You wouldn't know it from the sublime confidence with which "Enlightenment values" have been invoked in recent years by the self-proclaimed descendants of Voltaire (Dawkins, Hitchens et al), but today there reigns among scholars something close to a consensus that there was not one "Enlightenment" but several. As John V Fleming observes at the beginning of this engaging, if rather eccentric, book, the "very term 'Enlightenment' … is elastic if not protean". There were political and scientific Enlightenments, he notes, and "local Enlightenments galore" – in Scotland and in France, by the Baltic Sea and deep in Bavaria too.

In any serious account of "the" Enlightenment, therefore, the definitional question – what are we talking about when we talk about the Enlightenment? – will always take centre stage. Another recent book on the topic, Anthony Pagden's The Enlightenment and Why It Still Matters, is a case in point. Pagden argues that contemporary debates over the legacy of the Enlightenment have been focused in the wrong place: in his view, the great achievement of the Enlightenment thinkers of the 18th century was not simply to replace the authority of divine revelation with that of reason, but to offer a "cosmopolitan" account of what we owe to each other when God is no longer on the scene, a "universalising vision of the human world".

There is one aspect of the more familiar version of the Enlightenment that Pagden takes for granted, however: the claim that it is, almost by definition, anti-religious. He pays no attention, for instance, to the German sociologist Max Weber's demonstration that the "innerworldly asceticism" which shaped the modern, secular world was in fact rooted in certain currents of Judeo-Christian monotheism. And when he discusses the work of John Locke, a key Enlightenment thinker by any measure, he simply ignores what it owes to Christianity.

It is with some relief, then, that one finds Fleming acknowledging that "candid students of the European Enlightenment must soon discover that it had a great deal to do with religion" – it was either searching for a suitable replacement (in the form of human reason) or – and this is the bit of the story that is often missed out – "salvaging it in some way". (One assumes this is a reference to the deism that many Enlightenment thinkers subscribed to and which rejected, on moral grounds, the idea of God as an agent forever intervening in history.)

It's worth pointing out that the Enlightenment isn't really Fleming's period – he's a medievalist by trade (he taught "humanistic studies" at Princeton for 40 years) and this book, his ninth, is, in part at least, an attempt to rescue the middle ages from the condescension of posterity. To this end he emphasises the "medieval continuities" in the age of Enlightenment – alchemy and witchcraft among others – and what he calls an "enduring appetite for transcendental experience" that survived the atrophying of the "machinery of medieval Christianity".

On several occasions, Fleming cites some lines by perhaps the greatest Enlightenment thinker of them all, Immanuel Kant. Kant offered an answer to the question "What is Enlightenment?" in his celebrated 1784 essay of that name. His answer was that enlightenment is "man's emergence from self-incurred immaturity". It consists, he went on, in having the courage to use one's "own understanding" – to think for oneself, in other words.

But these aren't the lines that Fleming returns to. Instead, he quotes the much less well-known opening sentence to Kant's magnum opus, the Critique of Pure Reason, published in 1781. "Human reason," Kant wrote there, "has this peculiar fate that in one species of its knowledge it is burdened by questions which … it is not able to answer."

The aim of Kant's "critical" philosophy was to restrain the pretensions of philosophers to lay claim to knowledge of items – the soul, freedom and God – which lie beyond the spatial and temporal limits of human experience. But this wasn't just a matter of upbraiding his predecessors – Leibniz and Spinoza principal among them – for their hubris. On the contrary, Kant also recognised that the tendency of human reason to overreach itself is ineluctable. "Metaphysics" isn't just a regrettable episode in the history of philosophy; it is a "natural" disposition that can't be eradicated.

Fleming is interested in those who, during the Enlightenment assault on the claims of revealed religion and traditional metaphysics, were "unable to dispense altogether with 'transcendence'". All of which raises a number of rather profound questions – about the methodology of historical periodisation, particularly whether the Enlightenment marks a decisive and easily identifiable break with what preceded it, and the extent to which claims about an enduring appetite for transcendental experience are merely historical or in fact refer to certain permanent features of human nature. However, Fleming doesn't seem especially interested in attempting to answer them. His approach, breezy and charmingly belletristic, is unabashedly impressionistic.

He looks in the "crevices of history" for figures such as Valentine Greatrakes, an Anglo-Irish veteran of the Roundhead army during the English civil war, who claimed to be able to cure scrofula, a tubercular inflammation of the lymph nodes known as the "King's evil"; the adepts of secret religious societies such as the Rosicrucians and the Freemasons; and the Italian occultist Count Alessandro di Cagliostro, an early practitioner of the seance who was inducted into the masonic order and eventually arrested for his alleged role in the "Affair of the Diamond Necklace" in prerevolutionary France.

Fleming writes vividly and entertainingly about these episodes and makes some useful connections with the wider intellectual and historical context along the way – especially interesting is his suggestion that the flourishing of masonic lodges in England in the 18th century is best understood as a form of "sociability" analogous to that which was taking root in the coffeehouses of London during the same period.

But it remains unclear what all this is meant to tell us about the Enlightenment. Is he simply pointing out that certain occult practices survived well into what he calls the "Enlightenment period", a purely chronological category, or is he making a much more far-reaching claim about the internal contradictions of Enlightenment thought? Unfortunately, this book never properly confronts that question, let alone answers it.