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.

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)

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.

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 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)

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.

This paper explores the thesis that the concept of cultural techniques should be strictly limited to symbolic technologies that allow for self-referential recursions. Writing enables one to write about writing itself; painting itself can be depicted in painting; films may feature other films. In other words, cultural techniques are defined by their ability to thematize themselves; they are second-order techniques as opposed to first-order techniques like cooking or tilling a field. To illustrate his thesis, Macho discusses a sequence (...) of historical examples, from body signs and death masks to digital code and ID papers. These examples serve to reiterate another basic proposal that is already announced in the paper’s title. The recursive, self-observing qualities of cultural techniques make them a ‘technology of the self’ and thus render them indispensable for the generation, repetition and maintenance of identity. (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)

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)

The hypothesis of this paper is that language is one more Eigenform, the “external” description of which is impossible. It follows that the application of second-order cybernetics to Eigenform might be adequate. In this article, I would like to concentrate on one relatively small aspect of the idea of Eigenform suggested by Foerster, Kauffman and Spenser-Brawn. I will use Foerster`s recursive approach namely that neither observer nor the thing observed can precede each other, but instead mutually assume each other. In (...) my research, language would stand in the place of the observer, and in the place of the thing – the world itself. To specify further, I focus on the problem of noting, and in particular, on how signs correspond to things. Therefore, I will try to show that the sign and the object do not precede one another and do not exist isolated from each other, but on the contrary, condition each other. Thus, language creates the world of objects, but in turn, it is created by the world. Thus it is a model of self-referentiality, which arranges the form of language as Eigenform as the idea of “mutual referentiality,” as we see it in the relation between language and the world. (shrink)

It is proposed that subconscious retro-predictions in conjunction with brain state update cycles are instrumental in the physiological generation of conscious sensations and perceptions, and in all abstract thought. In this paper the hypothesis is supported by conducting a detailed a re-evaluation of the self-referential statements in Set Theory and Formal Logic known as antinomies. This study concludes that the recursive behavior exhibited by abstract enigmas such as "Russell’s Paradox" is analogous to the oscillations typical of bistable perceptual (...) phenomena. (shrink)

Results in recursion-theoretic inductive inference have been criticized as depending on unrealistic self-referential examples. J. M. Bārzdiņš proposed a way of ruling out such examples, and conjectured that one of the earliest results of inductive inference theory would fall if his method were used. In this paper we refute Bārzdiņš' conjecture. We propose a new line of research examining robust separations; these are defined using a strengthening of Bārzdiņš' original idea. The preliminary results of the new line (...) of research are presented, and the most important open problem is stated as a conjecture. Finally, we discuss the extension of this work from function learning to formal language learning. (shrink)

All information results from a process, intrinsic to living beings, of info-autopoiesis or information self-production; a sensory commensurable, self-referential feedback process immanent to Bateson’s ‘difference which makes a difference’. To highlight and illustrate the fundamental nature of the info-autopoietic process, initially, two simulations based on one-parameter feedback are presented. The first, simulates a homeostatic control mechanism (thermostat) which is representative of a mechanistic, cybernetic system with very predictable dynamics, fully dependent on an external referent. The second, simulates (...) a homeorhetic process, inherent to biological systems, illustrating a self-referenced, autonomous system. Further, the active incorporation/interference of viral particles by prokaryotic cells and the activation of CRISPR-Cas can be understood as info-autopoiesis at the most fundamental cellular level, as well as constituting a planetary network of self-referenced information. Moreover, other examples of the info-autopoietic nature of information are presented to show the generality of its applicability. In short, info-autopoiesis is a recursive process that is sufficiently generic to be the only basis for information in nature: from the single cell, to multi-cellular organisms, to consideration of all types of natural and non-natural phenomena, including tools and artificial constructions. (shrink)

There is a familiar derivation of G¨ odel’s Theorem from the proof by diagonalization of the unsolvability of the Halting Problem. That proof, though, still involves a kind of self-referential trick, as we in effect construct a sentence that says ‘the algorithm searching for a proof of me doesn’t halt’. It is worth showing, then, that some core results in the theory of partial recursive functions directly entail G¨ odel’s First Incompleteness Theorem without any further self-referential (...) trick. (shrink)

Brain functions are stochastic processes without intentionality whereas mind emerges from brain functions as a Hegelian “change from quantity”, that is, on the order of 1012 profusely interconnected neurons, “into a new quality”: the collective phenomenon of the brain's self-experience. This self-referential and self-observing quality we have in mind is capable of (recursively) observing its self-observations, i.e., interpreting change that is meaningful in relation to itself. The notion of self-interpretation embodies the idea of a (...) “hermeneutic circle”, that is, (in interpretation theory) the treatment of the whole in relation to its parts. (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.

