On Impossibility (1950-1974)

"Every organism represents a system, by which term we mean a complex of elements in mutual interaction. From this obvious statement the limitations of the analytical and summative conceptions must follow. First, it is impossible to resolve the phenomena of life completely into elementary units; for each individual part and each individual event depends not only on conditions within itself, but also to a greater or lesser extent on the conditions within the whole, or within superordinate units of which it is a part. Hence the behavior of an isolated part is, in general, different from its behavior within the context of the whole. [...] Secondly, the actual whole shows properties that are absent from its isolated parts." (Ludwig von Bertalanffy, "Problems of Life", 1952)

"The history of mathematics shows that the introduction of better and better symbolism and operations has made a commonplace of processes that would have been impossible with the unimproved techniques." (Morris Kline,"Mathematics in Western culture", 1953)

"There comes a stage, however, as the system becomes larger and larger, when the reception of all the information is impossible by reason of its sheer bulk. Either the recording channels cannot carry all the information, or the observer, presented with it all, is overwhelmed. When this occurs, what is he to do? The answer is clear: he must give up any ambition to know the whole system. His aim must be to achieve a partial knowledge that, though partial over the whole, is none the less complete within itself, and is sufficient for his ultimate practical purpose." (W Ross Ashby, "An Introduction to Cybernetics", 1956)

"Uncertainty is introduced, however, by the impossibility of making generalizations, most of the time, which happens to all members of a class. Even scientific truth is a matter of probability and the degree of probability stops somewhere short of certainty." (Wayne C Minnick,"The Art of Persuasion", 1957)

"The outstanding feature of behavior is that it is often quite easy to recognize but extremely difficult or impossible to describe with precision." (Anatol Rapoport. "An Essay on Mind", General Systems, 1962)

"A theory in its scientific context is not a static museum piece, but is always being extended and modified to account for new phenomena. […] Moreover, without a model, it will be impossible to use a theory for one of the essential purposes we demand of it, namely to make predictions in new domains of phenomena." (Mary B Hesse," Models and Analogies in Science", 1963)

"I shall not attempt to prove that mathematics is useful. I will admit it and so save myself the trouble that here is a great and respected discipline where all is impossible yet much is useful. The usefulness largely flows from the impossibility. Mathematical concepts have been simplified and generalized until they describe an imaginative world no part of which could possibly exist outside men’s minds." (Billy E Goetz, "The Usefulness of the Impossible", 1963)

"It is impossible to overstate the importance of problems in mathematics. It is by means of problems that mathematics develops and actually lifts itself by its own bootstraps. […] Every new discovery in mathematics, results from an attempt to solve some problem." (Howard W Eves, "A Survey of Geometry", 1963)

It is not impossible that our own Model will die a violent death, ruthlessly smashed by an unprovoked assault of new facts […]. (Clive S Lewis, "The Discarded Image: An Introduction to Medieval and Renaissance Literature", 1964) 

"In all of natural philosophy, the most deeply and repeatedly studied part, next to pure geometry, is mechanics. […] The picture of nature as a whole given us by mechanics may be compared to a black-and-white photograph: It neglects a great deal, but within its limitations, it can be highly precise. Developing sharper and more flexible black-and-white photography has not attained pictures in color or three-dimensional casts, but it serves in cases where color and thickness are irrelevant, presently impossible to get in the required precision, or distractive from the true content." (Clifford Truesdell, "Six Lectures on Modern Natural Philosophy", 1966)

"In order to define a concept we have to indicate first of all that it is a special case of a more general concept. This is impossible for the concept of set, since this concept is already as broad as possible and is thus not a special case of any other concept." (Naum Ya. Vilenkin, "Stories about Sets", 1968)

"It is impossible, and it has always been impossible, to grasp the meaning of what we nowadays call physics independently of its mathematical form." (Jacob Klein, "Greek Mathematical Thought and the Origin of Algebra", 1968)

"Scientific knowledge is not created solely by the piecemeal mining of discrete facts by uniformly accurate and reliable individual scientific investigations. The process of criticism and evaluation, of analysis and synthesis, are essential to the whole system. It is impossible for each one of us to be continually aware of all that is going on around us, so that we can immediately decide the significance of every new paper that is published. The job of making such judgments must therefore be delegated to the best and wisest among us, who speak, not with their own personal voices, but on behalf of the whole community of Science. […] It is impossible for the consensus - public knowledge - to be voiced at all, unless it is channeled through the minds of selected persons, and restated in their words for all to hear." (John M Ziman, "Public Knowledge: An Essay Concerning the Social Dimension of Science", 1968)

"The choice of model is often the most critical aspect of a design and development engineering job, but it is impossible to give explicit rules or techniques.' (Fred C Scweppe, "Uncertain dynamic systems", 1973)

"It is impossible to devise a scientific experiment to describe the creation process, or even to ascertain whether such a process can take place. The Creator does not create at the whim of a scientist." (Henry M. Morris, "Scientific Creationism", 1974) 

"The field of probability and statistics is then transformed into a Tower of Babel, in which only the most naive amateur claims to understand what he says and hears, and this because, in a language devoid of convention, the fundamental distinctions between what is certain and what is not, and between what is impossible and what is not, are abolished. Certainty and impossibility then become confused with high or low degrees of a subjective probability, which is itself denied precisely by this falsification of the language. On the contrary, the preservation of a clear, terse distinction between certainty and uncertainty, impossibility and possibility, is the unique and essential precondition for making meaningful statements (which could be either right or wrong), whereas the alternative transforms every sentence into a nonsense." (Bruno de Finetti, "Theory of Probability", 1974)