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"In the view of many social scientists, the more probable a theory is, the better it is, and if we have to choose between two theories which are equally strong in terms of their explanatory power, and differ only in that one is probable and the other is improbable, then we should choose the former."

From: http://plato.stanford.edu/entries/popper/#ProbKnowVeri

What is meant by "probable" and "improbable" theory?

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    The whole notion is specific to Popper, to whom the article is devoted, and "probable/improbable theory" is explained earlier in it with an example:"while Einstein’s theory was highly ‘risky’, in the sense that it was possible to deduce consequences from it which were, in the light of the then dominant Newtonian physics, highly improbable... and which would, if they turned out to be false, falsify the whole theory, nothing could, even in principle, falsify psychoanalytic theories." In other words, the notion is relative to a contested background theory.
    – Conifold
    Commented Nov 6, 2016 at 20:51

2 Answers 2

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We consider situations which put a given theory T to a test.

let N = the total number of possible outcomes,

and let n = the number of possible outcomes which do not falsify the theory.

Then the probability of the theory is

p(T) = n / N

When a theory T is falsification-oriented, as Popper demands from scientific theories, most possible outcomes will falsify the theory. Therefore n will be small, and the probability p(T) will also be small. Hence, the theory will be improbable.

The above account of probability is implied by the following sentence in the SEP article:

The higher the informative content of a theory the lower will be its probability, for the more information a statement contains, the greater will be the number of ways in which it may turn out to be false.

and by the general properties of a probability measure, in particular that it is a number between 0 and 1.

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Syed, basically an improbable theory is a theory which is unlikely but not impossible. A probable theory is more likely. Poppers point as described in the article is that improbable theories are more scientific because they are simpler to falsify.

For example, "it is improbable that a tornado full of frogs rained the animals into the exhaust stack resulting in the explosion, but the weather has been rather odd lately." To test this "theory", if the debris from the explosion contains frog matter, it might become more reasonable and worth further investigation.

Contrast this with, "It's more probable that the smokestack building exploded because even though the maintenance records indicate that the stack had been decoked regularly, we have good reason to suspect the records are false considering the labor unrest as of late. Recent change in maintenance staff also led to other oversights and we are not confident that the records are accurate and reliable. We've interviewed all the employees but so far none of them contradict the records. Furthermore, considering the waning profit margins in lieu of the labor strikes, management has been under increased pressure to maintain a facade of operating at normal capacities while shorting maintenance and safety staffing."

In either case, the smokestack blew, but which one would be easier to demonstrate as false? Would demonstrating the falsity of the latter scenario be the same as demonstrating that force does not equal mass times acceleration or that an object released midair doesn't fall to the ground? Would a conclusion that the former is accurate be demonstrably true, or a matter of agreement?

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