Intellectual Impostures
Page 6
The pl cannot, therefore, be a sub-code. It is the infinite ordered code, a complementary system of codes from which one may isolate (by operatory abstraction and by way of proof of a theorem) a usual language, a scientific metalanguage and all the artificial systems of signs – which are all only subsets of this infinite, externalizing the rules of its order over a restricted space (their power is lesser relative to that of the pl that is surjected onto them).
(Kristeva 1969, pp. 178–9)
These paragraphs are meaningless, though Kristeva has very ably strung together a series of mathematical terms. But it gets even better:
Having assumed that poetic language is a formal system whose theorization can be based on set theory, we may observe, at the same time, that the functioning of poetic meaning obeys the principles designated by the axiom of choice. This axiom specifies that there exists a single-valued correspondence, represented by a class, which associates to each non-empty set of the theory (of the system) one of its elements:
(∃A) {Un(A)·(x)[∼Em(x)·⊃·(∃y)[y∈x·〈yx〉∈A]]}
[Un(A) – ‘A is single-valued’; Em(x) – ‘the class x is empty’.]
Said otherwise, one can choose simultaneously an element in each of the non-empty sets that we consider. So stated, the axiom is applicable in our universe E of the pl. It makes precise how every sequence contains the message of the book.
(Kristeva 1969, p. 189, italics in the original)
These paragraphs (as well as the following ones) illustrate brilliantly the acerbic comments of the sociologist Stanislav Andreski quoted in our Introduction (p. 10). Kristeva never explains the relevance of the axiom of choice for linguistics (in our opinion it has none). The axiom of choice says that if we have a collection of sets, each of which contains at least one element, then there exists a set containing exactly one element ‘chosen’ from each of the original sets. This axiom permits one to assert the existence of certain sets without constructing them explicitly (one does not say how the ‘choice’ is made). The introduction of this axiom in mathematical set theory is motivated by the study of infinite sets, or of infinite collections of sets. Where does one find such sets in poetry? To say that the axiom of choice ‘makes precise how every sequence contains the message of the book’ is ludicrous – we’re unsure whether this assertion does more violence to mathematics or to literature.
Nevertheless, Kristeva continues:
The compatibility of the axiom of choice and the generalized continuum hypothesis41 with the axioms of set theory places us at the level of reasoning about the theory, thus in a metatheory (and such is the status of semiotic reasoning) whose metatheorems have been perfected [mis au point] by Gödel.
(Kristeva 1969, p. 189, italics in the original)
Here again, Kristeva is trying to impress the reader with technical jargon. She has indeed cited some very important (meta)theorems of mathematical logic, but without bothering to explain to the reader the content of these theorems, much less their relevance for linguistics. (Let us note that the set of all texts ever written, in the entirety of human history, is a finite set. Moreover, any natural language – for example, English or Chinese – has a finite alphabet; a sentence, or even a book, is a finite sequence of letters. Therefore, even the set of all finite sequences of letters in all conceivable books, without any restriction on their length, is a denumerable infinite set. It is hard to see how the continuum hypothesis, which concerns nondenumerable infinite sets, could have any application in linguistics.)
All this does not prevent Kristeva from pushing onward:
One finds there precisely the existence theorems that we do not intend to develop here, but that interest us to the extent that they provide concepts allowing us to pose in a new way – a way that would be impossible without them – the object that interests us: poetic language. The generalized existence theorem postulates, as one knows, that:
‘If φ(x1,...,xn) is a primitive propositional function containing no free variables other than x1,...,xn, without necessarily containing all of them, there exists a class A such that, for all sets x1,...,xn, 〈x1,...,xn〉 ∈ A. ≡ . φ(x1,...,xn).’42
In the poetic language, this theorem denotes the different sequences as equivalent to a function encompassing all of them. Two consequences follow from this: 1) it stipulates the non-causal chaining [enchaînement] of poetic language and the expansion of the letter in the book; 2) it stresses the range [portée] of this literature which puts forth its message in the smallest sequences: the meaning (φ) is contained in the mode of junction of words, of sentences ...
Lautréamont was one of the first consciously to practice this theorem.43
The notion of constructibility implied by the axiom of choice associated to what we have just set forth for poetic language, explains the impossibility of establishing a contradiction in the space of poetic language. This observation is close to Gödel’s observation concerning the impossibility of proving the inconsistency [contradiction] of a system by means formalized within the system.
