A representationalist analysis of strong first-person phenomena is developed (Baker 1998), and it is argued that conscious, cognitive self-reference can be naturalized under this representationalist analysis. According to this view, the phenomenal first-person perspective is a condition of possibility for the emergence of a cognitive first-person perspective. Cognitive self-reference always is reference to the phenomenal content of a transparent self-model. The concepts of phenomenal transparency and introspection are clarified. More generally, I suggest that the concepts of phenomenal opacity (...) and phenomenal transparency are interesting instruments for analyzing conscious, self-representational content, and that their relevance in understanding reflexive, i.e., cognitive subjectivity may have been overlooked in the past. (shrink)
Reflection on the self's way of being "in" consciousness yields two arguments for a theory of self-reference not based in any way all all on self-cognition. First, I show that one theory of self-reference predicts an experience of the self because the theory inadequately analyzes the semantical facts about indexicality. I construct a dilemma for this cognitivism, which it cannot get out of, for it requires even solitary self-reference to be based on some original self-knowledge, which is (...) not available. I describe my "kinetic model" of unspoken self-reference, and I show how it fits the facts of four forms of consciousness, all of which presuppose self-reference, rather than yield it. Second, a speaker uses the first person pronoun in sentences because she is aware of the unmediated role in agency of the beliefs she would express, and not because she is aware of herself in their content. The cognitive model, in contrast, succumbs to a vicious regress and is exposed as an obstacle to an understanding of consciousness. (shrink)
In this paper I want to propose that we see solipsism as arising from certain problems we have about identifying ourselves as subjects in an objective world. The discussion will centre on Wittgenstein.
All paradoxes of self-reference seem to share some structural features. Russell in 1908 and especially Priest nowadays have advanced structural descriptions that successfully identify necessary conditions for having a paradox of this kind. I examine in this paper Priest’s description of these paradoxes, the Inclosure Scheme (IS), and consider in what sense it may help us understand and solve the problems they pose. However, I also consider the limitations of this kind of structural descriptions and give arguments against Priest’s (...) use of IS in favour of dialetheism. IS fails to identify sufficient conditions for having a paradox of self-reference. That means that, even if we identified a problem common to any reasoning satisfying IS, that problem would not explain why some of those reasonings are paradoxical and some others are not. Therefore IS cannot justify by itself the claim that some particular theory offers the best solution to the paradoxes of self-reference. We still need to consider aspects concerning the content and context of occurrence of every paradox. (shrink)
I here investigate the sense in which diagonalization allows one to construct sentences that are self-referential. Truly self-referential sentences cannot be constructed in the standard language of arithmetic: There is a simple theory of truth that is intuitively inconsistent but is consistent with Peano arithmetic, as standardly formulated. True self-reference is possible only if we expand the language to include function-symbols for all primitive recursive functions. This language is therefore the natural setting for investigations of self-reference.
emantic pathologies of self-reference include the Liar (‘this sentence is false’), the Truth-Teller (‘this sentence is true’) and the Open Pair (‘the neighbouring sentence is false’ ‘the neighbouring sentence is false’). Although they seem like perfectly meaningful declarative sentences, truth value assignment to their uses seems either inconsistent (the Liar) or arbitrary (the Truth-Teller and the Open-Pair). These pathologies thus call for a resolution. I propose such a resolution in terms of relative-truth: the truth value of a pathological sentence (...) use varies with the context of its assessment. It always has a determinate truth value, but this truth value is relative to the context of its assessment. I start by considering a fairly esoteric pathology: the Truth-Teller, that is, sentences which assert nothing but their own truth. I make the case that truth value of a given truth-teller use must in general depend on the context of its assessment, and that one can indeed change its truth value at will. I then show how the notion of assessment-sensitive truth can help us provide solutions to other semantic paradoxes such as the Liar and the Open Pair and that those solutions are immune to revenge problems. I conclude by situating my proposal among the main approaches to the semantic paradoxes, and by drawing a very broad moral about pathological self-reference and intentionality. (shrink)
Self-reference in semantics, which leads to well-known paradoxes, is a thoroughly researched subject. The phenomenon can appear also in decision theoretic situations. There is a structural analogy between the two and, more interestingly, an analogy between principles concerning truth and those concerning rationality. The former can serve as a guide for clarifying the latter. Both the analogies and the disanalogies are illuminating.
