Graham Priest has argued that Yablo’s paradox involves a kind of ‘hidden’ circularity, since it involves a predicate whose satisfaction conditions can only be given in terms of that very predicate. Even if we accept Priest’s claim that Yablo’s paradox is self-referential in this sense—that the satisfaction conditions for the sentences making up the paradox involve a circular predicate—it turns out that there are paradoxical variations of Yablo’s paradox that are not circular in this sense, since they involve (...) satisfaction conditions that are not recursively specifiable, and hence not recognizable in the sense required for Priest’s argument. In this paper I provide a general recipe for constructing infinitely many such noncircular Yabloesque paradoxes, and conclude by drawing some more general lessons regarding our ability to identify conditions that are necessary and sufficient for paradoxically more generally. (shrink)

Graham Priest has argued that Yablo’s paradox involves a kind of ‘hidden’ circularity, since it involves a predicate whose satisfaction conditions can only be given in terms of that very predicate. Even if we accept Priest’s claim that Yablo’s paradox is self-referential in this sense—that the satisfaction conditions for the sentences making up the paradox involve a circular predicate—it turns out that there are paradoxical variations of Yablo’s paradox that are not circular in this sense, since they involve (...) satisfaction conditions that are not recursively specifiable, and hence not recognizable in the sense required for Priest’s argument. In this paper I provide a general recipe for constructing infinitely many such noncircular Yabloesque paradoxes, and conclude by drawing some more general lessons regarding our ability to identify conditions that are necessary and sufficient for paradoxically more generally. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Is Literature Self-Referential?Eric MillerIIs literary language necessarily self-referential? And does this put paradox at the heart of literature? For at least two decades now, affirmative answers to both questions have been articles of faith among critics in the structuralist and poststructuralist mainstream. Literature’s ineluctable paradoxicality attracts us so because a paradox suggests that there are limits to human rationality, and thus strikes a blow for (...) literature and against science. Paradox ensures literature its own special realm, safe from the culturally imperialistic inroads of science’s orderly, rational-empirical constructions. Literature thus gets to be seen as “bigger” than reason, because only literature can live with paradox, and thus only literature reveals those “deeper” truths of contradiction-ridden human existence, whereas science can never penetrate beyond rational manipulations of phenomenal surfaces. Indeed, for anyone who holds all human existence to be fundamentally paradoxical, this special capacity makes literature the only genuine, demystified species of human knowledge. In the war between C. P. Snow’s Two Cultures, a war humanists are now losing badly, we like to regard paradox as our ultimate weapon.Belief in the paradoxicality of literature may also be found among the New Critics, 1 and in fact goes back at least to the Romantics, 2 but they did not derive this belief from a necessary self-referentiality of literary language. This newer way of deriving paradox appears to offer several competitive advantages. Self-reference seems to be the ultimate version of “art for art’s sake”: if all literary language is necessarily self-referential, then literature must be something totally self-contained, and is thus legitimized solely in and through itself. In addition, deriving [End Page 475] literature’s paradoxicality from self-reference seems to ground it in the same conceptual realm as mathematical logic, and thus tempts us to claim for literature a “rigor” normally conceded only to logic, mathematics, and theoretical physics. Self-referentiality would thus seem both to protect literature’s autonomy and to raise its cultural status into the company of mathematics and science.But it is a trap. For behind this new strategy lurks a capitulation to the underlying conceptual scheme of natural science, and literature thus comes to be conceived, in effect, as a science. Self-reference is, after all, still a kind of reference; paradox is still a kind of truth-relational construction;—and truth-relations built around reference constitute the correspondence theory of truth. From such a foundational commitment to reference and correspondence-truth, flows the rest of the scientific worldview: the dualism of referring expression and referent, word and object, sentence and fact, theory and data, language and world, culture and nature. The presentation of literature as a quasi-negation of this ontology changes nothing. The dualism of reference still functions as literature’s conceptual starting point, as its arche. We only appear to be defining a peculiar and radically distinct sphere for literature when we insist on its self-referentiality, on the (recursive) identity, for it, of referring expression and referent. For, this is still to treat the conceptual distinction between the two as foundational, and literature thereby tacitly assimilates science’s fundamental categorial division: the referential language-world duality of correspondence truth. Indeed, literature thus comes to live even more completely in the margins of science: it will have no essence of its own; it will differ at most in being a photo-negative image of science’s positiv(istic) project. In Snow’s war, self-reference is a Trojan horse.With self-reference as the essence of literature, we are thus staking our reputations on literature’s being a special field of formalizable “knowledge about...,” rather than, say, a quality or kind or realm of possible experience—which is to adopt science’s understanding of what is important. Matters are only made worse by that other attempt to define literary studies as a negation of the theory-data dualism of natural science: the poststructuralist denial of the distinction between criticism and literature. For the institutional need professional critics have to be seen as a discipline with a method and a subject, as a form of “knowledge about,” hardly disappears with... (shrink)

