Quotes & Sayings About Mathematics And Logic

Mathematics and logic have been proved to be one; a fact from which it seems to follow that mathematics may successfully deal with non-quantitative problems in a much broader sense than was suspected to be possible. — Alfred Korzybski

Only mathematics and mathematical logic can say as little as the physicist means to say. — Bertrand Russell

And this is what I mainly learned up there, that the Parthenon was not a thing to study but to feel. It wasn't aloof, rational, timeless, pure. I couldn't locate the serenity of the place, the logic and steady sense. It wasn't a relic species of dead Greece but part of the living city below it. This was a surprise. I'd thought it was a separate thing, the sacred height, intact in its Doric order. I hadn't expected a human feeling to emerge from the stones but this is what I found, deeper than the art and mathematics embodied in the structure, the optical exactitudes. I found a cry for pity. — Don DeLillo

The totality of our so-called knowledge or beliefs, from the most casual matters of geography and history to the profoundest lawsof atomic physics or even of pure mathematics and logic, is a man-made fabric which impinges on experience only along the edges. Or, to change the figure, total science is like a field of force whose boundary conditions are experience. — Willard Van Orman Quine

Logic, n. The art of thinking and reasoning in strict accordance with the limitations and incapacities of the human misunderstanding. The basic of logic is the syllogism, consisting of a major and a minor premise and a conclusion - thus:
Major Premise: Sixty men can do a piece of work sixty times as quickly as one man.
Minor Premise: One man can dig a post-hole in sixty seconds; Therefore-
Conclusion: Sixty men can dig a post-hole in one second.
This may be called syllogism arithmetical, in which, by combining logic and mathematics, we obtain a double certainty and are twice blessed. — Ambrose Bierce

Mathematics had never had more than a secondary interest for him [her husband, George Boole]; and even logic he cared for chiefly as a means of clearing the ground of doctrines imagined to be proved, by showing that the evidence on which they were supposed to give rest had no tendency to prove them. — Mary Everest Boole

We know that mathematicians care no more for logic than logicians for mathematics. The two eyes of science are mathematics and logic; the mathematical set puts out the logical eye, the logical set puts out the mathematical eye; each believing that it sees better with one eye than with two. Note that De Morgan, himself, only had sight with only one eye. — Augustus De Morgan

Its very nature, scientific investigation takes for granted such assumptions as that: there is a physical world existing independently of our minds; this world is characterized by various objective patterns and regularities; our senses are at least partially reliable sources of information about this world; there are objective laws of logic and mathematics that apply to the objective world outside our minds; — Edward Feser

In the Principia Mathematica, Bertrand Russell and Alfred Whitehead attempted to give a rigorous foundation to mathematics using formal logic as their basis. They began with what they considered to be axioms, and used those to derive theorems of increasing complexity. By page 362, they had established enough to prove 1 + 1 = 2. — Ted Chiang

Take this neat little equation here. It tells me all the ways an electron can make itself comfortable in or around an atom. That's the logic of it. The poetry of it is that the equation tells me how shiny gold is, how come rocks are hard, what makes grass green, and why you can't see the wind. And a million other things besides, about the way nature works. — Richard Feynman

Mathematics is not arithmetic. Though mathematics may have arisen from the practices of counting and measuring it really deals with logical reasoning in which theorems - general and specific statements - can be deduced from the starting assumptions. It is, perhaps, the purest and most rigorous of intellectual activities, and is often thought of as queen of the sciences. — Christopher Zeeman

I use logic all the time in mathematics, and it seems to yield "correct" results, but in mathematics "correct" by and large means "logical", so I'm back where I started. I can't defend logic because I can't remove my glasses. — Richard J. Trudeau

Mathematics is, as it were, a sensuous logic, and relates to philosophy as do the arts, music, and plastic art to poetry. — Karl Wilhelm Friedrich Schlegel

