The Baconian method is the investigative method developed by Sir Francis Bacon. The method was put forward in Bacon's book Novum Organum (1620), or 'New Method', and was supposed to replace the methods put forward in Aristotle's Organon. This method was influential upon the development of scientific method in modern science; but also more generally in the early modern rejection of medieval Aristotelianism.
Baconian method 
By reasoning using "induction", Bacon meant the ability to gradually generalize a finding based on accumulating data - he advised proceeding by this method (building a case from the ground up). Isaac Newton, a noted Baconian, used such principles in the Philosophy section of his Principia, writing "hypotheses non fingo" (I don't make hypotheses). He also wrote in his Optiks that "hypotheses have no place in experimental science." Bacon wrote (In the Novum Organum) that, "Our only hope, then is in genuine Induction... There is the same degree of licentiousness and error in forming Axioms, as in abstracting Notions: and that in the first principles, which depend in common induction. Still more is this the case in Axioms and inferior propositions derived from Syllogisms." (see for example, aphorism XVII of the Novum Organum)
The method consists of procedures for isolating and further investigating the form nature, or cause, of a phenomenon, including the method of agreement, method of difference, and method of concomitant variation.
Bacon suggests that you draw up a list of all things in which the phenomenon you are trying to explain occurs, as well as a list of things in which it does not occur. Then you rank your lists according to the degree in which the phenomenon occurs in each one. Then you should be able to deduce what factors match the occurrence of the phenomenon in one list and don't occur in the other list, and also what factors change in accordance with the way the data had been ranked.
Thus, if an army is successful when commanded by Essex, and not successful when not commanded by Essex: and when it is more or less successful according to the degree of involvement of Essex as its commander, then it is scientifically reasonable to say that being commanded by Essex is causally related to the army's success.
From this Bacon suggests that the underlying cause of the phenomenon, what he calls the "form," can be approximated by interpreting the results of one's observations. This approximation Bacon calls the "First Vintage." It is not a final conclusion about the formal cause of the phenomenon but merely a hypothesis. It is only the first stage in the attempt to find the form and it must be scrutinized and compared to other hypotheses. In this manner, the truth of natural philosophy is approached "by gradual degrees," as stated in his Novum Organum.
The "Baconian method" does not end at the first vintage. Bacon described numerous classes of Instances with Special Powers, cases in which the phenomenon one is attempting to explain is particularly relevant. These instances, of which Bacon describes 27 in Novum Organum, aid and accelerate the process of induction.
Aside from the First Vintage and the Instances with Special Powers, Bacon enumerates additional "aids to the intellect" which presumably are the next steps in his method. These additional aids, however, were never explained beyond their initial limited appearance in Novum Organum.
Idols of the Mind 
Bacon also listed what he called the Idols (false images) of the mind - some are similar to what is now called cognitive bias. He described these as things which obstructed the path of correct scientific reasoning.
- Idols of the Tribe (Idola tribus): This is humans' tendency to perceive more order and regularity in systems than truly exists, and is due to people following their preconceived ideas about things.
- Idols of the Cave (Idola specus): This is due to individuals' personal weaknesses in reasoning due to particular personalities, likes and dislikes.
- Idols of the Marketplace (Idola fori): This is due to confusions in the use of language and taking some words in science to have a different meaning than their common usage.
- Idols of the Theatre (Idola theatri): This is the following of academic dogma and not asking questions about the world.
- Idols of the School (Idola schola): This is due to a belief in a blind rule reasoning.
The English physician Sir Thomas Browne (1605–82) was one of the earliest scientists to adhere to the scientific empiricism of the Baconian method. His encyclopaedia Pseudodoxia Epidemica (1646–76) includes numerous examples of Baconian investigative methodology; its preface even paraphrases lines from Bacon's essay On Truth from his 1605 work The Advancement of Learning. Isaac Newton was a noted Baconian—his famous quote hypotheses non fingo (I don't frame hypotheses) was featured in later editions of the Principia, demonstrating his preference for rules that could be demonstrated by formal proof, as opposed to unevidenced hypotheses.
The Baconian method was further developed and promoted by English philosopher John Stuart Mill. His 1843 book, A System of Logic, was an effort to shed further light on issues of causation. In this work, he formulated the five principles of inductive reasoning now known as Mill's methods.
See also 
- Hesse, M. B. (1964), “Francis Bacon's Philosophy of Science”, in A Critical History of Western Philosophy, ed. D. J. O'Connor, New York, pp. 141—52.
-  Article on Francis Bacon by Stanford University Encyclopedia of Philosophy. Juergen Klein.