Refutability (опровержимость) is property of a scientific concept, that determines the possibility of its negation, refutation.
Refutability is one of necessary requirements, postulated for the scientific knowledge at the Main Page of TORI, as Third TORI axiom.
History and terminology
The first attempt to formulate refutability as basic property of the scientific knowledge is usually attributed to Karl Popper, although he used the term falsifiability instead  . The term falsifiability is ambiguous. Requirement of flsifiability allows to qualify as pseudo-science all the official Russian versions of the Russian history, as the falsifications are prohibited there, and there is special presidential commission to fight against those who are qualified as "falsifiers" . The falsifiability may mean fraud, and it is desirably to avoid it, at least in science.
In TORI, the term falsifiabication is not used in any of its meanings. In the case of dishonest distortion of data, the term fraud is used. In the case of indication of inconsistency of a concept the term refutation is used. Accordingly, the property is not called falsifiability, but refutability.
The requirement of reproducibility  implies both, the Verifiability and Refutability. If the repetition of some experiment reproduces the prediction of some concept, it is interpreted as verification; if the results disagree, the disagreement can be matter for the search of mistakes and for the refutation. In particular, the reproducibility is essential for computational mathematics; the results of evaluation of some quantity, results of simulations are supposed to be reproduced, if performed with different facilities (another hardware, another software, another code). For the tracing of any possible disagreements and errors, it is important to specify the software used and to provide the initial codes . In order to provide the reproducibility, simplifying the refutation of concepts, in TORI, the figures are supplied with generators, id est, codes, used for the generation. Stability of figures is verified, running the generators at different operational systems (some macintosh and linux); so, the figures are expected to reproduce also at running with other operational systems.
Reproducibility allows both, refutation and verification. If the result of a new experiment of calculus reproduces the previously reported results, this is considered as verification. If not, this may be matter for the refutation. In such a way, verifiability is closely related to refutability; these two qualities can be combined to the requirement of reprodicibility. However, the practice of analysing of the scientific (and pseudo–scientific) claims indicate, that lack of refutability is most often defect of the concepts suggested. For this reason, it worth to separate refutability in a special TORI axiom, and keep reproducibility as a special case.
Range of validity
For commonly accepted paradigms, the refutation usually means the setting of the new limit of the range of applicability. This allows the scientific revolutions. . The concept still may be valid in the reduced range of validity. This prevents loss of the scientific knowledge at a scientific revolution.
The Newtonian mechanics with its universal time and certain trajectories of all particles had been successfully refuted twice: once, by the theory of the special relativity, and then, by the Quantum mechanics. The third attempt to refute it with the inertioids like gravitsapa (developed under the leadership of the RAEN functionary Valery Menshikov in the Khrunichev's Center) is not successful: Up to year 2011, after several years of research and attempts, including the launching of the perpetual motion machines, inertioids to the Earth's orbit, no one additional criterion that would narrow the range of validity of mechanics has not been formulated; no new criterion for the range of validity of the law of conservation of energy–momentum is suggested. The claim for the realization of the inertial propulsion should be qualified as fraud : the creators of gravitsapa cannot claim that they do not know about the conservation of momentum .
Within the axioms of TORI ANY scientific concept allows the refutation, even of the axioms of arithmetics. Such an example is described in the article Mizugadro number. But even if the Mizugadro number exists, the arithmetics remains as very useful approximation with wide range of applicability.
The refutability makes the scientific concept extremely efficient in the description of phenomena and predictions. It is one of the most important tools in the research. This property forces the researcher to arrange the experiments and observations in such a way, that any result appears as benefit.
If the experiment is aimed to confirm some paradigm (id set, the commonly–accepted concept), and it confirms it, this is supposed to be a benefit.
If such an experiment contradicts the paradigm, refutes it - even better. The conditions where the paradigm, theory fails should be carefully described, allowing the colleague reproduce the deduction or the observation and confirm the failure.
For example, the violation of the conservation of energy–momentum, even if it happens in the twelve's digit, is of interest for highest rank physical journal rather than for a technical application. For example, the category pseudoscience includes any attempt to use any inertioid for the propulsion of a spacecraft without to formulate criteria, hypothesis, that would indicate the limit of applicability of the law of conservation of energy-momentum, a way to see the violation in the laboratory, estimates, how strong deviation is expected in each case.
Application of the criterion
The practical use of the criterion of refutability may lead to counter-intuitive conclusions. Some concepts the society, often conceded as a "scientific fact", happen to belong to a religion rather than to any science. Below, few such examples are considered.
Creation of first life
The concept about the spontaneous creation of the first life on the Earth was compulsory in the USSR. It was one of the key statements of the Marx-Lenin philosophy.
