A number of contemporary philosophers think that the unqualified statement “X is unspeakable” faces the danger of self-referential absurdity: if this statement is true, it must simultaneously be false, given that X is speakable by the predicate word “unspeakable.” This predicament is in this chapter formulated as an argument that I term the “ineffability paradox.” After examining the Buddhist semantic theory of apoha (exclusion) and an apoha solution to the issue, I resort to a few Chinese Buddhist and (...) Hindu philosophical materials to rationally reconstruct a strategy for resolving the paradox. By introducing the mode of expression termed “indication,” together with the relevant notions of superimposition and of gesturing beyond the horizon, I show that expressing the ineffable does not necessarily involve irresoluble contradiction. It is also suggested that philosophers may need to acknowledge the relevance of the notion of ineffability for contemporary philosophizing. (shrink)

Saying that x is ineffable seems to be paradoxical – either I cannot say anything about x, not even that it is ineffable – or I can say that it is ineffable, but then I can say something and it is not ineffable. In this article, I discuss Alston’s version of the paradox and a solution proposed by Hick which employs the concept of formal and substantial predicates. I reject Hick’s proposal and develop a different account based on some (...) passages from Pseudo-Dionysius’ Mystica Theologia. ‘God is ineffable’ is a metalinguistic statement concerning propositions about God: not all propositions about God are expressible in a human language. (shrink)

In this paper, I analyze the concept of ineffability: what does it mean to say that something cannot be said? I begin by distinguishing ineffability from paradox: if something cannot be said truly or without contradiction, this is not an instance of ineffability. Next, I distinguish two different meanings of ‘saying something’ which result from a fundamental ambiguity in the term ‘language’, viz. language as a system of symbols and language as a medium of communication. Accordingly, (...) ‘ineffability’ is ambiguous, too, and we should make a distinction between weak and strong ineffability. Weak ineffability is rooted in the deficiencies of a particular language while strong ineffability stems from the structure of a particular cognitive system and its capacities for conceptual mental representation. Mental contents are only sayable if we are able to conceptualize them and then create signs to represent them in communication. (shrink)

While physicists know how to use quantum mechanics, there is no consensus on what quantum mechanics is a mechanics of. The aim of this paper is to introduce the beginning of what might turn out to be an interpretation of quantum mechanics—one that leaves all calculated probabilities intact. The basic idea is that quantum mechanics describes the objective world, but there must be added to it ineffable variables, one of which is the temporal 'now'. Ineffable variables are not 'hidden variables'.

Ineffability is a long-time partner of the philosophy of religion and mysticism. Through apophatic conceptions of the divine, it can act to guarantee the transcendence of the divine, elevate it to something beyond our conceptions. It has also held the central role in defining if not the nature, then at least the characteristics of mystical experience. Sometimes it is that which affirms the unique nature of mystical experience, and sometimes it is what challenges the concept of mysticism as incoherent (...) and paradoxical. In this article, I will explore if there could be a Being Ineffable that unites both the mystical experience and its (purportedly) transcendent object, while acknowledging the problem of coherence that ineffability entails. I will do so by forming an argument for ineffability that attempts to both validate and define absolute ineffability as the point of convergence between three meanings of Being Ineffable: as a definition of absolute (ineffability), as a mystical experience of it, and finally, as the Ineffable, that is, the God/Absolute/Ultimate; all the meanings are held together by an argument from ineffability—a permeating and silently expressed attempt to turn ineffability from its usual role of a negation into a necessary affirmation. (shrink)

This paper is about the relevance of the ineffable and the singular to hermeneutics. I respond to standard criticisms of Friedrich Schleiermacher by Karl Barth and Hans-Georg Gadamer in order to clarify his understanding of language, interpretation, and religion. Schleiermacher’s “indicative hermeneutics” is developed in the context of the ethical significance of communication and the ineffable. The notion of trace is employed in order to interpret the paradox of speaking about that which cannot be spoken. The trace is not (...) a brute singularity but bears a fundamental relationship to the word—and ultimately the word of God—for Schleiermacher. (shrink)

