The Death of Philosophy

by Thomas-Fogiel, Isabelle; Lynch, Richard;

  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.

  Having grasped the genesis of what Récanati unhesitatingly calls the first wave of analysis’s “phobia of reflexivity,” we are now in a position to relativize Russell’s prohibition, for

  1. what turns out to be insoluble in a given domain—formal logic, for example—is not necessarily so in another. No argument a priori authorizes an extension of the prohibition; there is nothing that permits, immediately and without proof, its universalization or its extension to other domains. In a word, that a type of statement is unanalyzable in one domain does not mean that it is so in all domains. On this point, as I will show in what follows, the liar’s paradox can be explained, and—in a context other than Russell’s—no longer need be classified among the insolubilia. A question thus arises about the limits of this prohibition of self-referential statements,24 because it is illicit to decree a priori that the prohibition holds universally. All the less so, as

  2. the universalization of this prohibition is de facto impossible, because it is contradictory. Karl-Otto Apel has demonstrated this through an analysis of the Russellian proposition that articulates the prohibition, that is, that “no sign of signs can relate to all signs and in the same way to itself.” This proposition means, if we display the assertion implicitly contained therein, that “it holds for all signs that no sign of signs . . .” Apel’s demonstration shows that a universalized prohibition is self-destructive and falls into the series of paradoxes that it had aimed to overcome. This is why the classical analysis is unable to consistently maintain its own conclusion, namely, its prohibition of self-referential statements.

  This relativization of the Russellian prohibition allows me to now attempt an objective comparison of the two proposed systems in light of self-referentiality.

  The Similarities and Differences Between Two Attitudes Toward Self-referentiality

  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?

  The Lessons of This Comparison

  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 co
ntext, 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.

  2. Furthermore, at a certain level of analysis, it seems impossible to eliminate this type of relation of self to self, even for analytic philosophy itself. On this point, to take a more contemporary example than Russell’s, Pascal Engel’s work, bearing the very title of La vérité [Truth], is extremely symptomatic of this quasi impossibility to eliminate the problem of self-reference. In this text, Engel reviews the various definitions of truth generated in the course of history (correspondence theories, coherence theories, pragmatic theories, etc.), and at no point in his survey does he mention truth as a proposition’s noncontradiction with itself—or as congruence between a statement and its utterance, what is said and its saying.

  But this omission is eminently paradoxical in light of the author’s own reasoning, for Engel uses this definition of truth at a critical moment in his demonstration. Thus, when he wants to establish, against the relativists, a “minimal concept of truth,” the argument to which he resorts is quite precisely the argument that Fichte employed without cease, namely, “those who make this claim contradict themselves in saying it.” Indeed, disputing that it must be admitted, with the relativists, that two theses are true because they are true relative to a perspective, Engel writes:

  Let’s now consider a thesis concerning the justification of the two theses … To defend relativism, regarding justification, it must be maintained that the rules of justification are equally justified for those who believe the first theory and for those who believe the second. Here, too, relativism will have to apply this to its own thesis and to admit that its rules of justification are just as good as those of its adversary. But by the same reasoning as above, it cannot admit as much without presupposing the validity of a point of view according to which some rules are better than others.26

  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.

  Consequently, we can say that the mode of reference ad extra is not the only one capable of being understood in terms of true and false, and that one can legitimately—despite Russell’s prohibition—consider that in certain circumstances reference to the utterance can enable a decision about truth and falsity (for example, in the case of the liar’s paradox). The opposition between traditions can no longer continue to be interpreted as an opposition between one definitively historically superannuated way of philosophizing and another, legitimate because more contemporary. This is why I am entitled here to answer the initial question—the question whether self-reference is strengthened by this confrontation with formal logic’s prohibition—in the affirmative.

  Conclusions: The Application of Propositions to Themselves

  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.