From: oz.start.the.riot!
Date: 2005-12-17 上午6:36
Subject: Fw: daily quote<2005-12-17>
To: bornvagabond.*******@spaces.msn.com
To develop the skill of correct thinking is in the first place to learn what you have to disregard. In order to go on, you have to know what to leave out: this is the essence of effective thinking.
Godel, 15 March 1972
In presenting these conversations, you should pay attention to three principles:(1) deal only with certain points; (2) separate out the important and the new; and (3) pay attention to connections
Godel, 5 February 1976
The possible worldviews [can be divided] into two groups [conceptions]: skepticism, materialism and positivism stand on one [the left] side; spiritualism,idealism and theology on the other [the right ]. The truth lies in the middle,or consists in a combination of these two conceptions.
Godel, ca. 1962
It is conceivable(although far outside the limits of present-day science)that brain physiology would advance so far that it would be known with empirical certainty(1) that the brain suffices for the explanation of all mental phenomena and is a machine in the sense of Turing; (2) that such and such is the precise material structure and physiological functioning of the part of the brain which performs mathematical thinking.
Godel, Gibbs Lecture, 1951 note 17
It is by viewing together a number of relevant facts that we come to believe in objectivism[in mathematics]. Philosophy consists of pointing things out rather than arguments .
Godel, 25 N,ovember 1975
Logic is the theory of the formal. It consists of set theory and the theory of concepts.... Set is a formal concept. If we replace the concept of set by the concept of concept, we get logic. The concept of concept is certainly formal and, therefore, a logical concept.... A plausible conjecture is : Every set is the extension of some concept.... The subject matter of logic is intensions(concepts); that of mathematics is extensions(set).
Godel, ca. 1976
For someone who considers mathematical objects to exist independently of our
constructions and of our having an intuition of them individually , and who
requires only that the general mathematical concepts must be sufficiently clear for us to be able to recognize their soundness and the truth of the axioms concerning them, there exists, I believe, a satisfactory foundation of Cantor's set theory in its whole original extent and meaning.
Godel, The Cantor Paper, 1964
General philosophy is a conceptual study, for which method is all-important.
Gadel, 23 January 1976
For approaching the central part of philosophy, there is good reason to confine one's attention to reflections on mathematics. Physics is perhaps less well suited for this purpose; Newtonian physics would be better.
Godel, 24 May 1972
The meaning of the world is the separation of wish and fact.
Godel, November 1975
For the physical world, the four dimensions are natural. But for the mind, there is no such natural coordinate system; time is the only natural frame of inference.
Godel, 15 March 1972
Godel, my philosophical viewpoint:
1. The world is rational.
2. Human reason can, in principle, be developed more highly(through certain
techniques).
3. There are systematic methods for the solution of all problems(also art, etc.).
4. There are other worlds and rational beings of a different and higher kind.
5. The world in which we live is not the only one in which we shall live or have lived.
6. There is incomparably more knowable a priori than is currently known.
7. The development of human thought since the Renaissance is thoroughly intelligible(durchaus einsichtige).
8. Reason in mankind will be developed in every direction.
9. Formal rights comprise a real science.
10. Materialism is false.
11. The higher beings are connected to the others by analogy, not by composition.
12. Concepts have an objective existence.
13. 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.
14. Religions are, for the most part, bad- but religion is not.
---
wang hao : a logical journey - from Godel to philosophy
> 我来回应