Top 1200 Mathematical Logic Quotes & Sayings - Page 2

You asked me how to get out of the finite dimensions when I feel like it. I certainly don't use logic when I do it. Logic's the first thing you have to get rid of.

Crime is common. Logic is rare. Therefore it is upon the logic rather than upon the crime that you should dwell.

Aristotle can be regarded as the father of logic. But his logic is too scholastic, full of subtleties, and fundamentally has not been of much value to the human understanding. It is a dialectic and an organon for the art of disputation.

I do know that you have to choose between the logic of reconciliation and the logic of justice. Pure justice leads to new civil war. I prefer the negotiable revolution.

There is no morality by instinct. There is no social salvation in the end without taking thought; without mastery of logic and application of logic to human experience.

If I were asked to name, in one word, the pole star round which the mathematical firmament revolves, the central idea which pervades the whole corpus of mathematical doctrine, I should point to Continuity as contained in our notions of space, and say, it is this, it is this!

Turin is a city which entices a writer towards vigor, linearity, style. It encourages logic, and through logic it opens the way towards madness.

I think the world on the other side of fossil fuel is more local - the logic of sun and wind is diffuse and spread out, not concentrated like the logic of coal and oil.

Every attempt to employ mathematical methods in the study of chemical questions must be considered profoundly irrational and contrary to the spirit of chemistry.... if mathematical analysis should ever hold a prominent place in chemistry -- an aberration which is happily almost impossible -- it would occasion a rapid and widespread degeneration of that science.

Logic is immaturity weaving its nets of gossamer wherewith it aims to catch the behemoth of knowledge. Logic is a crutch for the cripple, but a burden for the swift of foot and a greater burden still for the wise.

If one doesn't value logic, what logical argument would you invoke to prove they should value logic?

We will convert the entire world to Islam with our logic. We are confident that the Islamic logic, culture, and discourse can prove their superiority in all fields over all schools of thought and theories.

Logic doesn't really provide for loyalty. If your logic changes suddenly and things not make sense, you can alter your allegiance, but love stops you from being able to do that.

I end with a word on the new symbols which I have employed. Most writers on logic strongly object to all symbols. ... I should advise the reader not to make up his mind on this point until he has well weighed two facts which nobody disputes, both separately and in connexion. First, logic is the only science which has made no progress since the revival of letters; secondly, logic is the only science which has produced no growth of symbols.

All traditional logic habitually assumes that precise symbols are being employed. It is therefore not applicable to this terrestial life but only to an imagined celestial existence... logic takes us nearer to heaven than other studies.

Beneath words and logic are emotional connections that largely direct how we use our words and logic.

Poincaré was a vigorous opponent of the theory that all mathematics can be rewritten in terms of the most elementary notions of classical logic; something more than logic, he believed, makes mathematics what it is.

These algorithms, which I'll call public relevance algorithms, are-by the very same mathematical procedures-producing and certifying knowledge. The algorithmic assessment of information, then, represents a particular knowledge logic, one built on specific presumptions about what knowledge is and how one should identify its most relevant components. That we are now turning to algorithms to identify what we need to know is as momentous as having relied on credentialed experts, the scientific method, common sense, or the word of God.

If we did not have a sense of who we were, how we got here, why we want to achieve something - which, on the face of it, on the logic of it, is probably not worth trying - and prove that logic wrong, then you wouldn't succeed; then you would just evaporate.

In Iran's future Islamic system everyone can express their opinion, and the Islamic government will respond to logic with logic.

Through logic and inference we can prove anything. Therefore, logic and inference, in contrast to ordinary daily living experience, are secondary instruments of knowledge. Probably tertiary.

I think that's one of the problems with downloading mps these days. You never really get a chance to attune to a different logic, a different musical logic. If you hear a song and don't like it, you'll just delete it off your hard drive.

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.

Like Molière's M. Jourdain, who spoke prose all his life without knowing it, mathematicians have been reasoning for at least two millennia without being aware of all the principles underlying what they were doing. The real nature of the tools of their craft has become evident only within recent times A renaissance of logical studies in modern times begins with the publication in 1847 of George Boole's The Mathematical Analysis of Logic.

My brother is a genius. When we went to Italy, he was on the local television channel as a prodigy, who could solve very sophisticated mathematical equations. He was only seven or eight years old but he could solve mathematical problems for fourteen year olds.

What a mathematical proof actually does is show that certain conclusions, such as the irrationality of , follow from certain premises, such as the principle of mathematical induction. The validity of these premises is an entirely independent matter which can safely be left to philosophers.

Logic was puny in the face of my wrath. Logic was puny and magic was mighty: I had just gotten rebirthed, refilled and renewed, and was fast on my way to resentful.

The nineteenth century was completely lacking in logic, it had cosmic terms and hopes, and aspirations, and discoveries, and ideals but it had no logic.

I loved logic, math, computer programming. I loved systems and logic approaches. And so I just figured architecture is this perfect combination.

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.

