In the following example of paradox from Chapter 1, the historian/narrator gives an overview of the Muad'Dib's reign:
He did this because capture of Arrakis, that planet known more often as Dune, gave him a monopoly over the ultimate coin of the realm—the geriatric spice, melange, the poison that gave life.
In this passage, the speaker paradoxically refers to spice as the "poison that gives life." This "poison" has given Paul the prescience needed to bring about the Jihad, and, in turn, to bring more water to Arrakis: hence, the poison that gives life and understanding. Spice is also the poison that gives life to the mind, in the form of enhanced mental capacity and prescience. This new life for the mind begets power, in turn, for people like the Muad'Dib and the Bene Gesserit. However, just as spice is a poison that gives life, so does the life it gives, in turn, beget poison. Power is arguably a form of poison, corrupting everything it touches in due course. If spice is potent, the power it engenders is even more so. In a way, Paul has been poisoned by spice, cursed with a power that brings him misery and difficulty.
In the following example of paradox from the beginning of Chapter 3, Paul mulls over his life and the changes beset upon the planet Dune by his rule:
He stood naked and oddly attuned to his world. Dune was a world of paradox now—a world under siege, yet the center of power. To come under siege, he decided, was the inevitable fate of power. He stared down at the green carpeting, feeling its rough texture against his soles.
In this passage, Paul muses on Dune as a "world of paradox," simultaneously the center of power and a place of instability. Such is the nature of powerful places, often. Their power begets their fragility, as many grapple to seize the associated resources and latitude.
In many ways, Paul is himself an emblem of the empire he created, torn between the demands of the Bene Gesserit and powerful houses, and the demands of his heart—in which sit Chani and the Fremen. Paul is the center of power. His mind is the center of power, yet it too is under siege, threatened from without and within by malicious forces. Yet this siege is fated, according to Paul himself: one cannot claim the seat of power yet shirk from the challenges it creates.
In the following example of paradox from Chapter 8, Alia reflects on happier times, before her brother became the Muad'Dib:
There’d been much pleasure in those untrammeled days before her brother had mounted the throne—time for joking, time for small things, time to enjoy a cool morning or a sunset, time . . . time . . . time . . . Even danger had been good in those days—clean danger from known sources. No need then to strain the limits of prescience, to peer through murky veils for frustrating glimpses of the future.
Alia compares the time before her brother's reign to a time period of "good danger," a danger which, though present and threatening, was paradoxically preferable to the murkiness of the future.
This passage plays upon themes of longing in the novel: longing for the past, for another world, for another time or place. As it turns out, power can be a trap—and both Paul and Alia have power in droves. Alia longs for a simpler time, well before either she or Paul were beholden to the machinations of power. She wishes for a world not sculpted by the Bene Gesserit, one she and those she cares for could make their own.
In the following example of paradox, the narrator from the epigraph to Chapter 8 speaks abstractly about what Alia represents:
To pilgrims who seek her out with demands that she restore virility or make the barren fruitful, she is a form of antimentat. She feeds on that proof that the “analytic” has limits. She represents ultimate tension. She is the virgin-harlot—witty, vulgar, cruel, as destructive in her whims as a coriolis storm.
As a religious figure alongside her brother, Alia represents a rather tumultuous sexual force. She is a source of "tension"; simultaneously a virgin and a sexual object, like Mary in the Christian Bible. Undoubtedly, Alia herself does not wholly embody such an ideal. The words from this epigraph are words from a religious text; Alia is a religious figure. Yet one must ask—how should an abstract religious figure be considered, apart from the person whom they actually were? Martyrs are more stories than people, after a certain point, and this is clearly true of Alia. Her paradoxes and personal contradictions become scaffolding for an entire religious ideology. Such pressures are more than one human can typically bear: fame, let alone the kind associated with religion, is not a natural state.