The Death of Philosophy: Reference and Self-reference in Contemporary Thought

The most fertile of the currently espoused models of self-reference is, as I have already indicated, the one that Paul Ricoeur criticizes as a “doctrine of sui-reference,” which tends to reduce reference to self to a reference ad extra. This understanding of self-reference consists in reducing any self-referential statement, like “I speak,” to a referential statement, like “he speaks.” The act of utterance is interpreted, in fact, as a standard reference to an exterior being. For example, when I utter the sentence “He is speaking,” I refer to a being in the world who can be designated by his proper name (and his initials, like “L. W.”) or by a definite description (“the philosopher of the ‘Blue Book’”); moreover, my proposition can be verified or falsified by reference to the facts: either the individual “L. W.” is speaking right now, or not.

And yet the proposition “I am speaking” can be analyzed as a strictly referential expression because it can be replaced salve veritate by a proper name or a definite description. To secure a definitive trivialization of the self-referential phrase “I,” we can say that a statement like “I speak” has the same traits as referential statements of the sort “L. W. speaks” because, contradicting the proposition that “no one is speaking,” it implies the proposition that “someone is speaking” and behaves therefore as a value of the propositional function “x speaks.” This is the first argumentative strategy for making self-reference a worldly fact, one species among others of reference ad extra. There have been many critics of this reduction, such as Ricoeur, already mentioned, but also Wittgenstein, who himself challenged the referential dimension of the “I,”¹ or Colin McGinn, who tried to show the “infallible” or “incorrigible” character of the self-attribution of psychological states such as pain,² or even Sydney Shoemaker, who showed in “Self-reference and Self-Awareness”³ how self-reference is the condition of possibility for any other form of reference.

And yet however interesting these different conceptions may be and whatever importance this debate may have today, we must note that from my point of view, that is, from the viewpoint of the problem of the status of philosophical discourse, this problem is not relevant.⁴ Indeed, my model of self-reference as a principle of reflexivity does not try to answer the question, “What is being done when one says ‘I’ in sentences like ‘I have a toothache’?” but to ask, “What is said when one utters propositions like ‘The truth does not exist’ or ‘A proposition is true only if an intuition or an empirical fact verifies it,’ etc.?” The law of reflexivity is not identical with any of the versions of self-reference that I’ve cited—from Récanati’s “sui-reference” to the reflection sought by Ricoeur. The law of reflexivity can be explained as follows: given a certain number of propositions like those I’ve mentioned—here, relative to truth—what is presupposed in order to be able to utter these propositions; what is implied, or even what set of laws must they obey so that they do not destroy themselves? It is important to insist on this point, for we have here a very different problem of self-referentiality than before. Indeed, it is not a matter of knowing whether the “I,” a simple “shifter,”⁵ refers to an empirical fact of the world (“sui-reference”), nor of understanding the “I” as subjective in contrast to the body’s objectivity (Wittgenstein), nor even of making it an anchoring point—whether this anchoring point is defined as a shattered cogito (Ricoeur) or the “limit-point of the world” (Granger)—nor even of deciding in favor of a forever “infallible” “I” (Shoemaker) or conversely for an “I” that is a pure grammatical illusion (Nietzsche and the deconstructivists). Knowing what is said when one says “I” is not my problem because the problem of reflexivity here is the problem of a proposition’s reference to itself. My task is thus to circumscribe a type of propositions and to determine the grammar that governs them. Even admitting, with the philosophy of language, that philosophy is only one language game among others, the question nevertheless arises of what are the rules that structure it. And yet in this language game of philosophy, we find certain propositions that must encompass themselves under penalty of self-destruction. The problem of reflexivity is clearly circumscribed here relative to the other contemporary problems. Its domain of relevance and of analysis is precisely delimited as the class of propositions that must refer to themselves to avoid contradiction. Having now characterized this difference from other theories of self-reference, all of which are structured around the meaning of the pronoun “I,” I must next clarify the class of propositions that must be applied to themselves.