Mathematical demonstrations being built upon the impregnable Foundations of Geometry and Arithmetick are the only truths that can sink into the Mind of Man, void of all Uncertainty; and all other Discourses participate more or less of Truth according as their Subjects are more or less capable of Mathematical Demonstration.

They [the mathematicians of the Enlightenment] defined their terms vaguely and used their methods loosely, and the logic of their arguments was made to fit the dictates of their intuition. In short, they broke all the laws of rigor and of mathematical decorum. The veritable orgy which followed the introduction of the infinitesimals... was but a natural reaction. Intuition had too long been held imprisoned by the severe rigor of the Greeks. Now it broke loose, and there were no Euclids to keep its romantic flight in check.

The strength of the computer lies in its being a logic machine. It does precisely what it is programed to do. This makes it fast and precise. It also makes it a total moron; for logic is essentially stupid.

... mathematical knowledge ... is, in fact, merely verbal knowledge. "3" means "2+1", and "4" means "3+1". Hence it follows (though the proof is long) that "4" means the same as "2+2". Thus mathematical knowledge ceases to be mysterious.

There is a logic of language and a logic of mathematics.

String theory has had a long and wonderful history. It originated as a technique to try to understand the strong force. It was a calculational mechanism, a way of approaching a mathematical problem that was too difficult, and it was a promising way, but it was only a technique. It was a mathematical technique rather than a theory in itself.

The classes of problems which are respectively known and not known to have good algorithms are of great theoretical interest. [...] I conjecture that there is no good algorithm for the traveling salesman problem. My reasons are the same as for any mathematical conjecture: (1) It is a legitimate mathematical possibility, and (2) I do not know.

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.

In my work you often get an abrupt shift in time, a jolt. But the emotional logic will take the reader on. I hope. I trust. After all, our memories do not work with any sequential logic.

This common and unfortunate fact of the lack of adequate presentation of basic ideas and motivations of almost any mathematical theory is probably due to the binary nature of mathematical perception. Either you have no inkling of an idea, or, once you have understood it, the very idea appears so embarrassingly obvious that you feel reluctant to say it aloud.

[Before the time of Benjamin Peirce it never occurred to anyone that mathematical research] was one of the things for which a mathematical department existed. Today it is a commonplace in all the leading universities. Peirce stood alone-a mountain peak whose absolute height might be hard to measure, but which towered above all the surrounding country.

Eventually, Aristotle appeared among the Greeks. He improved the methods of logic and systematized its problems and details. He assigned to logic its proper place as the first philosophical discipline and the introduction to philosophy. Therefore he is called the First Teacher.

For generations, field guides to plants and animals have sharpened the pleasure of seeing by opening our minds to understanding. Now John Adam has filled a gap in that venerable genre with his painstaking but simple mathematical descriptions of familiar, mundane physical phenomena. This is nothing less than a mathematical field guide to inanimate nature.

The problem with cinema nowadays is that it's a math problem. People can read a film mathematically; they know when this comes or that comes; in about 30 minutes, it's going to be over and have an ending. So film has become a mathematical solution. And that is boring, because art is not mathematical.

The logic of the poet - that is, the logic of language or the experience itself - develops the way a living organism grows: it spreads out towards what it loves, and is heliotropic, like a plant.

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.

For me, all fiction is about prizing the logic of metaphors - which is the logic of narratives in general - over reality, which is irreducibly random and senseless.

Logic ridicules love, and love smiles knowingly at the whole foolishness of logic.

My heroes were always a combination of Captain Kirk and Mr Spock. You have to be ruled by logic, but if you're only ruled by logic and you don't touch your emotions, you will make the wrong instinctive call.

there are the two sides to a Frenchman, logic and fashion and that is the reason why French people are exciting and peaceful. Logic and fashion.

I'm not belittling the art world. Not at all. I take it quite seriously, actually. But the logic of art is a vanguard logic that pressures art to incorporate the quotient of risk.

It is possible--indeed possible even according to the old conception of logic--to give in advance a description of all 'true' logical propositions. Hence there can never be surprises in logic.

It can be shown that a mathematical web of some kind can be woven about any universe containing several objects. The fact that our universe lends itself to mathematical treatment is not a fact of any great philosophical significance.

There is no logic like the logic of the heart.

Arithmetic is where the content lies, and not logic; but logic prompts certainty, and not arithmetic.

The validity of mathematical propositions is independent of the actual world-the world of existing subject-matters-is logically prior to it, and would remain unaffected were it to vanish from being. Mathematical propositions, if true, are eternal verities.

In mathematical analysis we call x the undetermined part of line a: the rest we don't call y, as we do in common life, but a-x. Hence mathematical language has great advantages over the common language.

... each of the 24 modes in the Ramanujan function corresponds to a physical vibration of a string. Whenever the string executes its complex motions in space-time by splitting and recombining, a large number of highly sophisticated mathematical identities must be satisfied. These are precisely the mathematical identities discovered by Ramanujan.

Well it was not exactly a dissertation in logic, at least not the kind of logic you would find in Whitehead and Russell's Principia Mathematica for instance. It looked more like mathematics; no formalized language was used.

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.