The Unexpected Hanging Problem is also known as the Surprise Examination Problem. We here solve it by isolating what is logical reasoning from the rest of the human psyche. In a not-so-orthodox analysis, following our tradition (The Liar, Dichotomy, The Sorites and Russell’s Paradox), we talk about the problem from a perspective that is more distant than all the known perspectives. From an observational point that is in much farther than all the observational points used until now, (...) the reader can finally see why the problem has been perpetuated as a problem and can also see that the problem was never an actual problem: Once more, we have an allurement. The allurement this time makes us start paying attention to all the complexity of the human psyche when studying problems that involve human feelings. The main finding could be told to be that we have to understand and study more the human psyche, in all its intricacies, also when dealing with problems that seem to belong with exclusivity to Mathematics or Logic. (shrink)

I identify an assumption that the students should not rely on: if the teacher believes that the exam would not be a surprise on a certain day, the teacher will not give the exam on that day. The reason I present for not making this assumption does not involve doubting the moral goodness of the teacher. But it does involve making a value judgment.

The students’ argument against the possibility of a surprise exam assumes that the following would not occur: the teacher decides to give the exam on a certain day; the teacher believes that the exam would be a surprise on that day; but, actually, the exam would not be a surprise on that day. I give a reason to reject this assumption, and I point out that an attempt to reformulate the surprise exam paradox in order to allow for the (...) assumption does not result in an acceptable argument. (shrink)

In our research about Fuzzy Time and modeling time, "Unexpected Hanging Paradox" plays a major role. Here, we compare this paradox to the Zeno Paradox and the relations of them with our standard models of continuum and Fuzzy numbers. To do this, we review the project "Fuzzy Time and Possible Impacts of It on Science" and introduce a new way in order to approach the solutions for these paradoxes. Additionally, we have a more general discussion about (...) paradoxes, as Philosophical back ground of the subject and in this way, we introduce the concepts of General View, the first picture, BBF-General View. (shrink)

. In our research about Fuzzy Time and modeling time, "Unexpected Hanging Paradox" plays a major role. Here, we compare this paradox to the Zeno Paradox and the relations of them with our standard models of continuum and Fuzzy numbers. To do this, we review the project "Fuzzy Time and Possible Impacts of It on Science" and introduce a new way in order to approach the solutions for these paradoxes. Additionally, we have a more general discussion (...) about paradoxes, as Philosophical back ground of the subject and in this way, we introduce the concepts of General View, the first picture, BBF-General View. -/- . (shrink)

Although Fuzzy logic and Fuzzy Mathematics is a widespread subject and there is a vast literature about it, yet the use of Fuzzy issues like Fuzzy sets and Fuzzy numbers was relatively rare in time concept. This could be seen in the Fuzzy time series. In addition, some attempts are done in fuzzing Turing Machines but seemingly there is no need to fuzzy time. Throughout this article, we try to change this picture and show why it is helpful to consider (...) the instants of time as Fuzzy numbers. In physics, though there are revolutionary ideas on the time concept like B theories in contrast to A theory also about central concepts like space, momentum… it is a long time that these concepts are changed, but time is considered classically in all well-known and established physics theories. Seemingly, we stick to the classical time concept in all fields of science and we have a vast inertia to change it. Our goal in this article is to provide some bases why it is rational and reasonable to change and modify this picture. Here, the central point is the modified version of “Unexpected Hanging” paradox as it is described in "Is classical Mathematics appropriate for theory of Computation".This modified version leads us to a contradiction and based on that it is presented there why some problems in Theory of Computation are not solved yet. To resolve the difficulties arising there, we have two choices. Either “choosing” a new type of Logic like “Para-consistent Logic” to tolerate contradiction or changing and improving the time concept and consequently to modify the “Turing Computational Model”. Throughout this paper, we select the second way for benefiting from saving some aspects of Classical Logic. In chapter 2, by applying quantum Mechanics and Schrodinger equation we compute the associated fuzzy number to time. (shrink)

Abstract The Theory of Computation in its existed form is based on Church –Turing Thesis. Throughout this paper, we show that the Turing computation model of this theory leads us to a contradiction. In brief, by applying a well-known paradox (Unexpected hanging paradox) we show a contradiction in the Theory when we consider the Turing model as our Computation model.

Fitch's Paradox and the Paradox of the Knower both make use of the Factivity Principle. The latter also makes use of a second principle, namely the Knowledge-of-Factivity Principle. Both the principle of factivity and the knowledge thereof have been the subject of various discussions, often in conjunction with a third principle known as Closure. In this paper, we examine the well-known Surprise Examination paradox considering both the principles on which this paradox rests and some formal (...) characterisations of the surprise notion, crucial in this paradox. Standard formalizations of the Surprise Examination paradox in modal logic do not seem, at first glance, to depend on either factivity or knowledge-of-factivity, but we will argue that both factivity and knowledge-of-factivity play a key implicit role in the paradox. Namely, they are implicitly, perhaps unintentionally, used in order to simplify the definition of surprise. We analyze modal logical formalizations of three versions of the paradox concluding that the Surprise Examination paradox is the result of two flaws: the assumption of knowledge-of-factivity, and the over-simplification of the definition of "surprise" accordingly. By fixing these two flaws, the Surprise Examination paradox vanishes. (shrink)

This paper proposes a new framework to solve the surprise examination paradox. I survey preliminary the main contributions to the literature related to the paradox. I introduce then a distinction between a monist and a dichotomic analysis of the paradox. With the help of a matrix notation, I also present a dichotomy that leads to distinguish two basically and structurally different notions of surprise, which are respectively based on a conjoint and a disjoint structure. I describe (...) then how Quine's solution and Hall's reduction apply to the version of the paradox corresponding to the conjoint structure. Lastly, I expose a solution to the version of the paradox based on the disjoint structure. (shrink)

In this thesis, I examine how "truth" is never adequately defined yet still used as a foundation for meaning and purpose. The elephant which is ignored is the paradoxical nature of truth and how it relates to the infinite, which is something we have not yet come to understand well enough. I propose that it is still possible if we are open-minded enough to accept the unexpected.

