'Beauty in things exists merely in the mind which contemplates them." These words were penned in 1742 by David Hume, a key figure in the Scottish Enlightenment, and a close friend of the painter Allan Ramsay, born 300 years ago next month.

Walk down Glasgow's University Avenue from now until early January and lift your eyes and you'll see a host of banners featuring portraits by Allan Ramsay. There are some splendidly real faces on display; from a girlish Flora MacDonald to a haughty be-wigged Duke of Argyll and even the square-jawed, dark features of Ramsay himself at the age of 26.

Ramsay's gaze is sure and his bottom lip is set within an almost stubborn expression of defiance. He is this side of handsome and his features are far from picture-perfect, as if to reinforce Hume's observation that beauty is a concept which exists only in the mind.

The banners announce a new exhibition to mark the tercentenary of Ramsay's birth, which opens today in the University of Glasgow's Hunterian Art Gallery.

The exhibition, Portraits of the Enlightenment, features a selection of works in oil, pastel and paper by Ramsay. The faces on the wall are mostly his friends and intellectual equals. They include The Hunterian's founder, William Hunter, as well as Francis Hutcheson, the Ulster-born professor of moral philosophy at the university from 1730 until his death, also a leading figure of the Scottish Enlightenment.

A large oil painting of Frances Boscawen was painted around 1747-8, when this bright young 'bluestocking' was just 23 and newly married to Edward Boscawen, third son of the first Viscount Falmouth.

The stunning portrait was probably commissioned on a purely commercial basis, but before long, Ramsay and the Boscawens were close friends. It was a friendship based on high ideals, as well as a love of nature and literature. It is recorded that this portrait was viewed as a truthful rendering of his friend's features. Frances herself said of her appearance: "Beauty and I were never acquainted."

The story of Ramsay's intellectual life would not be complete without prints or mezzotints "after" Ramsay, many of which were produced by Ramsay's ambitious studio assistant, David Martin. One of the most intriguing is of Swiss-born writer and philosopher, Jean-Jacques Rousseau, a key figure in the European Enlightenment scene, whom Ramsay painted at the London home of David Hume.

Rousseau, who had served time as an apprentice to an engraver, was nervous about having his portrait painted at all.

Ramsay's portrait in oil, displayed next to the mezzotint, is a softly painted depiction of the man whose theories influenced the leading figures of the French Revolution. We see him looking directly at the artist, clad in his by-then trademark Armenian hat and robe, his black-gloved hand clasped to his chest.

This portrait was never meant to be publicly displayed and was not seen in public until it was acquired by the Scottish National Gallery in the late nineteenth century. In contrast, the Martin print, exhibited in 1766 at the Society of Artists exhibition in London, shows an exaggerated, almost cartoon-like version of Ramsay's Rousseau.

The resulting fall-out between Hume, Ramsay and a furious Rousseau who hated the Martin image was much talked about in the salons of the European intelligentsia of the day.

According to Mungo Campbell, deputy director of The Hunterian, and curator of this exhibition, the thread which binds all these works together is the fact they are all "reflections of Ramsay's relationship with these people."

"These are people he shared ideas with," he says of the artist who defined this Hanoverian era like no other. "We've made a point of not having Ramsay's royal pictures on show here. This is a much more intimate display. Having the royal pictures would have been another story altogether. The work here reflects where the intimate exchanges in Ramsay's life took place."

Allan Ramsay was born in 1713. The son of the Edinburgh poet and bookseller Allan Ramsay, he was raised by his father to feel he was on a level playing field with those who might be viewed as being on a superior social strata.

His relationship with his father was a close one and an early drawing of Ramsay Senior, made when his son was just 16, is one of the stand-out pictures in this show.

Ramsay was a precociously talented draughtsman who became the go-to portrait artist for London society from the early 1740s until the early 1760s. Some of his earlier theatrical drapery-festooned portraits of wealthy clients are on display in the main Hunterian gallery on the ground floor, and the contrast between these and the more intimate portraits in this new exhibition is marked.

The young Ramsay had studied in Edinburgh, London and Italy before establishing himself as a society portrait painter in London. By the 1750s, Joshua Reynolds was the new kid on the block and the rivalry between the two men was the subject of much discussion in the tea salons of the day.

The great chronicler of the Georgian era, Horace Walpole, said of the two men in 1759: "Mr Reynolds seldom succeeds in women: Mr Ramsay is formed to paint them."

Ramsay, an accomplished linguist who was fluent in French and German, was the Royal family's preferred portraitist and in 1767, was appointed German-speaking George III's "Principal Painter in Ordinary".

By 1770, Ramsay had stopped painting for purely commercial purposes, preferring to concentrate on his other interests, including politics, writing and business investments.

According to Mungo Campbell, one of things that divides Ramsay from Reynolds is his realism and his honesty.

He points to the 1749 portrait of Flora MacDonald, which was commissioned by Ramsay's mentor, the antiquarian and physician, Dr Richard Mead, (and is on loan from the Ashmolean Museum in Oxford) as an example of a work which highlights this honesty.

"She is portrayed swathed in tartan and holding flowers but there is the usual Ramsay honesty," he says. "She captivated London society and by that stage was a celebrity. David Martin made a print of this portrait literally before the paint dried and it was a sell-out."

This exhibition is not the ultimate survey of Ramsay's work. Instead it is an intimate and honest reflection of the way this great Scottish artist operated in his private life. Step inside the Hunterian from today, and you step behind the silk damask curtains of parlours where the sparks that made the spirit of the Enlightenment were ignited.

Along the way, feel the force of a master to whom the art of portraiture was second nature.

Allan Ramsay: Portraits of the Enlightenment is at Glasgow University's Hunterian Art Gallery from today until January 5 2014.