However, inductivism very soon began to face serious challenges. As early as 1740s and 1750s, there began to dawn the realization that many areas of scientific inquiry could not be forced into the inductivist framework. Franklin's Fluid Theory of Electricity, the Vibratory Theory of Heat, the Buffonian Theory of Organic Molecules and Phlogiston Chemistry, etc. that developed in the middle of the nineteenth century went against the spirit of the inductivist cult of observations as they involved reference to entities and processes. The scientific grounds against the inductivist position were cleared with the appearance of chemical and gravitational theories of George Le Sage, the Neurophysiological theories of David Hartley and the General Matter Theory of Roger Boscovich. These scientists accurately realized that their theories would face stiff opposition not so much on scientific considerations but due to the methodological implications considered absolutely undesirable by the prevailing methodological orthodoxy, namely, inductivism. Hence, they felt the need for methodological legitimization in terms of an alternative model. It is this need which motivated them to resurrect the method of hypothesis. In their attempt to develop the method of hypothesis, these thinkers produced works of immense significance. Their works were followed by those of Jean Senebier, best known for his work on Photosynthesis, Pierre Provost, the founder of the theory of heat exchange and many others. These scientists challenged the canons of scientific method as envisaged by inductivism and in doing so they had their professional interests at stake.

Apart from the above mentioned challenge from the protagonists of the method of hypothesis, the method of induction faced an internal crisis. David Hume, an eminent eighteenth century inductivist, undermined it from within. He showed that the very principle of induction which allowed us to proceed from observed to as yet unobserved phenomena itself stood unjustified. Any attempt to justify the principle of induction, Hume conclusively shows, results in circularity or infinite regress. Hume was himself an inductivist. He did not accept the method of hypothesis because of his commitment to empiricism. He concludes that since we have no alternative to the principle of induction, our belief is irrational; we have to boldly accept that the whole of our knowledge including science, the paragon of knowledge, rests on an irrational belief, an animal faith.