His father, who according to the son was a repository of all the Christian virtues, died while Greene was a boy, and it was through the generosity of his uncle, John Pretty, rector of Farley, Hampshire, that he was sent to Clare Hall, Cambridge.
In 1711 he published 'A Demonstration of the Truth and Divinity of the Christian Religion,' and in the following year 'The Principles of Natural Philosophy, in which is shown the insufficiency of the present systems to give us any just account of that science.'
The latter work was ridiculed and parodied in 'A Taste of Philosophical Fanaticism ... by a gentleman of the University of Gratz.'
Greene, while taking an active part in college and parochial work, was convinced that the whole field of knowledge was his proper province, and devoted many years' leisure to the production of his next work, a large folio volume of 980 pages, entitled 'The Principles of the Philosophy of the Expansive and Contractive Forces, or an Enquiry into the Principles of the Modern Philosophy, that is, into the several chief Rational Sciences which are extant,' 1727.
In the preface Greene, after being at some pains to prove himself a whig, declared his intention of proposing a philosophy, English, Cantabrigian, and Clarensian, which he ventured to call the 'Greenian,' because his name was 'not much worse in the letters which belonged to it than those of Galileo and Descartes.'