Self-reference and the Limits of Thought. This paper explores the connection between the natural language and a formal language from a particular point of view: self-referential constructions. Such constructions lead to some kind of limits of thought, either in the form of paradoxical constructions (Liar-type or Grelling-type), or in the form of the so called limitative theorems in mathematical logic (e.g. Gödel’s theorem). By deriving Gödel’s significant results from paradoxical constructions the limitative character of such self-referential (...) constructions is preserved, but they open the ways for a new representation of a great variety of arguments in the field of logic, mathematics and philosophy. (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)

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)

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)

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).

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)

Cognitive theories of depression assert that negative self-referent cognition has a causal role in the development and maintenance of depression symptoms, but few studies have examined temporal associations between these constructs using intensive, longitudinal sampling strategies. In three samples of undergraduate students, we examined associations between change in self-referent processing and depression across 5 daily assessments (Sample 1, N = 303, 1,194 measurements, 79% adherence), 7 daily assessments (Sample 2, N = 313, 1,784 measurements, 81% adherence), and 7 (...) weekly assessments (Sample 3; N = 155, 833 measurements, 81% adherence). Random intercept cross-lagged panel models indicated large cross-lagged effects in two of the three samples (Samples 1 and 3 but not Sample 2), such that more negative self-referent thinking than usual was significantly associated with a subsequent increase in depression symptoms at the next time lag. Notably, change in depression from usual was not associated with increases in negative self-referent processing at the next time point in any sample. These findings suggest that change in negative self-referent processing may be causally linked to future increases in depression on a day-to-day and week-to-week basis, although confidence in this conclusion is tempered somewhat by a lack of replication in Sample 2. (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.

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)

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)

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)

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)

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)

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.

A character in a novel pulls a book from a shelf and starts to read about himself in a novel. Puzzling, but what does it really mean? Does it force us to fundamentally reconsider the nature of fiction? Does it turn the novel into a kind of liar's paradox? And what exactly is a liar's paradox, anyway? Does the liar's paradox, despite its name, have anything to do with lying? What, if anything, does the liar's paradox have to tell us (...) about reality, beliefs, and fictional discourse? (shrink)

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.

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.

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)

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)

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

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)

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)

The quantum functionalist model of mentation provides an explanation of conscious and unconscious perception without the postulation of a central processing unit . Based on Goswami's idealist interpretation of quantum mechanics, the quantum model posits a dual quantum/classical system for the mind-brain with which consciousness is linked via self-reference. A comparative analysis of word-sense disambiguation data is conducted with a cognitive science model derived from the Posner and Snyder facilitation and inhibition and the Rummelhart, McClelland, and PDP group's (...) parallel-distributed-processing theories. A new line of experiments is proposed which distinguishes between the two models. (shrink)

In his paper on the incompleteness theorems, Gödel seemed to say that a direct way of constructing a formula that says of itself that it is unprovable might involve a faulty circularity. In this note, it is proved that ‘direct’ self-reference can actually be used to prove his result.

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 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)

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. (shrink)

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)

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)