On Facts (1990-1999)

"On this view, we recognize science to be the search for algorithmic compressions. We list sequences of observed data. We try to formulate algorithms that compactly represent the information content of those sequences. Then we test the correctness of our hypothetical abbreviations by using them to predict the next terms in the string. These predictions can then be compared with the future direction of the data sequence. Without the development of algorithmic compressions of data all science would be replaced by mindless stamp collecting - the indiscriminate accumulation of every available fact. Science is predicated upon the belief that the Universe is algorithmically compressible and the modern search for a Theory of Everything is the ultimate expression of that belief, a belief that there is an abbreviated representation of the logic behind the Universe's properties that can be written down in finite form by human beings." (John D Barrow, New Theories of Everything", 1991)

"The popular image of mathematics as a collection of precise facts, linked together by well-defined logical paths, is revealed to be false. There is randomness and hence uncertainty in mathematics, just as there is in physics." (Paul Davis, "The Mind of God", 1992)

„[...] there is no criterion for appreciation which does not vary from one epoch to another and from one mathematician to another. [...] These divergences in taste recall the quarrels aroused by works of art, and it is a fact that mathematicians often discuss among themselves whether a theorem is more or less ‚beautiful‘. This never fails to surprise practitioners of other sciences: for them the sole criterion is the 'truth' of a theory or formula." (Jean Dieudonné, „Mathematics - The Music of Reason", 1992)

"The word theory, as used in the natural sciences, doesn’t mean an idea tentatively held for purposes of argument - that we call a hypothesis. Rather, a theory is a set of logically consistent abstract principles that explain a body of concrete facts. It is the logical connections among the principles and the facts that characterize a theory as truth. No one element of a theory [...] can be changed without creating a logical contradiction that invalidates the entire system. Thus, although it may not be possible to substantiate directly a particular principle in the theory, the principle is validated by the consistency of the entire logical structure." (Alan Cromer, "Uncommon Sense: The Heretical Nature of Science", 1993)

"Worldviews are social constructions, and they channel the search for facts. But facts are found and knowledge progresses, however fitfully. Fact and theory are intertwined, and all great scientists understand the interaction." (Stephen Jay Gould, "Shields of Expectation - and Actuality", 1993)

"As a result, surprisingly enough, scientific advance rarely comes solely through the accumulation of new facts. It comes most often through the construction of new theoretical frameworks. [..]  To understand scientific development, it is not enough merely to chronicle new discoveries and inventions. We must also trace the succession of worldviews" (Nancy R Pearcey & Charles B Thaxton, "The Soul of Science: Christian Faith and Natural Philosophy", 1994)

"Clearly, science is not simply a matter of observing facts. Every scientific theory also expresses a worldview. Philosophical preconceptions determine where facts are sought, how experiments are designed, and which conclusions are drawn from them." (Nancy R Pearcey & Charles B. Thaxton, "The Soul of Science: Christian Faith and Natural Philosophy", 1994)

"Mathematics is not just a collection of isolated facts: it is more like a landscape; it has an inherent geography that its users and creators employ to navigate through what would otherwise be an impenetrable jungle." (Ian Stewart, "Nature’s Numbers", 1995)

"Mathematics is not the study of an ideal, preexisting nontemporal reality. Neither is it a chess-like game with made-up symbols and formulas. Rather, it is the part of human studies which is capable of achieving a science-like consensus, capable of establishing reproducible results. The existence of the subject called mathematics is a fact, not a question. This fact means no more and no less than the existence of modes of reasoning and argument about ideas which are compelling an conclusive, ‘noncontroversial when once understood’." (Philip J Davis & Rueben Hersh, "The Mathematical Experience", 1995)

"The shift of paradigms requires an expansion not only of our perceptions and ways of thinking, but also of our values. […] scientific facts emerge out of an entire constellation of human perceptions, values, and actions-in one word, out of a paradigm-from which they cannot be separated. […] Today the paradigm shift in science, at its deepest level, implies a shift from physics to the life sciences." (Fritjof Capra, "The Web of Life", 1996)

"Mathematics is the study of analogies between analogies. All science is. Scientists want to show that things that don’t look alike are really the same. That is one of their innermost Freudian motivations. In fact, that is what we mean by understanding." (Gian-Carlo Rota, "Indiscrete Thoughts", 1997)

"Theories rarely arise as patient inferences forced by accumulated facts. Theories are mental constructs potentiated by complex external prods (including, in idealized cases, a commanding push from empirical reality)." (Stephen J Gould, "Leonardo's Mountain of Clams and the Diet of Worms" , 1998)

"When we entrust the domain of values to those whose intellectual concerns are essentially centred on empirical facts, and whose conceptual frameworks are inevitably constructed around sets of empirical facts, we need not be surprised if the result is moral confusion." (Ronald W K Paterson, "The New Patricians", 1998)