Pure mathematics consists entirely of assertions to the effect that, if such and such a proposition is true of anything, then such and such another proposition is true of that thing. It is essential not to discuss whether the first proposition is really true, and not to mention what the anything is, of which it is supposed to be true. [ ... ] Thus mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true. People who have been puzzled by the beginnings of mathematics will, I hope, find comfort in this definition, and will probably agree that it is accurate. — Bertrand Russell

Ever since Plato most philosophers have considered it part of their business to produce 'proofs' of immortality and the existence of God. They have found fault with the proofs of their predecessors - Saint Thomas rejected Saint Anselm's proofs, and Kant rejected Descartes' - but they have supplied new ones of their own. In order to make their proofs seem valid, they have had to falsify logic, to make mathematics mystical, and to pretend that deepseated prejudices were heaven-sent intuitions. — Bertrand Russell

That's how you write novels actually. You suddenly hit upon something and you realize this is the path you were meant to take. You'd be a fool if you didn't follow it. Perhaps it's like solving a difficult question in pure mathematics. There must be a moment when the solution is so simple and evident that you wonder why you hadn't come upon it before. When you do come upon it, you know it in the deepest part of your being. It carries its own logic. — Don DeLillo

There is a logic of language and a logic of mathematics. — Thomas Merton

Mathematics as an expression of the human mind reflects the active will, the contemplative reason, and the desire for aesthetic perfection. Its basic elements are logic and intuition, analysis and construction, generality and individuality. Though different traditions may emphasize different aspects, it is only the interplay of these antithetic forces and the struggle for their synthesis that constitute the life, usefulness, and supreme value of mathematical science. — Richard Courant

Proofs exist only in mathematics and logic, not in science. — Satoshi Kanazawa

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. — Alonzo Church

Human logic [emphasis added] was forced on us by the physical world and is therefore consistent with it. Mathematics derives from logic. This is why mathematics is consistent with the physical world. — Jef Raskin

Mathematics consists of processes independent of the number. You must remove the number from your thinking and instead dwell on the idea and process of the underlying logic. The faster you do this, the quicker math will begin to make sense to you. Then maybe your life, but defiantly your grade, will get better. — John Weiss

The theories of the social sciences do not consist of "laws" in the sense of empirical rules about the behavior of objects definable in physical terms. All that the theory of the social sciences attempts is to provide a technique of reasoning which assists us in connecting individual facts, but which, like logic or mathematics, is not about the facts. It can, therefore, and this is the second point, never be verified or falsified by reference to facts. — Friedrich Hayek

I know that two and two make four - and should be glad to prove it too if I could - though I must say if by any sort of process I could convert 2 and 2 into five it would give me much greater pleasure. — George Gordon Byron

I earned my Ph.D. in philosophy, and one of my specializations was the logic and mathematics of game theory. I've also got a degree in drama, so I know about stories, characterizations, plot arcs, and the like. Lots of game designers can do one or the other: I've got the skills for both. — Brendan Myers

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. — Alfred Tarski

The philosophers make still another objection: "What you gain in rigour," they say, "you lose in objectivity. You can rise toward your logical ideal only by cutting the bonds which attach you to reality. Your science is infallible, but it can only remain so by imprisoning itself in an ivory tower and renouncing all relation with the external world. From this seclusion it must go out when it would attempt the slightest application. — Henri Poincare

The advantage is that mathematics is a field in which one's blunders tend to show very clearly and can be corrected or erased with a stroke of the pencil. — Norbert Wiener

What would mathematics have amounted to without the imagination of its devotees-its giants and their followers? There never was a discovery made without the urge of imagination-of imagination which broke the roadway through the forest in order that cold logic might follow. — David Eugene Smith

Mathematics expresses values that reflect the cosmos, including orderliness, balance, harmony, logic, and abstract beauty. — Deepak Chopra

