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Though I know what is a hypothesis, I'm not sure to fully really understand it and thus outlines the hypothesis in my context. I am abstracting my real problem in a common world problem.

Suppose I have a bag full of marbles of different colors and sizes. I want to be able to make different groups of these marbles. So my problem is that I want to be able to group the different marbles. For me, my hypothesis are:

  1. It is possible to group marbles based on their color
  2. It is possible to group marbles based on their size

Based on the above hypothesis, I perform two different grouping and show that the hypothesis is true. Are my hypothesis the right hypothesis in this situation ?

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Perhaps the best way to understand hypotheses is in terms of logic. We use hypotheses to learn about laws or principles that govern the behavior of things, and a common form of expressing such a principle is:

∀x[Px → Bx]

This might be read as: For every x which has some property P, x will exhibit a certain behavior B.

A hypothesis is nothing more than proposing such a principle so that it can be put to the test. In your example about grouping a marbles, the grouping would pertain to some particular property P whether it be of size or color. However, what is absent from your hypothesis is a behavior B. You are grouping the marbles arbitrarily without attributing any particular significance to the grouping.

You have to ask yourself: What effect can be brought about by grouping marbles by color (or size)? According to what principle? Once you answer that, you can put the hypothesis to the test to discover if it conforms to reality.

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I will give an answer from an applied sciences or engineering viewpoint: it depends on what exactly you are trying to achieve. Are you trying to simply group them together? In that case, the possibility expressed in your "hypotheses" have already been experimented with (and a mathematician could likely provide a rigorous demonstration), so they would rather count as facts.

The function of a hypothesis is to provide a statement that you are going to test.

If you say:

It is faster/more useful/more effective to sort them by color.

(obviously defining what you mean by this) then you would have a hypothesis that you could compare with the other possibility (typically against your other possibility of size).

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