How and why does Bacon's inductive method differ from the modern scientific method?

Bacon's inductive method begins by creating a kind of "data-bank" of information about the natural world through experiments and observation, then investigating this mine of information in order to find out about one particular nature or quality. It begins by looking at the natural world, and moves through various small steps to formulate axioms or true statements about nature. General axioms ("heat is a kind of motion") can be established only at the end of this process. The modern scientific method, although it is rarely followed in practice, begins with a hypothesis or specific question, then designs and refines experiments to test this hypothesis. Modern scientists are understandably skeptical about the possibilities for total knowledge that Bacon's inductive approach assumes. It is also important to remember that Bacon's methodology, particularly his emphasis on experimentation, was an important stage in the development of today's scientific method.

What did Aristotle's Organon get wrong, according to Bacon?

Essentially, almost everything. Bacon believes that Aristotle's philosophy relies on the useless and ambiguous device of the syllogism, and is concerned with categories and complex dialectical arguments at the expense of real inquiry into nature. Much of The New Organon is devoted to showing the flaws in Aristotle's method, and to rewriting Aristotle's Organon to fit with the demands of modern scientific inquiry. Bacon believes that an important reason for the poor progress that has been made so far in science is the excessive reliance on the authority of ancient authors, particularly Aristotle. Aristotle exemplifies the Sophistic style of philosophy, one of the three parts of the idols of the theater. Those medieval and contemporary philosophers who rely on Aristotelian categories are not impressed so much by the value and force of his arguments, as by his importance in Western universities and their own prejudices.

What hope does Bacon hold out for the progress of the sciences?

Bacon always makes it clear that his plan for the advancement of learning will take a long time, and require much effort. The obstacles preventing progress are considerable, and stem from many different aspects of human experience—from sense-perception, individual life-experience, language and philosophy. They can be overcome only if Bacon's scientific method is followed rigorously. He makes it clear that many things allow hope of progress: correcting past errors can give hope for the future, as can the fact that past discoveries were not always believed to be possible beforehand, as can the fact that humans waste energy on other projects that could be directed to scientific inquiry. Bacon's position is essentially one of cautious optimism; he knows that the creation of a comprehensive natural history is a great undertaking, hence his pleas for royal patronage, but believes that it could be possible after his lifetime. The potential benefits to humanity from scientific progress are so great that the task must be attempted.