What Is 'Semantic Bleaching'? How 'literally' can mean "figuratively". Literally How to use a word that literally drives some pe Is Singular 'They' a Better Choice? The awkward case of 'his or her'. Take the quiz. Our Favorite New Words How many do you know? How Strong Is Your Vocabulary? See synonyms for theorem on Thesaurus.
We could talk until we're blue in the face about this quiz on words for the color "blue," but we think you should take the quiz and find out if you're a whiz at these colorful terms. Words nearby theorem theophylline ethylenediamine , theor. Words related to theorem axiom , assumption , belief , deduction , dictum , doctrine , formula , fundamental , law , postulate , principle , proposition , rule , statement , theory , thesis , principium. Richeson January 26, Quanta Magazine.
One can test a scientific model by using the model to predict the results of an observation, then making the actual observation and comparing the results. If the model fails to accurately predict the result of the observation, then the model is in need of refinement; if the model's prediction matches the observation, then the model is consistent with the observation.
Consistency with an observation does not guarantee that the model will always match the phenomena for every future observation, but consistency with enough repeated observations does say that the model is reasonable candidate for an explanation of the phenomena. Over time, a model gets tested and refined, with details filled in by repeated observations and tests.
As mathematical models get tested and refined over time, we have increasing confidence in the effectiveness of our overall collection of mathematical models. That is, over time the current version of a set of models becomes a better and better description of reality. Note that, by contrast, common claims are often granted "fact" status after only a single observation or inference! Because of the difference in the levels of testing, the "facts" of everyday life are actually much more likely to be incorrect than are our scientific models.
As our hypotheses are being tested and refined until our level of confidence in them is very high, we seek a set of principles which provide a coherent explanation for the various laws and facts which we've assembled.
This kind of detailed explanation of some aspect of reality, incorporating all of the various well-tested hypotheses and mathematical models and explaining the various facts and laws that we've observed, is what we call a scientific theory. This is quite a different kind of thing entirely from what one might call a "theory" in day-to-day life. Our usual non-technical meaning of "theory" is much closer in meaning to the scientific term "hypothesis", that is, a simple idea which can be tested.
For example, a detective might have a "theory" about who committed the murder, or a student might have a "theory" about the best way to get a good grade. These are not "theories" in the scientific sense! A single individual never creates an entire scientific theory alone, for scientific theories are much too large and complex. Even theories which have an individual's name associated, such as "Einstein's theory of General Relativity" or "Darwin's theory of Evolution" are not the work of a single individual but are the cumulative results of the collaboration of many individuals over time.
A scientific theory is an extensive body of knowledge which brings together a great number of well-tested hypotheses and mathematical models, weaving them into a coherent explanation for the facts and laws we can observe. An everyday hypothesis is no more a scientific theory than a single bolt is an automobile.
A common related confusion is the idea that scientific theories are waiting to be tested and proved before becoming accepted as a fact or a law. To prove a statement means to derive it from axioms and other theorems by means of logic rules, like modus ponens. A proof is needed to establish a mathematical statement. A single counterexample suffices to refute such a statement. There is certainly an ambiguity mathematicians live with.
Some rules like the Law of Excluded Middle and some axioms like the Axiom of Choice are not universally accepted by all mathematicians. Commonly, auxiliary theorems of a lesser significance are called lemmas. If there is a need to emphasize an importance of a theorem in proving another theorem, the latter is called a corollary from the former, especially when the proof at hand is short.
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