Seeing of emptiness and mystical experience — the case of Madhyamaka: The problem of Buddhist religiosity is one of the most classic problems of Buddhist studies. A particular version of this issue is the search for mystical experience in Buddhism. This is due to the conviction that mystical experience is the essence of religious experience itself. The discovery of such an alleged experience fuels comparative speculations between Buddhism and the philosophical and religious traditions of the Mediterranean area. Madhyamaka is the (...) Buddhist tradition which many researchers saw as the fulfillment of such mystical aspirations in Buddhism. In this paper I specify the standard parameters of mystical experience (non‑conceptuality, ineffability, paradoxicality, silence, oneness, fullness) and I conclude that they either cannot be applied to Madhyamaka or that the application is only illusory. (shrink)

This article first defines the absolute discourse, then discusses its possibility in theology, as well as the relationships between language, thought, and reality as they derive from the spirituality and life of the Eastern Church. Theology must face several problems—including the paradox of transcendence, the violence of metaphysics, onto-theology, and the duplicity of language itself—, but the Revelation of the Absolute itself legitimizes the theological discourse. By using both affirmations and negations, theology reveals an iconic structure of discourse that (...) opens itself towards life and spirituality. The conclusion is that, in the absolute discourse of theology, words, even ineffable ones, are insufficient without life. (shrink)

This chapter focuses on Daoist praxeology and language in order to build something of a moral realist position (the contours of which may differ from most western versions insofar as it need not commit to moral cognitivism) that hinges on the seemingly paradoxical notions of ineffable moral truths and non-transferable moral skill.

Hegel's most interesting and controversial claims about nonconceptual knowledge arise in contexts of value. This paper examines the relation between nonconceptual and conceptual knowledge in Hegel's Phenomenology, specifically in connection with early Greek aesthetics. I take up Hegel's claim that the ancient Greeks expressed in their myths, religious narratives, sculpture, and artistic materials certain high powered philosophical truths which they shouldn't express in words. I raise a paradox about his claims and show how his claims about ineffable knowledge clash (...) with his general propositional criterion of knowledge, namely, that for something to count as knowledge it must be expressible in words. However I argue that Hegel's thoughts about the matter were coherent and I solve the paradox. (shrink)

Mahayana Buddhist philosophers’ attitude toward language is notoriously negative. The transcendental reality is often said to be ineffable. One’s obsession to apprehend the truth through words is an intellectual disease to be cured Attachment to verbal and conceptual proliferation enslaves oneself in the afflictive circle of life and death. Nevertheless, no Buddhist can afford to overlook the significance of language in preaching Buddhist dharmas as well as in day-to-day transactions. The point is not that of keeping silence. Rather, one should (...) understand and use language in such a way that one alludes to the unsayable reality and somehow escapes the bewitchment of language. Perhaps with this realization in mind, Mahayana Buddhist metaphysicians had fostered the penchant for using, at the sentential level, denials, negations and paradoxes to couch their views. In a similar vein but mainly at the word level, Dignaga (ca. 480-540 CE) the Yogacara epistemologist’ offered us a theory of language known as apoha doctrine in his landmark work Pramiinasamuccaya (henceforth PS). It is the purpose of this article to construe the doctrine. (shrink)

Kierkegaard, like Plato, though using different methods and conclusions, sought to ground knowledge in the ineffability of subjectivity. For Plato, knowledge comes subjectively (internally); for Kierkegaard, it comes by God's grace through faith. Socrates becomes the facilitator for the slave in the /Meno/, as does God for the man of faith. Again, Kierkegaard is also concerned with passion. "...the paradox is the passion of thought, and the thinker without the paradox is like the lover without passion; a (...) mediocre fellow" (p. 37). The paradox is necessitated by the metaphysical nature of the inquiry. Only knowledge through faith can approach the paradox since it is by definition beyond our knowledge. Passion must accompany the leap of faith, since knowledge acquisition for the man of faith is guided by God. (shrink)

Benardete paradoxes involve a beginningless set each member of which satisfies some predicate just in case no earlier member satisfies it. Such paradoxes have been wielded on behalf of arguments for the impossibility of an infinite past. These arguments often deploy patchwork principles in support of their key linking premise. Here I argue that patchwork principles fail to justify this key premise.

