What was Sir Francis Bacon's idea of 'induction' as a scientific method?
I would only add; 1) Bacon’s useful “eliminative induction” and 2) his difference from the Aristotelian inductionists.
Bacon’s eliminative induction; For instance, in order to find the root cause of something (like rain), you would inductively examine all the elements of many different situations, times and atmospheric conditions when it is raining. Then you would also look for those same elements and conditions when it is not raining. Thereby, you could eliminate some elements which do not contribute directly to the cause of rain. This has been very useful in the development of the scientific method.
Bacon's version of induction differed from the Aristotelian induction.
Think of a ladder to knowledge; you (inductively) pick up particulars on your way up to the top where you form a general theory about what you've been investigating and gathering data. Aristotelians say you could then move down the ladder (deductively) to about the middle and make general axioms there as well.
Where Bacon differed from the Aristotelians is that he advocated endlessly moving up the ladder, collecting more data and eliminating false propositions; as if he wanted to focus on the process itself; for the sake of the process, rather than for the sake of reaching a general deduction with which one could then move back down the ladder to apply to more particular things (general deduction: all new cars are shiny - all new BMW's are shiny). Bacon would say to take your time and keep moving up the ladder slowly because what if we find out that not all new cars are shiny; then all the middle of the ladder axioms could be false. His thinking is logical but not practical. Most scientists have accepted the idea that their general deductions may someday prove to be wrong, but have accepted that if they are currently applicable, to use them. For example, Newton’s theory of gravity predicted the movement of the planets to a great degree and scientists were able to use his theory for other particular (middle of the ladder) instances of gravity. Then Einstein came along and improved upon the theory. While we had to rethink all those instances in which we applied Newton’s gravity theory, it was still more beneficial for us that we did rely on Newton’s effective theory. (It served us well enough for over 200 years.)
The idea of induction is to be differentiated from the idea of deduction. They are opposite ways of trying to prove things or to find truth.
Before Bacon, most science was done on the Aristotelian method, which involved deduction. In deducation, a person takes a general principle and tries to apply it to a given situation. It is a type of reasoning by analogy.
Bacon, by contrast, wanted to reason by induction. In this method, a person gathers facts and then tries to draw conclusions from them. This is more compatible with science because it is based on empirical observation -- you are trying to make your theory fit the facts rather than trying to take a theory and use it to determine what the facts should be.