One of the global challenges addressed in this article, particularly in the Global South, is the high prevalence of child marriage. The author is situated in an area with one of the highest rates of child marriage in Indonesia. The rationale for selecting this case study is to examine the concept of spiritual freedom and its potential to empower women to challenge the oppression they face with regard to their bodies, rights, and futures. Child marriage should be (...) regarded as a criminal act in the context of Christianity. However, this issue does not appear to be a prominent topic in educational institutions, places of worship, or global discourse. This research employs a qualitative methodology, utilising interview techniques with women who have experienced child marriage. The author then engaged in a process of reflection with feminist philosopher Iris Marion Young, concurrently addressing theological concerns and the role of Christian education. The findings indicate that Christianity and government policy on health are inextricably linked, as health is a divine mandate for humanity to fulfil its responsibilities.Contribution: This article makes a contribution to the field of research in Central Kalimantan and serves to proclaim to the global community that Christian education must address the issue of child marriage as a matter of urgency. (shrink)

The claim that nonhuman animals lack foresight is common and intuitive. I propose an alternative whereby foresight is a gradual continuum in that it is present in animals to the extent that it is needed. A second aspect of this commentary points out that the requirements that the memory that mediates foresight be both specific yet flexible seem contradictory.

The article deals with Cantor's argument for the non-denumerability of reals somewhat in the spirit of Lakatos' logic of mathematical discovery. At the outset Cantor's proof is compared with some other famous proofs such as Dedekind's recursion theorem, showing that rather than usual proofs they are resolutions to do things differently. Based on this I argue that there are "ontologically" safer ways of developing the diagonal argument into a full-fledged theory of continuum, concluding eventually that famous semantic paradoxes based (...) on diagonal construction are caused by superficial understanding of what a name is. (shrink)

The value of autonomy is a hallmark of liberal doctrine. It would seem to follow that liberals must reject the practice of “arranged marriage” on the grounds that the “arranging” component of the practice eschews autonomy and individuality. However, in policy debates in Great Britain, the difference between “arranged marriage” and “forced marriage” has been defined as the presence of autonomy or free choice for an arranged marriage and their absence in cases of forced marriage. (...) A paradox seems to result: arranged marriage is defined as a marriage practice that both rejects autonomy and requires autonomy. In this article, I will show that the resultant paradox arises from the inadequacy of the autonomy analysis rather than from any intrinsically puzzling feature of arranged marriage. I then offer an alternative normative framework to assess arranged marriage’s potential contribution to a just society. My tri-metric analysis for arranged marriage includes the autonomy of the participants (Metric 1), as well as two societal metrics: the fairness of the distribution of care-giving labor (Metric 2) and the degree to which the society meets its members’ legitimate needs for care (Metric 3). (shrink)

논문은 한국의 가부장제적 의식이 다문화주의와 어떻게 갈등하는가를 한국에서의 다문화적 가족 상황을 통해서 살펴본다. 논문에서 이러한 문제의식은 한국의 가부장제와 가족제도에 중요한 기반을 제공하는 친친(親親) 개념을 통해 전개된다. 친친은 일차적으로 가부장 사회를 유지하기 위한 이념적 근거이며, 혈연을 강조하는 개념이다. 이러한 면에서 친친은 다문화주의와 정체성이라는 범주에서 배제와 분리, 그리고 동화라는 양 극단의 차별 모델을 산출한다는 부정적 의미를 지닌다. 하지만 논문은 여기에서 그치지 않고 친친이 지니는 역설적 측면에 주목하여, 친친이 다문화적 가치와 서로 갈등하고 반목하는 관계로 남지 않을 가능성을 시사하고자 한다.“친한 이는 친하게 대접받아야 한다.”는 (...) 친친의 논리에서 발견할 수 있는 역설의 지점을 살펴보고, 그것이 한국에서의 다문화주의 정착과 관련하여 어떤 긍정적 의미를 지닐 수 있는 것인지를 가늠해본다. (shrink)

