Both pure and applied science have gradually pushed further and further the requirements for accuracy and precision. However, applied science, particularly in the mass production of interchangeable parts, is even more exacting than pure science in certain matters of accuracy and precision.

The real problem in speech is not precise language. The problem is clear language. The desire is to have the idea clearly communicated to the other person. It is only necessary to be precise when there is some doubt as to the meaning of a phrase, and then the precision should be put in the place where the doubt exists. It is really quite impossible to say anything with absolute precision, unless that thing is so abstracted from the real world as to not represent any real thing.<p>Pure mathematics is just such an abstraction from the real world, and pure mathematics does have a special precise language for dealing with its own special and technical subjects. But this precise language is not precise in any sense if you deal with real objects of the world, and it is only pedantic and quite confusing to use it unless there are some special subtleties which have to be carefully distinguished.

The real problem in speech is not precise language. The problem is clear language. The desire is to have the idea clearly communicated to the other person. It is only necessary to be precise when there is some doubt as to the meaning of a phrase, and then the precision should be put in the place where the doubt exists. It is really quite impossible to say anything with absolute precision, unless that thing is so abstracted from the real world as to not represent any real thing.

The presentation of such material is not designed for any particular scientific group. Rather, the principal attempt is to be as specific as possible in language understandable to scientists and laymen alike, with avoidance of ambiguous generalities. The physicist, chemist, life scientist, psychiatrist, and philosopher may each use more technical or specialized terminology to state the same premise. Such interpretation is expected. It will indicate that the plan of communication is workable, that the "plain" talk does convey the proper meaning to a wide base rather than to a narrow pinnacle of specialists. It is expected, too, that many interpretations will be contradictory.

Everyday words are inherently imprecise. They work well enough in everyday life that you don’t notice. Words seem to work, just as Newtonian physics seems to. But you can always make them break if you push them far enough.

All exact science is dominated by the idea of approximation. When a man tells you that he knows the exact truth about anything, you are safe in inferring that he is an inexact man.

The precision of science depends not only on what we measure but on what we are structurally capable of acting on. Effort is not just output, it is a precondition.

A science only advances with certainty, when the plan of inquiry and the object of our researches have been clearly defined; otherwise a small number of truths are loosely laid hold of, without their connexion being perceived, and numerous errors, without being enabled to detect their fallacy.

No fact in the world is instant, infinitesimal and ultimate, a single mark. There are, I hold, no atomic facts. In the language of science, every fact is a field — a crisscross of implications, those that lead to it and those that lead from it. … We condense the laws around concepts. Science takes its coherence, its intellectual and imaginative strength together, from the concepts at which its laws cross, like knots in a mesh.

Among the various paradigmatic changes in science and mathematics in this century, one such change concerns the concept of uncertainty. In science, this change has been manifested by a gradual transition from the traditional view, which insists that uncertainty is undesirable in science and should be avoided by all possible means, to an alternative view, which is tolerant of uncertainty and insists that science cannot avoid it. According to the traditional view, science should strive for certainty in all its manifestations (precision, specificity, sharpness, consistency, etc.); hence, uncertainty (imprecision, nonspecificity, vagueness, inconsistency,etc.) is regarded as unscientific. According to the alternative (or modem) view, uncertainty is considered essential to science; it is not only an unavoidable plague, but it has, in fact, a great utility.

Science as a system of statements is always an object of discussion. Statements are to be compared with statements, and not with 'experience', or with 'the world', or with something else. All that meaningless doubling belongs to more or less subtle metaphysics and as such must be rejected. Every new statement is to be confronted with existing ones, already brought to a state of harmony between themselves. A statement will be considered correct if it can be joined to them.

Science presupposes the use of thoughtful, precise terminology, which leaves no room for ambiguity. Ideology, on the contrary, presupposes the use of meaningless, vague, equivocal terms. Scientific terminology does not need to be analyzed or interpreted. Ideological phraseology must be commented on, compared, rethought. Scientific assertions assume that we can at any time confirm them, refute them, or even in extreme cases, recognize their insoluble nature. The absurdity of ideological propositions means that they can neither be refuted nor confirmed p. 285

The more precise the measurement of position, the more imprecise the measurement of momentum, and vice versa.

Our language, in fact, is only approximate, and even in science it is so indefinite that if we lose sight of phenomena and cling to words, we are speedily outside of reality.… [W]e must always cling to phenomena and see in words only expressions empty of meaning, if the phenomena they represent are not definite, or if they are absent.