To have to apply to itself without self-contradiction is a requirement first for propositions relative to the concept of truth. I have shown this throughout my discussion, on the basis of three examples: skepticism, which claims that truth does not exist; Kantianism, which defines it as the connection between a concept and an intuition; and logical positivism, which understands a proposition’s truth in terms of its analyticity or its conformity with experience. Given that, it does not seem (contrary to Alfred Tarski’s view⁶) that the mention of the predicate of truth in a proposition would be the only case of a proposition’s necessary reflexivity. Thus, to cite only two further examples, when a historian, sociologist, or psychoanalyst asserts that “every man’s thinking is the reflection or the product of his social environment or of his contingent history,” he is simultaneously and in the same respect saying that the proposition that he has uttered is the product of his own specific and contingent social environment. In doing so, he cannot avoid this dilemma: On the one hand, because he admits that his proposition is the expression of a contingent moment, he can no longer claim that it is universal. That proposition thus becomes the expression of a contingent individual (whose name, for example, is Pierre Bourdieu), himself the product of a historical moment (the second half of the twentieth century) and a particular social milieu (the educated middle class), and no longer a proposition valid beyond this precise place and this particular time. Or, on the other hand, he acknowledges that his proposition has exceptions, in particular at least that very proposition, but, once again, he cannot claim that this proposition is universal because, at least for that individual’s proposition, “it is not the case,” as the logician’s canonical phrase would have it. However that may be, in both cases his proposition is false because it fails to apply to itself. We have here an example of a proposition that, although it does not immediately or indirectly contain the terms “truth” or “validity,” is self-refuting if it does not apply to itself, that is, in this case, if it does not take account of the entirety of the statement, in which the authority of the utterance is implicated, which authority must not be a counterexample of what is said at the level of contents.

To give another example, if, in the manner of an empiricist and anti-Cartesian psychologist, we define the “subject” (in contrast to animals or things) as a simple psychological singularity, inscribed here and now, we will see that to thus determine the subject is, at the same time and in the same respect, to claim the universal validity of what is said. If the psychologist says, for example against Descartes, that the subject is neither a substance nor a universal authority but is only an empirical individual hic et nunc, he claims that his proposition is valid and that Cartesianism is not. It follows that this proposition, which applies to the definition of a human subject in contrast to animals and things, must apply to the one who says it, or else it is not universal (see the preceding dilemma). And yet—and this is the key point—the psychologist, despite his definition of the subject, does not claim that the empirical individual x that is himself says that the subject is nothing other than an empirical individual but claims a much larger truth and thus in his very assertion presupposes another definition of the speaking authority, in this case the psychologist or philosopher or anthropologist who says, “The subject is defined as x and not as y.” Here again we encounter a proposition that must apply to itself in order to not be false but that for all that does not exclusively concern the concept of truth.

The last two propositions that I’ve discussed contain a hidden performative contradiction because of the noncongruence between the sentence’s contents (“Every thought is the expression of a contingent social environment” or else “Every subject is an empirical individual, singular, a hic et nunc viewpoint on the world”) and the authority of the utterance (the philosopher x who claims in saying this that he is not an empirical individual, a simple contingent point or product of his social environment, but an authority that overcomes it). Two subjects are to be taken into consideration in the proposition: the subject itself of the predicative proposition (“Every subject or every human or every speaking being is . . .”) and the authority of the utterance (the philosopher who says that “the subject is . . .”).⁷ And yet the authority of the utterance invalidates the predicative proposition’s definition of the subject (“all are … except me, who says so”), or again the subject of the proposition is in contradiction with the authority of the utterance. This is why the contents of the proposition, if they are applied to the authority that pronounces them, self-destruct and thereby show their falsity.

In the proposition “All swans are white,” the authority of the utterance (philosopher or naturalist in the ancient sense) claims the truth of what he says. This truth can be demonstrated or invalidated by different means (which I shall not enumerate), but the proposition does not have to apply to the speaker himself, who does not claim to be a swan. Neither does it include truth as a predicate because it says “All swans are white” and not “All true statements are x.” If we do find a claim to universality implied in this proposition, the required universality concerns exterior things or beings—to put it in terms of personal pronouns, the universality is relative to “them” (I could replace the term “swans” with “they”). These propositions pose no problem here,⁸ for even though they make a universality claim (which the “all” indicates), they do not require a test of self-application nor do they encompass the authority of the utterance.

