I have never received any formal training in the scientific method. This might sound a bit surprising given that I make a living as a scientist. Instead I have picked up bits and pieces ever since my undergraduate training in physics and throughout my scientific career. This intensified during the research that I did for a textbook on scientific modelling (currently only in Swedish, but an English version is under way), and I read extensively about the scientific revolution, empiricism, logical positivism and Thomas Kuhn's ideas on paradigm shifts.
My latest foray into philosophy of science is the book/extended essay Against Method by Paul Feyerabend. It was first published in 1975 and has ever since been both celebrated and strongly disliked by philosophers and scientists alike (but for different reasons that I will get back to). The main thesis is that there is no coherent scientific method and never has been. Instead Feyerabend proposes theoretical anarchy in which anything goes. For example he shows that introduction of hypotheses that contradict established theories is sometimes a sensible way forward, a move that would be strongly disliked by any philosopher of rationalist creed. He delves specifically into the Copernican revolution and suggests that Galileo used a great deal of propaganda and smoke and mirrors to expound the heliocentric world-view. For example telescopic observations, which are often cited as supporting evidence, were at the time highly speculative and required the development of auxiliary sciences (e.g. optics and meteorology) before they could be considered as solid evidence. Also, the Copernican model of the solar system was no better at explaining empirical observations than was the prevailing Ptolemaic model. Despite this (and hence in contradiction to reason) the Copernican world-view gained followers and was later supported by numerous independent evidence.
I find Feyerabends account quite convincing and also supported by my own experience of 'doing science'. Most of the models, theories and hypothesis investigated in the field of mathematical biology wouldn't stand much of a chance if they were exposed to the rigour of proper science (i.e. as defined by philosopher of science). In many cases the models aren't even falsifiable since their connection to actual phenomena is at best vague. Not to speak of the field of Artificial Life where models aren't even aimed at resembling any real phenomena. Rather they serve as means to aid and guide our feeble thinking. Much of my own work (devising and analysing mathematical models) has the goal of connecting with biology, not right now, but at some point in the future. But this doesn't render the research useless. It is speculative (in relation to existing knowledge, the models themselves are logically consistent), but it is heading somewhere.
This resonates with another conclusions drawn by Feyerabend, which is that the transition from one theory to the next entails a decrease in empirical content. We take a step back, speculate, and slowly approach the empirical facts and observations. My feeling is that mathematical (cancer) biology is in precisely this situation: we are exploring new concepts and ideas (i.e. developing or extending our ontology). And to me this makes perfect sense, and is something that should be encouraged.
My feeling is that philosophers of science dislike this book because it essentially makes them unemployed. If anything goes then there's no point devising or even describing a scientific method. Let the scientists have a go at it. Let anarchy rule. The cool reception from scientists I think has less to do with methodological anarchy (which most of us are quite familiar with) but rather with the perceived anti-scientism that Feyerabend has been accused of. If science does not rely on a specific method (not even reason or adherence to empirical fact) then it should be viewed as any other human activity such as religion or the arts. This is were many scientists (including me) start getting a bit uncomfortable. What I think he is trying to say is that there are many facets to human life and that science cannot and never will provide the full picture. There are always other views/stories/perspectives that inform us about the human condition.
EDIT: I think this quote by physisct Max Born sums up Feyerabend's thesis in a nice way:
"I believe there is no philosophical high-road in science, with
epistemological signposts. No, we are in a jungle and find our way by
trial and error, building our road behind us as we proceed."