In a passage in the Postmodern Condition on the way science legitimates itself, in the sense of obtaining the addressee’s assent, I came across this:
“The following question is more pertinent to legitimation : By what
criteria does the logician define the properties required of an axiomatic?
Is there a model for scientific languages? If so , is there just one ?
Is it verifiable ? The properties generally required of the syntax of
a formal system are consistency (for example , a system inconsistent
with respect to negation would admit both a proposition and its
opposite), syntactic completeness (the system would lose its consistency
if an axiom were added to it), decidability (there must be an
effective procedure for deciding whether a given proposition belongs
to the system or not), and the independence of the axioms in relation
to one another. Now Godel has effectively established the
existence in the arithmetic system of a proposition that is neither
demonstrable nor refutable within that system ; this entails that the
arithmetic system fails to satisfy the condition of completeness.
Since it is possible to generalize this situation , it must be accepted
that all formal systems have internal limitations. This applies to
logic: the metalanguage it uses to describe an artificial (axiomatic)
language is “natural ” or “everyday ” language ; that language is universal, since all other languages can be translated into it, but it is not
consistent with respect to negation – it allows the formation of paradoxes”
It seems I’ve been beaten to the punchline by Lyotard in assessing how Godel’s incompleteness theorem could apply to philosophy. I generally agree with Lyotard, but think I can offer something here. I think we have to clarify what Lyotard and Godel mean in order to avoid mistakes in interpretation, namely to correct the interpretation of Lyotard that all interpretations are equal and its all just “language games and metanarratives”. The term postmodernism in the title doesn’t help at all in this regard…but lets start with Godel.
If one were to apply the analogy (and Lyotard is here playing a bit of a language game himself) directly from Godel’s incompleteness theorem, one has to recognize that any formal system of logic, or at least the formal system of the rules of arithmetic logic, are incomplete by the fact in every formal arithmetic system that attempts to find the “basic axioms”, there can be found an axiom which agrees with the other axioms, i.e it isn’t refutable, but it can’t be derived from the foundational axioms. Therefore, there are missing rules. In fact, there might be an infinite number of basic arithmetic rules. Examples of these axioms are propositions like a=a, a+b=b+a, etc.
This should NOT be confused with the idea that all metalanguages or systems are fundamentally INCONSISTENT. Merely incomplete- as Lyotard says, this means that a set of axioms can prove or entail a certain number of other conclusions, but each theory has a “scope” or set of limits. This is so basic a proposition as to merit being common sense. For instance, general relativity is an accepted theory, it is viewed as legitimate science, certain calculations can be done on the basis of general relativity, but it has certain limitations at certain energy levels, special physical situations, etc. In fact, science often progresses by questioning the limitations of an existing theory and then creating a new theory that explains those previously unexplained phenomena.
So my grade- does Lyotard pass? Exceptionally well. He does a good job of translating Godel’s theory into basic language. But I’d give him a B, because we can derive more from Godel- Godel’s incompleteness theorem tells us even more about systems of knowledge. Moreover, Lyotard switches registers with regards to going into the realm of logic itself- do you notice? “All other languages can be translated into it, but it is not consistent with respect to negation”. To me this doesn’t necessarily follow from Godel. Even going with him that Godel’s theorem can be abstracted to all logical systems, incompleteness is NOT inconsistency!!! This may be some of the source of giving Lyotard a bad rap as a relativist.
It is true that science has to use the language of common sense, of discourse itself, to legitimate itself. Using the analogy of Godel can also be profitable. But a precise reading of what Godel’s incompleteness theorem actually is requires scientific literacy, requires (to make things even more complicated) not only an in depth knowledge of a concept, but also the intellectual tools to understand it. How’s that for an epistemological whopper!
Lyotard gets things 3/4 right, but opens himself up to the critique of pure relativism, instead of stating outright what he really is- a social constructivist. And one has to be an idiot to not be a social constructivist, because of course science is made by man. The question is whether the Knowledge (capital K) man has is fallible. And….it depends on the circumstance! And of course its incomplete!
