TORI

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This editable Main Article is under development and subject to a disclaimer.

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## Contents

* 1 TORI axioms
* 1.1 Applicability
* 1.2 Verifiability
* 1.3 Refutability
* 1.4 Self-consistency
* 1.5 Principle of correspondence
* 1.6 Pluralism
* 2 Collections of the TORI axioms
* 3 Criticism
* 4 Change of the host
* 5 References

TORI (Tools for Outstanding Research and Investigation) is a collection of tools for scientific research. These tools may include formulas, algorithms, figures, theorems, conjectures; and also some historical documents and products of art that are used (or are expected to be used in future) as illustrations. The content of TORI can be copied for free; the attribution is required in order to avoid circulation (and amplification) of rumors, if one finds his own formulas, pictures and statements published without indication of the source, and considers the new publication as an independent confirmation of his results.

Initially, TORI was expected to collect tools mainly about the Laser science. Then the applicability to other sciences had been discussed. Links that refer to other sciences had been collected at TORI in order to show, that the TORI axioms can be used in other sciences too.

A site with this name was created in March 2011 at http://tori.ils.uec.ac.jp/TORI and in February–March 2013 it moved to http://mizugadro.mydns.jp/t.[1]

## TORI axioms[edit]

TORI deals with concepts, satisfying the following axioms:

### Applicability[edit]

The concept has some limited range of validity, distinguishable from the empty set.

The empiric observation of development of science during centuries indicates, that often some concept appears that pretends to bring the "objective knowledge" and "absolute true", being applicable always and everywhere. The history of science indicate, that, in a best case, a "universal" scientific concept remains as a "theory or everything" during few centuries. Then, the limits of its applicability are revealed.

Among the most long-living concepts, the following can be named:
(1) round Earth as center of Universe,
(2) conservation of number of atoms of each kind in a closed system,
(3) biogenesis, impossibility of creation of life from non-living chemicals by natural processes (without God).
Lifetime of other "universal" concepts is even shorter.

The need to have limited range of validity for a scientific concept is not trivial not obvious. The suggestions to get the "objective knowledge" and the "absolute true" are repeated again and again from century to century, even after to reveal, that every self-consistent theory is not complete:  In any consistent axiomatizable theory (axiomatizable means the axioms can be computably generated) which can encode sequences of numbers (and thus the syntactic notions of "formula", "sentence", "proof") the consistency of the system is not provable in the system. [2]; more links against the "universal" theory are collected at the Mathematica site [3]

Summarizing the experience of the Human civilization during centuries, the limited range of applicability of any scientific concept is declared as axiom.

### Verifiability[edit]

In the terms of the already accepted concepts, some specific experiment with some specific result, that confirms the concept, can be described.

In various forms, the principle of verifiability comes from many philosophies. In particular, the idea to recognize the tree by its fruits is specified in the Bible; if some tree is declared to be fruitful, let it bring at least one good fruit [4].

Verifiability seems to be the oldest philosophical principle.

### Refutability[edit]

In the terms of the concept, some specific experiment with some specific result, that negates the concept, can be described.

Requirement of refutability had been suggested by Karl Popper [5][6][7]. Concept, that does not allow its refutation, cannot predict any non-trivial phenomenon: any result of any experiment, observation, calculus can be interpreted in favor of the concept.

Popper uses term falsifiability, that may have different (and sometimes opposite) meaning; in particular, at the transliteration to other languages. For this reason, term Refutability is suggested.

### Self-consistency[edit]

No internal contradictions of the concept are known.

Importance of self-consistency can be seen from the analysis of the official methodology, that was compulsory in the USSR. The dialectics had been postulated as the base of the all-mighty, omnipotent, and the only true Marx theory. Then, with this pretext, many branches of Science were attacked (Theory of relativity, Quantum mechanics, Genetics, Cybernetics, etc.). With Axiom 4, no dialectics, no doublethink [8] is allowed in any scientific concept; two independent researchers applying the concept to some case are supposed to come the same predictions.

In order to avoid phenomena, typical for the USSR and described by Orwell, the self-consistency is declared in the special axiom.

### Principle of correspondence[edit]

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.)

The correspondence principle (Axiom 5) had been suggested by Niels Bohr [9], aiming the application to Quantum Mechanics and its relation to the classical mechanics. However, the principle is more general; it is applied to other concepts too.

### Pluralism[edit]

Mutually-contradictive concepts may coexist; if two concepts, satisfying axioms 1-5, have some common range of validity, then, in this range, the simplest of them has priority.

Axiom 6 pluralism is necessary to protect the new, alternative concepts, while they are not yet developed sufficiently to get status of principal; the tolerance with respect to the new concepts is necessary for the scientific revolutions considered by Thomas Kuhn [10].

Criterion of simplicity had been formulated long ago. Usually it is attributed to William Ockam, although, perhaps, he was not first to declare and to use it.

## Collections of the TORI axioms[edit]

The axioms above were collected and suggested in the Russian journal Uspekhi [11] (in Russian) and in the First issue of the Far East Journal of Mechanical Engineering and Physics [12]. Then, the special site, TORI [1], had been designed to collect and develop concepts, based on axioms 1-6 above. Since that, these axioms can be referred as TORI axioms.