Although Fuzzy logic and Fuzzy Mathematics is a widespread subject and there is a vast literature about it, yet the use of Fuzzy issues like Fuzzy sets and Fuzzy numbers was relatively rare in time concept. This could be seen in the Fuzzy time series. In addition, some attempts are done in fuzzing Turing Machines but seemingly there is no need to fuzzy time. Throughout this article, we try to change this picture and show why it is helpful to consider (...) the instants of time as Fuzzy numbers. In physics, though there are revolutionary ideas on the time concept like B theories in contrast to A theory also about central concepts like space, momentum… it is a long time that these concepts are changed, but time is considered classically in all well-known and established physics theories. Seemingly, we stick to the classical time concept in all fields of science and we have a vast inertia to change it. Our goal in this article is to provide some bases why it is rational and reasonable to change and modify this picture. Here, the central point is the modified version of “Unexpected Hanging” paradox as it is described in "Is classical Mathematics appropriate for theory of Computation".This modified version leads us to a contradiction and based on that it is presented there why some problems in Theory of Computation are not solved yet. To resolve the difficulties arising there, we have two choices. Either “choosing” a new type of Logic like “Para-consistent Logic” to tolerate contradiction or changing and improving the time concept and consequently to modify the “Turing Computational Model”. Throughout this paper, we select the second way for benefiting from saving some aspects of Classical Logic. In chapter 2, by applying quantum Mechanics and Schrodinger equation we compute the associated fuzzy number to time. These, provides a new interpretation of Quantum Mechanics.More exactly what we see here is "Particle-Fuzzy time" interpretation of quantum Mechanics, in contrast to some other interpretations of Quantum Mechanics like " Wave-Particle" interpretation. At the end, we propound a question about the possible solution of a paradox in Physics, the contradiction between General Relativity and Quantum Mechanics. (shrink)

We examine two competing solutions to Benardete paradoxes: causal finitism, according to which nothing can have infinitely many causes, and the unsatisfiable pair diagnosis (UPD), according to which such paradoxes are logically impossible and no metaphysical thesis need be adopted to avoid them. We argue that the UPD enjoys notable theoretical advantages over causal finitism. Causal finitists, however, have levelled two main objections to the UPD. First, they urge that the UPD requires positing a ‘mysterious force’ that prevents paradoxes from (...) arising. Since such a force is implausible, the UPD is in trouble. Second, they employ recombination or patchwork principles to argue that paradoxical situations would be possible if causal finitism were false. Since such situations are not possible, causal finitism is true, and so a substantive metaphysical thesis is needed to avoid the paradoxes. We argue that the UPD proponent can successfully respond to these objections. (shrink)

We call something a paradox if it strikes us as peculiar in a certain way, if it strikes us as something that is not simply nonsense, and yet it poses some difficulty in seeing how it could make sense. When we examine paradoxes more closely, we find that for some the peculiarity is relieved and for others it intensifies. Some are peculiar because they jar with how we expect things to go, but the jarring is to do with imprecision (...) and misunderstandings in our thought, failures to appreciate the breadth of possibility consistent with our beliefs. Other paradoxes, however, pose deep problems. Closer examination does not explain them away. Instead, they challenge the coherence of certain conceptual resources and hence challenge the significance of beliefs which deploy those resources. I shall call the former kind weak paradoxes and the latter, strong paradoxes. Whether a particular paradox is weak or strong is sometimes a matter of controversy—sometimes it has been realised that what was thought strong is in fact weak, and vice versa,— but the distinction between the two kinds is generally thought to be worth drawing. In this Cchapter, I shall cover both weak and strong probabilistic paradoxes. (shrink)

Benardete paradoxes involve infinite collections of Grim Reapers, assassins, demons, deafening peals, or even sentences. These paradoxes have recently been used in arguments for finitist metaphysical theses such as temporal finitism, causal finitism, and discrete views of time. Here we develop a new finite Benardete-like paradox. We then use this paradox to defend a companions in guilt argument that challenges recent applications of patchwork principles on behalf of the aforementioned finitist arguments. Finally, we develop another problem for those (...) applications by examining the notion of exact duplication. (shrink)

Aside from bioethics, the main theme of Ronald Green's lifework has been an exploration of the relation between religion and morality, with special emphasis on the philosophies of Immanuel Kant and Søren Kierkegaard. This essay summarizes and assesses his work on this theme by examining, in turn, four of his relevant books. Religious Reason (1978) introduced a new method of comparative religion based on Kant's model of a rational religion. Religion and Moral Reason (1988) expanded on this project, clarifying that (...) religious traditions cannot be reduced to their moral grounding. Kierkegaard and Kant: The Hidden Debt (1992) offered bold new evidence that Kant, not Hegel, was the philosopher whose ideas primarily shaped Kierkegaard's overtly religious philosophy ; both philosophers focused on the problem of how to understand the relation between moral reasoning and historical religion. And Kant and Kierkegaard on Time and Eternity (2011) republished ten essays that explore various aspects of this theme in greater depth. I argue that throughout these works Green defends a " paradox of inwardness " : principles or ideals that are by their nature essentially inward end up requiring outward manifestation in order to be confirmed or fully justified as real. (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)

