Axiom

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An Axiom is a statement of logic, that is not proved within the discussion of a problem.

  1. The statement might be viewed as obvious. One example of such an axiom is the Principle of contradiction, which says that a statement and its opposite cannot both be true at the same time in the same place.
  2. The statement is based on physical laws and can easily be observed. An example for this are Newton's laws of motion
  3. A logical proposition, given at the start of an argument. This is the modern definition of axiom

Logic can be used to deduce other theorems from the axioms.

Euclid's axioms[change | edit source]

Euclid of Alexandria was a Greek mathematician. Around the year 300BC, he made a list of axioms:

  1. Two numbers that are both the same as a third number are the same number.
  2. If A and B are two numbers that are the same, and C and D are also the same, A+C is the same as B+D.
  3. If A and B are two numbers that are the same, and C and D are also the same, A-C is the same as B-D.
  4. Two shapes that fill exactly the same space are the same shape.
  5. If you divide a number by anything more than 1, the quotient (result) will be less than the original number.

Similar concepts[change | edit source]

When philosophers speak about paradigms or theologians about dogmas, they mean similar things.