Metahypothesis is formed by a number of other hypothesis - when you take some hypotheses and put them together, you get metahypothesis.
Lets look an example.
Assume that we consider two hypothesis - that A is two times B and that A is three times B. We think that they are both considerably strong hypothesis.
Thus, we will form a metahypothesis. It contains the following formulae:
A = (2 + C) * B
Where C is a constant variable. It's a variable on metalevel, with allowed values 0 and 1. It's constant on normal level. We can also use conditionals in case some variable completely changes the case.
Now, we do not have two hypothesis, but actually we have one unknown constant here, which is 0 or 1 - and we can speak about figuring out the value of this constant by clever tests.
Metahypothesis, at this point, have not yet shown their actual power - the actual power is that in many cases we can work out a complete metahypothesis, kind of theory. We can prove that by allowed constant values we cover the whole ground of possibilities - that one allowed set of constants must give us the correct result. As we allow all those values, we can actually prove our metahypothesis - it becomes a theory.
For example, if I don't know if I saw an apple or a banana, there are two hypotheses:
- "I saw an apple."
- "I saw a banana."
When I say that "I saw an apple or banana", I have formed a metahypothesis it covers all possibilities. There is only one conditional, expressed as "or". This conditional has two possible values and thus my theory is not exact - I can make it more exact by solving this constant. I can, also, calculate the probabilities of different values - which is not so simple with two different hypothesis.
This is a big step to correct theory if we are able to collect and join all possible hypothesis.
There is another big advantage of metahypothesis over a loose set of different hypothesis - hypothesis might overlap. There might be concurrent hypothesis, which are actually just variations over the same theme. In good metahypothesis (which is simplified to a degree that it can't be more simplified) all those variations will be expressed as different possible values of some set of constants. Now we can start proving that some values do not make sense, which allows additional simplifications step-by-step. What we have gained - instead of a book filled with hypothesis each page, most of them very similar, we have one a bit longer metahypothesis. We can say that if any of hypothesis in that book is correct, then our metahypothesis will be correct, too - with some unknown metaparameters. We can also calculate probabilities and have a good discussion over the values of variables instead of a lot of churches. We can put in less emotion and less personal beliefs in such case - as the metahypothesis states very clearly that we don't know everything -, but we can also have a better talk over which specific conditionals and metaparameters we think we have solved. We share a common language. And that's a plus.
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