This paper reports (in section 1 “Introduction”) some quotes from Nelson Goodman which clarify that, contrary to a common misunderstanding, Goodman always denied that “grue” requires temporal information and “green” does not require temporal information; and, more in general, that Goodman always denied that grue-like predicates require additional information compared to what green-like predicates require. One of the quotations is the following, taken from the first page of the Foreword to chapter 8 “Induction” of the Goodman’s book “Problems and Projects”: (...) “Nevertheless, we may by now confidently conclude that no general distinction between projectible and non- projectible predicates can be drawn on syntactic or even on semantic grounds. Attempts to distinguish projectible predicates as purely qualitative, or non-projectible ones as time-dependent, for example, have plainly failed”. Barker and Achinstein in their famous paper of 1960 tried to demonstrate that the grue-speaker (named Mr. Grue in their paper) needs temporal information to be able to determine whether an object is grue, but Goodman replied (in “Positionality and Pictures”, contained in his book “Problems and Projects”, chapter 8, section 6b) that they failed to prove that Mr. Grue needs temporal information to determine whether an object is grue. According to Goodman, since the predicates “blue” and “green” are interdefinable with the predicates “grue” and “bleen”, “if we can tell which objects are blue and which objects are green, we can tell which ones are grue and which ones are bleen” [pages 12-13 of “Reconceptions in Philosophy and Other Arts and Sciences”]. But this paper points out that an example of interdefinability is also that one about the predicate “gruet”, which is a predicate that applies to an object if the object either is green and examined before time t, or is non-green and not examined before time t. The three predicates “green”, “gruet”, “examined before time t” are interdefinable: and even though the predicates “green” and “examined before time t” are interdefinable, being able to tell if an object is green does not imply being able to tell if an object is examined before time t (the interdefinability among three elements is a type of interdefinability present, for example, also among the logical connectives). Thus, it is wrong the Goodman’s thesis according to which if it is possible to determine without having temporal information whether the predicate “green” has to be applied to an object, then it is also possible to determine without having temporal information whether a predicate interdefinable with “green” has to be applied to an object. Another example of interdefinability is that one about a decidable predicate PD, which is interdefinable with an undecidable predicate PU: therefore even though we can tell whether an object is PD and whether an object is non-PD, we cannot tell whether an object is PU (since PU is an undecidable predicate) and whether an object is non-PU. Although the predicates PD and PU are interdefinable, the possibility to determine whether an object is PD does not imply the possibility to determine whether an object is PU (since PU is an undecidable predicate). Similarly, although the predicates “green” and “grue” are interdefinable, the possibility to determine whether an object is “green” even in absence of temporal information does not imply the possibility to determine whether an object is “grue” even in absence of temporal information. These and other examples about “grue” and “bleen” point out that even in case two predicates are interdefinable, the possibility to apply a predicate P does not imply the possibility to apply a predicate interdefinable with P. And that the possibility to apply the predicate “green” without having temporal information does not imply the possibility to apply the predicate “grue” without having temporal information. Furthermore, knowing that an object is both green and grue implies temporal information: in fact, we know by definition that a grue object can only be: 1) either green (in case the object is examined before time t); 2) or blue (in case the object is not examined before time t). Thus, knowing that an object is both grue and green, we know that we are faced with case 1, the case of a grue object that is green and examined before time t. Then the paper points out why the Goodman-Kripke paradox is a paradox about meaning that cannot have repercussions on induction. Finally the paper points out why Hume’s problem is a problem different from Goodman’s paradox and requires a specific treatment. -/- . (shrink)

This article tackles an epistemic puzzle formulated by R. Smullyan that we call the ‘Surprise Deception Paradox'. On the morning of April 1st 1925, his brother announced that he would deceive him during the day, but apparently nothing happened. Since R. Smullyan waited all day to be deceived by some action, he was actually deceived, but by the lack of an action, that is to say by omission. Afterwards, Smullyan felt immediately puzzled: because he expected to be deceived, he (...) was not deceived; but since he was not deceived the way he expected, he was actually deceived. We use dynamic belief revision logic to look more clearly into this puzzle. We argue that Smullyan's reasoning is not a self-referential paradox but shares common features with the more famous Surprise Examination Paradox. In Smullyan's riddle, we show that a misleading default mechanism makes R. Smullyan surprised by the deception he has been preyed to. We also use this solution to discuss whether such defaults, compared to other forms of truth-telling deception, may qualify as lies or not. (shrink)

The Buddhist Nikāya Suttas frequently mention the concept of fear (bhaya) and related synonyms. This concept does not receive much scholarly attention by subsequent Buddhist philosophers. Recent scholars identify a ‘paradox of fear’ in several traditions of classical Indian Buddhism (Brekke 1999, Finnigan 2019, Giustarini 2012). Each scholar points out, in their respective textual contexts, that fear is evaluated in two ways; one positive and the other negative. Brekke calls this the “double role” of fear (1999: 443). Each also (...) identify fear as purposely elicited to motivate acts aimed at achieving fearlessness, where freedom from fear is characteristic of nibbāna. They all find this puzzling. Finnigan asks: “Why would one purposefully incite fear if one’s goal is its elimination?” (2019: 221). Giustarini says that fear has a “contradictory nature” (2012: 513); Brekke calls it “the paradox of fear” (1999: 442). This article introduces the ‘paradox of fear’ as it appears in the Bodhicaryāvatāra of Śāntideva and the Nikāya suttas. It then critically examines Brekke and Giustarini’s proposed solutions. It argues that they get some things right in ways that are both supported by the Nikāyas and relevant to Śāntideva but that they leave some important questions unanswered. The article contends that these questions are best answered if fear is analysed as appropriate when its objects are related to karma and rebirth. (shrink)