This paper discusses the nonconceptual theory of mystical ineffability which claims that mystical experiences can’t be expressed linguistically because they can’t be conceptualized. I discuss and refute two objections against it: (a) that unconceptualized experiences are impossible, and (b) that the theory is ad hoc because it provides no reason for why mystical experiences should be unconceptualizable. I argue against (a) that distinguishing different meanings of ‘object of experience’ leaves open the possibility of non-empty but objectless nonconceptual experiences. I (...) show that (b) is a valid objection but can be countered by a new theory of mystical non-conceptuality: mystical experiences are not conceptual because the specific mode of mystical consciousness prevents conceptualization. The dissolution of the subjectivity of consciousness during mystical experiences undermines the very foundation of the possibility of conceptual thought and thus renders them ineffable. (shrink)

Ronald de Sousa is one of the few analytic philosophers to have explored the ineffability of emotion. Ineffability arises, for de Sousa, from attempts to translate experience, which involves non-conceptual content, into language, which involves conceptual content. As de Sousa himself rightly notes, such a characterization construes all perceptual experience as ineffable and does not explain what might set emotional ineffability apart. I build on de Sousa’s insights regarding what makes emotional ineffability distinctive by highlighting that (...) in the case of emotion the content in question is, crucially, evaluative. Evaluative content has normativity that makes the ineffability of emotion both particularly salient as well as particularly relevant, as the way in which an object is valuable is felt to be merited despite the experience’s ineffability. After proposing an improved working definition of emotional ineffability, I move to the question of how language and emotional experience interact, and whether these interactions can be evaluated in any systematic way. While de Sousa is pessimistic regarding the prospects of such an evaluation, I argue that if we move beyond an individual level of analysis it is possible to characterize cases where the ineffability of emotion leaves members of particular social groups vulnerable to a range of epistemic and affective injustices. I argue that we can similarly characterize cases where the ineffability of emotion holds radical potential to challenge and transform unjust social arrangements. I end by proposing that the representational content of emotion involves what I call ‘modal complexity’ and that this makes emotions particularly well-suited to play such radical roles. (shrink)

Though largely neglected by philosophers, the concept of ineffability is integral to the Christian mystical tradition, and has been part of almost every philosophical discussion of religious experience since the early twentieth century. After a brief introduction, this article surveys the most important discussions of divine ineffability, observing that the literature presents two mutually reinforcing obstacles to a coherent account of the concept, creating the impression that philosophical reflection on the subject had reached an impasse. The article goes (...) on to survey some more recent work, which draws on the conceptual resources of existential phenomenology, pragmatism, and the later Wittgenstein. It shows that this work has made possible a new philosophical account of divine ineffability that surmounts the obstacles, overcomes the impasse and makes divine ineffability, once again, a live option in philosophy of religion. The article concludes with some brief remarks on how this alternative approach reflects recent trends in the discipline as a whole and has the potential to make a valuable contribution to live research questions in epistemology of religion. (shrink)

[A. W. Moore] There are criteria of ineffability whereby, even if the concept of ineffability can never serve to modify truth, it can sometimes serve to modify other things, specifically understanding. This allows for a reappraisal of the dispute between those who adopt a traditional reading of Wittgenstein's Tractatus and those who adopt the new reading recently championed by Diamond, Conant, and others. By maintaining that what the nonsense in the Tractatus is supposed to convey is ineffable understanding, (...) rather than ineffable truth, we can do considerable justice to each of these readings. We can also do considerable justice to the Tractatus. /// [Peter Sullivan] Moore proposes to cut between 'traditional' and 'new' approaches to the Tractatus, suggesting that Wittgenstein's intention is to convey, through the knowing use of nonsense, ineffable understanding. I argue, first, that there is indeed room for a proposal of Moore's general kind. Secondly, though, I question whether Moore's actual proposal is not more in tune with Wittgenstein's later thought than with the attitude of the Tractatus. (shrink)

[A. W. Moore] Criteria of ineffability are presented which, it is claimed, preclude the possibility of truths that are ineffable, but not the possibility of other things that are ineffable—not even the possibility of other things that are non-trivially ineffable. Specifically, they do not preclude the possibility of states of understanding that are ineffable. This, it is argued, allows for a reappraisal of the dispute between those who adopt a traditional reading of Wittgenstein’s Tractatus and those who adopt the (...) new reading recently championed by Cora Diamond, James Conant, and others. By maintaining that what the nonsense in the Tractatus is supposed to convey is ineffable understanding, rather than ineffable truth, we can do considerable justice to each of these readings. We can also do considerable justice to the Tractatus. /// [Peter Sullivan] Moore proposes to cut between 'traditional' and 'new' approaches to the Tractatus, suggesting that Wittgenstein's intention is to convey, through the knowing use of nonsense, ineffable understanding. I argue, first, that there is indeed room for a proposal of Moore's general kind. Secondly, though, I question whether Moore's actual proposal is not more in tune with Wittgenstein's later thought than with the attitude of the Tractatus. (shrink)