Contemporary theorists of constituent power recognize a tension in which the omnipotent novelty of constituent power is necessarily policed by constituted power. Beginning with Arendt’s claim that the categories of constitutional stability and political novelty should be thought together rather than treated as oppositional, this article presents an interpretation of her work that seeks to address this ‘paradox of constitutionalism’. While commentators have come to assert that Arendt repudiates ‘absolutes’ in favour of an account of ‘relative beginnings’, this article (...) demonstrates that Arendt’s argument involves a critical redescription of the absolute, rather than a repudiation. This is significant, for it illuminates the manner in which her account of founding seeks to dismantle the commonplace temporalizations we attribute to our political vocabulary. This is employed to argue that particular stylings of absolutes naturalize the appearance of the new only as temporal ruptures, allowing us to get a handl... (shrink)

Husserl’s first work formulated what proved to be an algorithmically complete arithmetic, lending mathematical clarity to Kronecker’s reduction of analysis to finite calculations with integers. Husserl’s critique of his nominalism led him to seek a philosophical justification of successful applications of symbolic arithmetic to nature, providing insight into the “wonderful affinity” between our mathematical thoughts and things without invoking a pre-established harmony. For this, Husserl develops a purely descriptive phenomenology for which he found inspiration in Mach’s proposal of a “universal (...) physical phenomenology.” To account for applications to any domain, Husserl envisages a theory of all possible deductive systems, which he develops extensively in his Göttingen lectures wherein he engages with Hilbert’s work on deductive systems for geometry, real arithmetic, and physics. This leads Husserl to formulate claims of decidability and proofs of completeness for various arithmetics that result from his analysis of Kronecker’s general arithmetic. Careful attention to these proofs seem to show that Husserl was not oblivious to problems that underlie our incompleteness theorems, namely that of showing that some inversions of his algorithmic arithmetic are undefined. His growing preoccupation with the issue of a pre-established harmony between mathematical thought and reality motivate his pursuit of a “supramathematics” of all possible complete theory forms to demystify such harmony, by having such a form on hand for describing any empirical domain. He soon decides that a transcendental idealism of nature will reveal the wonderful affinity of thoughts and things comprising such harmony, to be a wonderful “parallelism of objective unities and constituted manifolds of consciousness.” But the paradoxes of logic and set theory cloud the clarity of mathematics, which Weyl would restore with Brouwer’s intuitionism and Hilbert with his metamathematics. Husserl informed Weyl that his student Becker had formulated a phenomenological foundation not only for Weyl’s generalization of relativity theory but also for the Brouwer-Weyl continuum. But Weyl eventually rejected much of Becker’s work, especially when it became clear that his phenomenological intuitionism could not account for the success of Hilbert’s transfinite mathematics in quantum physics. Becker responded to this “crisis of phenomenological method” with his mantic phenomenology celebrating the magic of mathematical mysticism, which Husserl finally rejects in favor of a pluralistic phenomenology of mathematics and nature. (shrink)

Some philosophical accounts imply that masturbation is inferior sexual activity. Against this, Soble argues that masturbation is central. Relying on the physical-anatomical indistinguishability of sexual act-types, he derives a Zeno-style paradox about sexual activity: either all sexual activity (even ordinary coitus) is masturbatory or none of it is (not even solitary masturbation). Soble argues for the first horn of the dilemma, thus ensuring that solitary masturbation is a member of the continuum of sexual activities. Going beyond anatomy, Soble (...) also argues that the central psychological features of paired sexual activity are normally exhibited also by solitary masturbation, which further establishes that solitary masturbation is on the continuum of sexual activity. Altogether, Soble's arguments support a "unary" model of sexuality, compelling us to take seriously the genuine sexual nature of solitary masturbation, a result that is important for the philosophy of sex, the scientific study of sexuality, and the politics of human sexuality. (shrink)

In this chapter, the author explains Rorty's neopragmatist feminism and some feminist criticism of his work, limiting her to questions not yet settled in the literature. She argues that Rorty can defeat the criticisms that his reformism is too conservative and that his feminism flounders without representationalist truth. "Feminism and Pragmatism" discusses the apparent paradox that injustices, on a Rortyan view, are not injustices until they are so perceived. Thus, if our society begins to accept gay marriage, passes (...) legislation supporting gay marriage, and begins criticizing those who oppose gay marriage, we have made a significant change in our practices, norms, and language. Our society still, at least at this time, thinks of "gay marriage" as a somewhat different category than "marriage," despite the fact that we treat both as marriages. We still rely on legislatures and courts to determine the legality of our marriage practices. (shrink)