But if we turn to propositions of the type “All humans, subjects, or speaking beings are x,” we seem to have both the universality of the first case and the necessary self-referentiality of the second. Indeed, the proposition applies both to the “they” (“all humans or all speaking subjects” contained in the proposition) and at the same time must include the one who utters it. The relevant personal pronoun here is thus not the “I” nor the “they.” Not the “I,” for the proposition claims that it concerns all humans;⁹ nor the “they,” because it must include the one who utters it. Clearly, neither is it governed by a singular “you,” nor by a plural “you,” for once again the “I” must be included. Thus the authority of the utterance is indeed a “we” that has the peculiarity of combining the two required dimensions: the universality claim and self-referentiality. Neither the empirical “I,” nor the “I” of the Cartesian cogito, and even less the “he” of “God or nature” can account for the dual dimension revealed by these propositions.

Moreover, this discovery allows me to cut off any realist sort of questioning about the entity to which this or that personal pronoun would refer: “my own body” for the “I,” an additional “I” for the “we,” a set of things for the “they,” etc. What is important here is not to know what this “we” refers to (a group, a crowd, a nation, etc.) but to establish that some propositions—of key importance because they concern what humanity, thought, speech, etc., are—are governed by a pronoun, the “we,” which is regulated by definite usages and a precise grammar. This insight authorizes a remark: many contemporary discussions of the personal pronoun “I,” in common with classical metaphysics, search for a basis, a being, an external reference for the pronoun “I.” This realist quest shares the same hope: to answer the question, “Who is it that speaks?” rather than the different, less essentializing question, “How do these propositional categories function, and how must they function to be consistent?” Some realist (or, on the contrary, nominalist) currents of contemporary analytic philosophy have, with this realist antiphony, more in common than they realize with the metaphysics that they reject.

Furthermore, that my problem is not the realist problem also allows me to dismiss the dispute about the precedence of one pronoun over another. To know whether the “I,” the “you,” the “he,” or the “we” is first has absolutely no importance in my framework. It is not a matter of knowing how the “I” becomes a “we” (the problem of overcoming the solipsism of Cartesian philosophy or the problem of self-interest in political philosophy); nor of determining how the “we” becomes an “I” (the psychological problem, or the problem of the phenomenology of Dasein, where it is asked for example how the child individuates himself with regard to the entity that he initially forms with the maternal body). The question is, How can we more precisely describe this type of proposition that must be able to apply to itself without self-destructing?

Given these stakes, I can only regret that the “we” has been so neglected in the study of personal pronouns. This oversight in linguistic as well as philosophical studies is indisputably harmful, for the “we” is the pronoun that governs a good number of philosophical, and even anthropological, statements that apply to humanity in general, or to “the subject” or “the mind” or “the speaking authority,” or, if one likes a more naturalist expression, the “brain.” The neurologist, for example, cannot define the brain’s activity in general and exclude from this definition the scientist’s own cerebral activity. I will illustrate this type of paradox—very common today in the cognitive and the social sciences—at greater length in what follows. It will suffice for now to summarize what the present analysis has established: self-referentiality as the law of reflexivity applies to propositions and need not address any realist questions concerning the reference of indexicals (my own body, the shattered cogito, the metaphysical subject, the empirical individual, etc.). For the moment, I have discovered two kinds of propositions that must apply to themselves: propositions concerning truth and (to put it most succinctly) propositions concerning humanity (in contrast to things and animals). We have also seen that, within this second group, the speaking authority is the “we,” defined as “all the others” and “myself.” That said, if we have been led in the course of this analysis to distinguish two groups of propositions, the latter nonetheless belong to the same genre, of propositions that must apply to themselves or include themselves.