My first goal is to motivate a distinctively metaphysical approach to the problem of induction. I argue that there is a precise sense in which the only way that orthodox Humean and non-Humean views can justify induction is by appealing to extremely strong and unmotivated probabilistic biases. My second goal is to sketch what such a metaphysical approach could possibly look like. After sketching such an approach, I consider a toy case that illustrates the way in which such a metaphysics (...) can help us make progress on the problem of induction. (shrink)

In the first two sections of this reply article, I provide a brief introduction to the topic of ineffability and a summary of Ineffability and Religious Experience. This is followed, in section 3, by some reflections in reply to the response articles by Professors Metz and Cooper. Section 4 presents some concluding remarks on the future of philosophy of religion in the light of the most recent philosophical work on ineffability.

It is argued that, although there are no ineffable truths, the concept of ineffability nevertheless does have application—to certain states of knowledge. Towards the end of the essay this idea is related to religion: it is argued that the language that results from attempting (unsuccessfully) to put ineffable knowledge into words is very often of a religious kind. An example of this is given at the very end of the essay. This example concerns the Euthyphro question: whether what is (...) right is right because God wills it, or whether God wills it because it is right. (shrink)

This essay provides an overview of the ways in which contemporary philosophers have tried to make sense of ineffability as encountered in aesthetic contexts. Section 1 sets up the problem of aesthetic ineffability by putting it into historical perspective. Section 2 specifies the kinds of questions that may be raised with regard to aesthetic ineffability, as well as the kinds of answer each one of those questions would require. Section 3 investigates arguments that seek to locate aesthetic (...) ineffability within the object of aesthetic experiences, i.e. within aesthetic content. Section 4 discusses arguments that seek to locate aesthetic ineffability within the subject of aesthetic experience. (shrink)

Ineffability in Plato is a conundrum. There are at least four dimensions of ineffability in Platonic texts: epistemic (divine), strategic (religious), unspeakability and incommunicability. In this paper, I deal only with the first dimension, which is strictly epistemic in kind, and defend that Plato rejects divine ineffability, namely, the belief that the knowledge of the divine in general is inaccessible to the human mind. Several crucial passages attest to this rejection unequivocally. They show that Plato attached a (...) great philosophical relevance to what I call the equivalenceprinciple, namely, the interdependence or specularity between human and divine intelligence. The assertion of this principle represents the Platonic path to absolute knowledge, which I try to locate in the broader context of the history of philosophy, from early philosophers to Hegel. (shrink)

The discrepancy between individual women and the stereotypes attributed to the group as a ‎whole has become progressively greater and more explicit over the course of history. The stereotypes remain the same age-old ‎allegations whilst the ‎developments in the occupations of women and the traits they have opportunity to express have increased the distance between women and those ascribed traits. Stereotypes’ abstention from revision in light of contrary evidence constitutes an epistemic paradox for it entails conflict between the stereotypical (...) knowledge and empirical evidence, as well as between the stereotypical knowledge and other empirical knowledges. This paradox of stubbornness also raises the question as to the epistemic source of stereotypes. For, people at young ages encounter evidence which should have formed a more complex knowledge regarding women rather than the pervasive stereotypical knowledge. It is this extremity of absurdness of stereotypes regarding women that is utile to understanding stereotypes as a whole. The epistemic paradox that is engrained in all stereotypes is exposed uncompromisingly by this group. The paradox cannot be dismissed with excuses of having a small basis of evidence, such as may be said regarding other social groups with which one may have had minimal or no contact. Thus, stereotypes of women provide a limit case to understanding the epistemology of this paradoxical form of knowledge. The traits and epistemic phenomena which render stereotypes epistemically puzzling and intriguing is the relationship between knowledges. Stereotypical knowledge regarding women as a group conflict with one’s experience-founded knowledges of particular women, deeming the corporate body of knowledge incoherent. Quine’s theory of knowledge, with its holistic empirical approach endorsing conceptual schemes, provides fertile ground for this analysis. The novelty in his account is his establishment of the criteria of coherency, which shifts the focal point of epistemic inquiry away from the adequacy of individual knowledges with empirical evidence to the intra-knowledge relationships themselves. In his empiricism, Quine rather examines the interactions between knowledges and the overarching coherence of the body of knowledge as a holistic unit. Quine creates place in his account for mechanism which provide for the epistemic incongruences of stubbornness and conflict found between stereotypical knowledges and empirical evidence. These very mechanisms are what this paper requests to examine. Quine, ultimately, formulates knowledge as a collectively held fabric consisting of relations and of posits – socially constructed mechanisms which are empirically-irreducible and implemented pragmatically for the organisation of empirical evidence. According to Quine, the fabric formation is a conceptual scheme sourced in social heritage. People are bestowed with an eclectic framework of ‎knowledge to pragmatically merge between an inherited, collective conceptual scheme and the personally experienced empirical evidence. This paper will delve into Quine’s fabric of knowledge, its relations, and inner-mechanisms. The finding of stereotypes to be an age-old posit entrenched pragmatically – thus stubbornly – in the collective conceptual scheme, will explain the epistemic paradoxes they entail and offer insight to their revision in light of empiric reality and its women. (shrink)

