Quotes of All Topics . Occasions . Authors
I don't believe in natural science.
The axiomatic method is very powerful
Nothing new had been done in Logic since Aristotle!
The meaning of world is the separation of wish and fact.
I like Islam, it is a consistent idea of religion and open-minded.
Said to physicist John Bahcall. I don't believe in natural science.
The sentence 'snow is white' is true if, and only if, snow is white.
I don't believe in empirical science. I only believe in a priori truth.
All generalizations, with the possible exception of this one, are false.
The physical laws, in their observable consequences, have a finite limit of precision.
Either mathematics is too big for the human mind or the human mind is more than a machine.
The more I think about language, the more it amazes me that people ever understand each other at all.
You will not find in semantics any remedy for decayed teeth or illusions of grandeur or class conflict.
But every error is due to extraneous factors (such as emotion and education); reason itself does not err.
I am convinced of the afterlife, independent of theology. If the world is rationally constructed, there must be an afterlife
There can be no doubt that the knowledge of logic is of considerable practical importance for everyone who desires to think and to infer correctly.
...a consistency proof for [any] system ... can be carried out only by means of modes of inference that are not formalized in the system ... itself.
The development of mathematics towards greater precision has led, as is well known, to the formalization of large tracts of it, so that one can prove any theorem using nothing but a few mechanical rules.
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.
Logic is justly considered the basis of all other sciences, even if only for the reason that in every argument we employ concepts taken from the field of logic, and that ever correct inference proceeds in accordance with its laws.
It may be unpopular and out-of-date to say-but I do not think that a scientific result which gives us a better understanding of the world and makes it more harmonious in our eyes should be held in lower esteem than, say, an invention which reduces the cost of paving roads, or improves household plumbing.
... semantics ... is a sober and modest discipline which has no pretensions of being a universal patent-medicine for all the ills and diseases of mankind, whether imaginary or real. You will not find in semantics any remedy for decayed teeth or illusions of grandeur or class conflict. Nor is semantics a device for establishing that everyone except the speaker and his friends is speaking nonsense
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.
However the machine would permit us to test the hypothesis for any special value of n. We could carry out such tests for a sequence of consecutive values n=2,3,.. up to, say, n=100. If the result of at least one test were negative, the hypothesis would prove to be false; otherwise our confidence in the hypothesis would increase, and we should feel encouraged to attempt establishing the hypothesis, instead of trying to construct a counterexample.
If a mathematician wishes to disparage the work of one of his colleagues, say, A, the most effective method he finds for doing this is to ask where the results can be applied. The hard pressed man, with his back against the wall, finally unearths the researches of another mathematician B as the locus of the application of his own results. If next B is plagued with a similar question, he will refer to another mathematician C. After a few steps of this kind we find ourselves referred back to the researches of A, and in this way the chain closes.
The development of mathematics toward greater precision has led, as is well known, to the formalization of large tracts of it, so that one can prove any theorem using nothing but a few mechanical rules... One might therefore conjecture that these axioms and rules of inference are sufficient to decide any mathematical question that can at all be formally expressed in these systems. It will be shown below that this is not the case, that on the contrary there are in the two systems mentioned relatively simple problems in the theory of integers that cannot be decided on the basis of the axioms.