Here we will go beyond the variety of violence to show its unity, common points and continuities. For although there are multiple forms of violence, they are interrelated: they define a continuum from trivial to extreme violence. Violence against oneself, things, living things such as plants and animals, other nations, the other, one’s fellow human beings, therefore the violence of society against its members, which returns to self-violence. Another continuum is its spiral development, with violence generating violence and (...) pushing it to grow. Violence can also be learned, we progress ever further in violence: in gangs, in armies, in society... Everyone is capable of violence, sometimes to a good advantage as in self-defence. Here it resides in necessity, that of survival, but in general it is impunity that allows and encourages it. In closed, totalitarian, universes: family, work, hospital, army, state... The proximity and distance between the perpetrator and the victim defines yet another continuity. We will discuss the various elements that contribute to its development. And paradoxically, to see that violence also serves to avoid violence. In this way, evacuating it, refusing it, is in fact feeding it, which makes today’s violence, which is an evolution of previous violence and which prepares and defines tomorrow’s violence. (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)

Economics presents the paradox of the entropy of the law of diminishing returns and infinity of the substitution effect. Resolution assumes the substitution effect is greater than diminishing returns. Technology presupposing entropy, introduced is a new paradox of entropic technology generating infinite growth. Resolution assumes serial substitution of technologies, generating an infinite continuum. Physics and economics contest mechanic entropy and organic growth conceptions. A mechanic conception resolves set disjunctives exclusively, every set disjoined from a contiguous set, constituting (...) entropy. An organic conception resolves set disjunctives inclusively, every set conjoined with a contiguous set, constituting growth. Causally each instance of something decreases the preexistent set of all possible instances by one, dying. Functionally each instance of something increases the postexistent set of all possible instances by one, living. Economists have the advantage here. Endlessly divisible, substance is something constituted of nothing, ungoverned by the law of conservation of energy. Physicists implicitly concede this assuming substance emerges from a Big Bang. Alas lunch is not free. Product of an economic growth equation being endless and non-repetitive, calculation is irrational, rendering growth economics irrelevant. Calculation requires marginal analysis, sequences initiating anywhere within a set governed by conservation of energy and entropy converging in parallel upon a common limit, “the unseen hand.” Energy conserved, however, economic growth is bounded. (shrink)

Graham Priest has focused attention on an intriguing but neglected paradox posed by José Benardete in 1964. Benardete viewed the paradox as a threat to the intelligibility of the spatial and temporal continua and offered several different versions of it. Priest has selected one of those versions and formalized it. Although Priest has succeeded nicely in sharpening the paradox, the version he chose to formalize has distracting and potentially problematic features that are absent from some of Benardete's (...) other versions. I offer a formalization of a simpler version of the paradox, the one that presents most plainly Benardete's challenge to the spatial continuum. Proposed resolutions of Benardete's paradox should address this version of the paradox as well as the one formalized by Priest. (shrink)

Is "living together" in a marriage-like relationship compatible with the feminist ideal of individual self-development? Paradoxically, while the structure and social-historical context of marriage-like relationships seems in fundamental conflict with the goal of autonomous self-development, the development of individuality also seems to be better fostered by living with a significant other in a committed relationship than by living alone. This paradox is resolved through the suggestion of a three-stage account of self-development: inauthenticity, autonomous being oneself, and autonomous (...) being with others. At the third stage, living together in a marriage-like relationship is one social format in which autonomous relating to others is possible. Unless the partners have attained the second stage, however, such a relationship will be destructive rather than conducive to individuality. (shrink)

In recent years there has been a revitalised interest in non-classical solutions to the semantic paradoxes. In this paper I show that a number of logics are susceptible to a strengthened version of Curry's paradox. This can be adapted to provide a proof theoretic analysis of the omega-inconsistency in Lukasiewicz's continuum valued logic, allowing us to better evaluate which logics are suitable for a naïve truth theory. On this basis I identify two natural subsystems of Lukasiewicz logic which (...) individually, but not jointly, lack the problematic feature. (shrink)

