On Theories (2010-2019)

“All scientific theories, even those in the physical sciences, are developed in a particular cultural context. Although the context may help to explain the persistence of a theory in the face of apparently falsifying evidence, the fact that a theory arises from a particular context is not sufficient to condemn it. Theories and paradigms must be accepted, modified or rejected on the basis of evidence.”  (Richard P Bentall,  “Madness Explained: Psychosis and Human Nature”, 2003)

“A theory is like medicine (or government): often useless, sometimes necessary, always self-serving, and on occasion lethal. So, it needs to be used with care, moderation and close adult supervision.” (Nassim N Taleb, “The Black Swan: The Impact of the Highly Improbable”, 2007)

“With each theory or model, our concepts of reality and of the fundamental constituents of the universe have changed.” (Stephen Hawking & Leonard Mlodinow, “The Grand Design”, 2010)

 “A theory is a set of deductively closed propositions that explain and predict empirical phenomena, and a model is a theory that is idealized.” (Jay Odenbaugh, “True Lies: Realism, Robustness, and Models”, Philosophy of Science, Vol. 78, No. 5, 2011)

"Science would be better understood if we called theories ‘misconceptions’ from the outset, instead of only after we have discovered their successors." (David Deutsch, "Beginning of Infinity", 2011)

"Complexity has the propensity to overload systems, making the relevance of a particular piece of information not statistically significant. And when an array of mind-numbing factors is added into the equation, theory and models rarely conform to reality." (Lawrence K Samuels, "Defense of Chaos: The Chaology of Politics, Economics and Human Action", 2013)

“[…] if one has a theory, one needs to be willing to try to prove it wrong as much as one tries to provide that it is right […]” (Lawrence M Krauss et al, A Universe from Nothing, 2013)

"Another way to secure statistical significance is to use the data to discover a theory. Statistical tests assume that the researcher starts with a theory, collects data to test the theory, and reports the results - whether statistically significant or not. Many people work in the other direction, scrutinizing the data until they find a pattern and then making up a theory that fits the pattern." (Gary Smith, "Standard Deviations", 2014)

"Data clusters are everywhere, even in random data. Someone who looks for an explanation will inevitably find one, but a theory that fits a data cluster is not persuasive evidence. The found explanation needs to make sense and it needs to be tested with uncontaminated data." (Gary Smith, "Standard Deviations", 2014)

"Data without theory can fuel a speculative stock market bubble or create the illusion of a bubble where there is none. How do we tell the difference between a real bubble and a false alarm? You know the answer: we need a theory. Data are not enough. […] Data without theory is alluring, but misleading." (Gary Smith, "Standard Deviations", 2014)

"[...] it is one thing to posit a set of axioms for a putative discipline. It is quite another to show that those proposed axioms are not mutually contradictory. A set of axioms that is not mutually contradictory is also called a consistent axiom system. Of course, a set of mutually contradictory axioms might be such that one can easily see a contradiction or maybe a simple argument could reveal a contradiction. More worrisome is the possibility that an argument that is very clever or very long or both is needed to reveal a contradiction. Given a mathematical theory that seems to be free of internal contradictions, the way mathematicians show it is, in fact, free of contradictions is by constructing what is called a model for the theory. This involves using another mathematical theory, say set theory, to produce a concrete mathematical object that satisfies the axioms of the theory being investigated. Once a model has been constructed, then we know that if set theory itself is free of internal contradictions, then the same is true of the theory being investigated. In practice, one does not often go all the way back to set theory to construct a model - mathematicians work with higher level constructions - but, in principle, they could start with set theory and work up from there." (Steven G Krantz & Harold R Parks, "A Mathematical Odyssey: Journey from the Real to the Complex", 2014)

"We are hardwired to make sense of the world around us - to notice patterns and invent theories to explain these patterns. We underestimate how easily patterns can be created by inexplicable random events - by good luck and bad luck." (Gary Smith, "Standard Deviations", 2014)

"Mathematical modeling is the modern version of both applied mathematics and theoretical physics. In earlier times, one proposed not a model but a theory. By talking today of a model rather than a theory, one acknowledges that the way one studies the phenomenon is not unique; it could also be studied other ways. One's model need not claim to be unique or final. It merits consideration if it provides an insight that isn't better provided by some other model." (Reuben Hersh,"Mathematics as an Empirical Phenomenon, Subject to Modeling", 2017)

“Scientists generally agree that no theory is 100 percent correct. Thus, the real test of knowledge is not truth, but utility.” (Yuval N Harari, “Sapiens: A brief history of humankind”, 2017) 

"In mathematics, we often depend on the proof of a statement to offer not only a justification of its truth, but also a way of understanding its implications, its connections to other established truths - a way, in short of explaining the statement. But sometimes even though a proof does its job of showing the truth of a result it still leaves us with the nagging question of why.’ It may be elusive - given a specific proof - to describe in useful terms the type of explanation the proof actually offers. It would be good to have an adequate vocabulary to help us think about the explanatory features of mathematics (and, more generally, of science)." (Barry Mazur, "On the word ‘because’ in mathematics, and elsewhere", 2017)

“A theory is nothing but a tool to know the reality. If a theory contradicts reality, it must be discarded at the earliest.” (Awdhesh Singh, “Myths are Real, Reality is a Myth”, 2018)