The paper begins by acknowledging that weakened systematic precision in phenomenology has made its application in philosophy of science obscure and ineffective. The defining aspirations of early transcendental phenomenology are, however, believed to be important ones. A path is therefore explored that attempts to show how certain recent developments in the logic of self-reference fulfill in a clear and more rigorous fashion in the context of philosophy of science certain of the early hopes of phenomenologists. The resulting dual (...) approach is applied to several problems in the philosophy of science: on the one hand, to proposed rejections of scientific objectivity, to the doctrine of radical meaning variance, and to the Quine-Duhem thesis, and or. the other, to an analysis of hidden variable theory in quantum mechanics. (shrink)

In this paper we examine various requirements on the formalisation choices under which self-reference can be adequately formalised in arithmetic. In particular, we study self-referential numberings, which immediately provide a strong notion of self-reference even for expressively weak languages. The results of this paper suggest that the question whether truly self-referential reasoning can be formalised in arithmetic is more sensitive to the underlying coding apparatus than usually believed. As a case study, we show how (...) this sensitivity affects the formal study of certain principles of self-referential truth. (shrink)

If you were to build a world from Nothing, how would you do it? By investigating the nature of self-reference, we will show how this can be achieved, how starting from Nothing, Everything can be obtained. Various implications of the definition of self-reference will be investigated, showing how it can account for various aspects of the phenomenology of consciousness, thus showing how starting from only 1 principle, a world of infinite complexity can be obtained. Parallels with (...) set theory will be made along the way. (shrink)

If you were to build a world from Nothing, how would you do it? By investigating the nature of self-reference, we will show how this can be achieved, how starting from Nothing, Everything can be obtained. Various implications of the definition of self-reference will be investigated, showing how it can account for various aspects of the phenomenology of consciousness, thus showing how starting from only 1 principle, a world of infinite complexity can be obtained. Parallels with (...) set theory will be made along the way. (shrink)

In this paper, we examine a fundamental problem that appears in Greek philosophy: the paradoxes of self-reference of the type of “Third Man” that appears first in Plato’s 'Parmenides', and is further discussed in Aristotle and the Peripatetic commentators and Proclus. We show that the various versions are analysed using different language, reflecting different understandings by Plato and the Platonists, such as Proclus, on the one hand, and the Peripatetics (Aristotle, Alexander, Eudemus), on the other hand. We show (...) that the Peripatetic commentators do not focus on Plato’s solution but primarily on the formulation of the “Third Man” paradox. On the contrary, Proclus seems to be convinced that Plato suggests a sound solution to the paradox by defining the predicate of similarity (homogeneity) that demarcates two types of homogeneous entities – the eide and the participants in them in a way that their confusion would be inadmissible. We claim that Plato’s solution follows a sound line of reasoning that is formalisable in a language of Frege-Russell type; hence there exists a model in which Plato’s reasoning is valid. Furthermore, we notice that Plato’s definition of the second-order predicate of similarity is attained by resorting to first-order entities. In this sense, Plato’s definition is comparable to Eudoxus’ definition of ratio, which is also attained by resorting to first-order objects. Consequently, Plato seems to follow a logical practice established by the mathematicians of the 5th century, notably Eudoxus, in his solution to the paradox. (shrink)

The purpose of this paper is to open for investigation a range of phenomena familiar from dynamical systems or chaos theory which appear in a simple fuzzy logic with the introduction of self-reference. Within that logic, self-referential sentences exhibit properties of fixed point attractors, fixed point repellers, and full chaos on the [0, 1] interval. Strange attractors and fractals appear in two dimensions in the graphing of pairs of mutually referential sentences and appear in three dimensions in (...) the graphing of mutually referential triples. (shrink)

This article is a modern socratic dialogue between socrates and theaetetus presented in the "ordinary language." the discussion centers on self-Referring statements and their meaning. (staff).

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)

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 (...) class='Hi'>self-reference. (shrink)

An anthology of previously unpublished essays from some of the most outstanding scholars working in philosophy, mathematics, and computer science today, _Self-Reference_ reexamines the latest theories of self-reference, including those that attempt to explain and resolve the semantic and set-theoretic paradoxes. With a thorough introduction that contextualizes the subject for students, this book will be important reading for anyone interested in the general area of self-reference and philosophy.

