Kurt Gödel (1906 – 1978) was an Austrian, and later American, logician, mathematician, and philosopher. The notion of existence is one of the primitive concepts with which we must begin as given.
Quotations from Kurt Gödel
To every ω-consistent recursive class κ of formulae there correspond recursive class signs r, such that neither v Gen r nor Neg (v Gen r) belongs to Flg (κ) (where v is the free variable of r).
The more I think about language, the more it amazes me that people ever understand each other at all.
Ninety percent of [contemporary philosophers] see their principle task as that of beating religion out of men’s heads. … We are far from being able to provide scientific basis for the theological world view.
The meaning of world is the separation of wish and fact.
I don’t believe in empirical science. I only believe in a priori truth.
The formation in geological time of the human body by the laws of physics (or any other laws of similar nature), starting from a random distribution of elementary particles and the field is as unlikely as the separation of the atmosphere into its components. The complexity of the living things has to be present within the material [from which they are derived] or in the laws [governing their formation].
The illusion of the passage of time arises from the confusing of the given with the real. Passage of time arises because we think of occupying different realities. In fact, we occupy only different givens. There is only one reality.
There would be no danger of an atomic war if advances in history, the science of right and of state, philosophy, psychology, literature, art, etc. were as great as in physics. But instead of such progress, one is struck by significant regresses in many of the spiritual sciences.
What I call the theological worldview is the idea that the world and everything in it has meaning and reason, and in particular a good and indubitable meaning. It follows immediately that our worldly existence, since it has in itself at most a very dubious meaning, can only be means to the end of another existence. The idea that everything in the world has a meaning [reason] is an exact analogue of the principle that everything has a cause, on which rests all of science.
The notion of existence is one of the primitive concepts with which we must begin as given. It is the clearest concept we have.
In principle, we can know all of mathematics. It is given to us in its entirety and does not change. … That part of it of which we have a perfect view seems beautiful, suggesting harmony; that is that all the parts fit together although we see fragments of them only. … Mathematics is applied to the real world and has proved fruitful. This suggests that the mathematical parts and the empirical parts are in harmony and the real world is also beautiful.
Positivists decline to acknowledge any a priori knowledge. They wish to reduce everything to sense perceptions. Generally they contradict themselves in that they deny introspection as experience. … They use too narrow a notion of experience and introduce an arbitrary bound on what experience is ….
The brain is a computing machine connected with a spirit.
One bad effect of logical positivism is its claim of being intimately associated with mathematical logic. As a result, other philosophers tend to distance themselves from mathematical logic and therewith deprive themselves of the benefits of a precise way of thinking.
I don’t think the brain came in the Darwinian manner. In fact, it is disprovable. Simple mechanism can’t yield the brain. I think the basic elements of the universe are simple. Life force is a primitive element of the universe and it obeys certain laws of action. These laws are not simple, and they are not mechanical.
Philosophy as an exact theory should do for metaphysics as much as Newton did for 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
Philosophical thinking differs from thinking in general. It leaves out attention to objects but directs attention to inner experiences. (It is not so hard if one also directs attention to objects.) To develop the skill of introspection and correct thinking [is to learn] in the first place what you have to disregard. The ineffectiveness of natural thinking comes from being overwhelmed by an infinity of possibilities and facts. In order to go on, you have to know what to leave out; this is the essence of effective thinking.
To explain everything is impossible: not realizing this fact produces inhibition.
Without precision, one cannot do anything in philosophy.
Rules of right behavior are easier to find than the foundations of philosophy.
True philosophy is precise but not specialized.
Kurt Gödel – my philosophical viewpoint
- The world is rational.
- Human reason can, in principle, be developed more highly (through certain techniques).
- There are systematic methods for the solution of all problems.
- There are other worlds and rational beings of a different and higher kind.
- The world in which we live is not the only one in which we shall live or have lived.
- There is incomparably more knowable a priori than is currently known.
- The development of human thought since the Renaissance is thoroughly one-dimensional.
- Reason in mankind will be developed in every direction.
- Formal rights comprise a real science.
- Materialism is false.
- The higher beings are connected to the others by analogy, not by composition.
- Concepts have an objective existence.
- There is a scientific (exact) philosophy and theology, which deals with concepts of the highest abstractness; and this is also most highly fruitful for science.
- Religions are, for the most part, bad—but religion is not.
COMMENTS on the quotations of Kurt Gödel
Language is a diffuse method of communication; thus when an idea is stated with great clarity, the problems associated with the inherent diffuseness become vivid, but when ideas are stated in a confusing way, the problems remain invisible and potentially useful ideas remain unused.
Clear statements attract contradiction, but clear statements also attract clarification. Clear statements provide a path to better understanding. Clear statements provide the opportunity to restate the underlying idea in other words, and in the overlap of the collection of statements there may be a better idea than any statement previously made. Gödel said, To explain everything is impossible: not realizing this fact produces inhibition. Both parts of his statement are clear and thus useful but it doesn’t state the underlying reasons for the problem of inhibition and it doesn’t provide a method for moving forward. Of course people do quickly begin arguing with the statements other people make, but it is helpful to state clearly the process, and why it works.
On Gödel’s list of 14 philosophical viewpoints, it would appear they are simple unsupported assertions, and I or you could challenge every one of them because they are so overstated, but in our challenging them there is clarification and thus value to be had. The worrisome part for me is that he moves his assertions toward religion at the end of the list, and it is horrifying to think how some Dark Ages church scholars would have applied these ideas to the general populace. Clear ideas have the potential for terrible application; therefore there must be checks and balances as the Founding Fathers wrote into our Constitution. Unchecked power, even the power of abstract ideas, will interact with empowered humans’ application of that power and bring about unlimited human suffering.
As influential as Gödel was to mathematics, it must be remembered that he was a man, and a man with poor contact with ordinary human reality. The simple proof of that statement is his starving himself to death, because he wouldn’t eat anything unless it was prepared by his wife. Unfortunately, she was sick and in the hospital for several months. I would ask, why didn’t they take him to the hospital and put him in the same room with his wife so she could oversee the preparation of his food?
The world in which we live is not the only one in which we shall live or have lived. When Gödel made this statement the Drake Equation was available, and it seems reasonable that there is life beyond Earth, and yet an assertion doesn’t seem helpful. There isn’t much to be done with that assertion.
The assertion There is incomparably more knowable a priori than is currently known is more valuable because it encourages people to keep seeking for more basic knowledge, but it doesn’t give a general method for conducting the search, or any techniques. I have suggested, for example, observing examples of natural convergent-evolution and stating the underlying process, then find new methods for applying that idea.
I don’t think the brain came in the Darwinian manner. In fact, it is disprovable. Simple mechanism can’t yield the brain. The human brain and all of the other uniquely human attributes didn’t come about by simple Natural Selection, but by a more advanced form of selection I call Eveish Selection, which is a positive feedback selective system after rudimentary language is in place. Gödel would be right if the world came together by simple random crashing of atoms, but there are processes underlying the structure which permit evolutionary things to happen because of natural developments.
Even though absolute truth can never be stated absolutely; stating ideas precisely is the path forward approaching Truth.