The aim of this paper is to introduce a formal system STW of self-referential truth, which extends the classical first-order theory of pure combinators with a truth predicate and certain approximation axioms. STW naturally embodies the mechanisms of general predicate application/abstraction on a par with function application/abstraction; in addition, it allows non-trivial constructions, inspired by generalized recursion theory. As a consequence, STW provides a smooth inner model for Myhill's systems with levels of implication.

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. (shrink)

The proposed model overlooks the self-referential and self-perpetuating nature of ownership intuitions. Human knowledge is primarily formed through social interaction within power dynamics. Accordingly, we suggest that legitimate ownership of one object can influence perceptions of legitimate ownership of another object. Ultimately, we argue that ownership intuitions are not independent but embedded in a self-referential system that perpetuates inequality.

The author compares the theoretical elements of her grounded theory, Protecting Self: Experiencing Organizational Change, with autopoiesis, a biological theory of living systems. Autopoiesis, meaning self-production, is a closed system that recursively generates the same organization, components, and network of processes from which they are produced. A cautious extrapolation of theoretical similarities between the two theories is presented, including self-referentiality, self-maintenance, circularity, individuality, and the maintenance of identity. The author concludes that this comparison provides a thought-provoking (...) argument that supports the difficult process of individual and organizational learning, growth, and change. (shrink)

Can you find an xy-equation that, when graphed, writes itself on the plane? This idea became internet-famous when a Wikipedia article on Tupper’s self-referential formula went viral in 2012. Under scrutiny, the question has two flaws: it is meaningless (it depends on fonts) and it is trivial. We fix these flaws by formalizing the problem.

Are there ‘self-referential’ propositions? That is, propositions that say of themselves that they have a certain property, such as that of being false. There can seem reason to doubt that there are. At the same time, there are a number of reasons why it matters. For suppose that there are indeed no such propositions. One might then hope that while paradoxes such as the Liar show that many plausible principles about sentences must be given up, no such fate (...) will befall principles about propositions. But the existence of self-referential propositions would dash such hopes. Further, the existence of such propositions would also seem to challenge the widespread claim that Liar sentences fail to express propositions. The aim of this paper is thus to settle the question–at least given an assumption. In particular, I argue that if propositions are structured, then self-referential propositions exist. (shrink)

The aim of this paper is to examine a special subgroup of emotion: self-referential emo- tions such as shame, pride and guilt. Self-referential emotions are usually conceptualized as (i) essentially involving the subject herself and as (ii) having complex conditions such as the capacity to represent others’ thoughts. I will show that rather than depending on a fully fledged ‘theory of mind’ and an explicit language-based self-representation, (i) pre-forms of self-referential emotions appear at (...) early developmental stages already exhib- iting their characteristic structure of the intentional object of the emotion being identical with or intricately related to the subject experiencing the emotional state and that (ii) they precede and substantially contribute to the development of more complex representations and to the development of a self-concept, to social interaction and to ways of understand- ing of other minds. (shrink)

We study the structure of families of theories in the language of arithmetic extended to allow these families to refer to one another and to themselves. If a theory contains schemata expressing its own truth and expressing a specific Turing index for itself, and contains some other mild axioms, then that theory is untrue. We exhibit some families of true self-referential theories that barely avoid this forbidden pattern.

