Hill: The Sense of 17th Century English Radicals 
The 20th century's leading English historian of the 17th century, Christopher Hill, gives a detailed and complex account of dissenters in his 1972 The World Turned Upside Down: Radical Ideas during the English Revolution. The thing is, there were so many different kinds of dissenters in that messy century that things get complicated. Don't worry about the many names here, just notice how this fits with the comments of Berman, who only follows the big names in the scientific revolution. Hill sketches many disruptive movements, most of which were articulated in terms of some particular reading of the Bible, and often a belief in some secret ancient knowledge (hermeticism).

    So cool and level-headed a sceptic as John Selden was at once a supporter of the new heliocentric astronomy [Copernicus] and a great admirer of Robert Fludd [alchemist]. Francis Bacon himself had been inspired by the Hermetic [=ancient knowledge of magic] religio-social ideal of controlling nature. Although he rejected the superstitious claims of magic and astrology, which attempted to dominate nature from outside, he thought they contained a core of knowledge about the physical universe which could be used. He looked to the example of craftsmen as a model of scientific experiment: nature cannot 'be commanded except by being obeyed'.
    Bacon's influence was spread wide in England after 1640, thanks especially to the exertions of Samuel Hartlib, and to the invitation to Comenius to come to England. The Comenian fusion of Baconianism and Hermetic natural philosophy laid great emphasis on the social and democratic possibilities of the new science. Hartlib for two decades popularized in England a programme of social, economic, religious and educational reform which influenced men of the calibre of Boyle and Petty. In the euphoria of the early 1640s this programme, which appeared to have the blessing of the Parliamentary leaders, joined with millenarian enthusiasm in creating visions of a Utopia in England soon. (Cf. Hugh Peter's recommendation to Parliament in 1646 that the state should further 'the new experimental philosophy'.). The Comenians appealed especially to craftsmen, who formed the bulk of the religious sects, by their call for a wide extension of educational opportunity, for new teaching methods (using the vernacular, not Latin; emphasizing things, not words; experience, not books); for pooling and making widely available all existing scientific information (notably via Hartlib's Office of Addresses) and for directing science to the relief of man's estate - just as much as by their desire for peace and tolerance among protestants, and for union against the dark forces of papal reaction. 'We are all fellow-citizens of the world, all of one blood, all of us human beings,' wrote Comenius in words which Winstanley and Webster echoed. This was what attracted Boyle in 1646-7. The members of Hartlib's 'Invisible College' practised 'so extensive a charity that it reaches unto everything called man', taking 'the whole body of mankind for their care'.
    Mr [K.V.] Thomas [1971 Religion and the Decline of Magic] has shown how widespread was interest in alchemy and astrology in the 1640s and 50s, not least among religious and political radicals.... Mr. Thomas gives evidence to show that Richard Overton sought political advice from the astrologer Lilly at a crucial stage in April 1648; other serious rational politicians who consulted professional astrologers include Cornet Joyce, Mrs. John Lilburne, Hugh Peter, several Agitators, Anabaptists, Ranters and Quakers. Lawrence Clarkson took up astrology in 1650; John Pordage practised it. So did the members of Hartlib's Invisible College; Gerrard Winstanley [of the communist Diggers] and John Webster recommended that it should be taught. George Fox [of the Quakers] in 1649 was no less worried by the influence of astrologers than of priests....
    Alchemy/chemistry, and especially chemical medicine, had radical associations. For Familists and Behmenists, so influential on Ranters and Quakers, alchemy was an outward symbol of internal regeneration. John Webster, Erbery's heir, had been a pupil of the Transylvanian chemist Hans Hunneades, who worked at Gresham College. Webster also pressed the study of alchemy and natural magic on the universities, and was attacked as a proponent of the 'Familistical-Levelling Magical temper'. One alchemist, of whom Sir Isaac Newton thought very highly, hoped in 1645 that 'within a few years', thanks to alchemy, 'money will be like dross', and so 'that prop of the antichristian Beast will be dashed in pieces ... These things will accompany our so long expected and so suddenly approaching redemption,' when 'the new Jerusalem shall abound with gold in the streets'. That was nearly as subversive as Winstanley [i.e., the Diggers].
