Horkheimer and Adorno and Foucault see progress as a kind of trap in which we ensnare ourselves. Can this have any relation to the modern contradiction/condition? And if so, what have the postmodernists said about it?
Per Lyotard, for one, the crucible of the Second World War put paid to the "grand narratives" of revolution and the Enlightenment: the first of these argued that revolution was inevitable and would usher in beneficial social change; the second held that social advancement could be attained through technological progress. Postmodernist perspectives would have it that the destruction of grand narratives on account of Nazism, Stalinism, decolonization, postcolonialism, globalization, the collapse of belief systems, growing income inequality, climate change, etc. and the ensuing multiplication of competing, post-truth, "little narratives" has confounded the erstwhile legitimacy of knowledge: the only claims it now makes pertain to practicality and efficiency. From postmodernist perspectives, therefore, the "little narratives" explain the modern contradictions/conditions this query refers to.
I think that's right in some sense. Modernism can be thought of in lots of ways; it's often marked by comminution, empty signification, and transcendence. What does "progress" really mean? From what to what? It's not always clear. The tendency in modernism to try to divide things into smaller and smaller parts in order to (for no clear reason) achieve some all-encompassing greater good seems irrational at best. It distracts from the real embodied forms of suffering and difficulty that one could more easily attend to by noticing the immanence of in-the-moment practices and relations.
Like Horkheimer and Adorno, Foucault observed in the growth of the global accumulation of power, it can even be said that the attempts to escape from that power fed the oppressive power itself. The end of progress in Foucault's work on repression (sexual, moral, legal, mental) means repression by the state. Foucault draws on an anti-enlightenment tradition that rejects the equation of reason, emancipation, and progress, arguing that an interface between modern forms of power and knowledge has served to create new forms of domination. Hence his skepticism (Best & Kellner 1991).
In Theatrum Philosophicum, Foucault (1970), stated that “one day the century will be Deleuzian”. The criticism of modernity was based on "reversing Platonism". When his "inverted Platonism" consists of moving in the Platonic series and provoking in it the appearance of a relevant point: division. (Deleuze, 1969a: 82–85, 165–168; Deleuze, 1969b,1969: 292–300).
On the other hand, the State divides under the power to homogenize, to flatten society. The power that produces knowledge and not simply encourages it because it serves power. Likewise, the concentration of power is the ability to produce even more power in the capital.
Progress limits modern man and man limits himself. Foucault criticizes Horkheimer and Adorno's model of saying, showing how limited everything is. By showing how we are, we are caged. In the face of the crisis of the excessive growth of progress and therefore of power relations, Foucault asks how can the growth of capacities be disconnected from the intensification of power relations? It is a matter of finding in the exploration of possibilities without these becoming new forms of repression.
In Minima Moralia, Adorno mentions that Walter Benjamin's writings are his inspiration. In the "Theses on History", Benjamin offers a similar critique of Hegelian and Marxist philosophy of history. In the "Angel of History" on a painting by Klee called "Angelus Novus". Benjamin described progress as the storm that blows from Paradise and irresistibly propels the angel of history into the future. With his back to the future, the angel of history faces the past and sees only one catastrophe. Following Benjamin, Adorno in History and Freedom about the Auschwitz catastrophe "makes all talk of progress toward freedom seem ridiculous" and even makes the "affirmative mentality" involved in such talk seem "the mere assertion of a mind that is incapable of looking horror in the face and therefore perpetuates it" (Wohlfarth, 1979).
Adorno tried to radically unite what Allen (2015) has called progress as an imperative versus progress as a "fact"; the former is only possible when the latter is rigorously problematized. This is what motivates his paradoxical statement that "progress happens where it ends. Adorno's skepticism about progress as a "fact" is shared by Foucault. In the History of Madness, Foucault announced his intention to write a history that "would eliminate all chronology and historical succession from the perspective of 'progress', to reveal in the history of an experience, a movement in itself, cleared by a teleology of knowledge or the orthogenesis of learning. That experience is neither progress nor regression in relation to any other" (Allen, 2015). Foucault's skepticism was motivated by a somewhat different moral sensibility than Adorno's.
This critique of progress stems from a sensitivity to the ways in which progress in the human sciences is based on the exclusion of the insane, the socially deviant, homosexuals and others considered "abnormal", but Adorno and Foucault agreed on the philosophical point that conceptions of historical progress imply the need for a supra-historical, timeless and universal point of view that we now know to be a metaphysical illusion. In an attempt to think about the possibilities of a fully historicized understanding of critical philosophy, which also reflexively historicizes itself and its own notion of historicity. This is a radical adoption of the Hegelian legacy, precisely charged with skepticism about progress (Allen 2015).
References
Allen A. (2015). Adorno, Foucault, and the End of Progress: In ed. Penelope Deutscher and Cristina Lafont, Critical Theory in Postcolonial Times. Columbia University Press. Retrieved from https://www.law.berkeley.edu/wp-content/uploads/2015/04/Adorno-Foucault-and-the-End-of-Progress-Critical-Theory-in-Post-colonial-times.pdf
Best S., Kellner D. (1991) Foucault and the Critique of Modernity. In: Postmodern Theory. Communications and Culture. Palgrave, London.
Deleuze, G. (1969a). Différence et repetition. Paris: P.U.F.
Deleuze, G. (1969b). Logique du sens. Paris: Minuit.
Foucault, M. (November 1970). Theatrum Philosophicum, Critique, 282, 1970.
Wohlfarth, I. (1979). Walter Benjamin's Image of Interpretation. New German Critique, (17), 70-98. doi:10.2307/488011
Trap is an understatement. Postmodern see to be sponsored project of modernity as it makes sense to the modern and is not in a position to reach its constituency outside modernity, be it premodern or non-modern.