fact, as far as I can understand, the argument for Har Sinai can only be understood if this concept of rationality is accepted.
Stay Tuned!

Bibliography
Hofstadter, Douglas. Godel Escher Bach. New York: Basic Books Inc, 1979.