A confrontation between this model of reflexivity and Bertrand Russell’s prohibition requires that I return in the first case to the reasons that led Russell to prohibit self-referentiality. To briefly retrace this history, recall that Russell, spurred by G. E. Moore to abandon his initial Hegelianism,¹⁰ undertook to demonstrate that all mathematical operations can be reduced to noncontradictory expressions and that logic thus grounds mathematics.¹¹ Concerned to reduce set theory to a pure logical calculus, Russell boiled the mathematical concept of sets down to the logical concept of classes. The set of humans corresponds to the class determined by the function “is a human.” In doing this, Russell came up against a still famous paradox.¹² This paradox stems from the following: Certain sets can be members of themselves, thus the set or the class of inanimate objects is itself an inanimate object and the set of sets is a set. Other sets are not members of themselves: the set of all humans is not a human, and the set of pipes can say, without batting an eyelid, that “this is not a pipe.” Taking this last type of classes into consideration, Russell wondered whether, in the final analysis, “this class contains itself or not.”¹³ This question cannot be answered with a yes or a no, as true or false. Indeed, if w (the set of all sets that do not contain themselves) contains itself, then it does not (because w contains only sets that do not contain themselves); but if it does not contain itself, then it does (because it is the set of all sets that do not contain themselves). Thus true and false, yes and no, reciprocally imply each other: if the set contains itself, then it does not; if it does not contain itself, then it does. As Russell writes, “From each answer its opposite follows,”¹⁴ and there is a contradiction. This contradiction cannot be reduced, nor transformed, nor overcome—unlike many paradoxes, major or minor, that adorn the history of logic or mathematics. Nor does this contradiction belong to the category of statements that are neither true nor false, neither a nor not-a. Indeed, in logic, statements that are neither true nor false, that is, statements to which no truth value can be attributed, are either statements that have not yet been determined, which is what Russell has in mind when he writes, “‘x is human’ is a propositional function; so long as x remains undetermined, it is neither true nor false, but when a value is assigned to x it becomes a true or false proposition”; ¹⁵ or else statements that are neither true nor false are undeterminable statements, in which case we have what logical analysis called nonsense, like the statement “Caesar is a prime number,” which is neither true nor false, to which no value a or not-a can be attributed. And yet the paradoxical statement that Russell discovered is not a statement that is neither true nor false, nor is it an undetermined or undeterminable statement; it is purely and simply a statement that is both true and false, a and not-a, itself and its contrary, in that if it is the one, it is the other. As Philippe de Rouilhan notes in Russell et le cercle des paradoxes, “this paradox stated in logical terms carries a contradiction without any possible escape in logic itself.”¹⁶ In a word, the reduction of rational procedures to a logical calculus leads, in the end, to the pure and simple transgression of logic’s very basis, namely, the principle of noncontradiction. Indeed, if logic has not always been defined in the same way, if it has not employed the same techniques throughout its history, if there is a gulf between Aristotelian predicate logic and the Megarian school’s propositional logic, between Russell’s logic and the various logics that have succeeded it, if—to take up Otto Neurath’s metaphor—the history of logic is comparable to Theseus’s ship, which must be constantly reconstructed on the open sea in order to continue sailing, the fact nevertheless remains that however diverse its forms, logic cannot violate the principle of noncontradiction, nor can the ship go without the very condition for navigation.

Russell compares this logical paradox to a much older semantic paradox, known as the liar’s paradox or Eubulides’ paradox, whose purest formulation we owe to Eubulides of Miletus.¹⁷ Eubulides states, “I lie.” His statement ought to be true or false; either he is lying or he is not lying (a, not-a). But if it is true that he is lying, then he is telling the truth in saying that he lies and thus he does not lie. It follows that if he is lying then he is not lying. On the other hand, if it is false that he is lying, then what he says (in saying that he lies) is false and thus he lies. There again, he is lying and is not lying. The medievals classified the liar’s paradox among the insolubilia, and the Stoics’ adversaries presented it as the ultimate limit of human rationality. Russell, for his part, makes it the prototype of serious paradoxes, of absolute contradictions that are both true and false, which simultaneously affirm and deny.