    Chemistry became almost equated with radical theology. Webster himself hailed Erbery as 'chemist of truth and gospel'. Francis Osborne in 1656 said that the Socinians were 'looked upon as the most chemical and rational part of our many divisions'. Samuel Fisher in 1662 praised 'that chemical divinity, that God is declaring forth the mysteries of his kingdom by', in reply to Bishop Gauden's sneer at 'canting or chemical divinity, which bubbles forth many specious notions in fine fancies and short-lived conceptions'. Richard Overton in 1643 had proposed a scientific experiment to test the immortality of the soul; George Fox and Edward Burrough in 1658 similarly proposed experiments to test the miracle of the mass. Henry Pinnell translated Paracelsus in 1657, with an Apology in which the translator praised the Hermetic philosophy and insisted that, so far from making 'void the Word of the Lord by his works', he wanted to 'establish the one by the other'. 'Every part of the creation doth its part to publish the great mysteries of man's salvation.' One of the Fellows of the short-lived Durham College was Israel Tonge, an alchemist; another, William Sprigge, agitated for the teaching of chemistry in the universities.
    So astrology, alchemy and natural magic contributed, together with Biblical prophecy, to the radical outlook. In 1646 Benjamin Bourne declared that 'the Familists are very confident that by knowledge of astrology and strength of reason they shall be able to conquer over the whole world'. As Mr Thomas points out, in the astrologers' 'assumption that the principles underlying the development of human society were capable of human explanation we can detect the germ of modern sociology'. 'Astrology, though beginning as a system of explanation, ... ended as one which held out the prospect of control.' That is why conservative theologians were so hostile to it. It also explains its attractions for the radicals: rather like sociology in mid-twentieth century English universities.
    Reliance on dreams and visions - Descartes and Lord Herbert of Cherbury no less than Fox or Winstanley - was also not entirely irrational. The sudden insight, summing up mental processes that have been continuing for some time, is something we are all familiar with. It could seem like a revelation, especially when it came in the hours of darkness. But if you believed the insight was divinely inspired, this gave it authority both for you and for your audience. So new and unconventional insights could be propounded and accepted. A group which Fox met in 1647, who 'relied much on dreams', ultimately became Quakers. Many Anabaptists, Ranters and Quakers practised faith healing, a layman's medicine, or rather the medicine of lay believers. But the miraculous cures claimed by the early Quakers were suppressed by their successors: Penn and Ellwood do not refer to them.
    The supporters of alchemy, astrology and magic were unfortunate in backing the right horse at the wrong time. Alchemy was to develop into the science of chemistry, though it had to wait for the next great upheaval of the French Revolution for this to be completed. Social sciences have emerged more slowly in the nineteenth and twentieth centuries, and they are not conscious of any debt to astrology. But the cosmic hopes which the Hermetic philosophy seemed to open up were not wholly unreasonable in the mid-seventeenth century when magic and science were still advancing side by side. Isaac Newton first turned to the study of mathematics in order to investigate the scientific claims of judicial astrology. He remained interested in alchemy throughout the creative period of his life. 'The last of the magicians,' Lord Keynes called him. From our twentieth-century vantage point we see the path of science advancing inexorably through the mechanical philosophy and the gradual elimination of magic from all spheres - except, unfortunately, the core of Newton's law of gravity, the unexplained 'force' which acts by apparently non-material, non-mechanical means across vast distances. Ignoring this, we assume that the triumph of mechanism was inevitable from the start. But Winstanley, for whom God and matter were one, said 'God is still in motion', and urged us to pursue 'the motional knowledge of a thing as it is'. For 'truth is hid in every body'. Great though the achievements of the mechanical philosophy were, a dialectical element in scientific thinking, a recognition of the 'irrational' (in the sense of the mechanically inexplicable) was lost when it triumphed, and is having to be painfully recovered in our own century. We smile when we read Samuel Hering asking for special university courses on Jacob Boehme; but at least one modern historian of science has suggested that it was exactly Boehme's sort of leaven that was missing in English scientific thinking during the later seventeenth and eighteenth centuries. The radicals were wrong; but they are beginning to look less stupidly wrong than they did once.