An examination of case law on forced marriage reveals that in addition to physical force, the role of emotional pressure is now taken into consideration. However, in both legal and policy discourse, the difference between arranged and forced marriage continues to be framed in binary terms and hinges on the concept of consent: the context in which consent is constructed largely remains unexplored. By examining the socio-cultural construction of personhood, especially womanhood, and the intersecting structural inequalities that constrain (...) particular groups of South Asian women in the UK, we argue that consent and coercion in relation to marriage can be better understood as two ends of a continuum, between which lie degrees of socio-cultural expectation, control, persuasion, pressure, threat and force. Women who face these constraints exercise their agency in complex and contradictory ways that are not always recognised by the existing exit-centred state initiatives designed to tackle this problem. (shrink)

Emile Borel regards the Banach-Tarski Paradox as a reductio ad absurdum of the Axiom of Choice. Peter Forrest instead blames the assumption that physical space has a similar structure as the real numbers. This paper argues that Banach and Tarski's result is not paradoxical and that it merely illustrates a surprising feature of the continuum: dividing a spatial region into disjoint pieces need not preserve volume.

This article centres on the legal recognition of same-sex marriage with a view to exploring the issue of unspeakability; that is, the condition whereby some questions cannot be articulated because of a lack of words. More specifically, the article will explore what happens to those social practices that are not given legal speakability and thereby legal recognition/protection. To this end, I first focus on how words are produced in the sphere of everyday life and their dependence on the existence (...) of a widespread normality. I then discuss how the law sees to the preservation and the reproduction of normality by providing a set of categories which are made available to law-abiders to settle disputes when they arise. In doing so, I elucidate the twofold role played by law as both a selective and a creative device. To cast some light on the particular way law operates, I discuss an important decision by the Italian Constitutional Court in 2010, which provides a telling example of how legal officials are able to seal off the set of legal categories and to leave some issues in the sphere of the unspeakable. I then unearth a paradox: while unspeakability reveals a condition of powerlessness, the acquisition of speakability could bring about even harsher exclusionary effects. I conclude by arguing that the entry into the sphere of official law is always a Janus-faced achievement, but can play as an effective instrument of critique. (shrink)

In The Struggle for Democracy, Christopher Meckstroth looks at history and context in the development of democratic theory to provide a principled way of sorting out deep conflicts over who has the right to speak for the democratic people. He tests this theory by applying it to contemporary debates over same-sex marriage, military intervention, and gun control.

Neuro-education, a new frontier for educational researchers, has its passionate advocates and equally passionate detractors. Some philosophers, including Noel Purdy and Hugh Morrison, Andrew Davis, and Ralph Schumacher, have argued that the entire enterprise is misguided. I evaluate and challenge their arguments. This permits me to articulate my own position: Neuroscience may make impressive contributions to education but, perhaps paradoxically, not by guiding the work of teachers.

The five participants in this dialogue critically discuss Zeno of Elea's paradox of Achilles and the tortoise. They consider a number of solutions to and restatements of the paradox, together with their philosophical implications. Among the issues investigated include the appearance-reality distinction, Aristotle's distinction between actual and potential infinity, the concept of a continuum, Cantor's continuum hypothesis and theory of transfinite ordinals, and, as a solution to Zeno's puzzle, the distinction between infinite and indeterminate or inexhaustible (...) divisibility. (shrink)

Events between which we have no epistemic reason to discriminate have equal epistemic probabilities. Bertrand’s chord paradox, however, appears to show this to be false, and thereby poses a general threat to probabilities for continuum sized state spaces. Articulating the nature of such spaces involves some deep mathematics and that is perhaps why the recent literature on Bertrand’s Paradox has been almost entirely from mathematicians and physicists, who have often deployed elegant mathematics of considerable sophistication. At the (...) same time, the philosophy of probability has been left out. In particular, left out entirely are the philosophical ground of the principle of indifference, the nature of the principle itself, the stringent constraint this places on the mathematical representation of the principle needed for its application to continuum sized event spaces, and what these entail for rigour in developing the paradox itself. This book puts the philosophy and its entailments back in and in so doing casts a new light on the paradox, giving original analyses of the paradox, its possible solutions, the source of the paradox, the philosophical errors we make in attempting to solve it and what the paradox proves for the philosophy of probability. The book finishes with the author’s proposed solution—a solution in the spirit of Bertrand’s, indeed—in which an epistemic principle more general than the principle of indifference offers a principled restriction of the domain of the principle of indifference. (shrink)

