A Quote by Paul Feyerabend
Mathematical Reasoning is not only exact; it has its own criteria of reality.
Related Quotes
Many persons entertain a prejudice against mathematical language, arising out of a confusion between the ideas of a mathematical science and an exact science. ...in reality, there is no such thing as an exact science.
It is a common observation that a science first begins to be exact when it is quantitatively treated. What are called the exact sciences are no others than the mathematical ones.
The Reader may here observe the Force of Numbers, which can be successfully applied, even to those things, which one would imagine are subject to no Rules. There are very few things which we know, which are not capable of being reduc'd to a Mathematical Reasoning, and when they cannot, it's a sign our Knowledge of them is very small and confus'd; and where a mathematical reasoning can be had, it's as great folly to make use of any other, as to grope for a thing in the dark when you have a Candle standing by you.
Mathematics is not only real, but it is the only reality. That is that entire universe is made of matter, obviously. And matter is made of particles. It's made of electrons and neutrons and protons. So the entire universe is made out of particles. Now what are the particles made out of They're not made out of anything. The only thing you can say about the reality of an electron is to cite its mathematical properties. So there's a sense in which matter has completely dissolved and what is left is just a mathematical structure.
The criteria or the paradigm for us is not the West, not the Western paradigm, because the West has its own culture, we have our own culture, they have their own reality, we have our own reality.
Mathematical reasoning may be regarded.
We feel certain that the extraterrestrial message is a mathematical code of some kind. Probably a number code. Mathematics is the one language we might conceivably have in common with other forms of intelligent life in the universe. As I understand it, there is no reality more independent of our perception and more true to itself than mathematical reality.
Nature seems to take advantage of the simple mathematical representations of the symmetry laws. When one pauses to consider the elegance and the beautiful perfection of the mathematical reasoning involved and contrast it with the complex and far-reaching physical consequences, a deep sense of respect for the power of the symmetry laws never fails to develop.
Do mathematics have a relation to reality or are they only a mathematical symbol?
[Albert] Camus always insisted that historical criteria and historical reasoning were not the only things to take into account, and that they weren't all powerful, that history could always be wrong about man. Today, this is how we are starting to think.
The moving power of mathematical invention is not reasoning but imagination.
Mathematics may be the only exception in the sciences that leaves no room for skepicism. But, if mathematical results are exact as no empirical law can ever be, philosophers have discovered that they are not absolutely novel - instead, they are tautological.
To do any important work in physics a very good mathematical ability and aptitude are required. Some work in applications can be done without this, but it will not be very inspired. If you must satisfy your "personal curiosity concerning the mysteries of nature" what will happen if these mysteries turn out to be laws expressed in mathematical terms (as they do turn out to be)? You cannot understand the physical world in any deep or satisfying way without using mathematical reasoning with facility.
The deep paradox uncovered by AI research: the only way to deal efficiently with very complex problems is to move away from pure logic.... Most of the time, reaching the right decision requires little reasoning.... Expert systems are, thus, not about reasoning: they are about knowing.... Reasoning takes time, so we try to do it as seldom as possible. Instead we store the results of our reasoning for later reference.
If philosophy is still necessary, it is so only in the way it has been from time immemorial: as critique, as resistance to the expanding heteronomy, even if only as thought's powerless attempt to remain its own master and to convict of untruth, by their own criteria, both a fabricated mythology and a conniving, resigned acquiescence.
Not only in geometry, but to a still more astonishing degree in physics, has it become more and more evident that as soon as we have succeeded in unraveling fully the natural laws which govern reality, we find them to be expressible by mathematical relations of surprising simplicity and architectonic perfection. It seems to me to be one of the chief objects of mathematical instruction to develop the faculty of perceiving this simplicity and harmony.
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