Themost important step is to get out of the idea of ideology as mere superstructure, a sort of passive reflection of what goes on in the economic base. Even if this simple picture can be complexified by notions of relative autonomy, non-expressive totalities, different sorts of contradictions, uneven development and heterogeneous phases co-present in the same structur, this more sophisticated picture still leads to trouble as long as we are stuck in the definition of ideology as (1) a system of ideas that (2) is the Other of science.
This Althusserian dualism can’t work because there is no magic criterion of demarcation to discern and attribute the status of scientificity or not. However, if we take ideology in some wider sense than merely ideas, such as the unawareness of the material (political, economic and technological) origins and/or conditions of our ideas, then it becomes a more plausible notion, but it can no longer be the Other of science, and we have left the space of structuralist epistemology.
This is what Bernard Stiegler is proposing under the name of “organology”, and he finds only fragmentary examples of it in intellectual history. His idea is that with the advent and dissemination of digital technologies we are at a point where the technical conditioning (here too in a wide sense, as he recards the invention and spread of alphabetic writing as one major form of technical conditioning) is being transformed in depth and so we may be able to become more aware of it, and if not control it, as this is not possible, at least inflect it in a favorable direction (as its influence is conditioning but not determining), and orient it towards a more curative and less toxic bifurcation.
Having taken this step outside structuralist epistemology the poststructuralists began to riff on the tension between the psychoanalytic and the structuralist strands. Structuralism was scientistic and tended to read Lacan from a rationalist perspectiver, but Lacan’s vision of misrecognition as a systemic feature led the poststructuralists to see that even science contained “ideological” features, hence the decomposition of the notion of ideology into sub-components, that are then conserved under other names, except for the treatment of ideology as the other of science.
But poststructuralist French theory balked at a barrier that in other countries Science and Technology Studies (STS) breached. Foucault did genealogies of human sciences, but did not touch the natural sciences (except biology). Lyotard briefly toyed with relativising the authority of the sciences but eventually just limited it to the cognitive domain, where he gave it unrivalled hegemony. Deleuze talked about “nomad” vs “sedentary” science, but this constituted a distinction at the level of its content (fluids vs solids) and its procedures (problematic vs theorematic) rather than involving a heuristic analysis of the processes of construction of scientific results.
The Althusserian conception has certain advantages as it situates ideology not just in ideas but as a structuring principle in practices and institutions e.g. in the definition of the roles and functions available within a social formation. It also contributes the notion of a sort of systemic cognitive bias, or blindness, concerning the factors that structure the very type of subjectivity pervading a society.
These two other strands (psychoanalytical and structural) are far more radical than the epistemological (ideology is the “Other of science”) strand, which makes alchemy for example a case of ideology and chemistry a science, situating them in radically different categories separated by an epistemological rupture. The problem is that by rejecting the crude binary demarcations of the epistemological strand many theorists threw the baby out with the bathwater and lost sight of, or expressed cryptically, the positive aspects of the two other strands of ideology as structuration of embodied practice and of ideology as misrecognition or cognitive blindness.
Certain theoretical figures have emerged that are situated halfway between structuralism and post-structuralism. One could call them “demi-post-structuralists”. Badiou is a good example, with his scientism intact. Still stuck in the problematic of the conceptual space opened up by the Althusser-Lacan conjuncture, they privilege Lacan as an alternative way out of structuralism yet they try to “rationalise” their problematic by appeals to notions of scientificity based on methodological rigour.
The problem with the primacy of method is that it is not content neutral. A formal method has substantive claims about its domain coded into it. The opponents of “method” are not crazy spontaneity-addicted narcissists but people like Bohr and Einstein who claimed that explicit scientific method was a bottom up, post hoc clarification, not an a priori top-down imperative. The stakes are not blindly insisting on the priority of creation but maintaining a place open for the possibility of novelty and creation versus closing off in advance some possible developments, often without even noticing.
The status of mathematics, is a totally different affair, and the question of the research heuristics of mathematics is not well discussed. For it is heuristics we must look at when we talk about maths, not “eternal” content. Cantor had some very strange ideas fueling his research. That such philosophies are not always detachable from the technical aspects can be seen in that intuitionist maths is not the same as formalist maths.
Lacan would consign most ideas about methodological rigour to the binaries (or dualisms) of the imaginary, the domain of constitution of the ego, narcissistic by definition, so it is amusing to hear the imaginary “anti-methodists” being called narcissistic, when they are a spectre constructed precisely to comfort the methodological rigorists.
It is only by concentrating on the end-product, i.e. scientific results, that one can have the impression that methods are somehow detachable from the processes they are embedded in, in some absolute way. It is no use trying to retreat to a detached context of justification or to a separate “space of implications”. Such a separate methodical space is just as bad in the formal mode as OOO’s retreat to a separate space of objects is in the material mode.