The paradoxes of self-reference are genuinely paradoxical. The liar paradox, Russell’s paradox and their cousins pose enormous difficulties to anyone who seeks to give a comprehensive theory of semantics, or of sets, or of any other domain which allows a modicum of self-reference and a modest number of logical principles. One approach to the paradoxes of self-reference takes these paradoxes as motivating a non-classical theory of logical consequence. Similar logical principles are used in each of the paradoxical (...) inferences. If one or other of these problematic inferences are rejected, we may arrive at a consistent (or at least, a coherent) theory. In this paper I will show that such approaches come at a serious cost. The general approach of using the paradoxes to restrict the class of allowable inferences places severe constraints on the domain of possible propositional logics, and on the kind of metatheory that is appropriate in the study of logic itself. Proof-theoretic and model-theoretic analyses of logical consequence make provide different ways for non-classical responses to the paradoxes to be defeated by revenge problems: the redefinition of logical connectives thought to be ruled out on logical grounds. Non-classical solutions are not the “easy way out” of the paradoxes. (shrink)
In this paper, we present a framework in which we analyze three riddles about truth that are all (originally) due to Smullyan. We start with the riddle of the yes-no brothers and then the somewhat more complicated riddle of the da-ja brothers is studied. Finally, we study the Hardest Logic Puzzle Ever (HLPE). We present the respective riddles as sets of sentences of quotational languages , which are interpreted by sentence-structures. Using a revision-process the consistency of these sets is established. (...) In our formal framework we observe some interesting dissimilarities between HLPE’ s available solutions that were hidden due to their previous formulation in natural language. Finally, we discuss more recent solutions to HLPE which, by means of self-referential questions , reduce the number of questions that have to be asked in order to solve HLPE . Although the essence of the paper is to introduce a framework that allows us to formalize riddles about truth that do not involve self-reference, we will also shed some formal light on the self-referential solutions to HLPE. (shrink)
In this paper I will give an analysis of what I call ‘generalizing detached self-reference’ within a general account of reference to the first person. With generalizing detached self-reference an agent attributes properties to a range of individuals by putting himself into their shoes, or simulating them. I will show that generalizing detached self-reference plays an important role in the semantics of natural language, in particular in the English generic one and in what syntacticians call arbitrary PRO.
Although it was traditionally thought that self-reference is a crucial ingredient of semantic paradoxes, Yablo (1993, 2004) showed that this was not so by displaying an infinite series of sentences none of which is self-referential but which, taken together, are paradoxical. Yablo’s paradox consists of a countable series of linearly ordered sentences s(0), s(1), s(2),... , where each s(i) says: For each k (...) > i, s(k) is false (or equivalently: For no k > i is s(k) true). We generalize Yablo’s results along two dimensions. First, we study the behavior of generalized Yablo-series in which each sentence s(i) has the form: For Q k > i, s(k) is true, where Q is a generalized quantifier (e.g., no, every, infinitely many, etc). We show that under broad conditions all the sentences in the series must have the same truth value, and we derive a characterization of those values of Q for which the series is paradoxical. Second, we show that in the Strong Kleene trivalent logic Yablo’s results are a special case of a more general fact: under certain conditions, any semantic phenomenon that involves self-reference can be emulated without self-reference. Various translation procedures that eliminate self-reference from a non-quantificational language are defined and characterized. An Appendix sketches an extension to quantificational languages, as well as a new argument that Yablo’s paradox and the translations we offer do not involve self-reference. (shrink)
Self-referential sentences have played a key role in Tarski's proof  of the non-definibility of arithmetic truth within arithmetic and Gödel's proof  of the incompleteness of Peano Arithmetic. In this article we consider some new methods of achieving self-reference in a uniform manner.