Chinese Chan or Zen Buddhism is renowned for its improvisational, atypical, and perplexing use of words. In particular, the tradition’s encounter dialogues, which took place between Chan masters and their interlocutors, abound in puzzling, astonishing, and paradoxical ways of speaking. In this chapter, we are concerned with Chan’s use of paradoxical language. In philosophical parlance, a linguistic paradox comprises the confluence of opposite or incongruent concepts in a way that runs counter to our common sense and ordinary rational thinking. (...) One naturally wonders about Chan masters’ rationales for their use of paradox. There are also concerns about whether the use violates the logical principle of noncontradiction to the effect that nothing can be both P and not-P all over in the same way at the same time. Chan became a viable Chinese Buddhist tradition during the Tang dynasty (618−907) and continued to develop for several centuries. The tradition had produced a huge literature; consequently, our investigation of its use of paradox cannot but be limited and selective. In the second section, I first sketch key ideas of Chan that are pertinent to our investigation and then examine the use of paradox in the sermons associated with certain Tang masters of the southern Chan. In the third section, I analyze the presence of paradoxical language in post-Tang encounter dialogues. The fourth section concludes. (shrink)

This paper explores the liar paradox and its implications for logic and philosophical reasoning. It analyzes the paradox using classical logic principles and paraphrases it as "affirmation of the falsity of the very affirmation." The study draws connections between the liar paradox and Hegel's speculative sentence and suggests it functions as a "quasi-speculative sentence." Additionally, it examines parallels with the logocentric predicament and the determinist's assertion, highlighting their paradoxical nature. Through these analyses, the paper aims to illuminate (...) the fundamental paradoxes in our reasoning and logic. (shrink)

The current debates in social sciences show that the paradox of observing—the embeddedness of observer in the process of observing—is at the heart of the controversy about their cognitive status and future. Although the problem of observing has been addressed in numerous theoretical perspectives—some of which (Habermas, Leydesdorff, Maturana, and Luhmann) are examined in this article—the prospects for resolving this paradox remain problematic. Locating a point that allows reflection on the process of autopoiesis in general, not just the (...) operation of a particular autopoietic system, may be one condition for resolving this paradox. Such point will offer reflection on all autopoietic systems, including the observer. The dynamic balance between equilibrium and disequilibrium is the mechanism which regulates the process of autopoiesis. Since the function of regulation is essentially a reflective function, this equilibrium between equilibrium and disequilibrium, which can be identified with the concept of homeorhesis introduced by Conrad Waddington, may offer a possibility to reflect on the process of observing. (shrink)

The paper describes the solution to semantic paradoxes pioneered by Pavel Tichý and further developed by the present author. Its main feature is an examination (and then refutation) of the hidden premise of paradoxes that the paradox-producing expression really means what it seems to mean. Semantic concepts are explicated as relative to language, thus also language is explicated. The so-called ‘explicit approach’ easily treats paradoxes in which language is explicitly referred to. The residual paradoxes are solved by the (...) ‘implicit approach’ which employs ideas made explicit by the former one. (shrink)

Throughout this paper, we are trying to show how and why our Mathematical frame-work seems inappropriate to solve problems in Theory of Computation. More exactly, the concept of turning back in time in paradoxes causes inconsistency in modeling of the concept of Time in some semantic situations. As we see in the first chapter, by introducing a version of “Unexpected Hanging Paradox”,first we attempt to open a new explanation for some paradoxes. In the second step, by applying this (...) paradox, it is demonstrated that any formalized system for the Theory of Computation based on Classical Logic and Turing Model of Computation leads us to a contradiction. We conclude that our mathematical frame work is inappropriate for Theory of Computation. Furthermore, the result provides us a reason that many problems in Complexity Theory resist to be solved.(This work is completed in 2017 -5- 2, it is in vixra in 2017-5-14, presented in Unilog 2018, Vichy). (shrink)

The lottery paradox involves a set of judgments that are individually easy, when we think intuitively, but ultimately hard to reconcile with each other, when we think reflectively. Empirical work on the natural representation of probability shows that a range of interestingly different intuitive and reflective processes are deployed when we think about possible outcomes in different contexts. Understanding the shifts in our natural ways of thinking can reduce the sense that the lottery paradox reveals something problematic about (...) our concept of knowledge. However, examining these shifts also raises interesting questions about how we ought to be thinking about possible outcomes in the first place. (shrink)

In this paper, I start by describing and examining the main results about the option of formalizing the Yablo Paradox in arithmetic. As it is known, although it is natural to assume that there is a right representation of that paradox in first order arithmetic, there are some technical results that give rise to doubts about this possibility. Then, I present some arguments that have challenged that Yablo’s construction is non-circular. Just like that, Priest (1997) has argued that (...) such formalization shows that Yablo’s Paradox involves implicit circularity. In the same direction, Beall (2001) has introduced epistemic factors in this discussion. Even more, Priest has also argued that the introduction of infinitary reasoning would be of little help. Finally, one could reject definitions of circularity in term of fixed-point adopting non-well-founded set theory. Then, one could hold that the Yablo paradox and the Liar paradox share the same non-well-founded structure. So, if the latter is circular, the first is too. In all such cases, I survey Cook’s approach (2006, forthcoming) on those arguments for the charge of circularity. In the end, I present my position and summarize the discussion involved in this volume. En este artículo, describo y examino los principales resultados vinculados a la formalización de la paradoja de Yablo en la aritmética. Aunque es natural suponer que hay una representación correcta de la paradoja en la aritmética de primer orden, hay algunos resultados técnicos que hacen surgir dudas acerca de esta posibilidad. Más aún, presento algunos argumentos que han cuestionado que la construcción de Yablo no sea circular. Así, Priest (1997) ha argumentado que la formalización de la paradoja de Yablo en la aritmética de primer orden muestra que la misma involucra implícitamente circularidad. En la misma dirección, Beall (2001) ha introducido factores epistémicos en esta discusión. Más aún, Priest ha también argumentado que la introducción de razonamiento infinitario como complemento de la formalización en la aritmética sería de poca ayuda. Finalmente, se podría rechazar todo intento de dar definiciones de circularidad en términos de puntos fijos adoptando teoría de conjuntos infundados. Entonces, se podría sostener que la paradoja de Yablo y la del mentiroso comparten la misma estructura infundada. Por eso, si la última es circular, también lo es la primera. En todos los casos, presento el enfoque de Roy Cook (2006, en prensa) sobre estos argumentos que atribuyen circularidad a la construcción de Yablo. En el final, presento mi posición y un breve resumen de la discusión involucrada en este volumen. (shrink)