Pure analysis puts at our disposal a multitude of procedures whose infallibility it guarantees; it opens to us a thousand different ways on which we can embark in all confidence; we are assured of meeting there no obstacles; but of all these ways, which will lead us most promptly to our goal? Who shall tell us which to choose? We need a faculty which makes us see the end from afar, and intuition is this faculty. It is necessary to the explorer for choosing his route; it is not less so to the one following his trail who wants to know why he chose it. — Henri Poincare

Brains operate ... not by logic but by pattern recognition. This process is not precise, as is logic and mathematics. Instead, it trades off specificity and precision, if necessary, to increase its range. It is likely, for example, that early human thought proceeded by metaphor, which, even with the late acquisition of precise means such as logic and mathematical thought, continues to be a major source of imagination and creativity in adult life. — Gerald Edelman

The principles of logic and mathematics are true universally simply because we never allow them to be anything else. And the reason for this is that we cannot abandon them without contradicting ourselves, without sinning against the rules which govern the use of language, and so making our utterances self-stultifying. In other words, the truths of logic and mathematics are analytic propositions or tautologies. — A.J. Ayer

Can you name a single one of the great fundamental and original intellectual achievements which have raise man in the scale of civilization that may be credited to the Anglo-Saxon? The art of letters, of poetry, of music, of sculpture, of painting, of the drama, of architecture; the science of mathematics, of astronomy, of philosophy, of logic, of physics, of chemistry, the use of the metals and principles of mechanics, were all invented or discovered by darker and what we now call inferior races and nations. — James Weldon Johnson

The rejection of all abstract formalism. Materialism reminds every science of its real source: the world men transform. No science can, whether in its history or its object, grasp its own origins within itself or constitute itself as a closed world, exhaustively defined by internal rules. Materialism refers every science and every activity to the reality they depend on, even if this dependence is masked by a great many abstract mediations: mathematics as well as logic, aesthetics as well as ethics and politics. — Louis Althusser

Bits also play a part in logic, that strange blend of philosophy and mathematics for which a primary goal is to determine whether certain statements are true or false. True — Charles Petzold

The general mental qualification necessary for scientific advancement is that which is usually denominated "common sense," though added to this, imagination, induction, and trained logic, either of common language or of mathematics, are important adjuncts. — Joseph Henry

It is impossible to discuss realism in logic without drawing in the empirical sciences ... A truly realistic mathematics should be conceived, in line with physics, as a branch of the theoretical construction of the one real world and should adopt the same sober and cautious attitude toward hypothetic extensions of its foundation as is exhibited by physics. — Hermann Weyl

It is perplexing to see the flexibility of the so-called 'exact sciences' which by cast-iron laws of logic and by the infallible help of mathematics can lead to conclusions which are diametrically opposite to one another. — Vasco Ronchi

So how does one go about proving something like this? It's not like being a lawyer, where the goal is to persuade other people; nor is it like a scientist testing a theory. This is a unique art form within the world of rational science. We are trying to craft a "poem of reason" that explains fully and clearly and satisfies the pickiest demands of logic, while at the same time giving us goosebumps. — Paul Lockhart

I am convinced that the act of thinking logically cannot possibly be natural to the human mind. If it were, then mathematics would be everybody's easiest course at school and our species would not have taken several millennia to figure out the scientific method. — Neil DeGrasse Tyson

But the science of operations, as derived from mathematics more especially, is a science of itself, and has its own abstract truth and value; just as logic has its own peculiar truth and value, independently of the subjects to which we may apply its reasonings and processes. — Ada Lovelace

By a combination of formal training and self study, the latter continuing systematically well into the 1940s, I was able to gain a broad base of knowledge in economics and political science, together with reasonable skills in advanced mathematics, symbolic logic, and mathematical statistics. — Herbert A. Simon

Further, the same Arguments which explode the Notion of Luck, may, on the other side, be useful in some Cases to establish a due comparison between Chance and Design: We may imagine Chance and Design to be, as it were, in Competition with each other, for the production of some sorts of Events, and many calculate what Probability there is, that those Events should be rather be owing to the one than to the other. — Abraham De Moivre