A logician will obviously try to determine the nature of this pure form of contradiction, that is, he will try to establish a diagnosis that aims to indicate why a certain class of propositions gives rise to this simultaneity of truth and falsehood, this juxtaposition of yes and no, this coexistence of opposites. The propositions that generate contradictions, Russell tells us, all have in common the fact that they are self-referential: “It will be found that in all the logical paradoxes there is a kind of reflexive self-reference which is to be condemned on the same ground: viz. that it includes, as a member of a totality, something referring to that totality.”¹⁸ Logical contradictions that can be neither reduced nor overcome all proceed to employ a particular relation, namely, the relation of self to self, of a proposition to itself, of a class to itself, of a system to itself, etc. And whether it is a matter of logical or semantic paradoxes, the disruptive element is, for Russell, always the same: in all contradictions, “there is a common characteristic, which we may describe as self-reference or reflexiveness. The remark of Epimenides must include itself in its own scope. If all classes, provided they are not members of themselves, are members of w, this must also apply to w; and similarly for the analogous relational contradiction.”¹⁹ Self-reference or reflexivity happens when a class, a proposition, or a system refers to itself: self-inclusion occurs in the case of classes that are members of themselves, and self-application in the case of propositions that apply to themselves. To put this differently, a statement that ought to say something about something in fact says something about itself. The sign’s transitive function is interfered with by a reflexive dimension. For example, the proposition “Snow is white” says something about something—we have here the traditional transitive or representative function of a statement. On the other hand, in Jan Lukasiewicz’s statement, “The proposition that I am uttering is false,” the reflexive function interferes with the transitive function. We have two levels: the sentence seems to say that p, but, in fact, it says itself. This confusion—between what is said and the speaking about what is said—is what leads to the absolute contradiction, to the incredible junction of opposites, and is what endangers logic’s very principle.

Having presented this diagnosis, it is clear that logicians will try to find a solution. The common thread in all these solutions is that they neither dissolve nor resolve the contradiction: the contradiction can be defined but it cannot be overcome—it is irreducible, so that the only solution seems to be to prohibit this kind of statement. Thus Russell proposes not to reduce, transform, or overcome it but quite simply to prohibit self-referential statements in the establishment of the logical calculus. This prohibition is articulated in his 1910 theory of types, which adds the condition that “a class cannot contain itself” to the construction of logical language. We are thus led to establish a hierarchy of domains of meaning, to classify different types of statements, and to proscribe all self-referential statements. This is, as writers as diverse as Karl-Otto Apel and Philippe de Rouilhan have noted,²⁰ a way to prevent the paradox but not to solve it. Tarski undertakes the same strategy of prohibiting this type of statements rather than resolving the contradiction. Indeed, he proposes to disassociate two levels, the object language and metalanguage. If the liar’s statement is paradoxical, it is indeed because he confounds two different types of statement, the proposition p itself and the proposition that is about p. This is why we must distinguish between what is said from a point of view and what is said about that point of view. It is clear that, for Tarski as well as Russell, we can ask whether the contradiction has been bypassed rather than resolved. In any case, this is what François Rivenc maintains, who points out in Sémantique et vérité: De Tarski à Davidson that what is commonly considered as Tarski’s solution to the liar’s paradox would be better interpreted as “giving up any attempt to analyze the paradox.”²¹ This is echoed by Philippe de Rouilhan, who notes that Tarski finally resolved, at the end of his reconstruction, to “call ‘regular’ those statements in which a truth-predicate (or any related predicate) does not appear, and to reserve judgment on other statements (and to take action, if necessary, for exceptional statements such as Eubulides’ and Lukasiewicz’s).”²² This strategy of avoidance can also be read in a project like Hans Reichenbach’s. Indeed, his proposed solution in The Theory of Probability²³ is to create a category of the undecidable, into which statements that produce contradictions can be placed. He tells us that we must accept a trivalent logic that rejects the principle of the excluded middle (a is true or false, and there is no third possibility). Between truth and falsity there is a third value, the undecidable. But we are compelled to note that the introduction of this category threatens logical analysis itself. Indeed, what is logic if not the determination of what is decidable, the articulation of decision procedures? For logic, a system is decidable if there is a finite procedure, a sort of algorithm, that determines whether all the system’s expressions are demonstrable or not, that is, whether a value a or not-a can be attributed to all the system’s propositions. In light of this definition, the undecidable is a paradoxical category that, in the final analysis, relativizes logic’s scope (if the principle of noncontradiction does not hold for some statements, then logical analysis cannot claim to be universal). It follows that whether we declare self-reference to be prohibited (Russell), exceptional (Tarski), or undecidable (Reichenbach), the fact remains that the contradictions that it engenders are not diminished but only isolated and, in the end, abandoned. In a word, classical logical analysis declares itself powerless to overcome the kind of contradiction that these statements are liable to produce—and therefore prohibits them. The reason for this prohibition thus resides in the impossibility to resolve the type of contradiction created by certain propositions’ self-reference.