The paradox of pain refers to the idea that the folk concept of pain is paradoxical, treating pains as simultaneously mental states and bodily states. By taking a close look at our pain terms, this paper argues that there is no paradox of pain. The air of paradox dissolves once we recognize that pain terms are polysemous and that there are two separate but related concepts of pain rather than one.

I present and discuss recent work in analytic philosophy of religion on apophaticism and divine ineffability. I focus on three questions: how can we call God ineffable without contradicting ourselves? How can we refer to an ineffable God? What is the point of talking about an ineffable God?

Can agents rationally inquire into things that they know? On my view, the answer is yes. Call this view the Compatibility Thesis. One challenge to this thesis is to explain why assertions like “I know that p, but I’m wondering whether p” sound odd, if not Moore-Paradoxical. In response to this challenge, I argue that we can reject one or both premises that give rise to it. First, we can deny that inquiry requires interrogative attitudes. Second, we can deny the (...) ignorance norm, on which agents are not permitted to both know and have interrogative attitudes, such as wondering. I argue that there are compelling reasons to deny the former and reasons to question the latter. Both options pave the way for further work on further inquiry. (shrink)

If I were to say, “Agnes does not know that it is raining, but it is,” this seems like a perfectly coherent way of describing Agnes’s epistemic position. If I were to add, “And I don’t know if it is, either,” this seems quite strange. In this chapter, we shall look at some statements that seem, in some sense, contradictory, even though it seems that these statements can express propositions that are contingently true or false. Moore thought it was paradoxical (...) that statements that can express true propositions or contingently false propositions should nevertheless seem absurd like this. If we can account for the absurdity, we shall solve Moore’s Paradox. In this chapter, we shall look at Moore’s proposals and more recent discussions of Moorean absurd thought and speech. (shrink)

Supererogatory acts—good deeds “beyond the call of duty”—are a part of moral common sense, but conceptually puzzling. I propose a unified solution to three of the most infamous puzzles: the classic Paradox of Supererogation (if it’s so good, why isn’t it just obligatory?), Horton’s All or Nothing Problem, and Kamm’s Intransitivity Paradox. I conclude that supererogation makes sense if, and only if, the grounds of rightness are multi-dimensional and comparative.

I aim at dissolving Kripke's dogmatism paradox by arguing that, with respect to any particular proposition p which is known by a subject A, it is not irrational for A to ignore all evidence against p. Along the way, I offer a definition of 'A is dogmatic with respect to p', and make a distinction between an objective and a subjective sense of 'should' in the statement 'A should ignore all the evidence against p'. For the most part, I (...) deal with Kripke's original version of the paradox, wherein the subject wishes, above all else, to avoid losing her true belief or gaining a false one; in the final section I investigate the possibility of having a paradox for a subject who values knowledge above anything else. (shrink)

I propose a revision of Cantor’s account of set size that understands comparisons of set size fundamentally in terms of surjections rather than injections. This revised account is equivalent to Cantor's account if the Axiom of Choice is true, but its consequences differ from those of Cantor’s if the Axiom of Choice is false. I argue that the revised account is an intuitive generalization of Cantor’s account, blocks paradoxes—most notably, that a set can be partitioned into a set that is (...) bigger than it—that can arise from Cantor’s account if the Axiom of Choice is false, illuminates the debate over whether the Axiom of Choice is true, is a mathematically fruitful alternative to Cantor’s account, and sheds philosophical light on one of the oldest unsolved problems in set theory. (shrink)