John McDowell articulated a radical criticism of normative inferentialism against Robert Brandom’s expressivist account of conceptual contents. One of his main concerns consists in vindicating a notion of intentionality that could not be reduced to the deontic relations that are established by discursive practitioners. Noticeably, large part of this discussion is focused on empirical knowledge and observational judgments. McDowell argues that there is no role for inference in the application of observational concepts, except the paradoxical one of justifying the content (...) of an observational judgment in terms of itself. This paper examines the semantical consequences of the analysis of the content of empirical judgments in terms of their inferential role. These, it is suggested, are distinct from the epistemological paradoxes that McDowell charges the inferentialist approach with. (shrink)

A Wittgensteinian Way with Paradoxes examines how some of the classic philosophical paradoxes that have so puzzled philosophers over the centuries can be dissolved. Read argues that paradoxes such as the Sorites, Russell’s Paradox and the paradoxes of time travel do not, in fact, need to be solved. Rather, using a resolute Wittgensteinian ‘therapeutic’ method, the book explores how virtually all apparent philosophical paradoxes can be diagnosed and dissolved through examining their conditions of arising; to loosen their grip and (...) therapeutically liberate those philosophers suffering from them (including oneself). The book contrasts such paradoxes with real, ‘lived paradoxes’: paradoxes that are genuinely experienced outside of the philosopher’s study, in everyday life. Thus Read explores instances of lived paradox (such as paradoxes of self-hatred and of denial of other humans’ humanity) and the harm they can cause, psychically, morally or politically. These lived paradoxes, he argues, sometimes cannot be dissolved using a Wittgensteinian treatment. Moreover, in some cases they do not need to be: for some, such as the paradoxical practices of Zen Buddhism (and indeed of Wittgenstein himself), can in fact be beneficial. The book shows how, once philosophers’ paradoxes have been exorcized, real lived paradoxes can be given their due. (shrink)

You may not know me well enough to evaluate me in terms of my moral character, but I take it you believe I can be evaluated: it sounds strange to say that I am indeterminate, neither good nor bad nor intermediate. Yet I argue that the claim that most people are indeterminate is the conclusion of a sound argument—the indeterminacy paradox—with two premises: (1) most people are fragmented (they would behave deplorably in many and admirably in many other situations); (...) (2) fragmentation entails indeterminacy. I support (1) by examining psychological experiments in which most participants behave deplorably (e.g., by maltreating “prisoners” in a simulated prison) or admirably (e.g., by intervening in a simulated theft). I support (2) by arguing that, according to certain plausible conceptions, character evaluations presuppose behavioral consistency (lack of fragmentation). Possible reactions to the paradox include: (a) denying that the experiments are relevant to character; (b) upholding conceptions according to which character evaluations do not presuppose consistency; (c) granting that most people are indeterminate and explaining why it appears otherwise. I defend (c) against (a) and (b). (shrink)

This article examines the prisoner's dilemma paradox and argues that confessing is the rational choice, despite this probably entailing a less-than-ideal outcome.

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)

The Kripke/Wittgenstein paradox and Goodman’s riddle of induction can be construed as problems of multiple redescription, where the relevant sceptical challenge is to provide factual grounds justifying the description we favour. A choice of description or predicate, in turn, is tantamount to the choice of a curve over a set of data, a choice apparently governed by implicitly operating constraints on the relevant space of possibilities. Armed with this analysis of the two paradoxes, several realist solutions of Kripke’s (...) class='Hi'>paradox are examined that appeal to dispositions or other non-occurrent properties. It is found that all neglect crucial epistemological issues: the entities typically appealed to are not observational and must be inferred on the basis of observed entities or events; yet, the relevant sceptical challenge concerns precisely the factual basis on which this inference is made and the constraints operating on it. All disposition ascriptions, the thesis goes on to argue, contain elements of idealization. To ward off the danger of vacuity resulting from the fact that any disposition ascription is true under just the right ideal conditions, dispositional theories need to specify limits on legitimate forms of idealization. This is best done by construing disposition ascriptions as forms of (implicit) curve-fitting, I argue, where the “data” is not necessarily numeric, and the “curve” fitted not necessarily graphic. This brings us full circle: Goodman’s and Kripke’s problems are problems concerning curve-fitting, and the solutions for it appeal to entities the postulation of which is the result of curve-fitting. The way to break the circle must come from a methodology governing the idealizations, or inferences to the best idealization, that are a part of curve-fitting. The thesis closes with an argument for why natural science cannot be expected to be of much help in this domain, given the ubiquity of idealization. (shrink)

The principle of indifference is supposed to suffice for the rational assignation of probabilities to possibilities. Bertrand advances a probability problem, now known as his paradox, to which the principle is supposed to apply; yet, just because the problem is ill‐posed in a technical sense, applying it leads to a contradiction. Examining an ambiguity in the notion of an ill‐posed problem shows that there are precisely two strategies for resolving the paradox: the distinction strategy and the well‐posing strategy. (...) The main contenders for resolving the paradox, Marinoff and Jaynes, offer solutions which exemplify these two strategies. I show that Marinoff’s attempt at the distinction strategy fails, and I offer a general refutation of this strategy. The situation for the well‐posing strategy is more complex. Careful formulation of the paradox within measure theory shows that one of Bertrand’s original three options can be ruled out but also shows that piecemeal attempts at the well‐posing strategy will not succeed. What is required is an appeal to general principle. I show that Jaynes’s use of such a principle, the symmetry requirement, fails to resolve the paradox; that a notion of metaindifference also fails; and that, while the well‐posing strategy may not be conclusively refutable, there is no reason to think that it can succeed. So the current situation is this. The failure of Marinoff’s and Jaynes’s solutions means that the paradox remains unresolved, and of the only two strategies for resolution, one is refuted and we have no reason to think the other will succeed. Consequently, Bertrand’s paradox continues to stand in refutation of the principle of indifference. (shrink)