Of course scientific research in this regard plays the political game, and it forms the kind of pursuits and questions they are after. But the “paradox” is that the science produced in the meantime as a result is not untrue- atomic physics is all too real. It would be better if we take what we need from Lyotard et. al. as social theorists, productive concepts like postmodern informational society, and use them to enter into a dialogue on what exactly is going on now. Zizek uses the critique that postmodern digital society concept actually can obscure the dynamics of capitalism- yes but maybe only the appropriation of this idea, not within the confines of Lyotard, where he is definitely employing Marxian analysis of social phenomena. Take this passage from the same chapter on the “Pragmatics of Science”:
“—-what happened at the end of the eighteenth century , with the first
industrial revolution , is that the reciprocal of this equation was discovered: no technology without wealth , but no wealth without technology. A technical apparatus requires an investment; but since it optimizes the efficiency of the task to which it is applied, it also optimizes the surplus-value derived from this improved performance.
All th at is needed is for the surplus-value to be realized , in other
words, for the product of the task performed to be sold . And the system
can be sealed in the following way : a portion of the sale is
recycled into a research fund dedicated to further performance
improvement. It is at this precise moment that science becomes a
force of production , in other words, a moment in the circulation of
It was more the desire for wealth than the desire for knowledge
that initially forced upon technology the imperative of performance
improvement and product realization. The “organic” connection
between technology and profit preceded its union with science.
Techn ology became important to contemporary knowledge only
through the mediation of a generalized spirit of performativity. Even
today, progress in knowledge is not totally subordinated to technological investment.”
The obvious employment of terms like surplus-value means that Lyotard is faithful to the Marxist cause of identifying science as a force of production, as Marx elaborates on in the German Ideology. Lyotard takes this history of science and abstracts it to the development of technology and capitalism itself. He demonstrates that science was not always synonymous with technological advancement- today those two are intimately connected, due to the development of research institutions, which he goes into. Lyotard’s critique here seems to be that while there are some “pure research institutions”, the goal is not knowledge as such, but technological advancement for profit.
Of course, one could apply this critique to the field of medical research in pharmaceuticals, for example, with great effect, and that would have to be done in detail and in the concrete. Some anthropologists have done things to that effect, looking at the Monsanto Corporation and how research on safety is rushed in order to put out a product in as quick a time as possible, specifically for fertilizers, pesticides, etc. I.e things that are necessary for the survival of the human species at the moment. But what does this level of abstraction miss?
It misses the fact that in the politics of Science in the abstract, there are many fields, many different social interactions. Yes there is one principle axiomatic that has corrupted this field, that has been correctly identified by Lyotard, and that is the axiom of Capital, of gaining power and notoriety, but often what comes out of this is not only the commodification of knowledge, as Lyotard has so presciently realized is happening, but also the creation of new real powerful technologies. This is why I believe that instead of postmodern informational society, media society, even society of the spectacle, or bureaucratic society of controlled consumption (as Jameson has identified as parallels for Lyotard’s concepts), what is the society of today? It is the digital society of control. This is the immanent, concrete way we should talk about the world, because you know, in your heart, that these mechanisms of control operate. They will find you if you don’t pay your credit card bill- believe me, they will find you. The knowledge of how that credit card operates is well known, well defined, almost perfect. There is a margin of error, things that can be exploited, but in objective, solid (or should I say fluid) reality. So is there such a thing as “objective reality”? Again, I want to make this perfectly clear- it depends on your definition!! If your definition of objective reality is something separate from human consciousness, something inherently stable, then no. If it means that reality simply exists, then yes. Of course there is reality! And as we are beginning to show in quantum physics, that reality is no different than virtual reality. It’s one big show, and the advertisers know just how to manipulate it.
Have a happy Christmas season, and remember, Never Work, fuck Trump, and don’t buy beyond necessity.
P.S: Do I even need to mention how horrible Trump’s tax plan is? The bank robbery has begun