This concept satisfies some of the TORI axioms. In particular, it is verifiable; it allows the experiment, that confirms it. Such an experiment could be creation of new living objects from the "dead" chemical components in the laboratory. The axioms do not require that the concept "is already confirmed"; it requires, that the confirming experiment can be described.
As for refutability.. In terms of that philosophy, no experiment that refutes such a concept can be described.
The concept of creation of life by God, contrary, is scientific: it can be refuted. It predicts that no new life can be created in the laboratory by the spontaneous arrangement of atoms and molecules.
The refutability does not make the concept truth, but it is necessary for the qualification as "science".
Creation of artificial intellect
The concept of impossibility of creation of an artificial intellect looks similar to that about creation of first life. However, the criteria of intelligence should be adjusted. For example, the recognition of a non-human creature as subject of the International Law with rights equivalent to the Human Rights might be used as the criterion.
Then, the concept about impossibility of the artificial intellect can be considered as scientific: at least, it can be refuted.
The hypothesis of this existence cannot be refuted, it is not scientific.
Conservation of Energy-momentum
The fundamental law of conservation of energy-momentum follows from the symmetry of our Universe. This conservation allows to make the atomic clock and in this sense, is verged with about 16 decimal digits; the following increase of the precision is limited by the curvature of the space-time, caused by the gravitational interaction.
The statement There exist some tornado–like style of movement of a liquid, at which the total momentum of the isolated system does not preserve  is not refutable: there is no experiment that would refute it. While violation of the First Law of Newton is not specified with numbers, not expressed qunantitatively, any result of any experiment with violation of energy-momentum can be qualified as "successful in general" . No predictions can be made on the base of the irrefutable concept.
Equivalence of gravitational and inertial forces
According to the General Theory of Relativity (GTR)
, the gravity provides equal acceleration to all fields.
According to the Logunov Theory of Gratity (LTR) , the gravitate provides equal acceleration to all fields, except the gravitational field.
Both theories give the identical prediction for the barely-relativistic systems (similar to the Solar system). Due to the exception, mentioned above, from the Axiom of pluralism, the GTR is principal, and the RTG should be qualified as an "alternative" concept. Nevertheless, this LTG is still refutable: narrow beam of gravitons is not supposed to deviate in vicinity of a massive body, as the beam of photons does; if the beam of gravitons deviate, as an electromagnetic beam does, this would refute the LTG, indicating the limits of applicability. (Even in this case, the range of applicability of LTG seems to remain larger than that of the Newtonian mechanics). Up to technological achievement of 21 century, the narrow beams of gravitons are not available (as beams of photons); yet, it is not possible to perform an experiment to negate the LTG.
First, Marxism claimed that in the century 20, during the life of the generation that already past away, the communism is built. First, this prediction had been formulated in the speech by V.Lenin in 1920; then, again, in 1956. Such a conclusion is deduced from the assumption about the good will and honesty of the soviet veterans, and written in the canonized text of the Khruschev's Program of the Communist Party of the USSR.
Second, from the same assumption about good will and honesty of the soviet veterans, there was deduced the conclusion that the USSR will last forever; this was fixed in the national hymn of the USSR.
Both concepts were refutable, and were refuted in the same century 20.
More Irrefutable concepts
The irrefutable concepts are used to build–up religions. Here are examples of irrefutable conceits:
0. God had created our Universe.
1. Communism is future of all the humanity.
2. God blesses America.
3. Imperialism is evil.
4. God gives the immortal soul to everyone.
5. The righteous will be at Heaven.
Even the statement by O.Bender (personage of the Novel "12 chairs" by I.Ilf and E.Petrov  ) about the "Interplanetary Chess Tournament" in village "Vasyuki" is irrefutable: Bender does not specify the date of the tournament, and does not guarantee that the "Interplanetary Chess Tournament" will take place during the lifetime of victims of his fraud. In the similar way, the statement, that the tornado-like movement of a liquid may produce an inertial support-less force, may be considered as irrefutable: it suggests no estimate limiting the range of validity of the law of conservation of energy-momentum.
No predictions can be done on the basis of irrefutable concepts. In particular, in the experiments with gravitsapa, no estimates for the parameters of the orbit of the satellite Yubileiny due the vibrations of gravitsapa was announced, and no comparison with the measured parameters was published.
Some of the examples above are taken from the article Place of science in the human knowledge.
- http://www.stephenjaygould.org/ctrl/popper_falsification.html Karl R. Popper. Science as falsification. Karl Popper, Conjectures and Refutations. London: Routledge and Keagan Paul, 1963, pp. 33-39
- http://philosophyfaculty.ucsd.edu/faculty/rarneson/Courses/popperphil1.pdf Karl Popper. Science: Conjectures and refutations. - 'Philosophy of Science: a Personal Report', in British Philosophy in Mid-Century, ed. C. A. Mace, 1957.
