That Nature could be explained through abstract reasoning and experimentation.
The scientific belief that Francis Bacon and Rene Descartes shared was their belief that most of the knowledge that came before was weak, sloppy, and in some cases very wrong. They both believed knowledge should be received by personal observation.
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They both contributed to the Scientific method. Francis Bacon did this to make sure that they did not having false thoughts/teachings. Descartes said to gain knowledge to follow those steps. They helped create a new approach to science. Over time, people started calling this new approach the scientific method.
Yes they are considered the fathers of the enlightenment
Francis Bacon developed a theory of 'eliminative induction.' Induction is moving from specifics to generalities, and whilst it had been proposed as a key part of scientific method by Aristotle, Bacon adapted it. Aristotle proposed that scientific evidence should be gathered by observation, but Bacon proposed that evidence should be gathered by observation and experiments. this is known as eliminative induction as it eliminates variable factors which might be present through mere observation. Descartes' philosophy is based around doubt. he doubts everything, and can only establish his own existence through the presence of thought. This systematic doubt, and taking nothing for granted is, along with experimentation, the foundation of science.
Their fundamental ideas can. Certain parts of their theories such as Cartesian physics have been generally rejected, but their fundamental approaches are still valuable today. .