Formal Logic Quotes & Sayings

Science is not formal logic-it needs the free play of the mind in as great a degree as any other creative art. It is true that this is a gift which can hardly be taught, but its growth can be encouraged in those who already posses it. — Max Born

If you can't define something you have no formal rational way of knowing that it exists. Neither can you really tell anyone else what it is. There is, in fact, no formal difference between inability to define and stupidity. — Robert M. Pirsig

Theologians, and religionists in general, start with a fantasy premise and then proceed to apply rigorous formal logic to tease out its implications. Stark himself points out that "theology consists of formal reasoning about God." This is admirably exact. Theologians, beginning with a wished-for creation of their own minds, analyze that creation's characteristics by rigorous application of the principles of formal - that is, deductive - logic. — Andrew Bernstein

All rational knowledge is either material, and concerns some objects, or formal, and is occupied only with the form of understanding and reason itself and with the universal rules of thinking, without regard to distinctions among objects.
formal philosophy is called logic. Material philosophy, however, which has to do with definite object objects and the laws to which they are subject, is divided into two parts. This is because these laws are either laws of nature or laws of freedom. The science of the former is called physics, and that of the latter ethics. The former is also called theory of nature and the latter theory of morals. — Immanuel Kant

In [Aristotle's] formal logic, thought is organized in a manner very different from that of the Platonic dialogue. In this formal logic, thought is indifferent toward its objects. Whether they are mental or physical, whether they pertain to society or to nature, they become subject to the same general laws of organization, calculation, and conclusion but they do so as fungible signs or symbols, in abstraction from their particular "substance." This general quality (quantitative quality) is the precondition of law and order in logic as well as in society the price of universal control. — Herbert Marcuse

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

I believe that the emergence of postmodernism is closely related to the emergence of this new moment of late, consumer or multinational capitalism. I believe also that its formal features in many ways express the deeper logic of that particular social system. I will only be able, however, to show this for one major theme: namely the disappearance of a sense of history, the way in which our entire contemporary social system has little by little begun to lose its capacity to retain its own past, has begun to live in a perpetual present and in a perpetual change that obliterates traditions of the kind which all earlier social formations have had in one way or another to preserve. Think only of the media exhaustion of news: of how Nixon and, even more so, Kennedy are figures from a now distant past. One is tempted to say that the very function of the news media is to relegate such recent historical experiences as rapidly as possible into the past. — Fredric Jameson

Formality Thus the absence of all mention of particular things or properties in logic or pure mathematics is a necessary result of the fact that this study is, as we say, "purely formal". — Bertrand Russell

In other words, the propositions of philosophy are not factual, but linguistic in character - that is, they do not describe the behaviour of physical, or even mental, objects; they express definitions, or the formal consequences of definitions. Accordingly we may say that philosophy is a department of logic. For we will see that the characteristic mark of a purely logical enquiry, is that it is concerned with the formal consequences of our definitions and not with questions of empirical fact. — A.J. Ayer

Classical education was based on the seven liberal arts or sciences: grammar, the formal structures of language; rhetoric, composition and presentation of argument; dialectic, formal logic; arithmetic; geometry; music; astronomy.14 For centuries, the classics dominated the very idea of being educated and attempts at reform were resisted. — Ken Robinson

To argue that we humans are capable of complex multifarious thought and feeling, whereas the sheep's perception is probably limited by lowly sheepish perceptions, is no more to the point than if I were to slaughter and eat you on the grounds that I am a sophisticated personality able to enjoy Mozart, formal logic and cannibalism, whereas your imaginative world seems confined to True Romances and tinned spaghetti. — Brigid Brophy

1. God is (by definition) a being than which no greater being can be thought.
2. Greatness includes greatness of virtue.
3. Therefore, God is a being than which no being could be more virtuous.
4. But virtue involves overcoming pains and dangers.
5. Indeed, a being can only be properly said to be virtuous if it can suffer pain or be destroyed.
6. A God that can suffer pain or is destructible is not one than which no greater being can be thought.
7.For you can think of a greater being, that is, one that is nonsuffering and indestructible.
8. Therefore, God does not exist. — Douglas N. Walton

When you didn't force yourself to think in formal reconstructions, when you didn't catch these moments of ravishments under the lens of premises and conclusions, when you didn't impale them and label them, like so many splayed butterflies, bleeding the transcendental glow right out of them, then ... what? — Rebecca Goldstein

In formal logic, a contradiction is the signal of a defeat; but in the evolution of real knowledge it marks the first step in progress towards a victory. — Alfred North Whitehead

It (the talking, the telling) seemed (to him, to Quentin) to partake of that logic- and reason-flouting quality of a dream which the sleeper knows must have occurred, stillborn and complete, in a second, yet the very quality upon which it must depend to move the dreamer (verisimilitude) to credulity _horror or pleasure or amazement_ depends as completely upon a formal recognition of and acceptance of elapsed and yet-elapsing time as music or a printed tale. — William Faulkner

