The Death of Philosophy

by Thomas-Fogiel, Isabelle; Lynch, Richard;

  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.

  My analysis reveals two groups of self-referential propositions: The first is when a proposition must apply to itself directly, that is, at the level of the very content that is said—this is the case for propositions that aim to define truth, like the example of the Kantian definition (truth = intuition + concept), which is self-destructive because it is not included in the category that it aims to define. The second is when a proposition must encompass the authority that pronounces it—for example, the sociologist (example 1) and the psychological philosopher (example 2).

  We should dwell a little longer on this second group, which not only shows how propositions that must apply to themselves go beyond the single category of propositions aiming to define the true, but also conclusively clarifies the concept of the authority of the utterance.

  The Authority of the Utterance: Us

  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.

  And yet these details clarify the nature of the authority of the utterance. Indeed, in the given example, it appears that the authority, as a philosopher, is not an “I” but a “we”; a “we” that is immediately given as a “we” and not by the addition of several “I”s. Let’s try to clarify this key point, starting with a comparison of several propositions.

  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.

  If we now consider first-person propositions like “I have a toothache,” here we indeed have a direct reference to oneself, not a statement concerning an impersonal “he” or “she.” Nevertheless, in this case, the speaker does not claim that the entire world has a toothache. A universality claim is not included in this proposition. The “I” that speaks can thus be readily identified with a given empirical subject here and now.

  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.

  This discovery is important in more than one respect: First of all, it allows me to characterize the authority of the utterance that is a philosopher or an anthropologist or anyone who claims to truly say what humans, speaking beings, etc., are. The philosopher is a “we” and nothing other than a “we.” This “we” allows me to overcome the imputation of solipsism, whether it be understood in the Wittgensteinian sense of a “private language” or the Heideggerian sense of a “metaphysics of subjectivity.”

  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 psy
chological 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?

  Finally, this discovery allows me to refine our understanding of performative contradiction. What causes a performative contradiction in the second group of propositions that I’ve analyzed? The fact that the authority of the utterance excludes itself from what it says. The dual characteristic of making a universality claim and of including oneself in this universality is thus the mark of this group of self-referential propositions.

  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.

  But the insights just summarized can legitimately give rise to the following objection: self-referentiality as I have just defined it seems to be precisely the self-referentiality that Russell (and after him, all of formal logic) prohibited. Has all my research into the meaning and the consistency of self-referentiality today led me to revive a problem already settled by logic at the beginning of the twentieth century? This is the second major debate that I must address to better ensure the current viability of the model.

  The Theory of Reflexivity and the Prohibition Against Self-referential Propositions

  The Reasons for Russell’s Prohibition

  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.