Comments about "Axiom" in Wikipedia

This document contains comments about the article Axiom in Wikipedia
In the last paragraph I explain my own opinion.

Contents

Reflection


Introduction

The article starts with the following sentence.
An axiom or postulate is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments
If it is true requires experiments.

1. Etymology

2 Historical development

2.1 Early Greeks

2.2 Modern development

A set of axioms should be consistent; it should be impossible to derive a contradiction from the axiom.
That seems as common sense.
In particular, the monumental work of Isaac Newton is essentially based on Euclid's axioms, augmented by a postulate on the non-relation of spacetime and the physics taking place in it at any moment.
Newton considers a clear separation between space and time.
In 1905, Newton's axioms were replaced by those of Albert Einstein's special relativity, and later on by those of general relativity.
Newton's Law is one side of a coin. SR and GR are a different coin with his own postulates.
The next paragraph has nothing to do with axioms or postulates

2.3 Other sciences

Axioms play a key role not only in mathematics, but also in other sciences, notably in theoretical physics.
Okay.

3. Mathematical logic

3.1 Logical axioms

3.1.1 Examples

3.1.1.1 Propositional logic

3.1.1.2 First-order logic

3.2 Non-logical axioms

3.2.1 Examples

3.2.1.1 Arithmetic

3.2.1.2 Euclidean geometry

3.2.1.3 Real analysis

3.3 Role in mathematical logic

3.3.1 Deductive systems and completeness

3.4 Further discussion

4. See also

Following is a list with "Comments in Wikipedia" about related subjects


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Created: 3 November 2017

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