Elements of scientific reasoning
Elements of scientific reasoning in TORI terminology are the published, 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.
1. Statements
A **statement** (утверждение, высказывание) is a linguistic object that is either true or false. Examples:
- “The mass of the electron is 9.109×10⁻³¹ kg.”*
- “O lies inside triangle ABC.”*
Statements form the basic building blocks for more structured elements.
2. Axiom
An **axiom** is a published statement adopted without proof as a starting point for a theoretical system. Axioms define the domain, rules, and structure of a theory.
3. Conjecture
A **conjecture** is a statement believed to be true but not yet proven or refuted. Conjectures are typical in mathematics.
4. Hypothesis
A **hypothesis** is a published explanatory proposal that suggests a refutation test but does not yet form a complete, consistent concept.
5. Scientific concept
A **scientific concept** is a well-defined, refutable, internally consistent framework derived from one or more hypotheses.
6. Scientific fact
A **scientific fact** is a scientific concept that has survived at least one explicit, published refutation attempt and currently gives the best explanation for its domain.
7. Theorem
A **theorem** is a statement proven from axioms and previously accepted theorems. The proof is itself a structured logical object.
8. Theory
A **theory** is a hierarchical system of scientific concepts and rules describing a broad class of phenomena.
9. Models and emulations
A **model** is a simplified representation of a system. An **emulation** is a computational or constructive representation intended to replicate the behavior of a real system or theory.
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.
References