Critical Theory is an umbrella term to denote those theorists who take up the task described by Karl Marx as the self-clarification of the age struggles and wishes of the age. As such, two elements are crucial: (a) a connection to social and political struggles of emancipation, and (b) self-reflexivity.
Critical Theorists differ—sometimes quite fundamentally—about what these two elements require (and how they relate). For example, some such theorists (such as Max Horkheimer or Michel Foucault) take the normative orientations of struggles for emancipation as something that does not require grounding at the level of theorizing, while others (such as Jürgen Habermas) think such grounding is the main task of Critical Theory, securing moral validity for the struggles. These substantive differences also mean that there are no accepted methods on which all Critical Theorists would agree. To stay with the example, those Critical Theorists who reject discursive grounding of its normative standards tend to engage in genealogy and other disclosing forms of social critique; while those who seek discursive grounding employ reconstructive and/or constructivist methods.
The existence of fundamental substantive and methodological differences among proponents of Critical Theory means that it is difficult, or perhaps even impossible, to give a uniform characterization of it. Sometimes, Critical Theory is defined institutionally. Then it is denoting a succession of theorists (often classed into different generations) who are connected to the Institute of Social Research and/or the Philosophy Department in Frankfurt am Main, Germany—the so-called “Frankfurt School.” However, this institutional definition has only limited use. The disagreements among thinkers within the Frankfurt School tradition can run deep—sometimes deeper than they run with theorists, like Foucault, who are not connected institutionally to it. And it is an open and contested question whether everyone institutionally connected to the Frankfurt School is engaged in Critical Theory. Thinking systematically about the task of self-reflexively connecting to struggles of emancipation requires a different approach.
It is helpful to understand Critical Theory as a broad and varied tradition, with core cases (such as Horkheimer’s 1937 text “Traditional and Critical Theory”), but no sharp boundaries. Understood that way, there cannot be a fully comprehensive treatment of Critical Theory, but it is possible to think of this tradition as involving multiple morphing sequences, whereby approaches are amended in various ways over time and thereby change into something else. One important dividing line is how historical or transcendental one takes Marx’s task to be—some proponents of Critical Theory are, in effect, historical contextualists, while others seek to establish the conditions of possibility of human interaction as such.
Pseudo Schur complements, pseudo principal pivot transforms and their inheritance properties