    A generation ago even so sensitive a commentator as Sabine was a little embarrassed by Winstanley's suggestion that nature itself had been corrupted by the Fall of Man. He dismissed as 'naive' and 'simple-minded' the idea that natural disasters like 'the risings up of waters and the breakings forth of fire to waste and destroy are but that curse, or the works of man's own hands that rise up and run together to destroy their maker, and torment him that brought the curse forth'. Winstanley, however, as so often, is putting startlingly new content into traditional forms of language. If we bear in mind that for him the Fall was caused by covetousness and set up kingly power, we may rather think today that this is one of the profoundest of Winstanley's insights. As we contemplate our landscape made hideous by neon signs, advertisements, pylons, wreckage of automobiles; our seas poisoned by atomic waste, their shores littered with plastic and oil; our atmosphere polluted with carbon dioxide and nuclear fall-out, our peace shattered by supersonic planes; as we think of nuclear bombs which can 'waste and destroy' to an extent that Winstanley never dreamed of -we can recognize that man's greed, competition between men and between states, are really in danger of upsetting the balance of nature, of poisoning and destroying the fabric of the globe. We are better placed to appreciate Winstanley's insight, that in a competitive society the state is just a part of the competitive system. Perhaps it was over-simplified to believe that harmony and beauty will be restored to nature, as well as society, as soon as community of property is established. But what are the chances of priority being given to 'the beauty of the commonwealth' before there has been a change in social relations? For Winstanley social revolution is the same thing as men learning to 'live in community with the globe and ... the spirit of the globe', in accordance with the laws of nature: letting Reason rule in man as it does in the cosmos.
    Rejection of non-mechanistic explanations was in part - and only in part - ideologically motivated. Stable laws of nature went with a stable society. Now that God was located within every human heart, it was inconvenient to have him intervening in the day-to-day running of the universe. Both popular magic and catholic magic upset the ordered cosmos. After 1660 everything connected with the political radicals had to be rejected, including 'enthusiasm', prophecy, astrology as a rival system of explanation to Christianity, alchemy and chemical medicine. Proponents of the latter were dismissed as 'fanatics in physic', 'a sort of men not of academical but mechanic education', supporters of 'the late rebellion', who wanted to open medicine to 'batters, cobblers and tinkers'. Naturally enough, as the iatrochemists and alchemists failed to win acceptance, as they found themselves spurned by official scientific bodies, so they became increasingly wild and irrational. Thus society's verdicts are self-confirming.
    It was 'plebeians and mechanics' whom Bishop Parker denounced in 1681 for having 'philosophized themselves into principles of impiety'. They 'read their lectures of atheism in the streets and highways'. I was guilty of undue foreshortening when in my Intellectual Origins of the English Revolution I described the mechanical philosophy as the philosophy of rude mechanicals. I should have differentiated more sharply between 'mechanic atheism' and the mechanical philosophy proper. One part of the reason for the acceptance of the latter was that it seemed to offer an academic alternative to the mechanic atheism to which some of the radical congregations under mechanic preachers were tending.
    The triumph of the mechanical philosophy ultimately created further problems for Christianity, as some parsons had foreseen it would. Witches, malignant spirits and the devil had been useful explanations for the existence of evil and suffering, useful scapegoats. Who was to blame if they were not? 'Deny spirits and you are an atheist,' divines said.