In all of these cases, the error arose from accepting “loose” fits of a law to data, and the later, correct formulation provided a law that fit the data much more closely. If we wished to simulate this phenomenon with BACON, we would only have to set the error allowance generously at the outset, then set stricter limits after an initial law had been found.

In such a way, with much trouble and labor, the whole Canon has been established. For many hundreds of years, up to now, our ancestors have been using this method because they were not able to invent a better one. However, this method is uncertain and dilapidated as well as cumbersome and laborious. Therefore we want to perform this in a different, better, more correct, easier and more cheerful way. And we want to point out now how all sines can be found without the troublesome inscription [of polygons], namely by dividing a right angle into as many parts as one desires.

The "Baconian" sciences were the kind Francis Bacon had in mind when he issued a call to revitalize science by basing it on craftsmen's knowledge of nature. Bacon is remembered as the most effective critic of the traditional learning promulgated the elite institutions of his day. ...Bacon advocated compiling a "history of arts," or encyclopedia of crafts knowledge...

[Bacon's] philosophy resembles this religion, which protests continually: it is entirely negative and thinks only to contradict. In indulging himself without measure in this natural inclination, he ends by contradicting himself without perceiving it, and by insulting in others his own most characteristic traits. Thus he blames abstractions without respite, and he makes only abstractions, in always coming back to his middle, general, and most general axioms, and in maintaining that individual instances do not merit the philosopher's attention. He never ceases to shower abuse on the science of words, and he only makes words. He upsets all the received nomenclature to substitute for them new terms, baroque or poetic, or both. With Bacon, neologism is a real disease, and always he believes he has acquired an idea when he has invented a word. He looks with pity at the alchemy that was fully operative in his time, and all his physics is only another alchemy quite babbling and wholly similar to children who talk a lot and produce nothing, as he said very well and very badly with respect to the ancient Greeks.

Max Beer, in his History of British Socialism, points out that Bacon looked for the happiness of mankind chiefly in the application of science and industry. But by now it is plain that if this alone were sufficient, we could all live in heaven tomorrow. Beer points out that More, on the other hand, looked to social reform and religious ethics to transform society; and it is equally plain that if the souls of men could be transformed without altering their material and institutional activities, Christianity, Mohammedanism, and Buddhism might have created an earthly paradise almost any time this last two thousand years. The truth is, as Beer sees, that these two conceptions are still at war with each other: idealism and science continue to function in separate compartments; and yet "the happiness of man on earth" depends upon their combination.

After sketching his program for the scientific revolution that he foresaw, Bacon ends his account with a prayer: "Humbly we pray that this mind may be steadfast in us, and that through these our hands, and the hands of others to whom thou shalt give the same spirit, thou wilt vouchsafe to endow the human family with new mercies". That is still a good prayer for all of us as we begin the twenty-first century.

The skeptical view appears to me out of harmony with the inductive philosophy. Bacon gives us many warnings against preconceived opinions and prejudices; but he does not bid us despair of ascertaining facts from our own senses and from testimony. ...we do not find in Bacon any dogma like that of Mr. Faraday that the 'laws of nature are the foundation of our knowledge in natural things,' and that these form our only safe test for any new fact presented to our observation. Bacon's method is rather the contrary, namely, that facts are to serve as the foundation of the laws of nature.

In Bacon we see the culminating prime
Of British intellect and British crime.

To sum up the whole, we should say that the aim of the Platonic philosophy was to exalt man into a god. The aim of the Baconian philosophy was to provide man with what he requires while he continues to be man. The aim of the Platonic philosophy was to raise us far above vulgar wants. The aim of the Baconian philosophy was to supply our vulgar wants. The former aim was noble; but the latter was attainable.

Great as Bacon was, he was far from being free from the mistakes and prejudices of those who went before him. Even some of the most wild and absurd opinions of the antients have the sanction of his approbation and authority. He does not hesitate to assent to an opinion... that visual rays proceed from the eye; giving this reason for it, that every thing in nature is qualified to discharge its proper functions by its own powers, in the same manner as the sun, and other celestial bodies. He acknowledges, however, that the presence of light, as well as several other circumstances, is necessary to vision.

The main importance of Francis Bacon’s influence does not lie in any peculiar theory of inductive reasoning which he happened to express, but in the revolt against second-hand information of which he was a leader.

Anyone who wants to paint should read Bacon. He defined the artists as homo additus naturae.. .Bacon had the right idea, but listen Monsieur Vollard, speaking of nature, the English philosopher, [Bacon] didn't for-see our open-air school, nor that other calamity which has followed close upon its heels: open-air indoors.

I am saying to modern scientists and theologians: don't imagine that our latest ideas about the Big Bang or the human genome have solved the mysteries of the universe or the mysteries of life. Here are Bacon's words again: "The subtlety of nature is greater many times over than the subtlety of the senses and understanding". In the last four hundred years, science has fulfilled many of Bacon's dreams, but it still does not come close to capturing the full subtlety of nature.

One does not have to have experience raising children through school, dealing with family tragedies, and so forth, to be able to find three numbers whose fourth powers add up to another one.