The principle of universal instantiation plays a pivotal role both in the derivation of intensional paradoxes such as Prior’s paradox and Kaplan’s paradox and the debate between necessitism and contingentism. We outline a distinctively free logical approach to the intensional paradoxes and note how the free logical outlook allows one to distinguish two different, though allied themes in higher-order necessitism. We examine the costs of this solution and compare it with the more familiar ramificationist approaches to higher-order logic. (...) Our assessment of both approaches is largely pessimistic, and we remain reluctantly inclined to take Prior’s and Kaplan’s derivations at face value. (shrink)

By pooling together exhaustive analyses of certain philosophical paradoxes, we can prove a series of fascinating results regarding philosophical progress, agreement on substantive philosophical claims, knockdown arguments in philosophy, the wisdom of philosophical belief, the epistemic status of metaphysics, and the power of philosophy to refute common sense. As examples, this Element examines the Sorites Paradox, the Liar Paradox, and the Problem of the Many – although many other paradoxes can do the trick too.

This essay critically discusses the rising interest in process philosophy in recent years. I argue that the appeal of process philosophy lies in its ability to circumnavigate the binary dichotomies pervasive in European philosophy and defend an interpretation of process philosophy in terms of relationality, difference, and change. After outlining the central tenets of process philosophy, Graham Harman’s critique of a relational account of process philosophy is examined, particularly his assertion that this type of philosophy cannot fully explain genuine change. (...) Despite the merits of Harman’s critique, I will show that his object-oriented ontology faces similar limitations. Turning to Graham Priest’s dialethism I suggest that philosophy, instead of striving for a consistent representation of fundamental metaphysics, must embrace paradox to some extent. This leads the philosophical discipline to understand itself as a transformative process. This essay critically discusses the rising interest in process philosophy in recent years. I argue that the appeal of process philosophy lies in its ability to circumnavigate the binary dichotomies pervasive in European philosophy and defend an interpretation of process philosophy in terms of relationality, difference, and change. After outlining the central tenets of process philosophy, Graham Harman’s critique of a relational account of process philosophy is examined, particularly his assertion that this type of philosophy cannot fully explain genuine change. Despite the merits of Harman’s critique, I will show that his object-oriented ontology faces similar limitations. Turning to Graham Priest’s dialethism I suggest that philosophy, instead of striving for a consistent representation of fundamental metaphysics, must embrace paradox to some extent. This leads the philosophical discipline to understand itself as a transformative process. (shrink)

If we want to say that all truths are knowable Fitch’s Paradox leads us to conclude that all truths are known. Is it a real philosophical problem or a mere modeling problem? Is it possible to express the idea of knowability using modal logic? The Knowability Principle is expressed by the formula: if Phi is true then it is possible to know that Phi. But what is the meaning of possibility in this context? Using standard modal operators under what (...) condition can we express the idea of knowability? We will in particular examine the subjacent relations of the modal operators in a Kripke Model. We will define the possibility as the possibility of learning opposed to an unclear possibility. Then we will show that Fitch’s Paradox becomes clearer and we will examine how the Knowability Principle could be expressed in such frame. (shrink)

It is incontrovertible that the problem of insecurity is part of the ravening realities in the current civil society. It is a general problem facing the whole world. However, it is more pronounced in some parts of the world than in others. In African countries, especially in Nigeria, insecurity has been a seemingly insurmountable problem. It has rendered all attempts made by the government and individuals to stabilize the country thereby strengthening the principle of social co-operation, harmony and peaceful coexistence (...) among citizens, abortive. This paper argued that security seems to be an illusion in an African country like Nigeria because all attempts by the government to ensure stability do not put into consideration the ‘six paradoxes of violence’ largely responsible for insecurity. The paper examined the problem of insecurity in Nigeria and the paradoxes that need to be addressed if the nation ever hopes to deal meaningfully and honestly, with the challenge of insecurity that is drifting it apart. The paper identified the sixparadoxes of violence as outlined by Ali Mazrui, then analysed how these six paradoxes serve as the major barriers to the peaceful coexistence of people in Nigeria, and how they persistently threaten the unity of the nation at any slight provocation. The paper also suggested some ways by which these paradoxes can be addressed thereby ensuring a level of peace and social stability. (shrink)

It is often claimed that anti-realism is a form of transcendental idealism or that Kant is an anti-realist. It is also often claimed that anti-realists are committed to some form of knowability principle and that such principles have problematic consequences. It is therefore natural to ask whether Kant is so committed, and if he is, whether this leads him into difficulties. I argue that a standard reading of Kant does indeed have him committed to the claim that all empirical truths (...) are knowable and that this claim entails that there is no empirical truth that is never known. I extend the result to a priori truths and draw some general philosophical lessons from this extension. However, I then propose a re-examination of Kant’s notion of experience according to which he carefully eschews any commitment to empirical knowability. Finally I respond to a remaining problem that stems from a weaker, justified believability principle. (shrink)