Most people would have probably lost count around seven. This was, Harry knew
from his extensive reading on logic and arithmetic, the largest number that most people
could visually appreciate. Put seven dots on a page, and most people can take a quick
glance and declare, "Seven." Switch to eight, and the majority of humanity was lost. — Julia Quinn

When the twins asked what cuff-links were for - "To link cuffs together," Ammu told them - they were thrilled by this morsel of logic in what had so far seemed an illogical language. Cuff+link = cuff-link. This, to them, rivaled the precision of logic and mathematics. Cuff-links gave them an inordinate (if exaggerated) satisfaction, and a real affection for the English language. — Arundhati Roy

The fact that all Mathematics is Symbolic Logic is one of the greatest discoveries of our age; and when this fact has been established, the remainder of the principles of mathematics consists of the analysis of Symbolic Logic itself. — Bertrand Russell

A good part of 'The Information' is about the transition from an oral to a literary culture. Books effected such a great transformation in the way we think about the world, our history, our logic, mathematics, you name it. I think we would be greatly diminished as a people and as a culture if the book became obsolete. — James Gleick

Mathematics is the poetry of logic and the music of reason. — Albert Einstein

The person who wishes to attain human perfection should study logic first, next mathematics, then physics, and, lastly, metaphysics. — Maimonides

Inferences of Science and Common Sense differ from those of deductive logic and mathematics in a very important respect, namely, when the premises are true and the reasoning correct, the conclusion is only probable. — Bertrand Russell

Logic and mathematics are nothing but specialised linguistic structures. — Jean Piaget

The world of being is unchangeable, rigid, exact, delightful to the mathematician, the logician, the builder of metaphysical systems, and all who love perfection more than life. The world of existence is fleeting, vague, without sharp boundaries, without any clear plan or arrangement, but it contains all thoughts and feelings, all the data of sense, and all physical objects, everything that can do either good or harm, everything that makes any difference to the value of life and the world. According to our temperaments, we shall prefer the contemplation of the one or of the other. — Bertrand Russell

Mathematics does not grow through a monotonous increase of the number of indubitably established theorems but through the incessant improvement of guesses by speculation and criticism, by the logic of proofs and refutations. — Imre Lakatos

There is no "religious language" or "scientific language". There is rather the international notation of mathematics and logic; and English, French, Spanish and the like. In short, "religious discourse" and "scientific discourse" are part of the same overall conceptual structure. Moreover, in that conceptual structure there is a large amount of discourse, which is neither religious nor scientific, that is constantly being utilized by both the religious man and the scientist when they make religious and scientific claims. In short, they share a number of key categories. — Kai Nielsen

He who could write so easily, who could spend a thousand words down along his plunging fingers on the green-rubber keyboard of his machine, had stumbled like a first-grader over this single paragraph. A dozen times he had begun it and written into it a naked desperation; a dozen times he had begun it and written into it the frosted mathematics of logic. Finally he'd written out quickly the sentences that kept cropping up in all the versions. Those must be, to whatever censor there was in him, the most acceptable ones. He sealed it without rereading it and went out to mail it. An hour later he despised himself for having sent it. — Laura Z. Hobson

I lose faith in mathematics, logical and rigid. What with those that even zero doesn't accept? — Dejan Stojanovic

The subtleties of mathematics defecate the grossness of our apprehension, and supply the elements of a sounder and severer logic. — William Godwin

Jericho lowered himself carefully to his knees. He covered his eyes and moved his lips like all the others, but he had no faith in any of it. Faith in mathematics, yes; faith in logic, of course; faith in the trajectory of the stars, yes, perhaps. But faith in a God, Christian or otherwise? — Robert Harris

Science attempts to find logic and simplicity in nature. Mathematics attempts to establish order and simplicity in human thought. — Edward Teller

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

Logic, too, also rests on assumptions that do not correspond to anything in the real world, e.g., on the assumption that there areequal things, that the same thing is identical at different points in time: but this science arose as a result of the opposite belief (that such things actually exist in the real world). And it is the same with mathematics, which would certainly never have arisen if it had been understood from the beginning that there is no such thing in nature as a perfectly straight line, a true circle, and absolute measure. — Friedrich Nietzsche

