The hypothetico-deductive method derives primarily from the work of Karl Popper.
What is to count as corroborating evidence is philosophically problematic. The raven paradox is a famous example. The observation 'all swans are white' would appear to be collaborated only by observations of white swans. However, 'all swans are white' is logically equivalent to 'all non-white things are not swans'. 'This is a green tree' is an observation of a non-white thing that is not a swan, and therefore collaborates 'all non-white things are not swans'. It appears to follow that the observation 'this is a green tree' is collaborating evidence for the hypothesis 'all swans are white'.
This problem is related to the problem of induction, and arrises because one cannot logicaly infer a general case – a hypothesis – from any series of specific observations. Since it appears that virtually any observation can be seen as collaboration of any hypothesis, the choice of which observations the scientists involved should take seriously seems to be open, rather than a matter of the application of a strict method. The argument has also been taken as showing that both observations and theories are embedded in our overall understanding (holism), and so that it is not possible to make truly independent observations.
Evidence contrary to a hypothesis is also philosophically problematic. Such evidence is called a falsification of the hypothesis. However, under the theory of ontological relativity it is always possible to save a given hypothesis from falsification. This is so because any falsifying observation is embedded in a theoretical background, which can be modified in order to save the hypothesis. Popper anticipated this, noting that the falsification of a hypothesis is a matter of choice on the part of the scientists involved.
Despite these philosophical problems the hypothetico-deductive method remains perhaps the most popular and best understood theory of scientific method.