Elements of scientific reasoning

In TORI, the Scientific reasoning is way to interpret the observable phenomena and to bulid-up Science.

The Scientific reasoning serves both for creations of scientific tools and for convincing colleagues in their efficiency (if the tool is efficient) and/or revealing of errors, mistakes, bugs in these tools.

Elements of scientific reasoning in TORI terminology are structured objects that participate in the process of constructing, refuting, and improving scientific knowledge. They include axioms, statements, hypotheses, concepts, facts, theorems, theories, and related items.

The purpose of this classification is to provide a unified framework for describing objects that appear in scientific and mathematical texts, without relying on philosophical assumptions about “truth” or “belief”.

TORI emphasizes publication, refutability, and consistency rather than metaphysical truth.

Warning.
The first version of this article is generated by ChatGPT.
This article is under construction. The goal is to distribute possible meanings between the related terms.

1. Statements

Statement (утверждение, высказывание) is a linguistic object containing at least one sentence.

Here are examples:

1. «The transparent oil found in the cow, does not facilitate the cow’s nourishment, but being processed in an appropriate fashion, it provides the finest of nutrition.»
2. «Unbreakable Union of freeborn Republics // Great Russia has welded forever to stand..»
3. «Russia never attacked anyone first.»
4. «Quantum fluctuations annihilate an optical soliton.»
5. «Quantum fluctuations do not annihilate the optical soliton.»
6. «There exist no real-holomorphic solution \(F\) of equation \(F(z\!+\!1)=\exp(F(z))\) »
7. «There exist unique real-holomorphic solution \(F\) of equations \(F(z\!+\!1)=\exp(F(z))~\), \(~F(0)\!=\!1~\), \(~F(x\!+\!\mathrm i \infty)= - \)LambertW\((-1)~\), \(~F(x\!-\!\mathrm i \infty)= - \)LambertW\((-1)^*\)»
8. «The mass of the electron is 9.109×10⁻³¹ kg.»
9. «Point O lies inside triangle ABC.»

The statement may have no sense (no values can be assigned to the statement), example 1 above.
The statement may have value "false" or "true", examples 2,3,4,5,6,7 above
Value of a statement may depend on the precision required, example 8 above.
Value of a statement may depend on the notations used; how the objects mentioned are defined in the context, example 9 above.

Concepts

Developed, advanced statements that are believed to useful are denoted with term concepts.

Usually, a concept includes many statements.

Concepts form the essential part of the human knowledge.

In TORI, the Human knowledge is classified to 4 categories: Customs , art, religion, science.

The TORI axioms seem to be efficient tool in science, and, in particular, in physics .

Scientific concepts

Certain class of statements are especially interesting for TORI.

Such a statement is determined with term «Scientific concept».

In TORI, A scientific concept is concept that satisfies the 6 TORI axioms.

Definitions

Certain set of relations between statements often are used to simplify the deduction and reduce confusions.
Some terms are described in terms of other terms.

Such a description appears as Definition.

The use of definitions allows to reduce the number of terms that may cause confusions.

definition make deductions shorter.

Dictionaries are used to define one terms through others.

One of goals of TORI is to elaborate definitions that
A. Are maximally close to those from other cites and
B. Avoid contradictions that are typical if some ambiguous terms are used.

These contradictions can be considered as one of sources of conflicts including wars.

Hypothesis

Hypothesis is an assumption that is expected to be useful for building a concept; usually, a scientific concept.

Axioms

In order to perform the scientific deduction, some statements should be assumed.

In the Human civilization, during last kilo years, at the scientific research, especially in mathematics, it is convenient to formulate the statements, these assumption before the deduction.

Such an assumption is denoted with term Axiom.

The axioms can be considered as kind of definitions: any concept can be defined as deduction, based on the certain set of axioms.

In particular site TORI and significant part of the content of server Mizugadro are based on the TORI axioms.

Conjectures

A conjecture is a statement believed to be true but not yet proven or refuted. Conjectures are typical in mathematics.

The existence of Tetration first had been assumed, postulated as a a hypothesis. This hypothesis allowed to construct the efficient algorithm for the evaluation, and the conjecture of existence and uniqueness of tetration had been formulated . Only few years later, the formal proof has been presented.

Scientific fact

Scientific fact is a theory that has no competitors at least in some part of its applicability.

In such a way, scientific fact is scientific concept; this assumes its refutability.

No irrefutable scientific fact is allowed in TORI and in Science as this term is interpreted in TORI.

However, irrefutable concepts are allowed in religions. The whole Bible can be considered as a Religious concept, but not as a Scientific fact.

Theorems

Theorem is a statement proven from axioms and previously accepted theorems. The proof is itself a structured logical object.

Theory

Theory is a hierarchical system of scientific concepts and rules describing a broad class of phenomena.

Theory appears as a hypothesis that has survived at least one attempt to refute it.

Models and emulations

Model is a simplified representation of a system. Model appears as a scientific concept with narrow (in comparison with other scientific concepts) range of applicability.

If a model it related to historical event(s), it is denoted with term "historic model".

Emulation is a computational or constructive representation intended to replicate the behavior of a real system or theory. Usually, Emulation is constructed as a substitute, perhaps, temporal, of some document, that is supposed to exist, but is not available in the free access.

Relations between elements

Statements
   ↓
Hypotheses
   ↓ (structure)
Scientific concepts
   ↓ (refutation survives)
Scientific facts
   ↘
     → Theory
```

Mathematical objects follow a parallel chain:

Statements
   ↓
Conjectures
   ↓ (proof)
Theorems
   ↘
     → Axiomatic theory

Purpose

This classification system helps avoid ambiguity and prevents mixing:

• mathematical proof with empirical testing;
• hypotheses with facts;
• models with theories;
• statements with inferences.

It ensures that TORI terminology remains consistent across different sciences.

Warning

The definitions of the Elements of scientific reasoning in TORI may deviate from their usual meanings.

References

Keywords

«Elements of scientific reasoning», «Proposition», «Refutability», «Science», «Scientific concept», «Statement», «Theory», «TORI axioms»,