In the first place, I should note that there are common points between the birth of German idealism and the birth of logical positivism, that is, between these two historical moments in which the problem of propositions’ reference to themselves becomes fully clear. There are four commonalities: First of all, the two moments are situated at the same level—the epistemological—and not at an ontological level. Next, these two moments are based on the problem of grounding a discourse or a discipline. For German idealism, this is an interrogation of the grounds for the Kantian discourse; for Russell, it is an interrogation of the foundations of mathematics. Moreover, in both cases, this question about the grounds for a type of discourse gives rise to a serious contradiction that challenges the definition of the discipline itself (the failure of Kantianism, the crisis of mathematics). Finally, in both cases, the contradiction brings to light a specific mode of relation, the relation of an x to itself. For Russell, this is a proposition’s or a class’s relation to itself; for Fichte, it is philosophical propositions’ relation to themselves.

But the analogy stops there, for if we consider how this concept of relation to oneself is treated, the difference is twofold. Whereas Russell understands the contradiction’s origins as induced by the reference of an x to itself, Fichte traces the contradiction back to the absence of philosophical propositions’ reference to themselves. And whereas Russell prohibits all self-reference, Fichte makes it the fundamental basis for all philosophical knowledge. In a word, on the one hand, the reference of an x to itself is considered to be the source of insurmountable paradoxes and is thereby slapped with a prohibition, while on the other hand, this relation allows the creation of authentically philosophical propositions and is thereby promoted to the rank of a first principle, itself understood as the task or the model that we must fulfill when we do philosophy. Will this identification of real differences allow me to show that it is not only possible but even necessary to ignore the Russellian prohibition?

This comparison allows us to rethink the nature of the opposition between these two philosophical moments. Indeed, if self-reference is slapped with a prohibition in one case and, in the other, considered as one of the conditions that philosophical propositions must honor, this is not at all because the former wonder about language and its mechanisms while the latter dwell on consciousness and its nature. Nor is it because the former are good contemporary logicians and the latter poor, obsolete metaphysicians. Indeed, the denial of any self-reference, in the Russellian context, is explained by the fact that truth is there defined from the following principle: “All statements are true that are obtained from the schema ‘x is a true statement if and only if p’ by replacing x with the name of a statement and p with the statement itself.”²⁵ Self-referential statements are not paradoxical in themselves; but they only become so within this conception because the source of the paradox is located in the application of the schema “x is a true statement if and only if p” to statements already containing a truth predicate. Therefore, we can legitimately ask whether we must maintain the universality of this schema. But all German idealism has answered that we need not do so. The uniquely and purely representational conception of truth (as reference to an exterior x or to the world spoken of) was criticized by Fichte as well as Hegel. Self-reference does not have to be understood on the model of reference ad extra. It clearly follows that to establish a relevant debate between the two philosophical approaches requires understanding the opposition not as an opposition between the paradigm of language and the paradigm of the subject, nor as the opposition between a past historical moment and our necessarily true present, but as the opposition between different conceptions of truth. Must we understand self-reference in terms of the model of reference ad extra, or must we recognize another type of “reference” as well as the first that does not obey the same rules but can, however, produce propositions that can be understood in terms of true and false? Various arguments lead me to answer this question by reaffirming the rights of self-reference:

1. First of all, if we consider the liar’s argument, we can show that its paradoxical character is born from a certain definition of truth but is not in itself insurmountable. Indeed, if the liar’s argument is both true and false, in the context of early analytic philosophy, this is because it was held that every proposition must say something about something, that the proposition must refer to a “state of affairs.” But in the context of revitalized pragmatism, the same liar’s argument does not pose any particular problems. The statement is not both true and false but simply false, because it is self-destructive. In saying “I lie,” Eubulides cannot claim that his proposition is true without contradicting himself in the very contents of his statement. The truth claim is denied by the contents of what is said. It follows that the proposition “I lie” is a pragmatically false proposition—or possibly, because it shows that it cannot claim what it says is true, a proposition that belongs to a different discursive register from philosophical or scientific propositions. In saying “I lie,” I show my interlocutor that I invalidate—consciously, if I am being ironic—my claim to say the truth; I thus situate myself in a different framework from the one for truth-claiming propositions. As we can see, the diagnosis (serious contradiction or, on the contrary, a pragmatically false statement) is a function of the very conception of truth that is brought forward in each of these traditions. Therefore, the mode of reference ad extra does not appear to be the only one likely to express truth and falsity, and we should be able to consider that reference to an utterance—if it is not of the same order as reference to the world—ought not be understood with the same definition of truth. We can see that extending the prohibition to the liar’s argument is illegitimate; conversely, nothing prevents us from making self-referentiality a hypothesis to explore as the starting point for new propositions.