Following the phenomenology that is revealed by the emergent structure of consciousness, the path will lead to the acknowledgement of consciousness having a self-referential aspect. By following phenomenological clues, properties of self-reference will be revealed. The two most prominent properties of self-reference will be shown to be inclusion and transcendence that will be shown to be found everywhere in the phenomenology of consciousness. Also, self-reference will turn out to be unformalizable, this imposing limits on what (...) a theory of consciousness can ever achieve. The unformalizability of self-reference would be shown to be because self-reference: is itself, includes itself, and transcendes itself, all at the same time. Nevertheless, unformalizability will be shown to be an essential feature needed to bring essences into existence. (shrink)

Episodic memory has a distinctive phenomenology. One way to capture what is distinctive about it is by using the notion of mental time travel: When we remember some fact episodically, we mentally travel to the moment at which we experienced it in the past. This way of distinguishing episodic memory from semantic memory calls for an explanation of what the experience of mental time travel is. In this paper, I suggest that a certain view about the content of memories can (...) shed some light on the experience of mental time travel. This is the view that, when a subject remembers some fact episodically, their memory represents itself as coming from a perception of that fact. I propose that the experience of mental time travel in memory is the experience of representing one of the elements in this complex content, namely, the past perceptual experience of the remembered fact. In defence of this proposal, I offer two considerations. Firstly, the proposal is consistent with the idea that memories enjoy a temporal phenomenology (specifically, a feeling of pastness). Secondly, the proposal is consistent with the possibility that some of our other cognitive capacities might yield an experience of mental time travel which can be oriented towards the future. I argue that the received conception of mental time travel is in tension with those two ideas. (shrink)

I suggest two valid and sound arguments refuting physicalism, whether it is reductive or supervenience physicalism. The first argument is a self-referential one that is not involved with any self-referential inconsistency. The second argument demonstrates that physicalism is inescapably involved with self-referential inconsistency. Both arguments show that arguments and propositions (to be distinguished from sentences) are not physical existents. They are rather mental existents that are not reducible to any physical existent and do not (...) supervene on anything physical. From these two arguments, it clearly follows that any physicalist argument or proposition, as a mental existent, is self-refuting. (AN PHL2326365) Subjects: EXISTENTS; INCONSISTENCY; METAPHYSICS; MIND; PHYSICALISM; SELF-REFERENCE. (shrink)

The Ouroboros Model features a biologically inspired cognitive architecture. At its core lies a self-referential recursive process with alternating phases of data acquisition and evaluation. Memory entries are organized in schemata. The activation at a time of part of a schema biases the whole structure and, in particular, missing features, thus triggering expectations. An iterative recursive monitor process termed "consumption analysis" is then checking how well such expectations fit with successive activations. Mismatches between anticipations based on previous experience (...) and actual current data are highlighted and used for controlling the allocation of attention. In case no directly fitting filler for an open slot is found, activation spreads more widely and includes data relating to the actor, and Higher-Order Personality Activation, HOPA, ensues. It is briefly outlined how the Ouroboros Model produces many diverse characteristics and thus addresses established criteria for consciousness. Coarse-grained relationships to selected previous conceptualizations of consciousness and a sketch of how the Ouroboros Model could shed light on current research themes in artificial general intelligence and consciousness conclude this paper. (shrink)

The Gödel–Artemov framework offered a formalization of the Brouwer–Heyting–Kolmogorov semantics of intuitionistic logic via classical proofs. In this framework, the intuitionistic propositional logic IPC is embedded in the modal logic S4, S4 is realized in the Logic of Proofs LP, and LP has a provability interpretation in Peano Arithmetic. Self-referential LP-formulas of the type ‘t is a proof of a formula ϕ containing t itself’ are permitted in the realization of S4 in LP, and if such formulas are (...) indeed involved, it is then necessary to use fixed-point arithmetical methods to explain intuitionistic logic via provability. The natural question of whether self-referentiality can be avoided in realization of S4 was answered negatively by Kuznets who provided an S4-theorem that cannot be realized without using directly self-referential LP-formulas. This paper studies the question of whether IPC can be embedded in S4 and then realized in LP without using self-referential formulas. We consider a general class of Gödel-style modal embeddings of IPC in S4 and by extending Kuznetsʼ method, show that there are IPC-theorems such that, under each such embedding, are mapped to S4-theorems that cannot be realized in LP without using directly self-referential formulas. Interestingly, all double-negations of tautologies that are not IPC-theorems, like ¬¬, are shown to require direct self-referentiality. Another example is found in IPC→, the purely implicational fragment of IPC. This suggests that the BHK semantics of intuitionistic logic is intrinsically self-referential. (shrink)