Three distinct turning points (“bottleneck breakings”) in universal evolution are discussed at some length in terms of “self-reference” and (corresponding) “Reality Principles.” The first (origin and evolution of animate Nature) and second (human consciousness) are shown to necessarily precede a third one, that of Marxist philosophy. It is pointed out that while the previous two could occupy a natural (so in a sense neutral) place as parts of human science, the self-reference of Marxism, as a _social_ human phenomenon, (...) through its direct bearings on the _practice_ of society, did have a stormy history. I conclude that the fall of Bolshevism was unavoidable, and still, we might uphold our hope for a truly free society of humankind, just on the very basis of what we have learned of the fate of Marxist philosophy as such, as a _recursively evolving_ social _practice_: the freedom of humankind of its own ideological burdens (constraints). (shrink)
Arithmetical self-reference through diagonalization is compared with self-recognition in a mirror, in a series of diagrams that show the structure and main stages of construction of self-referential sentences. A Gödel code is compared with a mirror, Gödel numbers with mirror images, numerical reference to arithmetical formulas with using a mirror to see things indirectly, self-reference with looking at one’s own image, and arithmetical provability of self-reference with recognition of the mirror image. The comparison turns arithmetical self-reference (...) into an idealized model of self-recognition and the conception(s) of self based on that capacity. (shrink)
This article focuses on theoretical reflections on sovereignty and constitutionalism in the context of the globalization and Europeanisation of the nation states, their politics, and legal systems. Starting from a critical assessment of the Kelsen-Schmitt polemic, the author claims that sovereignty needs to be analysed by the sociological method in order to disclose its current structural differentiation. The constitution of society may be imagined as the multitude of self-constituted and functionally differentiated social subsystems. The constitutional pluralism argument subsequently reconceptualizes sovereignty (...) as socially differentiated and divided between specific subsystems. The EU's differentiated constitutional domain and the paradox of divided sovereignty are used as examples of profound structural and semantic changes in contemporary national and transnational societies. While the sovereign nation-state institutions have become marginalized in political structures of European societies, the self-constitutionalization of the functionally differentiated EU legal system proceeds by internalizing the concept of divided sovereignty and using it semantically as its mode of self-reference. (shrink)
The paradoxes of self reference have to be dealt with by anyone seeking to give a satisfactory account of the logic of truth, of properties, and even of sets of numbers. Unfortunately, there is no widespread agreement as to how to deal with these paradoxes. Some approaches block the paradoxical inferences by rejecting as invalid a move that classical logic counts as valid. In the recent literature, this deviant logic analysis of the paradoxes has been called into question.This disagreement motivates (...) a re-examination of the philosophy of formal logic and the status of logical truths and rules. In this paper I do some of this work, and I show that this gives us the means to defend the deviant approaches against such criticisms. As a result I hope to show that these analyses of the paradoxes are worthy of more serious consideration than they have so far received. (shrink)
In this paper I present two new paradoxes, a definability paradox (related to the paradoxes of Berry, Richard and König), and a paradox about extensions (related to Russell’s paradox). However, unlike the familiar definability paradoxes and Russell’s paradox, these new paradoxes involve no self-reference or circularity.
