Kurt Gödel – (April 28, 1906, Brno, Moravia, Austria–Hungary – January 14, 1978, Princeton, New Jersey, United States) was an Austrian logician, mathematician and philosopher. Later in his life he emigrated to the United States to escape the effects of World War II. One of the most significant logicians of all time, Gödel made an immense impact upon scientific and philosophical thinking in the 20th century, a time when many, such as Bertrand Russell, A. N. Whitehead and David Hilbert, were pioneering the use of logic and set theory to understand the foundations of mathematics.
Gödel is best known for his two incompleteness theorems, published in 1931 when he was 25 years of age, one year after finishing his doctorate at the University of Vienna. The more famous incompleteness theorem states that for any self-consistent recursive axiomatic system powerful enough to describe the arithmetic of the natural numbers (Peano arithmetic), there are true propositions about the naturals that cannot be proved from the axioms. To prove this theorem, Gödel developed a technique now known as Gödel numbering, which codes formal expressions as natural numbers.
Quotes by Kurt Gödel – (wiki)
Either mathematics is too big for the human mind or the human mind is more than a machine.
The notion of existence is one of the primitive concepts with which we must begin as given. It is the clearest concept we have.
The brain is a computing machine connected with a spirit.
Consciousness is connected with one unity. A machine is composed of parts.
The active intellect works on the passive intellect which somehow shadows what the former is doing and helps us as a medium.
Philosophy as an exact theory should do to physics as much as Newton did to physics. I think it is perfectly possible that the development of such a philosophical theory will take place within the next hundred years or even sooner.
Reason and understanding concern two levels of concept. Dialectics and feelings are involved in reason.
General philosophy is a conceptual study, for which method is all-important.
Don’t collect data. If you know everything about yourself, you know everything. There is no use burdening yourself with a lot of data. Once you understand yourself, you understand human nature and then the rest follows.
Intuition is not proof; it is the opposite of proof. We do not analyze intuition to see a proof but by intuition we see something without a proof.
To explain everything is impossible: not realizing this fact produces inhibition.
It is a mistake to argue rather than report. This is the same mistake the positivists make: to prove everything from nothing. A large part is not to prove but to call attention to certain immediately given but not provable facts. It is futile to try to prove what is given.
To be overcritical and reluctant to use what is given hampers success. To reach the highest degree of clarity and general philosophy, empirical concepts are also important.
Learn to act correctly: everybody has shortcomings, believes in something wrong, and live to carry out his mistakes.
Rules of right behavior are easier to find than the foundations of philosophy.
True philosophy is precise but not specialized.
By definition, wish is directed to being something. Love is wish directed to the being of something, and hate is wish directed to the nonbeing of something.
The meaning of the world is the separation of wish and fact. Wish is a force as applied to thinking beings, to realize something. A fulfilled wish is a union of wish and fact. The meaning of the whole world is the separation and the union of fact and wish.
The maximum principle for the fulfilling of wishes guides the building up of the world by requiring that it be the best possible.
When an extremely improbable situation arises, we are entitled to draw large conclusions from it.
Time is no specific character of being… I do not believe in the objectivity of time. The concept of Now never occurs in science itself…
Quotes about Gödel – (by Rudy Rucker)
Despite his vast knowledge, he still could discuss ideas with the zest and openness of a young man. If I happened to say something particularly stupid or naive, his response was not mockery, but rather an amused astonishment that anyone could think such a thing.
Gödel’s certainly impressed me as a man who had freed himself from the mundane struggle. I visited him in the Institute office three times in 1972, and if there is one single thing I remember most, it is his laughter. … The conversation and laughter of Gödel were almost hypnotic. Listening to him I would be filled with the feeling of perfect understanding. He, for his part, was able to follow any of my chains of reasoning to its end almost as soon as I had begun it. What with his strangely informative laughter and his practically instantaneous grasp of what I was saying, a conversation with Gödel was very much like direct telepathic communication.
The last time I spoke with Kurt Gödel was on the telephone, in March 1977. I had been studying the problem of whether machines can think, and I had become interested in the distinction between a system’s behavior and the underlying mind or consciousness, if any.
… I had begun to think that consciousness is really nothing more than simple existence. By way of leading up to this, I asked Gödel if he believed there is a single Mind behind all the various appearances and activities of the world.
He replied that, yes, the Mind is the thing that is structured, but that the Mind exists independently of its individual properties.
I then asked if he believed that the Mind is everywhere, as opposed to being localized in the brains of people.
Gödel replied, “Of course. This is the basic mystic teaching.”