Jordan Peterson, in his Oxford Union address, said,
It is obvious that there is a contradiction between Marxism and post-modernism.
In what sense is there a contradiction?
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I don't know what Peterson means by this, but according to Wikipedia's definition of postmodernism:
While encompassing a wide variety of approaches and disciplines, postmodernism is generally defined by an attitude of skepticism, irony, or rejection of the grand narratives and ideologies of modernism, often calling into question various assumptions of Enlightenment rationality. Consequently, common targets of postmodern critique include universalist notions of objective reality, morality, truth, human nature, reason, science, language, and social progress.
If you criticize objective reality or morality generally, it's not hard to see how that can also encompass criticism of Marxist notions like class struggle etc.
For example, Foucault (which Wikipedia gives a as prime example of a postmodernist)
never adopted an orthodox Marxist viewpoint, refuting core Marxist tenets such as class struggle.
Likewise Jean-François Lyotard
distanced himself from Marxism because he felt that Marxism had a rigid structuralist approach and they were imposing 'systematization of desires' through strong emphasis on industrial production as the ground culture.