This thesis focuses on expressively rich languages that can formalise talk about probability. These languages have sentences that say something about probabilities of probabilities, but also sentences that say something about the probability of themselves. For example: (π): “The probability of the sentence labelled π is not greater than 1/2.” Such sentences lead to philosophical and technical challenges; but can be useful. For example they bear a close connection to situations where ones confidence in something can affect whether it is (...) the case or not. The motivating interpretation of probability as an agent's degrees of belief will be focused on throughout the thesis. -/- This thesis aims to answer two questions relevant to such frameworks, which correspond to the two parts of the thesis: “How can one develop a formal semantics for this framework?” and “What rational constraints are there on an agent once such expressive frameworks are considered?”. (shrink)

베르그손이 『의식에 직접 주어진 것들에 관한 시론』에서 발견하고 규정한 변화로서의 지속은 『물질과 기억』을 거치면서 과거의 보존으로 그리고 『창조적 진화』로 가면서 자기에 의한 자기 창조로 계속적으로 재규정되는 과정을 볼 수 있다. 이 세 가지 특징은 이미 첫 저서에서 그 맹아를 볼 수 있고 상당히 일관된 논리로 서술되고 있다. 우리는 이를 ‘자기지시성’(autoréférentialité)이라는 개념으로부터 재구성해 보고 이를 통해 지속의 개념이 점차 명료화되는 동시에 확장되는 과정을 살펴보고자 한다. 이를 위해 우리는 변화에 대한 『시론』의 분석에서 자기지시적 운동의 세 측면을 구분하고 이것이 새로운 규정으로 이어지는 실마리를 (...) 드러낸 후에 『물질과 기억』의 분석에서 물질적 현재로의 열림이라는 계기와 더불어 자기지시성이 창조적 의미로 확장되는 실마리를 살펴본다. (shrink)

Contrary to the early media semioticians' claim that semiotics is a metalanguage of the media and the media are a metalanguage of reality, the present paper gives evidence of how the media represent a world that is itself highly mediated. It is argued that media representations involve self-referential loops in which communication turns out to be communication about communication, reports are reports about reports, and mediations are mediations of mediations. Self-reference in the media is interpreted as a (...) symptom of postmodernity with its tendency towards historical self-reflection in scenarios in which even catastrophic current events are being interpreted as mere media events or even déjà-vu scenarios in a culture in which everything seems to have been said and shown before. (shrink)

The proof of the Second Incompleteness Theorem consists essentially of proving the uniqueness and explicit definability of the sentence asserting its own unprovability. This turns out to be a rather general phenomenon: Every instance of self-reference describable in the modal logic of the standard proof predicate obeys a similar uniqueness and explicit definability law. The efficient determination of the explicit definitions of formulae satisfying a given instance of self-reference reduces to a simple algebraic problem-that of solving the corresponding (...) fixed-point equation in the modal logic. We survey techniques for the efficient calculation of such fixed-points. (shrink)