I argue that absolutism, the view that absolutely unrestricted quantification is possible, is to blame for both the paradoxes that arise in naive set theory and variants of these paradoxes that arise in plural logic and in semantics. The solution is restrictivism, the view that absolutely unrestricted quantification is not possible. -/- It is generally thought that absolutism is true and that restrictivism is not only false, but inexpressible. As a result, the paradoxes are blamed, not on illicit quantification, but (...) on the logical conception of set which motivates naive set theory. The accepted solution is to replace this with the iterative conception of set. -/- I show that this picture is doubly mistaken. After a close examination of the paradoxes in chapters 2--3, I argue in chapters 4 and 5 that it is possible to rescue naive set theory by restricting quantification over sets and that the resulting restrictivist set theory is expressible. In chapters 6 and 7, I argue that it is the iterative conception of set and the thesis of absolutism that should be rejected. (shrink)

Humility is a paradoxical virtue. This should come as no great surprise. It doesn’t take much explanation for one to realize that if someone is boasting about how humble he is, then he probably is not humble. In fact, as we shall see, the paradoxical nature of humility has a long history, going back to at least Thomas Aquinas in the thirteenth century. While it may not be a novel claim that there exists an apparent paradox of humility, I (...) will argue that there is more than one humility paradox, perhaps as many as five: the epistemic paradox, the paradox of self-attribution, the inculcation paradox, the agentic paradox, and the axiological paradox. All these paradoxes are distinct, yet seemingly intertwined. Upon examining them each in turn, we will be left with a Gordian knot of humility paradoxes. (shrink)

On page 14 of "Reconceptions in Philosophy and Other Arts and Sciences" (section 4 of chapter 1) by Nelson Goodman and Catherine Z. Elgin is written: “Since ‘blue’ and ‘green’ are interdefinable with ‘grue’ and ‘bleen’, the question of which pair is basic and which pair derived is entirely a question of which pair we start with”. This paper points out that an example of interdefinability is also that one about the predicate “grueb”, which is a predicate that applies to (...) an object if the object either is green and examined before time b, or is non-green and not examined before time b. The three predicates “green”, “grueb”, “examined before time b” are interdefinable. According to Goodman, since the predicates “blue” and “green” are interdefinable with the predicates “grue” and “bleen”, “if we can tell which objects are blue and which objects are green, we can tell which ones are grue and which ones are bleen” [pages 12-13 of “Reconceptions in Philosophy and Other Arts and Sciences”]. But , even though the predicates “green” and “examined before time b” are interdefinable, being able to tell if an object is green does not imply being able to tell if an object is examined before time b. The interdefinability among three elements is a type of interdefinability present, for example, also among the logical connectives. Another example of interdefinability is that one about a decidable predicate PD, which is interdefinable with an undecidable predicate PU: therefore even though we can tell whether an object is PD and whether an object is non-PD, we cannot tell whether an object is PU (since PU is an undecidable predicate) and whether an object is non-PU. Although the predicates PD and PU are interdefinable, the possibility to determine whether an object is PD does not imply the possibility to determine whether an object is PU (since PU is an undecidable predicate). Similarly, although the predicates “green” and “grue” are interdefinable, the possibility to determine whether an object is “green” even in absence of temporal information does not imply the possibility to determine whether an object is “grue” even in absence of temporal information. These and other examples about “grue” and “bleen” point out that even in case two predicates are interdefinable, the possibility to apply a predicate P does not imply the possibility to apply a predicate interdefinable with P. And that the possibility to apply the predicate “green” without having temporal information does not imply the possibility to apply the predicate “grue” without having temporal information. According to Goodman, if it is possible to determine if an object is green without needing temporal information, then it is also possible to determine if an object is grue without needing temporal information. But, knowing that an object is both green and grue implies temporal information: in fact, we know by definition that a grue object can only be: 1) either green (in case the object is examined before time t); 2) or blue (in case the object is not examined before time t). Thus, knowing that an object is both grue and green, we know that we are faced with case 1, the case of a grue object that is green and examined before time t. Then the paper points out why the Goodman-Kripke paradox is a paradox about meaning that cannot have repercussions on induction. Finally the paper points out why Hume’s problem is a problem different from Goodman’s paradox and requires a specific treatment. (shrink)

This paper (first published under the same title in Journal of Mathematical Economics, 29, 1998, p. 331-361) is a sequel to "Consistent Bayesian Aggregation", Journal of Economic Theory, 66, 1995, p. 313-351, by the same author. Both papers examine mathematically whether the the following assumptions are compatible: the individuals and the group both form their preferences according to Subjective Expected Utility (SEU) theory, and the preferences of the group satisfy the Pareto principle with respect to those of the individuals. While (...) the 1995 paper explored these assumptions in the axiomatic context of Savage's (1954-1972) SEU theory, the present paper explores them in the context of Anscombe and Aumann's (1963) alternative SEU theory. We first show that the problematic assumptions become compatible when the Anscombe-Aumann utility functions are state-dependent and no subjective probabilities are elicited. Then we show that the problematic assumptions become incompatible when the Anscombe-Aumann utility functions are state-dependent, like before, but subjective probabilities are elicited using a relevant technical scheme. This last result reinstates the impossibilities proved by the 1995 paper, and thus shows them to be robust with respect to the choice of the SEU axiomatic framework. The technical scheme used for the elicitation of subjective probabilities is that of Karni, Schmeidler and Vind (1983). (shrink)

The reason ability of considering time as a fuzzy concept is demonstrated in [7],[8]. One of the major questions which arise here is the new definitions of Complexity Classes. In [1],[2],…,[11] we show why we should consider time a fuzzy concept. It is noticeable to mention that that there were many attempts to consider time as a Fuzzy concept, in Philosophy, Mathematics and later in Physics but mostly based on the personal intuition of the authors or as a style of (...) Fuzzifying different various of the concepts. Consequently, fuzzifying time doesn’t go to be popular. In the new attempts we are trying to show why we are somewhat forced to consider time as a Fuzzy concept. It is mostly based on the “Unexpected Hanging Paradox” introduced by a Swedish Mathematician Lennart Ekbom. Our question is:” what will be the impact of it in Theory of Computation and Physics?”. Here, we discuss about the impact of fuzzifying time on Theory of Computation. (shrink)

