6 ideas
Bacon sorts the systematic distortions of human understanding into four classes. Idols of the Tribe are rooted in human nature itself. Idols of the Cave come from an individual's temperament and upbringing, Idols of the Marketplace from the looseness of language, and Idols of the Theatre from inherited philosophical systems and faulty proof.
The mind is not a clear mirror. It is an uneven one that mixes its own nature with what it reflects. It assumes more order and regularity in the world than exists. It notices and remembers confirming instances while neglecting or dismissing contrary ones, as with people who recall the shipwreck survivors who prayed but not the drowned who also prayed.
Words are coined to suit ordinary understanding, so they carve up reality badly. Some name things that do not exist, like 'fortune' or 'prime mover'. Others are vague, muddled abstractions of real things, like 'humid'. Because people believe they control words while words actually react back on the mind, many disputes are really quarrels over ill-defined terms and never touch the things themselves.
Received philosophical systems are like stage plays. They are invented worlds with internal coherence, and audiences mistake them for reality. Bacon groups these errors into three kinds: sophistical philosophy built on a few observations and much argument, empirical philosophy built on a few narrow experiments, and superstitious philosophy that mixes theology with natural inquiry.
Syllogistic logic works on propositions, which are made of words, which stand for notions. If those notions are confused and hastily abstracted from things, no amount of valid deduction can repair them. The old logic therefore fixes errors in place rather than finding new truths. Only a method that builds sound notions directly from observed particulars can advance knowledge.
Genuine induction rises from particulars to lesser axioms, then to middle axioms, and only last to the most general ones. It refuses to leap straight to sweeping principles. It must organize observations into tables of presence, absence, and degree, and it gives decisive weight to negative instances, because a single contrary case can overturn a generalization that many agreeing cases can never prove.