The TORI axioms are formulated in 2009 as generalization, interpretation of the empiric observations of ways of the scientific research. The experience of dealing with as the honest errors, as the intentional frauds and demagogy is taken into account. These axioms are published in 2010 in the first article of the Far East Journal of Mechanical Engineering and Physics , and then, in 2011, in the more detailed article Place of science in the human knowledge written for the Russian journal Uspekhi .
In 2011, on the base of the TORI axioms, the site tori.ils.uec.ac.jp/TORI had been created. The name TORI axioms is shosen after the name of that site. The site is available since 2011 March to 2013 February. 2013February 27, the site had been attacked by the cruel opponents, and since that, it is not available at its original URL. Some articles from there are copypasted to http://budclub.ru/k/kuznecow_d_j and to http://mizugadro.mydns.jp . The TORI axioms are mentioned in at the Main Page of this site.
S1. Applicability: The concept has some limited range of validity, distinguishable from the empty set.
S2. Verifiability: In the terms of the already accepted concepts, some specific experiment with some specific result, that confirms the concept, can be described.
S3. Refutability: In the terms of the concept, some specific experiment with some specific result, that negates the concept, can be described.
S4. Selfconsistency: No internal contradictions of the concept are known.
S5. Principle of correspondence: If the range of validity of a new concept intersects the range of validity of another already accepted concept, then, the new concept either reproduces the results of the old concept, or indicates the way to refute it. (For example, the estimate of the range of validity of the old concept may be wrong.)
S6. Pluralism: Mutually-contradictive concepts may coexist; if two concepts satisfying S1-S5 have some common range of validity, then, in this range, the simplest of them has priority.
TORI as science
Some "popular" articles contain statements
(1) "Scientists have shown, that .." or (2) "Scientists have found, that ..", or even (3) "The science had proven, that.."
instead of to provide the link to the original publication. Often, the declaration, that follows such a statement, is wrong; the journalists do not know, what science is. (How many physicians know physics?)
However, If one believes, that some statement still refers to science, the prefix of kind (1)-(3) should be replaced to the specific link, for example,
"Professor Kuroi Black  suggests, that ..."
The common confusion is, that one believes, that the existence of the rigorous mathematical proof of some statement indicates, that that statement is true, better than the series of failures in the honest attempts to negate this statement. This is just observation, not a theorem, that the mathematical deductions often have mistakes; and sometimes, the results are also wrong .
In such a way, even if the serious references are provided, this does not guarantee the correctness of the statement borrowed, but some hopes. However, if there is some "Scientists have shown, that .." instead of references, there are no hopes that the statement is correct.
The observation above explains, why the existence of the rigorous mathematical proof is not even mentioned among the TORI axioms.
TORI as religion
The TORI axioms can be considered as dogmas of the special religion. These asioms are not very new. The main idea of this religion were developed by Karl Popper, Thomas Kuhn, George Orwell (See Orwell1984), Heils Bohr, Stanislav Lem, Strugatsky brothers and other colleagues.
The comparison of the TORI religion with other religions is difficult, if at al. If the scientific methods, id est, the TORI axioms, were used for the comparison of various religions, then it should be easy to demonstrate the priority and efficiency of TORI. However, as Dmitrii Becklemishev had mentioned, such a comparison would be methodologically non–correct, in the same way, as if someone would try to describe the Aristotle's logics using methods of the female logic .
For this reason, here, the TORI axioms are just postulated and suggested to the international (and, especially, scientific) community as the philosophic criterion. The Editor considers this criterion as very efficient and important.
- 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)
https://ufn.ru/ru/tribune/ Д.Ю.Кузнецов. Место науки и физики в человеческом знании. УФН, т.181, Трибуна, p.1-9 (2011), in Russian. English version: http://mizugadro.mydns.jp/PAPERS/2010mestoe.pdf Dmitrii Kouznetsov. Place of science in the human knowledge.
- http://www.scirp.org/journal/PaperInformation.aspx?PaperID=36560 http://mizugadro.mydns.jp/PAPERS/2013jmp.pdf D.Kouznetsov. TORI axioms and the applications in physics. Journal of Modern Physics, 2013, v.4, p.1151-1156.
- http://www.ams.org/notices/201304/rnoti-p418.pdf Joseph F. Grcar. Errors and Corrections in Mathematics Literature. Notices of the AMS,, April 2013, p. 418-425. .. There is no reason to think engineers and mathematicians make mistakes less often than other researchers, ..
- http://Guacatelamala.sci.ac.gu/2000/3/t/KuroiBlack.pdf K.Black. Original statement. Revista Scientifica de Guacatelamala, 2000, v.3, No.4, p.5-6. (this is just example; there exist neither the author, nor the Journal, nor even the country specified)
- http://www.ark.ru/ins/zapoved/zapoved/logika.html Беклемишев Дмитрий Владимирович (профессор кафедры высшей математики Московского Физико-технического института.) Заметки о женской логике. Издание 3, исправленное и дополненное. Цитируется по состоянию на 2012 год. (In Russian)