In this transdisciplinary article which stems from philosophical considerations (that depart from phenomenology—after Merleau-Ponty, Heidegger and Rosen—and Hegelian dialectics), we develop a conception based on topological (the Moebius surface and the Klein bottle) and geometrical considerations (based on torsion and non-orientability of manifolds), and multivalued logics which we develop into a unified world conception that surmounts the Cartesian cut and Aristotelian logic. The role of torsion appears in a self-referential construction of space and time, which will be further (...) related to the commutator of the True and False operators of matrix logic, still with a quantum superposed state related to a Moebius surface, and as the physical field at the basis of Spencer-Brown’s primitive distinction in the protologic of the calculus of distinction. In this setting, paradox, self-reference, depth, time and space, higher-order non-dual logic, perception, spin and a time operator, the Klein bottle, hypernumbers due to Musès which include non-trivial square roots of ±1 and in particular non-trivial nilpotents, quantum field operators, the transformation of cognition to spin for two-state quantum systems, are found to be keenly interwoven in a world conception compatible with the philosophical approach taken for basis of this article. The Klein bottle is found not only to be the topological in-formation for self-reference and paradox whose logical counterpart in the calculus of indications are the paradoxical imaginary time waves, but also a classical-quantum transformer (Hadamard’s gate in quantum computation) which is indispensable to be able to obtain a complete multivalued logical system, and still to generate the matrix extension of classical connective Boolean logic. We further find that the multivalued logic that stems from considering the paradoxical equation in the calculus of distinctions, and in particular, the imaginary solutions to this equation, generates the matrix logic which supersedes the classical logic of connectives and which has for particular subtheories fuzzy and quantum logics. Thus, from a primitive distinction in the vacuum plane and the axioms of the calculus of distinction, we can derive by incorporating paradox, the world conception succinctly described above. (shrink)

One way speakers can refer to themselves in conversation is with a stressed first-person pronoun accompanied by a movement of the hand to or toward the chest. This can be produced alone or in tandem with a reference and gesture to another person. Close analysis of several instances of self-referential gesture demonstrates that this form of self-reference is designed to achieve interactional work beyond simple reference, specifically relational disaggregation and self-referential extraction.

Glas's rich article makes several useful points about both anxiety and enactivism, and about how enactivism can help to conceptualize anxiety in a suitably complex way. I agree that we need to characterize anxiety as an embedded, context-sensitive and temporally evolving phenomenon with layered symptoms. As Glas points out, the enactive approach has useful conceptual tools for doing so, because of its incorporation of the theoretical apparatus of dynamical systems theory. I am sympathetic with most of what Glas says about (...) this point, so I shall not dwell on it any further.I want to focus instead on Glas's discussion of self-referentiality, which I found interesting and valuable but also in need of further... (shrink)

As computational systems burgeon with advancing artificial intelligence (AI), the deterministic frameworks underlying them face novel challenges, especially when interfacing with self-modifying code. The Executioner Paradox, introduced herein, exemplifies such a challenge where a deterministic Executioner Machine (EM) grapples with self-aware and self-modifying code. This unveils a self-referential dilemma, highlighting a gap in current deterministic computational frameworks when faced with self-evolving code. In this article, the Executioner Paradox is proposed, highlighting the nuanced interactions between (...) deterministic decision-making and self-aware code, and the ensuing challenges. This article advocates for a re-evaluation of existing deterministic frameworks, emphasizing the need for adaptive decision-making mechanisms in computational systems. By dissecting the Executioner Paradox, the aim is to foster a robust discussion on evolving deterministic frameworks to accommodate the dynamic nature of self-modifying code, thereby contributing a forward-looking lens to the discourse on computational systems amidst advancing AI. (shrink)

The model of self-referential truth presented in this paper, named Revision-theoretic supervaluation, aims to incorporate the philosophical insights of Gupta and Belnap’s Revision Theory of Truth into the formal framework of Kripkean fixed-point semantics. In Kripke-style theories the final set of grounded true sentences can be reached from below along a strictly increasing sequence of sets of grounded true sentences: in this sense, each stage of the construction can be viewed as an improvement on the previous ones. I (...) want to do something similar replacing the Kripkean sets of grounded true sentences with revision-theoretic sets of stable true sentences. This can be done by defining a monotone operator through a variant of van Fraassen’s supervaluation scheme which is simply based on ω-length iterations of the Tarskian operator. Clearly, all virtues of Kripke-style theories are preserved, and we can also prove that the resulting set of “grounded” true sentences shares some nice features with the sets of stable true sentences which are provided by the usual ways of formalising revision. What is expected is that a clearer philosophical content could be associated to this way of doing revision; hopefully, a content directly linked with the insights underlying finite revision processes. (shrink)

