The 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 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 stick to the definition of ideology as (1) a system of ideas that (2) is the Other of science. This can’t work because there is no magic criterion of demarcation to discern and attribute the status of scientificity or not. If we take ideology in some wider sense as the unawareness of the material (ie 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 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), orient it towards a more curative and less toxic bifurcation.
I think that having taken this step outside structuralist epistemology the poststructuralists began riffing on the tension between the psychoanalytic and the structuralist strands. Structuralism was scientistic and tended to read Lacan in a rationalist vein, but Lacan’s vision of misrecognition as a systemic feature led the poststructuralists to see that even science had “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 I think that poststructuralistFrench theory balked at a barrier that in other countries Science Studies breached. Foucault did genealogies of human sciences, but did not touch the natural sciences. Lyotard 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 science” but it was more a content-level distinction than any heuristic analysis of the processes of construction of scientific results.
The Althusserian idea has certain advantages as situates ideology not just in ideas but as a structuring principle in practices and institutions, eg in the definition of roles and functions. It also adds the notion of a sort of systemic cognitive bias, or even blindness, concerning the factors that structure the very type of subjectivity pervading a society. All this is far more radical than the “Other of science” strand, which makes alchemy for example a case of ideology and chemistry a science. The problem is that by rejecting the crude binary demarcations of the last strand, theorists threw the baby out with the bathwater and lost sight of, or expressed more cryptically, the positive aspects of the two other strands of ideology as structuration embodied practice and of ideology as misrecognition or cognitive blindness.
Certain figures have emerged that are 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 space opened up by the Althusser-Lacan conjuncture, they try to 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 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 having a place for the possibility of novelty and creation versus closing off in advance some possible developments, often without even noticing.
The question of mathematics, which is often raised, 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 can be seen in that intuitionist maths is not the same as formalist maths, even if it is for the moment a minority position. Lacan would consign most ideas about methodological rigour to the binaries (or dualisms) of the imaginary, 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, ie scientific results, that one can have the impression that methods are somehow detachable from the processes they are embedded in, in some absolute way. I think 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 Harman’s retreat to a separate space of objects is in the material mode.