Thomas Kroedel argues that the lottery paradox can be solved by identifying epistemic justification with epistemic permissibility rather than epistemic obligation. According to his permissibility solution, we are permitted to believe of each lottery ticket that it will lose, but since permissions do not agglomerate, it does not follow that we are permitted to have all of these beliefs together, and therefore it also does not follow that we are permitted to believe that all tickets will lose. I present (...) two objections to this solution. First, even if justification itself amounts to no more than epistemic permissibility, the lottery paradox recurs at the level of doxastic obligations unless one adopts an extremely permissive view about suspension of belief that is in tension with our practice of doxastic criticism. Second, even if there are no obligations to believe lottery propositions, the permissibility solution fails because epistemic permissions typically agglomerate, and the lottery case provides no exception to this rule. (shrink)

Mysticism and the sciences have traditionally been theoretical enemies, and the closer that philosophy allies itself with the sciences, the greater the philosophical tendency has been to attack mysticism as a possible avenue towards the acquisition of knowledge and/or understanding. Science and modern philosophy generally aim for epistemic disclosure of their contents, and, conversely, mysticism either aims at the restriction of esoteric knowledge, or claims such knowledge to be non-transferable. Thus the mystic is typically seen by analytic philosophers as a (...) variety of 'private language' speaker, although the plausibility of such a position is seemingly foreclosed by Wittgenstein's work in the Philosophical Investigations. Yorke re-examines Wittgenstein's conclusion on the matter of private language, and argues that so-called 'ineffable' mystical experiences, far from being a 'beetle in a box', can play a viable role in our public language-games, via renewed efforts at articulation. (shrink)

This paper presents and motivates a new philosophical and logical approach to truth and semantic paradox. It begins from an inferentialist, and particularly bilateralist, theory of meaning---one which takes meaning to be constituted by assertibility and deniability conditions---and shows how the usual multiple-conclusion sequent calculus for classical logic can be given an inferentialist motivation, leaving classical model theory as of only derivative importance. The paper then uses this theory of meaning to present and motivate a logical system---ST---that conservatively extends (...) classical logic with a fully transparent truth predicate. This system is shown to allow for classical reasoning over the full (truth-involving) vocabulary, but to be non-transitive. Some special cases where transitivity does hold are outlined. ST is also shown to give rise to a familiar sort of model for non-classical logics: Kripke fixed points on the Strong Kleene valuation scheme. Finally, to give a theory of paradoxical sentences, a distinction is drawn between two varieties of assertion and two varieties of denial. On one variety, paradoxical sentences cannot be either asserted or denied; on the other, they must be both asserted and denied. The target theory is compared favourably to more familiar related systems, and some objections are considered. (shrink)

In this essay I defend a solution to a skeptical paradox. The paradox I focus on concerns epistemic justification (rather than knowledge), and skeptical scenarios that entail that most of our ordinary beliefs about the external world are false. This familiar skeptical paradox hinges on a “closure” principle. The solution is to restrict closure, despite its first appearing as a fully general principle, so that it can no longer give rise to the paradox. This has some (...) extra advantages. First, it suggests a general strategy that provides solutions to other versions of the paradox, not just those that depend on closure. Second, it clarifies the relation between the paradox and other kinds of skeptical problem. (shrink)

According to Aristotle if a universal proposition (for example: “All men are white”) is true, its contrary proposition (“All men are not white”) must be false; and, according to Aristotle, if a universal proposition (for example: “All men are white”) is true, its contradictory proposition (“Not all men are white”) must be false. I agree with what Aristotle wrote about universal propositions, but there are universal propositions which have no contrary proposition and have no contradictory proposition. The proposition X “All (...) the propositions that contradict this proposition are true” does not have the contrary proposition and does not have the contradictory proposition. In fact: FEX “All the propositions that contradict this proposition are not true” has a different subject: the subject of the proposition X is constituted by all the propositions that contradict the proposition X; by contrast, the subject of the proposition FEX is constituted by all the propositions that contradict the proposition FEX. And FOX “Not all the propositions that contradict this proposition are true” has a different subject: the subject of the proposition X is constituted by the propositions that contradict the proposition X; by contrast, the subject of the proposition FOX is constituted by the propositions that contradict the proposition FOX. According to Aristotle, a singular proposition (in his example: "Socrates is white") which is true must have its negative proposition ("Socrates is not white") which is false. I agree with Aristotle, but there are singular propositions which do not have the corresponding negative proposition. The proposition (or, rather, the pseudo-proposition) L “This same statement is not true” does not have the negative proposition because the proposition FNL “This same statement is true” has a different subject from the subject of the proposition L: the subject of the proposition L is the proposition L; by contrast, the subject of the proposition FNL is the proposition FNL. L and FNL cannot have the same subject. By contrast, the proposition M “This mount is entirely in Swiss territory” and the proposition NM “This mount is not entirely in Swiss territory” can have the same subject (for example, the Mount Eiger): in case the subject of the proposition M and the subject of the proposition NM is the same, M and NM are opposite propositions, NM is the negative proposition of M. By contrast, the proposition (or, rather, the pseudo-proposition) L "This same statement is not true" cannot have the corresponding negative proposition because FNL "This same statement is true" has a different subject: the subject of L is L ; by contrast, the subject of FNL is FNL. Then the paper continues by analyzing some variants of the liar’s paradox: L1 “The statement L1 is not true”; the so-called liar cycle; and the so-called Yablo’s paradox. (shrink)

