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Is pseudo-science considered a logico-mathematical knowledge? Is history a physical or social knowledge?

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Hey guys. So i am currently writing my tok essay relating my ideas to natural science and history. I divided my knowledge into three different criterias based on the theory about knowledge created by philosopher jean piaget, that is knowledge can be divided into 3 different types:

1)physical knowledge which refers to knowledge about objects in the world, which can be gained through perceptualprerties

2) social-arbitrary knowledge- culture specific knowledge learnt from people within one's culture group

3) logico-mathematical knowledge- abstract knowledge that must be invented

However, i am confused as to whether pseudoscience is considered logico-mathematical knowledge or not since from what i gather, pseudoscience are claims that are not testable unlike natural science and therefore cannot be proved by experiments unlike the natural science. On the other hand, pseudoscience does carry with it scientific substance. So back to the main question, can it be treated as logico-mathematical knowledge?

On another note, is history considered to be physical knowledge or social knowledge? Cause history involves the use of our perception in the gathering of sources to examine the past. And yet, it also gives ay to the study of our culture too.. So what could it be then?

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I don't know about the pseudosciences per se... I mean the answer should be in your query. If it is an unprovable, untestable theory, then it's not even worth being called a theory. It would become a belief in scientific fact, which is rooted in a vague idea at best. 'Pseudo'-science means that it's not really science (pseudo = lying, false) in the title itself. So I would be wary about using pseudoscientific examples in lieu of natural science.

History would be a social science in my view because when history intermingles with the study of cultures it generally becomes known by the more specialised field of 'anthropology' from what I am aware.

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