On Facts (1940-1949)

"[…] there is probably less difference between the positions of a mathematician and of a physicist than is generally supposed, [...] the mathematician is in much more direct contact with reality. This may seem a paradox, since it is the physicist who deals with the subject-matter usually described as 'real', but [...] [a physicist] is trying to correlate the incoherent body of crude fact confronting him with some definite and orderly scheme of abstract relations, the kind of scheme he can borrow only from mathematics." (Godfrey H Hardy, "A Mathematician's Apology", 1940)

"What the diagram has in common with the symbolic schema is the fact that the diagram spatially represents an abstract and unextended object. But there is here nothing other than a determinate location in space. This location serves as a mooring, an attachment, an orientation for our memory, but does not play any role in our thought." (Jean-Paul Sartre, "The Imaginary: A phenomenological psychology of the imagination", 1940)

"Mathematicians deal with possible worlds, with an infinite number of logically consistent systems. Observers explore the one particular world we inhabit. Between the two stands the theorist. He studies possible worlds but only those which are compatible with the information furnished by observers. In other words, theory attempts to segregate the minimum number of possible worlds which must include the actual world we inhabit. Then the observer, with new factual information, attempts to reduce the list further. And so it goes, observation and theory advancing together toward the common goal of science, knowledge of the structure and observation of the universe." (Edwin P Hubble, "The Problem of the Expanding Universe", 1941)

"Different kinds of facts, having different degrees of scientific value, are ascertainable in these two ways. Facts ascertainable by mere observation are what are called common-sense facts, i.e. facts accessible to a commonplace mind on occasions frequent enough to be rather often perceived and of such a kind that their characteristics can be adequately perceived without trouble: so that the facts concerning them can be familiar to persons not especially gifted and not especially alert." (Robin G Collingwood, "The New Leviathan: Or Man, Society, Civilization and Barbarism", 1942)

"The atomic theory plays a part in physics similar to that of certain auxiliary concepts in mathematics: it is a mathematical model for facilitating the mental reproduction of facts." (Ernst Mach, "The Science of Mechanics" 5th Ed, 1942)

"The faith of scientists in the power of mathematics is so implicit that their work has gradually become less and less observation, and more and more calculation. The promiscuous collection and tabulation of data have given way to a process of assigning possible meanings, merely supposed real entities, to mathematical terms, working out the logical results, and then staging certain crucial experiments to check the hypothesis against the actual, empirical results. But the facts [...] accepted by virtue of these tests are not actually observed at all." (Susanne K Langer, "Philosophy in a New Key", 1942)

"A material model is the representation of a complex system by a system which is assumed simpler and which is also assumed to have some properties similar to those selected for study in the original complex system. A formal model is a symbolic assertion in logical terms of an idealised relatively simple situation sharing the structural properties of the original factual system." (Arturo Rosenblueth & Norbert Wiener, "The Role of Models in Science", Philosophy of Science Vol. 12 (4), 1945)

"Every time one combines and records facts in accordance with established logical processes, the creative aspect of thinking is concerned only with the selection of the data and the process to be employed, and the manipulation thereafter is repetitive in nature and hence a fit matter to be relegated to the machines." (Vannevar Bush, "As We May Think", 1945)

"We can put it down as one of the principles learned from the history of science that a theory is only overthrown by a better theory, never merely by contradictory facts." (James B Conant, "On Understanding Science", 1947)

"A man desiring to understand the world looks about for a clue to its comprehension. He pitches upon some area of commonsense fact and tries to understand other areas in terms of this one. The original area becomes his basic analogy or root metaphor." (Stephen Pepper, "World Hypotheses: A Study in Evidence", 1948)

"To some people, statistics is ‘quartered pies, cute little battleships and tapering rows of sturdy soldiers in diversified uniforms’. To others, it is columns and columns of numerical facts. Many regard it as a branch of economics. The beginning student of the subject considers it to be largely mathematics." (The Editors, "Statistics, The Physical Sciences and Engineering", The American Statistician, Vol. 2, No. 4, 1948)

"[…] science, properly interpreted, is not dependent on any sort of metaphysics. It merely attempts to cover a maximum of facts by a minimum of laws." (Herbert Feigl, "Naturalism and Humanism", American Quarterly, Vol. 1, No. 2, 1949)

"Facts are the raw material of science - the bricks from which our model of the universe must be built - and we are rightly taught to search for sound and solid facts, for strong and heavy bricks that will serve us well in building foundations, for clean and polished bricks that will fi t neatly into ornamental towers. But while accumulating the bricks may be a contribution to science, we must take care that the pile does not become a hopelessly discouraging jumble. For science itself is not brickmaking - it is, at the workaday and technical level, bricklaying; and at the creative and artistic level, architecture, the designing of an edifice that will utilize all the bricks to the very best of advantage." (Marston Bates, "The Natural History of Mosquitoes", 1949)

"However obvious these facts may appear at first glance, they are actually not so obvious as they seem except when we take special pains to think about the subject. Symbols and things symbolized are independent of each other; nevertheless, we all have a way of feeling as if […] there were necessary connections." (Samuel I Hayakawa, "Language in Thought and Action", 1949)