## Criticism[edit]

TORI do not compete with big sites like Citizendium, Wikipedia and [Proofwiki], but collect the "outstanding" results, that, for some reason, cannot be placed there (contradict the common paradigm, or not published, or lack the mathematically rigorous proof, etc.). The serious consideration of any "outstanding", "non-traditional" approach should be justified. This justification appears as critics. In such a way, TORI is very critical site.

The criticism of TORI caused serious problems; not all authors consider the critic in the academic way. The criticism could be main reason for the attack 2013.02.27 and following change the hosting domain.

## Change of the host[edit]

2013 February 27, the site TORI had been attacked [13]. This attack happened within a week since the Editor of the Physics Today had sent to the reviewers the critical manuscript 'Corruption in Russian science' [14]. The links in support of the statements of the manuscript were collected at TORI; and the hypothesis had been formulated, that the author of criticized article had bribed the attackers, because no other feedback from Toni Feder [15] had been received.

In 2013 March, the clone of TORI had been arranged at server http://mizugadro.mydns.jp/t (and since that, the link should be corrected in sites that refer to TORI). In addition, the detailed description of the TORI axioms had been prepared as a manuscript [16]. That manuscript suggests, that the TORI axioms are declared as requirements for the scientific presentations and scientific publications.

## References[edit]

1. ↑ 1.0 1.1 TORI, Tools for Outstanding Research and Investigation:
http://tori.ils.uec.ac.jp/TORI (2011 March - 2013 February)
http://mizugadro.mydns.jp/t (2013 March – )
2. ↑ Dale Myers. 'Godel's Incompleteness Theorem'. http://www.math.hawaii.edu/~dale/godel/godel.html
3. ↑ http://mathworld.wolfram.com/GoedelsIncompletenessTheorem.html
4. ↑ http://bible.oremus.org/?passage=Matthew+7 Bible, Matthew 7, songs 15-20.  'Beware of false prophets, who come to you in sheep’s clothing but inwardly are ravenous wolves. You will know them by their fruits. Are grapes gathered from thorns, or figs from thistles? In the same way, every good tree bears good fruit, but the bad tree bears bad fruit. A good tree cannot bear bad fruit, nor can a bad tree bear good fruit. Every tree that does not bear good fruit is cut down and thrown into the fire. Thus you will know them by their fruits'.
5. ↑ Karl Popper. Science: Conjectures and refutations. - 'Philosophy of Science: a Personal Report', in British Philosophy in Mid-Century, ed. C. A. Mace, 1957. http://philosophyfaculty.ucsd.edu/faculty/rarneson/Courses/popperphil1.pdf
6. ↑ Popper, Karl R. The logic of scientific discovery. Oxford, England: Basic Books. (1959). http://psycnet. apa.org/psycinfo/1961-02882-000
7. ↑ Karl R. Popper. 'Science as falsification'. Karl Popper, Conjectures and Refutations. London: Routledge and Keagan Paul, 1963, pp. 33-39 http://www.stephenjaygould.org/ctrl/popper\\_falsification.html
8. ↑ George Orwell. 1984. (1949) http://www.george-orwell.org/1984
9. ↑ Alisa Bokulich. 'Bohr's Correspondence Principle'. Oct 14, 2010. http://plato.stanford.edu/entries/bohr-correspondence/
10. ↑ T.S.Kuhn. The Structure of Scientific Revolutions. 2nd. ed., Chicago: Univ. of Chicago Pr., 1970 http://www.des.emory.edu/mfp/Kuhn.html
11. ↑ D.Kouznetsov. 'Place of science and physics in human knowledge'. Uspekhi, Tribune, 2010-2011, No.110
Official Russian version: http://ufn.ru/tribune/trib120111.
English versions: http://samlib.ru/k/kuznecow_d_j/2010mestoe.shtml
http://mizugadro.mydns.jp/PAPERS/2010mestoe.pdf
http://mizugadro.mydns.jp/t/index.php/Place_of_science_in_the_human_knowledge

12. ↑ D.Kouznetsov. 'Support of non-traditional concepts'. Far East Journal of Mechanical Engineering and Physics, 1, Issue 1 (2010) 1. http://mizugadro.mydns.jp/PAPERS/2010support.pdf
13. ↑ D.Kouznetsov. 'Tori attacked', 2013. http://samlib.ru/k/kuznecow_d_j/toriattacked.shtml
14. ↑ D.Kouznetsov. 'Corruption in Russian science'. 2013, preprint http://mizugadro.mydns.jp/PAPERS/2013physToday.pdf
15. ↑ Toni Feder. 'Russia launches S&T university'. Physics Today, January 2013, page 20. http://www.physicstoday.org/resource/1/phtoad/v66/i1/p20_s1
16. ↑ D.Kouznetsov. 'TORI axioms and the application in Physics'. Journal of Modern Physics, 2013, accepted. http://mizugadro.mydns.jp/PAPERS/2013jmp.pdf