This contribution focuses on strategic ineffability in Plato. Strategic ineffability serves different purposes. In Plato, it is mainly used to express a religious feeling of dependence and to emphasize the remoteness of the divine. However, its meaning is not only religious. It is also part of a complex narrative device that often resorts to irony in order to de-emphasize the most arduous and controversial metaphysical speculations. Whereas topoi of affected modesty and unspeakability may only play an aesthetic role, (...) strategic ineffability has to do with relevant communication: it is a way to share with (and induce in) other people feelings, goals and morally relevant beliefs, without entailing any accurate conceptual content. Knowledge is not the primary goal here. The paper argues that Plato, Plotinus and other ancient philosophers used the notion of divine ineffability strategically to share beliefs with their selected audiences and lead their disciples to spiritual change. (shrink)

Silence is a multifaceted concept which is not merely as an absence of sound but a presence with significant ontological, existential, and phenomenological implications. Through a thematic analysis, this paper deconstructs silence into various dimensions—its ontology, linguistic universality, and its function as cessation of speech, a form of listening, an act of kenosis, a form of ascesis, and a way of life. The study employs philosophical discourse and mathematical notation to delve into these aspects, demonstrating that while each perspective sheds (...) light on certain facets of silence, none can comprehensively encapsulate its essence. The research underscores the paradoxical nature of silence. It is both a universal phenomenon recognised across cultures and an intimate, personal experience that resists definitive categorisation. The paper concludes that the true nature of silence, particularly when considering the state of "being silent," remains indefinable and elusive, inviting deeper contemplation on its role in human experience. (shrink)

I distinguish paradoxes and hypodoxes among the conundrums of time travel. I introduce ‘hypodoxes’ as a term for seemingly consistent conundrums that seem to be related to various paradoxes, as the Truth-teller is related to the Liar. In this article, I briefly compare paradoxes and hypodoxes of time travel with Liar paradoxes and Truth-teller hypodoxes. I also discuss Lewis’ treatment of time travel paradoxes, which I characterise as a Laissez Faire theory of time travel. Time travel paradoxes are impossible according (...) to Laissez Faire theories, while it seems hypodoxes are possible. (shrink)

Philosophers have long argued that duties to oneself are paradoxical, as they seem to entail an incoherent power to release oneself from obligations. I argue that self-release is possible, both as a matter of deontic logic and of metaethics.

It is widely accepted that there is what has been called a non-hypocrisy norm on the appropriateness of moral blame; roughly, one has standing to blame only if one is not guilty of the very offence one seeks to criticize. Our acceptance of this norm is embodied in the common retort to criticism, “Who are you to blame me?”. But there is a paradox lurking behind this commonplace norm. If it is always inappropriate for x to blame y for (...) a wrong that x has committed, then all cases in which x blames x (i.e. cases of self-blame) are rendered inappropriate. But it seems to be ethical common-sense that we are often, sadly, in position (indeed, excellent, privileged position) to blame ourselves for our own moral failings. And thus we have a paradox: a conflict between the inappropriateness of hypocritical blame, and the appropriateness of self-blame. We consider several ways of resolving the paradox, and contend none is as defensible as a position that simply accepts it: we should never blame ourselves. In defending this startling position, we defend a crucial distinction between self-blame and guilt. (shrink)