(Kristeva 1969, pp. 189–90, italics in the original)
In this excerpt, Kristeva shows that she does not understand the mathematical concepts she invokes. First of all, the axiom of choice does not imply any ‘notion of constructibility’; quite the contrary, it allows one to assert the existence of some sets without having a rule to ‘construct’ them (see above). Secondly, Gödel proved exactly the opposite of what Kristeva claims, namely the impossibility of establishing, by means formalizable within the system, the system’s consistency (i.e. non-contradiction).44
Kristeva has also tried to apply set theory to political philosophy. The following excerpt is taken from her book Revolution in Poetic Language (1974):
A discovery of Marx, which has not heretofore been sufficiently emphasized, can be sketched here. If each individual or each social organism represents a set, the set of all sets that the State should be does not exist. The State as set of all sets is a fiction, it cannot exist, just as there does not exist a set of all sets in set theory.45 [Footnote: On this topic, cf. Bourbaki46, but also, concerning the relations between set theory and the functioning of the unconscious, D. Sibony, ‘Infinity and castration’, in Scilicet, No. 4, 1973, pp. 75–133.] The State is, at most, a collection of all the finite sets. But for this collection to exist, and for finite sets to exist too, there must be some infinity: the two propositions are equivalent. The desire to form the set of all finite sets puts the infinite on stage, and reciprocally. Marx, who noticed the illusion of the State to be the set of all sets, saw in the social unit as presented by the bourgeois Republic a collection that nevertheless constitutes, for itself, a set (just as the collection of the finite ordinals is a set if one poses it as such) from which something is lacking: indeed, its existence or, if one wants, its power is dependent on the existence of the infinite that no other set can contain.
(Kristeva 1974, pp. 379–80, italics in the original)
But Kristeva’s mathematical erudition is not limited to set theory. In her article ‘On the subject in linguistics’, she applies mathematical analysis and topology to psychoanalysis:
[I]n the syntactic operations following the mirror stage, the subject is already sure of his uniqueness: his flight towards the ‘point ∞’ in the signifying [signifiance] is stopped. One thinks for example of a set C0 on a usual space R3 where for every continuous function F on R3 and each integer n > 0, the set of points X where F(X) exceeds n is bounded, the functions of C0 tending to 0 when the variable X recedes towards the ‘other scene’. In this topos, the subject placed in C0 does not reach this ‘centre exterior to language’ about which Lacan speaks and where he loses himself as subject, a situation that would translate the relational group that topology calls a ring.
(Kristeva 1977, p. 313, italics in the original)
This is one of the best examples of Kristeva’s attempts to impress the reader with fancy words that she obviously does not understand. Andreski ‘
advised’ the budding social scientist to copy the less complicated parts of a mathematics textbook; but the definition given here of the set of functions C0(R3) is not even correctly copied, and the errors stand out to anyone who understands the subject.47 But the real problem is that the purported application to psychoanalysis is nonsense. How could a ‘subject’ be ‘placed in C0’?
Among the other examples of mathematical terminology that Kristeva uses without explanation or justification, let us note in Kristeva (1969): stochastic analysis (p. 177), Hilbert’s finitism (p. 180), topological space and abelian ring (p. 192), union (p. 197), idempotence, commutativity, distributivity, ... (pp. 258–64), Dedekind structure with orthocomplements (pp. 265–6), infinite functional Hilbert spaces (p. 267), algebraic geometry (p. 296), differential calculus (pp. 297–8). And in Kristeva (1977): articulation set in graph theory (p. 291), predicate logic (which she bizarrely calls ‘modern proportional logic’48) (p. 327).
To summarize, our evaluation of Kristeva’s scientific abuses is similar to the one we gave for Lacan. In general, Kristeva has at least a vague idea of the mathematics she invokes, even if she manifestly does not always understand the meaning of the words she uses. But the main problem raised by these texts is that she makes no effort to justify the relevance of these mathematical concepts to the fields she is purporting to study – linguistics, literary criticism, political philosophy, psychoanalysis – and this, in our opinion, is for the very good reason that there is none. Her sentences are more meaningful than those of Lacan, but she surpasses even him for the superficiality of her erudition.
4
INTERMEZZO: EPISTEMIC RELATIVISM IN THE PHILOSOPHY OF SCIENCE
I did not write this work merely with the aim of setting the exegetical record straight. My larger target is those contemporaries who – in repeated acts of wish-fulfillment – have appropriated conclusions from the philosophy of science and put them to work in aid of a variety of social cum political causes for which those conclusions are ill adapted. Feminists, religious apologists (including ‘creation scientists’), counterculturalists, neoconservatives, and a host of other curious fellow-travelers have claimed to find crucial grist for their mills in, for instance, the avowed incommensurability and underdetermination of scientific theories. The displacement of the idea that facts and evidence matter by the idea that everything boils down to subjective interests and perspectives is – second only to American political campaigns – the most prominent and pernicious manifestation of anti-intellectualism in our time.
(Larry Laudan, Science and Relativism, 1990, p. x)
Since much postmodern discourse flirts with one form or another of cognitive relativism or invokes arguments that can support it, it seems useful at this point to include an epistemological discussion. We are aware that we will be dealing with difficult problems concerning the nature of knowledge and objectivity, which have worried philosophers for centuries. It is not necessary to share our philosophical positions in order to agree with the rest of what we say. In this chapter we shall criticize ideas that are in our view erroneous, but which are sometimes (not always) so for subtle reasons, contrary to the texts we criticize in the rest of this book. Our philosophical argumentation will, in any case, be rather minimalist; we shall not enter into the more delicate philosophical debates between, for example, moderate forms of realism and instrumentalism.