This article reinterprets the Kelsen-Schmitt debate in the context of social systems theory and rethinks its major concepts as part of legal and political self-reference and systemic differentiation. In Kelsen?s case, it is the exclusion of sovereignty from juridical logic that opens a way to the self-reference of positive law. Similarly, Schmitt constructed his concept of the political as a self-referential system of political operations protected from the social environment by the medium of power. The author argues that (...) the process of legal and political globalisation rules out the possibility of formulating substantive theories of the state associating this particular social organisation with metaphysical values and a self-validating collective identity. Kelsen and Schmitt continue to inspire current theories of non-metaphysical globalised law and politics. However, the constitutional state and sovereignty need to be reformulated as a meeting point of functionally differentiated and globalised legal and political communications and not as their ultimate end. (shrink)
We provide a systematic recipe for eliminating self-reference from a simple language in which semantic paradoxes (whether purely logical or empirical) can be expressed. We start from a non-quantificational language L which contains a truth predicate and sentence names, and we associate to each sentence F of L an infinite series of translations h 0(F), h 1(F), ..., stated in a quantificational language L *. Under certain conditions, we show that none of the translations is self-referential, but that any (...) one of them perfectly mirrors the semantic behavior of the original. The result, which can be seen as a generalization of recent work by Yablo (1993, Analysis, 53, 251–252; 2004, Self-reference, CSLI) and Cook (2004, Journal of Symbolic Logic, 69(3), 767–774), shows that under certain conditions self-reference is not essential to any of the semantic phenomena that can be obtained in a simple language. (shrink)
This note argues against Barwise and Etchemendy's claim that their semantics for self-reference requires use of Aczel's anti-foundational set theory, AFA, and that any alternative would involve us in complexities of considerable magnitude, ones irrelevant to the task at hand (The Liar, p. 35).Switching from ZF to AFA neither adds nor precludes any isomorphism types of sets. So it makes no difference to ordinary mathematics. I argue against the author's claim that a certain kind of naturalness nevertheless makes AFA (...) preferable to ZF for their purposes. I cast their semantics in a natural, isomorphism invariant form with self-reference as a fixed point property for propositional operators. Independent of the particulars of any set theory, this form is somewhat simpler than theirs and easier to adapt to other theories of self-reference. (shrink)
Self-Knowledge and Self-Reference is a defense and reconciliation of the two apparently conflicting theses that the self is peculiarly elusive and that our basic, cogito-judgments are certain. On the one hand, Descartes seems to be correct that nothing is more certain than basic statements of self-knowledge, such as "I am thinking." On the other hand, there is the compelling Humean observation that when we introspect, nothing is found except for various "impressions." The problem, then, is that the Humean and (...) Cartesian insights are both initially appealing, yet they appear to be in tension with one another. In this paper I attempt to satisfy both intuitions by developing a roughly descriptivist account of self-reference according to which our certainty in basic beliefs stems precisely from our needing to know so little in order to have them. (shrink)
Abstract Buddhist egology concurs with the Husserlian claim that the enipirical ego is ?constituted?. The Buddhist ?deconstruction? of the ego will not, however, pace Husserl, permit the pronoun ?I? to refer to a purported extra?linguistic entity. The insights here distilled from the unique mode of self?reference functional within the Vietnamese language secure for us an unmistakable confirmation of the Buddhist thesis and have profound consequences for the philosophical problems surrounding the existence and nature of the self and the existence of (...) other minds. (shrink)
The semantic paradoxes are often associated with self-reference or referential circularity. Yablo (1993), however, has shown that there are infinitary versions of the paradoxes that do not involve this form of circularity. It remains an open question what relations of reference between collections of sentences afford the structure necessary for paradoxicality. In this essay, we lay the groundwork for a general investigation into the nature of reference structures that support the semantic paradoxes and the semantic hypodoxes. We develop a (...) functionally complete infinitary propositional language endowed with a denotation assignment and extract the reference structural information in terms of graph-theoretic properties. We introduce the new concepts of dangerous and precarious reference graphs, which allows us to rigorously define the task: classify the dangerous and precarious directed graphs purely in terms of their graph-theoretic properties. Ungroundedness will be shown to fully characterize the precarious reference graphs and fully characterize the dangerous finite graphs. We prove that an undirected graph has a dangerous orientation if and only if it contains a cycle, providing some support for the traditional idea that cyclic structure is required for paradoxicality. This leaves the task of classifying danger for infinite acyclic reference graphs. We provide some compactness results, which give further necessary conditions on danger in infinite graphs, which in conjunction with a notion of self-containment allows us to prove that dangerous acyclic graphs must have infinitely many vertices with infinite out-degree. But a full characterization of danger remains an open question. In the appendices we relate our results to the results given in Cook (2004) and Yablo (2006) with respect to more restricted sentences systems, which we call F-systems. (shrink)