We begin by showing that every theory of the value of uncertain prospects must have one of three unpalatable properties. _Reckless_ theories recommend giving up a sure thing, no matter how good, for an arbitrarily tiny chance of enormous gain; _timid_ theories permit passing up an arbitrarily large potential gain to prevent a tiny increase in risk; _non-transitive_ theories deny the principle that, if A is better than B and B is better than C, then A must be better than (...) C. Having set up this trilemma, we study its horns. Non-transitivity has been much discussed; we focus on drawing out the costs and benefits of recklessness and timidity when it comes to axiology, decision theory, and normative uncertainty. (shrink)

This paper gives a definition of self-reference on the basis of the dependence relation given by Leitgeb (2005), and the dependence digraph by Beringer & Schindler (2015). Unlike the usual discussion about self-reference of paradoxes centering around Yablo's paradox and its variants, I focus on the paradoxes of finitary characteristic, which are given again by use of Leitgeb's dependence relation. They are called 'locally finite paradoxes', satisfying that any sentence in these paradoxes can depend on finitely many sentences. I (...) prove that all locally finite paradoxes are self-referential in the sense that there is a directed cycle in their dependence digraphs. This paper also studies the 'circularity dependence' of paradoxes, which was introduced by Hsiung (2014). I prove that the locally finite paradoxes have circularity dependence in the sense that they are paradoxical only in the digraph containing a proper cycle. The proofs of the two results are based directly on König's infinity lemma. In contrast, this paper also shows that Yablo's paradox and its nested variant are non-self-referential, and neither McGee's paradox nor the omega-cycle liar paradox has circularity dependence. (shrink)

This paper is concerned with the paradox of decrease. Its aim is to defend the answer to this puzzle that was propounded by its originator, namely, the Stoic philosopher Chrysippus. The main trouble with this answer to the paradox is that it has the seemingly problematic implication that a material thing could perish due merely to extrinsic change. It follows that in order to defend Chrysippus’ answer to the paradox, one has to explain how it could be (...) that Theon is destroyed by the amputation without changing intrinsically. In this paper, I shall answer this challenge by appealing to the broadly Aristotelian idea that at least some of the proper parts of a material substance are ontologically dependent on that substance. I will also appeal to this idea in order to offer a new solution to the structurally similar paradox of increase. In this way, we will end up with a unified solution to two structurally similar paradoxes. (shrink)

Counterfactuals are somewhat tolerant. Had Socrates been at least six feet tall, he need not have been exactly six feet tall. He might have been a little taller—he might have been six one or six two. But while he might have been a little taller, there are limits to how tall he would have been. Had he been at least six feet tall, he would not have been more than a hundred feet tall, for example. Counterfactuals are not just tolerant, (...) then, but bounded. This paper presents a surprising paradox: If counterfactuals are tolerant and bounded, then we can prove a flat contradiction using natural rules of inference. Something has to go then. But what? (shrink)

Paradoxes have played an important role both in philosophy and in mathematics and paradox resolution is an important topic in both fields. Paradox resolution is deeply important because if such resolution cannot be achieved, we are threatened with the charge of debilitating irrationality. This is supposed to be the case for the following reason. Paradoxes consist of jointly contradictory sets of statements that are individually plausible or believable. These facts about paradoxes then give rise to a deeply troubling (...) epistemic problem. Specifically, if one believes all of the constitutive propositions that make up a paradox, then one is apparently committed to belief in every proposition. This is the result of the principle of classical logical known as ex contradictione (sequitur) quodlibetthat anything and everything follows from a contradiction, and the plausible idea that belief is closed under logical or material implication (i.e. the epistemic closure principle). But, it is manifestly and profoundly irrational to believe every proposition and so the presence of even one contradiction in one’s doxa appears to result in what seems to be total irrationality. This problem is the problem of paradox-induced explosion. In this paper it will be argued that in many cases this problem can plausibly be avoided in a purely epistemic manner, without having either to resort to non-classical logics for belief (e.g. paraconsistent logics) or to the denial of the standard closure principle for beliefs. The manner in which this result can be achieved depends on drawing an important distinction between the propositional attitude of belief and the weaker attitude of acceptance such that paradox constituting propositions are accepted but not believed. Paradox-induced explosion is then avoided by noting that while belief may well be closed under material implication or even under logical implication, these sorts of weaker commitments are not subject to closure principles of those sorts. So, this possibility provides us with a less radical way to deal with the existence of paradoxes and it preserves the idea that intelligent agents can actually entertain paradoxes. (shrink)