The goal of this paper is to present Yabloesque versions of Grelling’s and Zwicker’s paradoxes concerning the notions of “heterological” and “hypergame” respectively. We will offer counterparts of these paradoxes that do not seem to involve self-reference or vicious circularity.El objetivo de este artículo es ofrecer versiones de las paradojas de Grelling (sobre el predicado “heterológico”) y de Zwicker (sobre el hiperjuego) inspiradas en la paradoja de Yablo. Nuestras versiones de estas paradojas no parecen involucrar ni autorreferencia ni (...) circularidad viciosa. (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 self-reference effect refers to better memory for self-relevant than for other-relevant information. Generally, the SRE is found in conditions in which links between the stimuli and the self are forged in the encoding phase. To investigate the possibility that such conditions are not prerequisites for the SRE, this research developed two conditions by using two recognition tasks involving abstract geometric shapes. One was the cue-in-encoding condition in which self- and other-cues were presented to construct (...) links with AGSs during the encoding phase, and the other was the cue-in-retrieval condition in which self- and other-cues were presented to construct links with AGSs during the retrieval phase. The SRE was found in both conditions. The findings reveal that self-cues merely presented during the retrieval phase are sufficient to induce the SRE. Links between the stimuli and the self constructed during the encoding phase may not be necessary prerequisites for the SRE. (shrink)

From the Editor’s Introduction: -/- THE INTERNAL LIMITATIONS OF HUMAN UNDERSTANDING -/- We carry, unavoidably, the limits of our understanding with us. We are perpetually confined within the horizons of our conceptual structure. When this structure grows or expands, the breadth of our comprehensions enlarges, but we are forever barred from the wished-for glimpse beyond its boundaries, no matter how hard we try, no matter how much credence we invest in the substance of our learning and mist of speculation. -/- (...) The limitations in view here are not due to the mere finitude of our understanding of ourselves and of the world in which we live. They are limitations that come automatically and necessarily with any form of understanding. They are, as we shall see, part and parcel of any organization or ordering of data that we call information. -/- The consequences of these limitations are varied: As a result of them, hermeneutics cannot help but be hermetic; scientific theories of necessity are circumscribed by the boundaries of the ideas that define them; formal systems must choose between consistency and comprehensiveness; philosophical study, because it includes itself within its own proper subject matter, is forced to be reflexive in its self-enclosure. The fundamental dynamic shared by all forms of understanding testifies to an internal limitative keystone. (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)

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)

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)

In lieu of an abstract, here is a brief excerpt of the content:Self-Reference:Theory and Didactics between Language and LiteratureSvend Erik Larsen (bio)Semiotics of Self-ReferenceLiterary metafiction constitutes the extreme case of self-referential texts. Therefore we can either discard it as generally irrelevant for the understanding of the cultural functions of texts, or use it as a point of departure for the formulation of both general and basic aspects of such functions. The position taken in this essay will (...) opt for the last possibility, although I know full well that already the term "metafiction" itself inevitably triggers a variety of skeptical reactions. Does it not just refer to some author's self-centered ruminations in the ivory tower? Or a topic for the nerds of literary studies with a taste for theoretical acrobatics? If so, in both cases following metafictional inclinations results in complete isolation from both the context of literature and its readers.However, one may also adopt the opposite position. The metafictional features of literature constitute one of the means by which literature reaches out to its context and also engages its readers. And critical endeavors are not necessarily devoid of anything but their own concepts. They may instead pave the way for methodological and didactic considerations that ultimately make difficult literature more accessible as a cultural phenomenon. Rather than dwelling upon subtle theoretical differences in the definition of what metafiction is, I will therefore engage in a methodological approach: what kind of questions can we put to the texts, and what kind of answers can we reasonably come up with when using metafiction in a methodological and didactic framework?I shall begin by proposing a set of definitions broader than metafiction that will allow me to zoom in on it as a relevant methodological concept that opens for didactic reflections. The notion of metalevel will constitute my starting point. In its broadest sense, a metalevel indicates a position outside a given field of objects or meanings and in relation to it. But rather than relating [End Page 13] to the content of the field in question, the metalevel is supposed to serve as a platform enabling us to observe and evaluate basic principles and function of the field. This is the role of, for example, the theory of science or of epistemology in relation to the particular knowledge of various sciences. We may call it an epistemological metalevel.In a more restricted sense, a metalevel comprises a level in relation to a given sign system — rather than to a given field of objects — from which we can observe and evaluate the basic principles defining the function, range and validity of the sign system. This is the role of, for example, musicology in relationto the acoustic arts, art criticism in relation to the visual arts, medicine in relation to bodily symptoms. We may call it an inter-semiotic metalevel.Finally, in its most restricted sense, a metalevel points toward a level inside a given sign system from which we can refer to this sign system itself,but not in relation to a given field of objects or in relation to another sign system. We may call this level an intra-semiotic metalevel. In this context, language is a unique system, which in this capacity shapes literature as a particular linguistic phenomenon. Only inside the semiotic system of language can the intra-semiotic metalevel have two different functions:The first function is as a science of language, linguistics, which is itself a verbal sign system. In verbal scientific descriptions and arguments we may scrutinize the natural or everyday language as a medium, that is, its basic linguistic structures and principles, without taking into consideration its content, which it may share with other media. Texts and pictures may refer to the same phenomenon even if such references do not overlap completely. All other sciences differ from linguistics in this respect, because they cannot deal scientifically with their non-verbal objects through the same non-verbal medium as that which makes up the object, but need the support of a linguistic metalevel or at least of signs that are linguistically anchored. Even mathematics or other strictly formal sign systems are based on natural languages. We may refer to... (shrink)

