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Science is an internally-consistent system

That’s a mouthful, but what do we mean by internally-consistent?

To answer that question we need to look at how a scientific discipline is actually built.

Any scientific discipline begins with a small number of concepts that cannot be proven and are accepted as true. They are called axioms.

For example in Mathematics, they are:

  • Reflexive: a=a therefore a=a (things are equal to each other)
  • Symmetric: a=b therefore b=a (if things are equal then they are equal from any direction)
  • Transitive: a=b and b=c therefore a=c (things equal to the same thing are equal to each other)
  • Additive: a=b therefore a + c = b + c (things equal continue to be equal when an equal amount is added)
  • Multiplicative: a=b therefore a x c = b x c (since multiplication is repeated addition, it follows the Additive axiom).

Bit by bit that discipline uses those axioms and logic to build more and more complex models. It is hard to believe, but the entire structure of Mathematics is based on those 5 simple axioms!

No matter how complex the model, it must comply to the original axioms because if they would not do so, then they would negate the original truth of the discipline.

In practical terms, this means that within a scientific discipline one can build a complex model starting with axioms, but one can also re-discover the axioms by decomposing a complex model. This is to go full circle and it is what it means to be internally-consistent.

At the same time, this strictly observed internal-consistency can be used to test a model.

This method is called “testing by absurdity”. The process is quite simple. One assumes that the model is correct and begins to decompose it. If one arrives to the inevitable conclusion that an axiom is incorrect, then the model is false.

For example, it is quite common in mathematical tests to arrive to the conclusion that 1 = 0, which is obviously absurd.

Internal-consistency effectively isolates scientific models from external influences such as axioms and models from other disciplines. So yes, different scientific disciplines sometimes may seem at odds with each other. This is normal because they are internally-consistent. Basically, although they usually talk to each other and are constantly getting closer and closer, they don’t take each other too seriously.

This is a scientific necessity simply because the scientific domain is too large. Specialization is required. However, eventually, it is expected that all scientific disciplines will comply with a unified set of axioms. The Grand Unification.

The power of axioms is that an entire scientific structure can be built on them. This makes scientific models extremely robust. On one hand any model can be deduced from axioms, which removes subjectivity. On the other hand, external axioms and systems cannot affect the discipline because it is closed to them.

Powerful stuff indeed!

Note: please see the Glossary if you are unfamiliar with certain words.

 

 

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