Julia Kristeva wrote about many different subjects. The texts we quote are quite old, and we emphasize that she gave up this approach a long time ago. However, they illustrate perfectly the attitude which consists in trying or claiming to do science while merely introducing scientific words and formulas into one's discourse.
In the book that we quote, Semeiotike, Kristeva tries to construct a ``logic" of poetic language. She appeals to various notions of formal logic and of set theory. Here is an example:
Having admitted that poetic language is a formal system whose theorization belongs to set theory , we may observe at the same time that the functioning of poetic meaning obeys to the principles designated by the axiom of choice. The latter 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.
[Un(A) - ``A is single-valued''; Em(x) - ``the class x is empty''.]
Said otherwise, one may choose simultaneously an element in each of the non-empty sets which we consider. So stated, the axiom is applicable in our universe
of the pl
. It specifies how every sequence contains the message of the book. ... [Kristeva (1969).]
To put it mildly, it is bizarre to introduce the axiom of choice, which is used in mathematics to establish the existence of infinite sets, into a theory of poetic language. And of course, the relevance of this axiom is merely asserted, not argued. Reading further, one starts to wonder whether Kristeva knows the mathematics that she invokes:
The notion of constructibility implied by the axiom of choice, associated to what we have just postulated for the poetic language, explains the impossibility to establish a contradiction in the space of poetic language. This observation is close to Gödel's observation concerning the impossibility of proving the contradiction of a system by means formalized within the system. [Kristeva (1969)]
First of all, the axiom of choice allows to prove the existence of sets that one cannot ``construct". But, what is more striking is that Kristeva does not seem to understand ``Gödel's observation": in fact Gödel showed exactly the contrary, namely the impossibility of proving the absence of contradiction of a system by means formalized within the system. It is trivial to construct a contradictory system of axioms and to prove that it is contradictory.
Semeiotike was Kristeva's first book, and made her famous. It is interesting to see how it was acclaimed:
Julia Kristeva changes the order of things: she always destroys the latest preconception, the one we thought we could be conforted by, the one of which we could be proud: what she displaces is the already said, that is to say, the insistence of the signified; what she subverts is the authority of monologic science and of filiation. [Roland Barthes (1970).]
In another work, Kristeva ``applies" technical concepts of mathematical analysis:
In the syntactic operations following the mirror stage, the subject is already sure of his uniqueness: his flight towards the ``point" in the signifying is stopped. One thinks for example of a set
on the usual space
where for each continuous function F in
The definition that she gives of the space 
of continuous function vanishing at infinity is not correct, but the main problem is: what
does this
have to do with psychology? How
could a subject be ``placed in "?
Despite such obvious abuses and name-dropping, an American commentator writes:
What is most striking about Kristeva's work ... is the competence with which it is presented, the intense singlemindedness with which it is pursued, and finally, its intricate rigour. No resources are spared: existing theories of logic are invoked and, at one point, quantum mechanics ... [John Lechte (1990).]