The novel has always provided a vehicle for commenting on various aspects of human existence. We are familiar with the political novel, the historical novel, or the metaphysical novel, and in this sense Sorrentino's Mulligan Stew, with its running commentary on novels, novelists, critics and publishers, may be viewed as a critical novel. A critical novel, however, has a striking feature which it does not share with the other sorts of novels mentioned above in that a critical novel is itself (...) a novel, and a member of the class of objects on which it is commenting. This is a structure that logicians call “self-reference” and the phenomenon of self-reference has provided a central theme in twentieth century logic and philosophy. (shrink)

This is a book that every logician will want to read. The well-worn topics of self-reference and the paradoxes have been given new life in these papers by a distinguished group of logicians.

The goal of this paper is to present Yabloesque versions of Grelling’s and Zwicker’s paradoxes concerning the notions of “heterological” and “hypergame” respectively. We will offer counterparts of these paradoxes that do not seem to involve self-reference or vicious circularity.El objetivo de este artículo es ofrecer versiones de las paradojas de Grelling y de Zwicker inspiradas en la paradoja de Yablo. Nuestras versiones de estas paradojas no parecen involucrar ni autorreferencia ni circularidad viciosa.

Self-referential sentences have played a key role in Tarski's proof [9] of the non-definibility of arithmetic truth within arithmetic and Gödel's proof [2] of the incompleteness of Peano Arithmetic. In this article we consider some new methods of achieving self-reference in a uniform manner.

This is the introduction to Self-reference: Reflections on Reflexivity, edited by Steven James Bartlett and Peter Suber. The introduction identifies and describes a wide range of varieties of self-reference, some which have become important topics of investigation in philosophy, and others which are of significance in other disciplines. /// The anthology is the first published collection of essays to give a sense of depth and breadth of current work on this fascinating and important set of issues. (...) The volume contains 13 essays by well-known authors in this field, written on special invitation for this collection. In addition, the book includes the first general bibliography of works on self-reference, comprising more than 1,200 citations. (shrink)

In this paper, I start by showing that sorites paradoxes are inclosure paradoxes. That is, they fit the Inclosure Scheme which characterizes the paradoxes of self-reference. Given that sorites and self-referential paradoxes are of the same kind, they should have the same kind of solution. The rest of the paper investigates what a dialetheic solution to sorites paradoxes is like, connections with a dialetheic solution to the self-referential paradoxes, and related issues—especially so called "higher order" vagueness.

John Buridan was a fourteenth-century philosopher who enjoyed an enormous reputation for about two hundred years, was then totally neglected, and is now being 'rediscovered' through his relevance to contemporary work in philosophical logic. The final chapter of Buridan's Sophismata deals with problems about self-reference, and in particular with the semantic paradoxes. He offers his own distinctive solution to the well-known 'Liar Paradox' and introduces a number of other paradoxes that will be unfamiliar to most logicians. Buridan also (...) moves on from these problems to more general questions about the nature of propositions, the criteria of their truth and falsity and the concepts of validity and knowledge. This edition of that chapter is intended to make Buridan's ideas and arguments accessible to a wider range of readers. The volume should interest many philosophers, linguists and logicians, who are increasingly finding in medieval work striking anticipations of their own concerns. (shrink)

In this sequel toSelf-reference in arithmetic Iwe continue our discussion of the question: What does it mean for a sentence of arithmetic to ascribe to itself a property? We investigate how the properties of the supposedly self-referential sentences depend on the chosen coding, the formulae expressing the properties and the way a fixed point for the expressing formulae are obtained. In this second part we look at some further examples. In particular, we study sentences apparently expressing their Rosser-provability, (...) their own${\rm{\Sigma }}_n^0$-truth or their own${\rm{\Pi }}_n^0$-truth. Finally we offer an assessment of the results of both papers. (shrink)