You know, in formal logic, an inconsistent set of axioms can be used to prove anything at all. Once you have a single contradiction, A and not A, there's nothing you can't derive from it. — Greg Egan

Dialectical logic undoes the abstractions of formal logic and of transcendental philosophy, but it also denies the concreteness of immediate experience. To the extent to which this experience comes to rest with the things as they appear and happen to be, it is a limited and even false experience. It attains its truth if it has freed itself from the deceptive objectivity which conceals the factors behind the facts that is, if it understands its world as a historical universe, in which the established facts are the work of the historical practice of man. — Herbert Marcuse

There is one basis of science," says Descartes , "one test and rule of truth, namely, that whatever is clearly and distinctly conceived is true." A profound psychological mistake. It is true only of formal logic, wherein the mind never quits the sphere of its first assumptions to pass out into the sphere of real existences; no sooner does the mind pass from the internal order to the external order, than the necessity of verifying the strict correspondence between the two becomes absolute. The Ideal Test must be supplemented by the Real Test, to suit the new conditions of the problem. — George Henry Lewes

Xenology is an unnatural mixture of science fiction and formal logic. At its core is a flawed assumption - that an alien race would be psychologically human. — Arkady Strugatsky

It has been a long road from Plato's Meno to the present, but it is perhaps encouraging that most of the progress along that road has been made since the turn of the twentieth century, and a large fraction of it since the midpoint of the century. Thought was still wholly intangible and ineffable until modern formal logic interpreted it as the manipulation of formal tokens. And it seemed still to inhabit mainly the heaven of Platonic ideals, or the equally obscure spaces of the human mind, until computers taught us how symbols could be processed by machines. — Allen Newell

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

Such revolutions in formal learning and felt experience needed new modes to express their understanding, beyond sonorous Ciceronian periods and the rigid structure of heroic couplets. It needed something looser, longer, and above all historical, which could not only link events, data, ideas, and context through time, but in which history could itself serve as an informing principle. The age craved creation stories in which the logic and moral order were manifest in and through the unfolding of the story. — Lydia Pyne

The practical utility of Formal Logic to-day lies not so much in the establishment of positive conclusions as in the prompt detection and exposure of invalid inference. — Dorothy L. Sayers

I know a person who will poke the fire, set chairs straight, pick dust specks from the floor, arrange his table, snatch up a newspaper, take down any book which catches his eye, trim his nails, waste the morning anyhow, in short, and all without premeditation - simply because the only thing he ought to attend to is the preparation of a noonday lesson in formal logic which he detests. - William James — Mason Currey

Inference is essentially rationality or logic, that which our current formal education system teaches and valorizes; however, direct perception is a level/avenue of knowledge above inference and accessible only through specialized forms of training or unique and rare forms of spontaneous awakening (for example, the "satori" of Zen). Similarly, the — Layli Phillips Maparyan

By abstaining from all definite content, whether as formal logic and theory of science or as the legend of Being beyond all beings, philosophy declared its bankruptcy regarding concrete social goals. — Theodor Adorno

The key-exercise will be Formal Logic. It is here that our curriculum shows its first sharp divergence from modern standards. The disrepute into which Formal Logic has fallen is entirely unjustified; and its neglect is the root cause of nearly all those disquieting symptoms which we have noted in the modern intellectual constitution. Logic has been discredited, partly because we have fallen into a habit of supposing that we are conditioned almost entirely by the intuitive and the unconscious. — Dorothy L. Sayers

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

Even to-day the masses of the Negroes see all too clearly the anomalies of their position and the moral crookedness of yours. You may marshal strong indictments against them, but their counter-cries, lacking though they be in formal logic, have burning truths within them which you may not wholly ignore, O Southern Gentlemen! — W.E.B. Du Bois

[Aristotle formal logic thus far (1787)] has not been able to advance a single step, and hence is to all appearances closed and completed. — Immanuel Kant

For the artist himself art is not necessarily therapeutic; he is not automatically relieved of his fantasies by expressing them. Instead, by some perverse logic of creation, the act of formal expressions may simply make the dredged-up material more readily available to him. — Al Alvarez

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

Logic is something the mind has created to conceal its timidity, a hocus-pocus designed to give formal validity to conclusions we are willing to accept if everybody else in our set will too. — Carl Lotus Becker

It remains to mention some of the ways in which people have spoken misleadingly of logical form. One of the commonest of these is to talk of 'the logical form' of a statement; as if a statement could never have more than one kind of formal power; as if statements could, in respect of their formal powers, be grouped in mutually exclusive classes, like animals at a zoo in respect of their species. But to say that a statement is of some one logical form is simply to point to a certain general class of, e.g., valid inferences, in which the statement can play a certain role. It is not to exclude the possibility of there being other general classes of valid inferences in which the statement can play a certain role — Peter Frederick Strawson

In life two negatives don't make a positive. Double negatives turn positive only in math and formal logic. In life things just get worse and worse and worse. — Robert McKee