This simple reasoning calls upon the entirety of my definition of self-reference. The thesis “must apply to itself,” and yet, if it is applied to itself, it self-terminates. It follows that it is false. This is a conception of truth and falsity (as the success or failure of a proposition’s application to itself) that thus ought to be listed along with the other conceptions, since it is mobilized at the most critical moment of the argument. Moreover, the employment of this type of relation to self (the application of a proposition to itself) is what makes possible, in Engel’s specific case, an outline of an answer to the question of reference to the world. Indeed, to reject relativism is to reject the idea that our discourse does not refer to anything tangible and is only the expression of contingent and isolated constructions. And yet what leads to Engel’s rejection is clearly the use of a reference that is not a reference to the world but a reference or a relation to self.

This analysis—which reveals how much even those who mean to challenge or ignore it are led to self-reference—shows us on the one hand that the mode of relation of an x to itself, far from having to be considered as something that we must track down and exclude, can be proposed as what will be likely to assure consistency for propositions that claim to be philosophical. On the other hand, it leads us to think that the question of reference (in the name of which the prohibition of self-reference was pronounced) actually goes through a consideration of the question of self-reference. Far from being a sterile “metaphilosophical” problem that enquires as far as the eye can see into the conditions of conditions—and so on to infinity—of the philosophical discourse,²⁷ the question of philosophical propositions’ relations to themselves could indeed constitute a part of the answer to the question of a proposition’s relation to what it is not.

More generally, the results of this dual confrontation (contemporary theories of self-reference and the prohibition of formal logic) are as follows:

1. First of all, I have been able to further clarify my model of self-reference. Self-reference is strictly defined as the possibility of a proposition’s application to itself. Two groups of propositions have emerged from my analyses: propositions concerning truth and propositions concerning humanity. If universality is indeed required in these two groups, the fact remains that not all propositions with a universality claim are necessarily called to be directly self-referential, as we saw with the example of “All swans are white.” This apparently insignificant insight is important in that it enables a strict delineation of the field of self-reference: self-reference does not concern all propositions with a universality claim but only propositions that contain the terms truth or humanity.²⁸ It follows if a specialist in leeches’ brains can certainly continue to develop in a uniquely referential and classically “scientific” microcosmos, without ever posing the question of self-reference, a specialist in human brains, on the other hand, is much less able to do so because his propositions do not apply to an objective “it” and must answer to the principle of identity that I have revealed (congruence between a statement and its utterance). Here again, the division between science (“All swans are x”) and philosophical knowledge (“Every human is z”) is clearly defined without either having at any point to be dissolved in the other. This division between science and knowledge can just as well be understood as a division between the question of reference as a question of validity and the question of self-reference as a question of truth. We do not have to prohibit the study of leeches’ brains in order to proclaim the distinctiveness of philosophical analysis; we have to show how each discipline, legitimate in itself, moves in domains that call for different ways of reasoning and arguing. Learning and knowledge, reference and self-reference, validity and truth—these are the categories that appear, at the end of these developments, capable of articulating this division.

But if self-reference as a principle of reflexivity (congruence between a statement and its utterance) is now not only entirely elucidated but moreover justified, the question again arises as to what such a principle engenders. Is it an isolated principle, a simple criterion to apply to external propositions, a negative principle in the sense that it indicates only falsity? Or is this principle the source for a way to link together and produce propositions? Can we define the distinctive laws of reasoning from this first principle? Does the law of self-referentiality permit the construction of a “logic” or a method of argumentation that is then likely to unfurl a network of interdependent truths? Moreover, does this principle enable the capture of authentic content? I must now address this crucial question of the fecundity of the reflexive principle.