Before the twentieth century, the Universe was usually imagined as a large spatially extended thing unfolding in time. The past was fixed and the future was open; unfolding was conceived as an asymmetric process of coming into being. Relativity introduced a new vision in which space and time are presented together as a single four-dimensional manifold of events. That, together with the fact that the fundamental laws of our classical theories are symmetric in time, made understanding why the past and (...) future present themselves so differently in our experience one of the central challenges of physics. The last two centuries have seen a great deal of progress in understanding various of the so-called arrows of time: the thermodynamic arrow, the cosmological arrow, the arrow of knowledge or information. There remains an outstanding piece of this puzzle that has seen little progress, one that Roger Penrose described in his beautiful paper Singularities and Time-Asymmetry in 1979 as: “The arrow most difficult to comprehend … namely the feeling of relentless forward temporal progression, according to which potentialities seem to be transformed into actualities.”I will propose that the insight needed to resolve the problem involves taking into account that we are part of the universe and that any attempt to model it as a totality involves self-reference. I will argue specifically that self-reference, against the background of a thermodynamic gradient, creates an instability in an embedded agent’s ability to know the future or even treat it as a potential object of knowledge. That instability captures the sense in which the future remains for her perpetually open and the passage of time resolves openness into the fixity of fact. (shrink)

This paper argues that a certain type of self-referential sentence falsifies the widespread assumption that a declarative sentence's meaning is identical to its truth condition. It then argues that this problem cannot be assimilated to certain other problems that the assumption in question is independently known to face.

An anthology of previously unpublished essays from some of the most outstanding scholars working in philosophy, mathematics, and computer science today, _Self-Reference_ reexamines the latest theories of self-reference, including those that attempt to explain and resolve the semantic and set-theoretic paradoxes. With a thorough introduction that contextualizes the subject for students, this book will be important reading for anyone interested in the general area of self-reference and philosophy.

Central to the liar paradox is the phenomenon of 'self-reference'. The paradox typically begins with a sentence like: -/- (L): (L) is not true -/- Historically, doubts about the intelligibility of self-reference have been quite common. In some sense, though, these doubts were answered by Kurt Gödel's famous 'diagonal lemma'. This paper surveys some of the methods by which self-reference can be achieved, focusing first on purely syntactic methods before turning attention to the 'arithmetized' (...) methods introduced by Gödel. It's primary lesson is that we need to be more careful than we usually have been about self-reference. (shrink)

A dialogue among statements that try to explain to each other the mechanisms and peculiarities of self-referential assertions and, particularly, of their context-dependence.

This paper argues that Anscombe's arguments against appealing to the self-reference rule that 'I" refers to its producer are ineffective.

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)

If a semantically open language has no constraints on self-reference, one can prove an absurdity. The argument exploits a self-referential function symbol where the expressed function ends up being intensional in virtue of self-reference. The prohibition on intensional functions thus entails that self-reference cannot be unconstrained, even in a language that is free of semantic terms. However, since intensional functions are already excluded in classical logic, there are no drastic revisionary implications here. Still, (...) the argument reveals a new sort of intensional context, one which does not depend on a propositional attitude verb, a modal operator, an idiom like 'so called', etc. Moreover, since classical logicians do not seem aware of the potential danger with self-reference, a word of warning is in order. (shrink)

This volume contains a selection of nine essays with an interdisciplinary perspective. They were originally presented at the Sixth International Conference on Word and Music Studies, which was held at Edinburgh University in June 2007 and was organized by the International Association for Word and Music Studies (WMA). The contributions to this volume focus on self-reference in various systematic, historical and intermedial ways. Self-reference - including, as a special case, metareference (the self-conscious reflection on music, (...) literature and other medial concerns) - is explored, among others, in instrumental music by Mozart, Mahler and Satie, in the structure and performance of (meta-)operas, in operatic adaptations of drama and filmic adaptations of opera, as well as in intermedial novelistic references to music. The essays cover a historical range from the 18th century to the present and are of interest to literary and opera scholars and students, musicologists as well as all readers generally interested in medial self-reference and intermediality studies. (shrink)

I favour an analysis of selfhood which ties it to the possession of certain kinds of first-person knowledge, in particular de re knowledge of the identity of one's own conscious thoughts and experiences. My defence of this analysis will lead me to explore the nature of demonstrative reference to one's own conscious thoughts and experiences. Such reference is typically ‘direct’, in contrast to demonstrative reference to all physical objects, apart from those that are parts of one's own (...) body in which one can localize sensations or which are directly subject to one's will. My conclusion will be that the semantic distinction between ‘direct’ and ‘indirect’ demonstrative reference helps to delineate the metaphysical boundary between oneself and the rest of the world. But I do not contend that one is to be identified with one's own body: indeed, I shall try to show that one can know a priori that no such identity can obtain. (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)