In 1783, Johann Friedrich Zöllner, a theologian, posed a question that we are in some ways no nearer to answering. "What", he asked in a footnote to an essay on civil marriages, "is enlightenment?" Should we be discussing "the" Enlightenment, as if it were a singular phenomenon, or "enlightenments"? If there are plural schools of thought, to what extent are they nationalistically inflected? What unites and what divides the French Enlightenment of Voltaire, d'Alembert, Diderot, Condorcet, Montesquieu and De Tocqueville from the Scottish Enlightenment of Hume, Smith, Kames, Ferguson, Robertson and Hutcheson, from the German Aufklärung, dominated by Kant, but also including Goethe, Stäudlin, Leibniz, Humboldt and Lichtenberg? Was there an English Enlightenment, a tradition of rationalism stretching from Bacon and Hobbes to Locke and Shaftesbury and eventually Paine and Wollstonecraft? And even if we admit to several concurrent lines of thoughts in different countries, how do we account for the vast contradictions within them – is there common ground between, say, Rousseau and La Mettrie?

Anthony Pagden is very much of the camp that believes an "Enlightenment", across several countries and with broad similarities of purpose and method, did indeed occur. His is the Enlightenment of the "long 18th century". It is typified by scepticism, by an ideal of universalism – sometimes referred to as cosmopolitanism both here and in the period (the idea that we are "citizens of the world") – and by scientism: the view that universal human nature can be analysed by philosophy with the same precision and predictability as billiard balls ricocheting around the baize is by Newtonian mechanics. In addition to these broad and contradictory areas of similarity, Pagden also identifies an increasing trend towards what was then called "freethinking" and is now called atheism. From Hobbes reading the Bible with critical analysis (how could Moses be the author of the Pentateuch if it recounts the death of Moses?) to Baron d'Holbach's Critical History of Jesus Christ, which identified the vicious circle of naive theology (how do we know the Bible is true? Because the Bible, at II Timothy 3:16 says all scripture is God-breathed), there was a perceptible burgeoning of distrust in religion, or at least conventional religious authority.

Pagden does highlight that it is naiveto conflate the Enlightenment with rationalism, citing Hume's idea that "reason is and ought only to be the slave of the passions", and paying due attention to the contemporaneous cult of sensibility and concept of sociability. But Pagden's selections from writers of the period are markedly partial. Take scientism: it is understandable that Edmund Burke is presented in a slightly villainous light here, but he wrote the following in An Appeal from the New to the Old Whigs: "No universal can be rationally affirmed on any moral or political subject. Pure metaphysical abstraction does not belong to these matters. The lines of morality are not like the ideal lines of mathematics. They are broad and deep as well as long. They admit of exceptions; they demand modifications." This requires at least a counterargument, especially since a similar position about the difference between geometry and philosophy can be found in Kant's Critique of Pure Reason. Other branches of the Enlightenment were clearly not of the universalising tendency: although Pagden is good on how both China and Tahiti were figured in Enlightenment taxonomies (in fact, it is the best part of the book), he barely mentions, for example, Adam Ferguson's less optimistic investigations into international rivalry as a check on universal despotism. Of course, it is possible to depict the Enlightenment as being inherently sceptical, but only at the expense of ignoring the whole of Kant's project: that which "roused him from his dogmatic slumbers" was an attempt to find a solution to Hume's scepticism. Equally, the Enlightenment can be typified as a predominantly secularising phenomenon as long as one omits the theism of Kant, Voltaire, Priestley, Hutcheson and Berkeley as well as the more typically theological writers such as Joseph Butler, Alexander Geddes and Moses Mendelssohn.

Pagden's 18th century is long: just not long enough. To assert, as he does, that "the entire Enlightenment ambition" was "to create a historically grounded human science which would one day lead to the creation of a universal civilisation capable of making all individuals independent, autonomous, freed of dictates from above and below, self-knowing and dependent solely on each other for survival" without referencing Marx is to write the history of ideas without ideas or history. He makes much of the various pamphlets on universal peace – Kant's "Toward Perpetual Peace" but also the work of William Penn, Pierre-André Gargaz, Jeremy Bentham and Charles-Irénée Castel – without acknowledging that what did preserve the peace in post-Napoleonic Europe was the far less philosophical, far grubbier and far more pragmatic Congress system.

The final chapter is on the "enemies" of Enlightenment, and continues the polemic first raised in Pagden's equally broad-brush book Worlds At War: The 2,500 Year Struggle Between East and West. He ends with a bizarre counterfactual on the Protestant Reformation and the Enlightenment never happening, whereby Sultan Selim III of the Ottoman empire marches into Paris in 1789. The chief enemy of Enlightenment here is the moral philosopher Alasdair MacIntyre, and it is curious that so little attention is paid to non-Anglophone critiques of Enlightenment: there are a few glancing references to Lyotard and Foucault, but nothing on Derrida, Ricoeur, Stirner, Deleuze or Virilio. It's worth remembering that MacIntyre's work in After Virtue and Whose Justice? Which Rationality? is driven in part by exposing the internal contradictions of Enlightenment moral philosophy. If we take the Kantian categorical imperative seriously – that there could be a moral code binding across space, time, agent and circumstance – then we will have to deal, eventually, with the "Anne Frank dilemma". If, as it is according to Kant, lying is always and absolutely a moral wrong, what do you say to the Gestapo?

This is a big but not a deep book. Compared to the affability, the clubbable nature of many of the thinkers it describes, it is strident, partisan and always willing to overlook a fact in favour of a thesis. Pagden asserts that the Enlightenment matters because it has given rise to international law, "global justice" and human rights legislation, while admitting that we see these at the moment but through a glass darkly. Would this be the international law that prosecutes some war criminals but not others; the "global justice" that applies to Kentucky but not Kandahar; the human rights that are suspended whenever enduring freedom needs a little quiet shock and awe? That Pagden does not mention Toussaint Louverture at all means an important vector in thinking about race, Enlightenment and a queasy sense of European presumed superiority is absent.

Nevertheless there was one moment when the book made me laugh out loud. Pagden quotes Adam Smith on the occupation of Edinburgh by the Jacobites – "four or five thousand naked Highlanders". He glosses this, in parentheses, with "the Highlanders were famous for running into battle dressed only in their shirts", which conjures a vision of a platoon of Wee Willie Winkies. If I were being generous, I would consider this a spellchecking error and assume that Pagden means "skirts", having shied away from the word "kilts" – except that a horde of bellicose Highlanders sprinting topless seems rather unlikely, too.

• Stuart Kelly will be appearing at the Edinburgh international book festival on 15 August at 11am and on 26 August at 1pm. edbookfest.co.uk