Quotes & Sayings About Mathematical Logic

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. — Tobias Dantzig

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

No human investigation can claim to be scientific if it doesn't pass the test of mathematical proof. — Leonardo Da Vinci

Two moral forces shaped how we think and live in this shining twentieth century: the Virgin, and the Dynamo. The Dynamo represents the desire to know; the Virgin represents the freedom not to know.

What's the Virgin made of? Things that we think are silly, mostly. The peculiar logic of dreams, or the inexplicable stirring we feel when we look on someone that's beautiful not in a way that we all agree is beautiful, but the unique way in which a single person is. The Virgin is faith and mysticism; miracle and instinct; art and randomness.

On the other hand, you have the Dynamo: the unstoppable engine. It finds the logic behind a seeming miracle and explains that miracle away; it finds the order in randomness to which we're blind; it takes the caliper to a young woman's head and quantifies her beauty in terms of pleasing mathematical ratios; it accounts for the secret stirring you felt by discoursing at length on the nervous systems of animals. — Dexter Palmer

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

And I think that if God did exist, he had many children. I think Jesus proves this. Jesus must be the seventh son of God. A-sus, B-sus, C-sus, D-sus, E-sus, F-sus, G-sus. That's just logic. That's just mathematical. And T-sus would always be fucking about. And P-sus does deliveries. C-sus started the Roman Empire. Cae-sus. F-sus, City in Turkey. B-sus was covered in something. Some people applauding there; other people going, "What?" ... B-sus was covered in bees. — Eddie Izzard

Consider a cognitive scientist concerned with the empirical study of the mind, especially the cognitive unconscious, and ultimately committed to understanding the mind in terms of the brain and its neural structure. To such a scientist of the mind, Anglo-American approaches to the philosophy of mind and language of the sort discussed above seem odd indeed. The brain uses neurons, not languagelike symbols. Neural computation works by real-time spreading activation, which is neither akin to prooflike deductions in a mathematical
logic, nor like disembodied algorithms in classical artificial intelligence, nor like derivations in a transformational grammar. — George Lakoff

All exact science is dominated by the idea of approximation. — Bertrand Russell

Much of what I make is geometric, and has a kind of almost mathematical logic to the form. — Anish Kapoor

Dr. Karel Culik is an outstanding applied mathematician, a specialist in algebra, logic, computer sciences and mathematical linguistics. In 1965, he visited the linguistics research program at MIT, and we have worked together on several projects since. — Noam Chomsky

Logic is the hygiene the mathematician practices to keep his ideas healthy and strong. — Hermann Weyl

It is all about numbers. It is all about sequence. It's the mathematical logic of being alive. If everything kept to its normal progression, we would live with the sadness
cry and then walk
but what really breaks us cleanest are the losses that happen out of order. — Aimee Bender

Satan, on the contrary, is thin, ascetic and a fanatical devotee of logic. He reads Machiavelli, Ignatius of Loyola, Marx and Hegel; he is cold and unmerciful to mankind, out of a kind of mathematical mercifulness. He is damned always to do that which is most repugnant to him: to become a slaughterer, in order to abolish slaughtering, to sacrifice lambs so that no more lambs may be slaughtered, to whip people with knouts so that they may learn not to let themselves be whipped, to strip himself of every scruple in the name of a higher scrupulousness, and to challenge the hatred of mankind because of his love for it
an abstract and geometric love. — Arthur Koestler

To understand this for sense it is not required that a man should be a geometrician or a logician, but that he should be mad. — Thomas Hobbes

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. — Tarleton Gillespie

What governs what we choose to notice? The first (which we shall have to qualify later) is whatever seems advantageous or disadvantageous for our survival, our social status, and the security of our egos. The second, again working simultaneously with the first, is the pattern and the logic of all the notation symbols which we have learned from others, from our society and our culture. It is hard indeed to notice anything for which the languages available to us (whether verbal, mathematical, or musical) have no description. This is why we borrow words from foreign languages. — Alan W. Watts

What seems certain is that Pythagoras developed the idea of mathematical logic ... He realized that numbers exist independently of the tangible world and therefore their study was untainted by inaccuracies of perception. This meant he could discover truths which were independent of opinion of prejudice and which were more absolute then any previous knowledge. — Simon Singh

Russell's books should be bound in two colours, those dealing with mathematical logic in red - and all students of philosophy should read them; those dealing with ethics and politics in blue - and no one should be allowed to read them. — Ludwig Wittgenstein

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

What is this film (Mirror) about?It is about a Man. No, not the particular man whose voice we hear from behind the screen, played by Innokentiy Smoktunovsky. It's a film about you, your father, your grandfather, about someone who will live after you and who is still "you". About a Man who lives on the earth, is a part of the earth and the earth is a part of him, about the fact that a man is answerable for his life both to the past and to the future. You have to watch this film simply, and listen to the music of Bach and the poems of Arseniy Tarkovsky; watch it as one watches the stars, or the sea, as one admires a landscape. There is no mathematical logic here, for it cannot explain what man is or what is the meaning of his life. (Sculpting in Time) — Andrey Tarkovsky

Simplify? Let me try. In school days, we are taught that if there are four animals in a room and you add two more, the total will be six. That is logic. But behind this logic, there are underlying assumptions. Now, if somebody tells you, there are four rats in the room and if you add two more cats in the room, how many animals in total exist in the room now? The answer will depend upon assumption. If you just use your mathematical brain, you will say six animals. If you use your human brain, you will say two animals. Why two animals? Because the two cats will eat the four rats in no time. — Ravindra Shukla

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

I think part of the appeal of mathematical logic is that the formulas look mysterious - You write backward Es! — Hilary Putnam

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

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

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

Sets are fundamental because every mathematical structure,
object or entity can be described as a set. Logic is fundamental because it
allows us to understand the meanings of statements, to deduce information
about mathematical structures and to uncover further structures. — Richard Heath Hammack

A fist is more than the sum of its fingers. — Margaret Atwood

There isn't an equation that can confirm something as self-evident (to us humans) as "muggy weather is uncomfortable" or "mothers are older than their daughters." There has been some progress made in translating this sort of information into mathematical logic, but to catalog the common sense of a four-year-old child would require hundreds of millions of lines of computer code. As Voltaire once said, "Common sense is not so common. — Michio Kaku

We never know what we are talking about. — Karl Popper

Six is a number perfect in itself, and not because God created the world in six days; rather the contrary is true. God created the world in six days because this number is perfect, and it would remain perfect, even if the work of the six days did not exist. — Saint Augustine

Here at Wisconsin we didn't get an undergraduate course in mathematical logic until the '60s. — Stephen Cole Kleene

I am allowed to use plain English because everybody knows that I could use mathematical logic if I chose. — Bertrand Russell