This thesis proposes that an account of first-person reference and first-person thinking requires an account of practical knowledge. At a minimum, first-person reference requires at least a capacity for knowledge of the intentional act of reference. More typically, first-person reasoning requires deliberation and the ability to draw inferences while entertaining different 'I' thoughts. Other accounts of first-person reference--such as the perceptual account and the rule-based account--are criticized as inadequate. An account of practical knowledge is provided by an interpretation of GEM (...) Anscombe's account in her landmark monograph "Intention". (shrink)
The paper presents a new, intuitive formal language, L E , that fits in with a world view in which experiences are central entities. It is shown how classical logic and an "objective making" adaptive logic can be applied to formulas of L E . The latter logic sheds an interesting light on the creation of theories about "the objective world". The paper also contains a small comment on sentences that are not translatable in L E . In the last (...) section, I revise self-referring sentences by means of their translations in L E. (shrink)
In this paper I want to propose that we see solipsism as arising from certain problems we have about identifying ourselves as subjects in an objective world. The discussion will centre on Wittgenstein’s treatment of solipsism in his Tractatus Logico- Philosophicus. In that work Wittgenstein can be seen to express an unusually profound understanding of the problems faced in trying to give an account of how we, who are subjects, identify ourselves as objects in the (...) world. We have in his compressed remarks, the kernels of a number of arguments which all come together to form what can be called the problem of self-identification. I want to argue that the solipsism of the Tractatus arises at least in part as a solution to, or – to put it less optimistically – as a symptom or articulation of this problem. In approaching Wittgenstein’s early discussion of solipsism in this way I will obviously be in disagreement with some other interpretations of the work. For example, there are those who think that there is no ‘solipsism of the Tractatus’.1 In fact, the Tractarian arguments presented below as motivating solipsism have been seen as fulfilling the quite opposite function of refuting it. I do not intend in this piece to engage with alternative interpretations. Let me say a little bit about why I have granted myself the licence not to do so. First, the focus of my concern with solipsism is on how it connects with what I have called the problem of self-identification. While it is a concern that emerged in an attempt to make sense of Wittgenstein’s remarks in.. (shrink)
Alasdair MacIntyre's account of tradition-based rationality has been the subject of much discussion, as well as the object of some recent charges of inconsistency. The author considers arguments by Jennifer Herdt, Peter Mehl, and John Haldane which attempt to show that MacIntyre's account of rationality is, in some way, inconsistent. It is argued that the various charges of inconsistency brought against MacIntyre by these critics can be understood as variations on two general types of criticism: (1) that MacIntyre's account of (...) tradition-based rationality presents a picture of rationality with inconsistent internal elements, and (2) that MacIntyre, in the act of presenting his picture of rationality, makes the sort of claims to which his own account of rationality denies legitimacy, and thus MacIntyre's account is self-referentially incoherent. In response to criticisms of the first sort, it is argued that MacIntyre can further clarify or develop his position to take the current criticisms into account without altering the fundamental aspects of his picture of rationality. In response to the charge of self-referential incoherence, it is argued that the charge rests on a mistaken understanding of MacIntyre's position and of the nature of justification. In dealing with these arguments, the author hopes to not only vindicate MacIntyre's account of rationality against the charges of some of its recent critics, but also to shed some light on the nature of arguments both for and against relativism and historicism. (shrink)
We know from more than two millenia of experience that self-referential statements, such as the liar's ("This very statement is false"), can be debated by philosophers and logicians for millenia without producing consensus on their solutions. We should not be surprised, then, if self-referential laws produce paradoxes which puzzle lawyers. What is surprising, though, is that some of these paradoxes bother only the logicians and philosophers who study law from outside, and do not bother lawyers at all. This fact should (...) interest philosophers of law even more than the paradoxes themselves. (shrink)
Graham Priest (1994) has argued that the following paradoxes all have the same structure: Russell’s Paradox, Burali-Forti’s Paradox, Mirimanoff’s Paradox, König’s Paradox, Berry’s Paradox, Richard’s Paradox, the Liar and Liar Chain Paradoxes, the Knower and Knower Chain Paradoxes, and the Heterological Paradox. Their common structure is given by Russell’s Schema: there is a property φ and function δ such that..
that all the paradoxes of set theory and logic fall under one schema; and (2) hence they should be solved by one kind of solution. This reply addresses both claims, and counters that (1) in fact at least one paradox escapes the schema, and also some apparently 'safe' theorems fall within it; and (2) even for the (considerable) range of paradoxes so captured by the schema, the assumption of a common solution is not obvious; each paradox surely depends upon the (...) theory and context in which it arises. Details of Priest's proposed solution are also sought. (shrink)