- http://psycnet.apa.org/psycinfo/1961-02882-000 Popper, Karl R. The logic of scientific discovery. Oxford, England: Basic Books. (1959).
- http://www.rg.ru/2009/05/20/komissia-dok.html Д.Медведев. О Комиссии при Президенте Российской Федерации по противодействию попыткам фальсификации истории в ущерб интересам России. Указ президента РФ, Русская Газета, 15 мая 2009 г. N 549 . (In Russian)
- http://press.princeton.edu/chapters/i7022.pdf Robert Ehrlich: Nine Crazy Ideas in Science. © 2001, by Princeton University Press. .. the developer of a new theory must do everything possible to prove the theory is incorrect, find its flaws, and even make any weaknesses known to the community. .. Revolutionary new ideas in physics and other sciences are rarely accepted immediately by the scientific community. ..
- http://calteches.library.caltech.edu/3043/1/CargoCult.pdf Richard P. Feynman. Cargo Cult Science. Caltech;s 1974 commencement address. .. if you're doing an experiment, you should report everything that you think might make it invalid - not only that you think is right about it: other cases that could possibly explain your result; and things you thought of that you've eliminated by some other experiment, and how they worked – to make sure the other fellow can tell they have been eliminated.
- http://icerm.brown.edu/tw12-5-rcem Reproducibility in Computational and Experimental Mathematics (December 10-14, 2012).
- http://www.ams.org/notices/201306/rnoti-p679.pdf D.H.Bailey, J.M.Borwein, Victoria Stodden. Set the Default to “Open”. Notices of the American Mathematical Society, 2013, v.60, No.6, p. 679-680.
- http://www.des.emory.edu/mfp/Kuhn.html T.S.Kuhn. The Structure of Scientific Revolutions. 2nd. ed., Chicago: Univ. of Chicago Pr., 1970.
- http://pphmj.com/abstract/5076.htm D.Kouznetsov. Support of non-traditional concepts. Far East Journal of Mechanical Engineering and Physics, 1, No.1, p.1-6 (2010)
- http://ufn.ru/tribune/trib120111 D.Kouznetsov. Place of science and physics in the human knowledge. Physics-Uspekhi, v.181, Трибуна, p.1-9 (2011, in Russian)
- Place of science in the human knowledge
- http://www.grani.ru/Society/Science/m.174440.html Академик Александров: "Гравицапа" противоречит законам физики. Грани.Ру, 06.02.2010. .."Инновационный" двигатель, основанный "на новых физических принципах получения тяги", который в ближайшее время будет тестироваться на борту спутника "Юбилейный", нарушает фундаментальный закон сохранения импульса, и разработчики двигателя не могут этого не понимать. Об этом заявил Граням.Ру член Комиссии РАН по борьбе с лженаукой и фальсификацией научных исследований, академик Евгений Александров.(in Russian)
- http://en.rian.ru/analysis/20050329/39700712.html Andrei KISLYAKOV. RUSSIA TO HELP DEVELOP NUCLEAR-POWERED SPACECRAFT. 15:34 29/03/2005. ... the R&D institute of space systems near Moscow is busy developing a perpetuum mobile (perpetual-motion engine), of sorts. This engine that will have a virtually unlimited service life could be used on Earth and in outer space.// Our institute's staffers have been developing a non-jet propulsion unit for several years in a row, Valery Menshikov, who heads this institute, said in mid-March. A liquid or solid-state propulsive mass moves along a preset tornado-shaped trajectory inside this engine, thereby ensuring sustainable propulsion.
- http://english.pravda.ru/science/tech/14-04-2009/107399-Russian_scientists-0 Russian scientists test perpetual motion machine in space. "Pravda", 14.04.2009. Specialists of the Institute for Space Systems conducted successful tests of the perpetual motion machine in space. Valery Menshikov, the director of the institute, said that the machine was installed at Yubileiny satellite which was launched into orbit almost a year ago. The satellite can now move from one orbit to another with the help of the engine, which discharges no reaction mass.// The first tests were conducted in June and July of 2008. The tests revealed some problems that need further developments of the machine, but the orbital experiment was conducted successfully in general.
- http://math.ucr.edu/home/baez/einstein/ J.C.Baez, E.F.Bunn. The Meaning of Einstein's Equation.(2006)
- http://ebookee.org/The-Theory-of-Gravity-A-A-Logunov_308692.html A.A.Logunov. The Theory of Gravity. (2001)
- Ilf and Petrov. The Twelve Chairs. (transition from Russian "Двенадцать стульев", 19 Oct 2002).