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)

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)

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)

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)

This is a paper about The Causal Self-Referential Theory of Perception. According to The Causal Self-Referential Theory as developed by above all John Searle and David Woodruff Smith, perceptual content is satisfied by an object only if the object in question has caused the perceptual experience. I argue initially that Searle's account cannot explain the distinction between hallucination and illusion since it requires that the state of affairs that is presented in the perceptual experience must exist (...) in order for the perception to be veridical. Smith's account is interestingly different in that the descriptive content, i.e. the content that presents the perceptual object as having certain properties, does not determine the object of the experience. His account consequently does not require that the state of affairs that is presented in perception exists in order for the perception to have an object. Smith argues instead that perceptual reference is determined by a specific kind of demonstrative content. In this paper it is argued that Smith's account of demonstrative content is too indeterminate and in certain circumstances prescribes the wrong object. It is subsequently argued that the theory of demonstrative content can be modified so as to avoid these consequences. This modification involves deriving the conditions of satisfaction of seeing an object from the conditions of satisfaction of seeing the shape of the object, where the shape of the object is conceived of as a particularized property, what is also called a ‘trope’. (shrink)

This contribution investigates the idea that an act of signification can be understood in terms of the self-referentiality that is typical of the biological organization. The capacity of a living being to interpret and appreciate its own environment can be understood as being grounded in its ability to perform self-referential experiences. We may call this the living being’s capacity of sense. In any act that generates sense, it is possible to distinguish a process of signification from its (...) outcome, but such a distinction between logical levels inevitably demands an external observer’s point of view. Hence, the concept of ‘subjectivity’ can be defined in terms of an absence of such distinction between logical levels. This absence is considered pivotal both for the self-referential organization of the living and for the generation of sense. A case example from the field of psychotherapy is added to illustrate the distinction as well as the non-distinction between logical levels of description. (shrink)

All the known non-self-referential paradoxes share a reference pattern of Yablo’s paradox in that they all necessarily contain infinitely many sentences, each of which refers to infinitely many sentences. This raises a question: Does the reference pattern of Yablo’s paradox underlie all non-self-referential paradoxes, just as the reference pattern of the liar paradox underlies all finite paradoxes? In this regard, Rabern et al. [J Philos Logic 42(5): 727–765, 2013] prove that every dangerous acyclic digraph contains infinitely (...) many points with an infinite out-degree. Building upon their work, this paper extends Rabern et al.’s result to the first-order arithmetic language with a primitive truth predicate, proving that all reference digraphs for non-self-referential paradoxes contain infinitely many sentences of infinite out-degree (called “social sentences”). We then strengthen this result in two respects. First, among these social sentences, infinitely many appear in one ray. Second, among these social sentences, infinitely many have infinitely many out-neighbors, none of which will eventually get to a sink. These observations provide helpful information towards the following conjecture proposed by Beringer and Schindler [Bull. of Symb. Logic 23(4): 442–492, 2017]: every dangerous acyclic digraph contains the Yablo digraph as a finitary minor. (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.

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)

The strategy I adopt in this paper is as follows. First I seek to show that the authors’ formulation of the notion of "determinism" is defective because it elides some important distinctions. Second, I go on to argue that these defects vitiate some of the contentions made in the paper and alert us to the inadequacy of the self-referential argument developed in it.

In his paper, “On paradox without self-reference”, Neil Tennant proposed the conjecture for self-referential paradoxes that any derivation formalizing self-referential paradoxes only generates a looping reduction sequence. According to him, the derivation of the Liar paradox in natural deduction initiates a looping reduction sequence and the derivation of the Yablo's paradox generates a spiral reduction. The present paper proposes the counterexample to Tennant's conjecture for self-referential paradoxes. We shall show that there is a (...) derivation of the Liar paradox which generates a spiraling reduction procedure. Since the Liar paradox is a self-referential paradox, the result is a counterexample to his conjecture. Tennant has believed that classical reductio has no essential role to formalize paradoxes. As our counterexample applies the rule of classical reductio, he may reject the counterexample. In this sense, it will be briefly argued that classical reductio and his rules for the liar sentence share some inferential role. If classical reductio should not be used in paradoxical reasoning, neither should be his rules for the liar sentence. (shrink)

Non-classical logic via approximation of self-referential sentences by dynamical systems are consistently presented. The new 6-valued truth values (here A=Liar, V=TruthTeller) are presented as a function of the classical truth values xi ∈ {0,1}, which resulted in a philosophical standpoint known as Suszko’s Thesis. Three-valued truth tables were created corresponding to Priest’s tables of the same name. In the process of constructing 4-valued truth tables, two more new truth values (va, av) were revealed that do not coincide with (...) the four original ones. Therefore, the closed tables turned out to be 6-valued. Prof Dunn’s 4-valued truth tables are compared with our 4-valued truth tables. De Morgan’s laws are confirmed by six-valued truth tables. Constructed 3-, 4- and 6-valued lattices obeying De Morgan’s laws. (shrink)

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)

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.

Anxiety disorders represent the most common class of mental illness. In fact, approximately one-third of adults report clinically significant symptoms of anxiety (Kessler et al., 2012), of which sy...

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)

Is postlapsarian sexual desire primarily altruistic or disordered? This paper utilizes the resources in the thought of St. Thomas Aquinas and in the contemporary magisterium to argue that recent phenomena such as the #MeToo movement underscore the inherently unstable and aggressive nature of sexual desire when it is uprooted from its natural end. Aquinas highlights three aspects of desire that more sex-positive accounts of sexuality would do well to heed: its natural infinity, its self-referential nature, and its power (...) of rationalization. By directing the motor of desire toward its natural ends, virtue—led by reason—can redirect desire away from self and toward the 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)

I argue that a self-referential sense of humor is positively self-accepting by acknowledging imperfection, abnormality, or average status, without genuinely intending ridicule on oneself. Instead, standards of perfection, normality, and greatness are the implicit targets of ridicule, which can provide a form of bonding among those having this sense of humor, who can then find commonality amongst themselves and relief from the pressure of those exacting standards. This self-accepting sense of humor helps to make life more (...) meaningful by facilitating contentment with imperfection both with respect to oneself and one’s situation. While a sense of humor can certainly be helpful for improving character, a perfectionist argument such as this should be balanced by acknowledgement of the value that can be gained from simply accepting ourselves just as we are. (shrink)