We are concerned here with a potpourri of ideas, often poorly formulated, that go under the generic name of ‘relativism’ and are nowadays rather influential in some sectors of the academic humanities and social sciences. This relativist Zeitgeist originates partly from contemporary works in the philosophy of science, such as Thomas Kuhn’s The Structure of Scientific Revolutions and Paul Feyerabend’s Against Method, and partly from extrapolations of these philosophers’ work by their successors.49 Of course, we do not purport to examine the entire work of the authors discussed in this chapter; that would be an unmanageable task. Rather, we shall limit ourselves to an analysis of certain texts that illustrate rather widespread ideas. We shall show that these texts are often ambiguous and can be read in at least two distinct ways: a ‘moderate’ reading, which leads to claims that are either worth discussing or else true but trivial; and a ‘radical’ reading, which leads to claims that are surprising but false. Unfortunately, the radical interpretation is often taken not only as the ‘correct’ interpretation of the original text but also as a well-established fact (‘X has shown that ...’) – a conclusion that we shall sharply criticize. It might, of course, be argued that no one holds this radical interpretation; and all the better if that is true. But the numerous discussions we have had during which the theory-ladenness of observation, the underdetermination of theory by evidence or the alleged incommensurability of paradigms have been put forward in order to support relativist positions leave us rather sceptical. And to show that we are not criticizing a figment of our imagination, we shall give, at the end of this chapter, a few practical examples of the relativism that is widespread in the United States, in Europe, and in parts of the Third World.
Roughly speaking, we shall use the term ‘relativism’ to designate any philosophy that claims that the truth or falsity of a statement is relative to an individual or to a social group. One may distinguish different forms of relativism according to the nature of the statement in question: cognitive or epistemic relativism when one is dealing with an assertion of fact (that is, about what exists or is claimed to exist); moral or ethical relativism when one is dealing with a value judgment (about what is good or bad, desirable or pernicious); and aesthetic relativism when one is dealing with an artistic judgment (about what is beautiful or ugly, pleasant or unpleasant). Here we shall be concerned only with epistemic relativism and not with moral or aesthetic relativism, which raise very different issues.
We are well aware that we will be criticized for our lack of formal philosophical training. In the Introduction we explained why this sort of objection leaves us cold, but it seems particularly irrelevant here. After all, there is no doubt that the relativist attitude is at odds with scientists’ idea of their own practice. While scientists try, as best they can, to obtain an objective view of (certain aspects of) the world,50 relativist thinkers tell them that they are wasting their time and that such an enterprise is, in principle, an illusion. We are thus dealing with a fundamental conflict. And as physicists who have long pondered the foundations of our discipline and of scientific knowledge in general, we think it important to try to give a reasoned answer to the relativist objections, even though neither of us holds a diploma in philosophy.
We shall start by sketching our attitude toward scientific knowledge,51 and shall then review briefly some aspects of twentieth-century epistemology (Popper, Quine, Kuhn, Feyerabend); our aim will mostly be to disentangle some of the confusions concerning notions such as ‘underdetermination’ and ‘incommensurability’. Finally, we shall examine critically some recent tendencies in the sociology of science (Barnes, Bloor, Latour) and shall give some practical examples of the effects of contemporary relativism.
Solipsism and radical scepticism
When my brain excites in my soul the sensation of a tree, or of a house, I pronounce, without hesitation, that a tree, or a house, really exists out of me, of which I know the place, the size, and other properties. Accordingly, we find neither man nor beast who calls this truth in question. If a peasant should take it into his head to conceive such a doubt, and should say, for example, he does not believe that his bailiff exists, though he stands in his presence, he would be taken for a madman, and with good reason; but when a philosopher advances such sentiments, he expects we should admire his knowledge and sagacity, which infinitely surpass the apprehensions of the vulgar.
(Leonhard Euler, 1997 [1761], pp. 428–9)
Let us start at the beginning. How can one possibly hope to attain an objective (albeit approximate and incomplete) knowledge of the world? We never have direct access to the wo
rld; we have direct access only to our sensations. How do we know that there even exists anything outside of those sensations?
The answer, of course, is that we have no proof; it is simply a perfectly reasonable hypothesis. The most natural way to explain the persistence of our sensations (in particular, the unpleasant ones) is to suppose that they are caused by agents outside our consciousness. We can almost always change at will the sensations that are pure products of our imagination, but we cannot stop a war, stave off a lion or start a broken-down car by pure thought alone. Nevertheless – and it is important to emphasize this – this argument does not refute solipsism. If anyone insists that he is a ‘harpsichord playing solo’ (Diderot), there is no way to convince him of his error. However, we have never met a sincere solipsist and we doubt that any exist.52 This illustrates an important principle that we shall use several times in this chapter: the mere fact that an idea is irrefutable does not imply that there is any reason to believe it is true.
Another position that one sometimes encounters, in place of solipsism, is radical scepticism: ‘Of course there exists an external world, but it is impossible for me to obtain any reliable knowledge of that world.’ In essence the argument is the same as that of the solipsist: I have immediate access only to my sensations; how can I know whether they accurately reflect reality? To be certain that they do, I would need to invoke an a priori argument, such as the proof of the existence of a benevolent deity in Descartes’ philosophy; and such arguments have fallen into disfavour in modern philosophy, for all sorts of good reasons that we need not rehearse here.