I think a strong claim can be made that the process of scientific discovery may be regarded as a form of art. This is best seen in the theoretical aspects of Physical Science. The mathematical theorist builds up on certain assumptions and according to well understood logical rules, step by step, a stately edifice, while his imaginative power brings out clearly the hidden relations between its parts. A well constructed theory is in some respects undoubtedly an artistic production. A fine example is the famous Kinetic Theory of Maxwell ... The theory of relativity by Einstein, quite apart from any question of its validity, cannot but be regarded as a magnificent work of art. — Ernest Rutherford

Another explanation for the failure of logic and observation alone to advance medicine is that unlike, say, physics, which uses a form of logic - mathematics - as its natural language, biology does not lend itself to logic. Leo Szilard, a prominent physicist, made this point when he complained that after switching from physics to biology he never had a peaceful bath again. As a physicist he would soak in the warmth of a bathtub and contemplate a problem, turn it in his mind, reason his way through it. But once he became a biologist, he constantly had to climb out of the bathtub to look up a fact. — John M Barry

Certainly one of the most important things I learned is that numbers can be deceiving. There is a logic to mathematics, but there is also the underlying human element that must be considered. Numbers can't lie, but the people who create those numbers can and do. As so many people have learned, forgetting to include human nature in an equation can be devastating. — Harry Markopolos

We especially need imagination in science. It is not all logic, nor all mathematics, but is somewhat beauty and poetry. — Maria Mitchell

Mathematics has always shown a curious ability to be applicable to nature, and this may express a deep link between our minds and nature. We are the Universe speaking out, a part of nature. So it is not so surprising that our systems of logic and mathematics sing in tune with nature. — George Zebrowski

Logic issues in tautologies, mathematics in identities, philosophy in definitions; all trivial, but all part of the vital work of clarifying and organising our thought. — Frank Plumpton Ramsey

Histories make men wise; poets, witty; the mathematics, subtle; natural philosophy, deep; moral, grave; logic and rhetoric, able to contend. — Francis Bacon

There is no great religion without a great schism. All of them have it. And that's because you're dealing with something called faith. And faith is not something you can prove; faith is personal opinion. Uh, when you're dealing with something with certainty, like, y'know, science or logic, you don't have the
there's no wiggle room; that's why history is not filled with warring math cults, y'know, because you can settle the issue; you can prove something to be right or wrong, and that's the end of the argument: next case. Whereas, when you're dealing with faith, you can forever argue your point, or another point, because you're dealing with intangibles. Personally, I think, faith is what you ask of somebody when you don't have the goods to prove your point. — Tom Quinn

Praxeology is a theoretical and systematic, not a historical, science. Its scope is human action as such, irrespective of all environmental, accidental, and individual circumstances of the concrete acts. Its cognition is purely formal and general without reference to the material content and the particular features of the actual case. It aims at knowledge valid for all instances in which the conditions exactly correspond to those implied in its assumptions and inferences. Its statements and propositions are not derived from experience. They are, like those of logic and mathematics, a priori. They are not subject to verification or falsification on the ground of experience and facts. — Ludwig Von Mises

Cort taught them to navigate by the sun and stars; Vannay showed them compass and quadrant and sextant and taught them the mathematics necessary to use them. Cort taught them to fight. With history, logic problems, and tutorials on what he called "the universal truths," Vannay taught them how they could sometimes avoid having to do so. Cort taught them to kill if they had to. Vannay, with his limp and his sweet but distracted smile, taught them that violence worsened problems far more often than it solved them. He called it the hollow chamber, where all true sounds became distorted by echoes. — Stephen King

Language is remarkable, except under the extreme constraints of mathematics and logic, it never can talk only about what it's supposed to talk about but is always spreading around. — Howard Nemerov