While Aristotle provides the crucial testimonies for the paradoxes of motion, topos, and the falling millet seed, surprisingly he shows almost no interest in the paradoxes of plurality. For Plato, by contrast, the plurality paradoxes seem to be the central paradoxes of Zeno and Simplicius is our primary source for those. This paper investigates why the plurality paradoxes are not examined by Aristotle and argues that a close look at the context in which Aristotle discusses Zeno holds the answer to (...) this question. (shrink)

In this paper, I examine recent phenomenological research on both depressive and manic episodes, with the intention of showing how phenomenologically oriented studies can help us overcome the apparently paradoxical nature of mixed states. First, I argue that some of the symptoms included in the diagnostic criteria for depressive and manic episodes in the DSM-5 are not actually essential features of these episodes. Second, I reconsider the category of major depressive disorder (MDD) from the perspective of phenomenological psychopathology, arguing that (...) severe depressive episodes should not be characterized by any particular moods (such as sadness, hopelessness, or guilt), and should instead be characterized by a diminished capacity for finding ourselves situated in and attuned to the world at all. In other words, the affective dimension of depression should be characterized as a change in the way we have moods, not as a change from one kind of mood to another. Third, I turn to mania, arguing that manic episodes, taken as the opposite of depressive episodes, should be characterized not by any particular moods (such as euphoria, grandiosity, or even irritability), but should instead be characterized by an enhanced or heightened capacity for finding ourselves situated in and attuned to the world. In other words, the affective dimension of mania, like the affective dimension of depression, should be understood as a change in the way we have moods, not as a change from one kind of mood to another. Fourth, I return to the phenomenon of mixed states and argue that the affective dimension of depression and mania, when conceived along the phenomenological lines I set forth in the previous sections, dissolves the paradox of mixed states by showing that the essential characteristics of depression and mania cannot and do not coincide. Many cases of mixed states are diagnosed because moods that we take to be essential features of either depression or mania arise within the context of what is considered to be the opposite kind of episode (e.g. dysphoria, typically associated with depression, often arises in what is otherwise considered a manic state). However, if we conceive of the affective dimension of depression as a decrease in the degree to which one is situated in and attune to the world through moods, and the affective dimension of mania as an increase in the degree to which one is situated in and attuned to the world through moods, then the particular mood one finds oneself in is simply irrelevant to the diagnosis of either depression or mania. As a result, the manifestation of any particular moods in what otherwise seems to be a pure manic or depressive episode does not constitute a mixed state. (shrink)

One of the possible solutions of the Fermi paradox is that all civilizations go extinct because they hit some Late Great Filter. Such a universal Late Great Filter must be an unpredictable event that all civilizations unexpectedly encounter, even if they try to escape extinction. This is similar to the “Death in Damascus” paradox from decision theory. However, this unpredictable Late Great Filter could be escaped by choosing a random strategy for humanity’s future development. However, if all civilizations (...) act randomly, this could be the actual cause of universal extinction, as no one will choose the most optimal strategy. Using a meta-random strategy, where the decision to start random actions is also made randomly, solves this. (shrink)

Some have argued that the right of national self-determination gives every national group the power to decide for itself whether to remain part of an existing state or to secede unilaterally and form its own state. Such a theory underpins the claim that Quebec is entitled to decide on its own whether or not to leave Canada. This paper examines the main philosophical arguments for the theory and finds them one-dimensional and inadequate; they fail to take account of the full (...) range of complex issues arising in actual cases of proposed secession. If the right of national self-determination is understood as involving a right of unilateral secession, it cannot be attributed to national groups across the board. It arises only in specific historical circumstances, usually involving oppression or other forms of grave injustice. (shrink)

This article critically examines McTaggart’s Paradox, which argues for the unreality of time based on inherent contradictions in the A-series and B-series of temporal order. McTaggart’s assertion that time is unreal stems from the premise that genuine change, essential for time, occurs within the A-series, where events transition from future to present to past. He contends that this series is inherently contradictory, as it requires events to simultaneously possess mutually exclusive properties of past, present, and future. This paradoxical nature (...) leads McTaggart to conclude that time is an illusion. The article challenges McTaggart’s conclusions by advocating for Presentism, the view that only the present moment exists. Presentism is supported by common-sense views and phenomenological experiences of time, which emphasize the experiential privilege of the present. By focusing on the reality of the present moment, Presentism offers a coherent and intuitive understanding of temporal experience, countering McTaggart’s paradox. Additionally, the article explores arguments from philosophers such as Sydney Shoemaker and William Rowe, who challenge McTaggart’s linkage of time with change. Shoemaker proposes that time can exist without change, while Rowe critiques the necessity of change for the existence of time. Through a comprehensive evaluation of McTaggart’s premises and the phenomenological evidence supporting Presentism, this article aims to refute the paradox and affirm the reality of time as experienced through the ever-present ‘Presentness.’ Presentism is thus presented as a robust framework for understanding time, consistent with both philosophical reasoning and everyday temporal experience. (shrink)

This paper takes into account the loops within the anti-suicide arguments - we can clearly understand that their theories were emerging either from their personal beliefs or irrelevant inferences. As discussed later, they overlooked the fact that human beings have ultimate freedom over their death and that is one thing that serves their ego. We see a mere categorical problem on behalf of Camus and his Sisyphus; that how he failed to realise the difference of circumstance and choices. How Kant’s (...) Categorical Imperative is like Plato’s Ideal World that can never exist and how Rousseau failed to recognise individuals as humans. The paper also examine the pro-suicide arguments of Arthur Schopenhauer, Phillip Mainlander, Max Stirner and David Hume. The paper concludes that although suicide is logical, however, there is a need to further categorise the types of suicides in order to create a better compass on this topic of self annihilation. (shrink)