The paper discusses the strengths and weaknesses of arguments of proper self-reference, arguments of self-application and arguments of iterative application. A formalization of the underlying logical structure of these arguments helps to identify the implicit premises on which these arguments rest. If the premises are plausible, the conclusions reached by these arguments must be taken seriously. In particular, all the types of argument discussed, when sound, show that certain theories that purport to be universally applicable are not tenable. (...) The argumentative power of such arguments then depends on how devastating it is for the theories in question to give up their claim of universal applicability. (shrink)

Augustine was undeniably a dogmatic thinker, but he also had an “aporetic side” which makes him more relevant to Christian philosophers today than isgenerally recognized. Augustine’s first experience of reading philosophy came from Cicero’s Hortensius, from which Augustine gained an appreciation for philosophical scepticism which he never lost. Thus, in all of his works and in all periods of his life, Augustine’s characteristic way of doing philosophy is aporetic, rather than either systematic or speculative. Paradoxically, Augustine’s faith in the truth (...) of Holy Scripture and Church Doctrine gave him a freedom to explore theological and philosophical conundra and, if he could not resolve them, admit frankly that he could not do so. Like Socrates, Augustine was wise partly because he admitted to being puzzled about things that others took for granted. Some of the perplexities which occupied him are: (a) the nature of time; (b) whether it is possible to show someone (without using words) what walking is if one is already walking; (c) whether one is responsible for what one does in one’s dreams; (d) whether one can think about sadness or pleasure by having an image of it in one’s mind, but without experiencing any sadness or pleasure in the thought, and (e) (perhaps most famously, in the Confessions) how one can want something that he does not believe to be good. (shrink)

Augustine was undeniably a dogmatic thinker, but he also had an “aporetic side” which makes him more relevant to Christian philosophers today than isgenerally recognized. Augustine’s first experience of reading philosophy came from Cicero’s Hortensius, from which Augustine gained an appreciation for philosophical scepticism which he never lost. Thus, in all of his works and in all periods of his life, Augustine’s characteristic way of doing philosophy is aporetic, rather than either systematic or speculative. Paradoxically, Augustine’s faith in the truth (...) of Holy Scripture and Church Doctrine gave him a freedom to explore theological and philosophical conundra and, if he could not resolve them, admit frankly that he could not do so. Like Socrates, Augustine was wise partly because he admitted to being puzzled about things that others took for granted. Some of the perplexities which occupied him are: (a) the nature of time; (b) whether it is possible to show someone (without using words) what walking is if one is already walking; (c) whether one is responsible for what one does in one’s dreams; (d) whether one can think about sadness or pleasure by having an image of it in one’s mind, but without experiencing any sadness or pleasure in the thought, and (e) (perhaps most famously, in the Confessions) how one can want something that he does not believe to be good. (shrink)

Following F. William Lawvere, we show that many self-referential paradoxes, incompleteness theorems and fixed point theorems fall out of the same simple scheme. We demonstrate these similarities by showing how this simple scheme encompasses the semantic paradoxes, and how they arise as diagonal arguments and fixed point theorems in logic, computability theory, complexity theory and formal language theory.

What is it, precisely, that an agent intends when he intends, as we might say, to clean his stove today? What is the content of his intention? In recent years, Gilbert Harman and John Searle have maintained that all intentions are self-referential -- that is, that an adequate expression of the content of any intention makes essential reference to the intention whose content is being expressed. I shall call this the self-referentiality thesis (SRT). Harman, in his paper (...) 'Practical Reasoning', argues that "the intention to do A is the intention that, because of that very intention, one will do A". Searle, in his book, Intentionality, contends similarly that the "Intentional content" of an agent's "prior intention" to A identifies that very intention as a cause of the agent's (prospective) A-ing. In Sections 1-3 below, I show that the main arguments for the SRT are unsuccessful and that the thesis is problematic. In Section 4, I sketch an alternative account of the contents of intentions. (shrink)