Wikipedia and the concept of the axiom

What an axiom does not mean?

 

Wikipedia says:

An axiom is a sentence or proposition that is accepted as the first and last line of a one-line proof and is considered as obvious or as an initial necessary consensus for the theory building or acceptation. Therefore, it is taken for granted as true, and serves as a starting point for deducing and inferencing other truths.

This is a wrong definition. I was writing a correct definition to Wikipedia in Finnish but theologians and philosophers were changing it. The reasons were ideological.

 

The axiom is never taken for granted as true because it is a part of the definition of the concepts.

What the axiom really means?

 

An axiom is a part of the definition of the concepts in the sentence.

Why we are not using axioms in everyday speech?

 

We can learn the language using many methods of definition:

 

  1. Implicit definition is a definition using axioms.

 

  1. Explicit definition is the definition using other terms.

 

  1. An ostensive definition conveys the meaning of a term by pointing out examples of what is defined by it.

 

  1. An operational definition of a quantity is a specific process whereby it is measured.

 

  1. In mathematics and computer science, recursion is a particular way of specifying (or constructing) a class of objects (or an object from a certain class) with the help of a reference to other objects of the class: a recursive definition defines objects in terms of the already defined objects of the class.

 

  1. A stipulative definition is a type of definition in which a new or currently-existing term is given a new meaning for the purposes of argument or discussion in a given context. This new definition may, but does not necessarily, contradict the dictionary (lexical) definition of the term. Because of this, a stipulative definition cannot be "correct" or "incorrect"; it can only differ from other definitions.

 

We learn words using all methods of definition.

 

Is there epistemological axioms?

 

Wikipedia says:

In certain epistemological theories, an axiom is a self-evident truth upon which other knowledge must rest, and from which other knowledge is built up. An axiom in this sense can be known before one knows any of these other propostions. Not all epistemologists agree that any axioms, understood in that sense, exist.

This is wrong because

1.      It is wrong to use the word “axiom” for “self-evident truths”.

2.      There are no self-evident truths.

 

Of course it is possible use axiomatic way to define the concepts of the epistemology. For example Alvin I. Goldman uses a weak definition of knowledge (in Knowledge in a Social World):

 

“...knowledge is here understood in the ‘weak’ sense of true belief”.

 

This is partial definition of the words knowledge, true anf belief.

 

This definition assumes that you know the meanings of the words is, here, understand, weak and sense.

 

Axioms in mathematics

 

Wikipedia says:

In logic and mathematics, an axiom is not necessarily a self-evident truth, but rather a formal logical expression used in a deduction to yield further results. To axiomatize a system of knowledge is to show that all of its claims can be derived from a small set of sentences that are independent of one another. This does not imply that they could have been known independently; and there are typically multiple ways to axiomatize a given system of knowledge (such as arithmetic). Mathematics distinguishes two types of axioms: logical axioms and non-logical axioms.

This is not exact. Axioms are implicit definitions of the fundandamental concepts.

 

In Euclidean geometry following sentences will define the concepts point, line and plane:

 

“For every two points A, B there exists a line a that contains each of the points A, B.

For every two points A, B there exists no more than one line that contains each of the points A, B.

There exists at least two points on a line. There exist at least three points that do not lie on a line.

For any three points A, B, C that do not lie on the same line there exists a plane α that contains each of the points A, B, C. For every plane there exists a point which it contains.

For any three points A, B, C that do not lie on one and the same line there exists no more than one plane that contains each of the three points A, B, C.

If two points A, B of a line a lie in a plane α then every point of a lies in the plane α.

If two planes α, β have a point A in common then they have at least one more point B in common.

There exist at least four points which do not lie in a plane”

 

Why Wikipedia contains much of false definitions?

 

The main reason to use false definitions of the concepts is theological or philosophical. Theologians can use for example following axioms:

 

There is only one god.

The god is all-mighty.

The god is all knowing.

The god is all-good.

 

This is one of the definitions of the Christian god. But there is no such god. We can use axioms to define being, but it is possible, that there is no such being.

 

There are mathematicians who think that the Euclidean definition of the line is wrong. It is not wrong because it is the definition of the Euclidean line. Non-Euclidean geometries have different axioms.

 

Why almost all dictionaries are using wrong definitions?

 

The publishing of the dictionary is one part of the use of the power.

 

Weak use of the language

 

Our use of the language is often weak. If somebody asks what we mean when we say for example “science” it is probable that we can not give a complete answer.

 

As atheists we can not accept the ideological use of the weak language. Most of the theology and the philosophy is opinions using emotional and weak language.

 

Is there good dictionaries?

 

I (Mr. Erkki Hartikainen from Finland) am trying to write Dictionary of Atheism. Please help me.