We outline Brentano’s theory of boundaries, for instance between two neighboring subregions within a larger region of space. Does every such pair of regions contain points in common where they meet? Or is the boundary at which they meet somehow pointless? On Brentano’s view, two such subregions do not overlap; rather, along the line where they meet there are two sets of points which are not identical but rather spatially coincident. We outline Brentano’s theory of coincidence, and show how he (...) uses it to resolve a number of Zeno-like paradoxes. (shrink)

The individualization thesis has been widely applied to explain women’s increasing autonomy in romantic relationships and marital decisions across both Western and non-Western contexts. In China, individualization is believed to have enhanced women’s freedom in love and marriage, supported by the 1950 Marriage Law, which abolished arranged marriages and granted women equal legal status to men. However, Chinese women still face notable constraints in exercising full autonomy over their choice of partners and the timing of marriage. Parental (...) involvement in matchmaking, pressure from media discourses that stigmatize “leftover women”, and social expectations continue to define women’s happiness in relation to timely marriage and childbearing. Importantly, Confucian family and gender norms now appear to have a greater influence on women’s romantic choices than they did during the early reform era. With the “return” of Confucian marital values and increasing parental involvement in matchmaking, does the individualization thesis still sufficiently explain Chinese women’s marital freedom? By addressing the “nonlinear” aspect of second modernity, this article aims to deconstruct the concept of “traditions” within the marital sphere. It argues that traditions have re-emerged in an “evolved” form, blending both traditional and modern requirements within China’s unique context of individualization. The nonlinear nature of individualization offers a dynamic perspective for understanding the complex relationship between tradition and modernity in rapidly transforming societies like China. (shrink)

DEFINING OUR TERMS A “paradox" is an argumentation that appears to deduce a conclusion believed to be false from premises believed to be true. An “inconsistency proof for a theory" is an argumentation that actually deduces a negation of a theorem of the theory from premises that are all theorems of the theory. An “indirect proof of the negation of a hypothesis" is an argumentation that actually deduces a conclusion known to be false from the hypothesis alone or, more (...) commonly, from the hypothesis augmented by a set of premises known to be true. A “direct proof of a hypothesis" is an argumentation that actually deduces the hypothesis itself from premises known to be true. Since `appears', `believes' and `knows' all make elliptical reference to a participant, it is clear that `paradox', `indirect proof' and `direct proof' are all participant-relative. PARTICIPANT RELATIVITY In normal mathematical writing the participant is presumed to be “the community of mathematicians" or some more or less well-defined subcommunity and, therefore, omission of explicit reference to the participant is often warranted. However, in historical, critical, or philosophical writing focused on emerging branches of mathematics such omission often invites confusion. One and the same argumentation has been a paradox for one mathematician, an inconsistency proof for another, and an indirect proof to a third. One and the same argumentation-text can appear to one mathematician to express an indirect proof while appearing to another mathematician to express a direct proof. WHAT IS A PARADOX’S SOLUTION? Of the above four sorts of argumentation only the paradox invites “solution" or “resolution", and ordinarily this is to be accomplished either by discovering a logical fallacy in the “reasoning" of the argumentation or by discovering that the conclusion is not really false or by discovering that one of the premises is not really true. Resolution of a paradox by a participant amounts to reclassifying a formerly paradoxical argumentation either as a “fallacy", as a direct proof of its conclusion, as an indirect proof of the negation of one of its premises, as an inconsistency proof, or as something else depending on the participant's state of knowledge or belief. This illustrates why an argumentation which is a paradox to a given mathematician at a given time may well not be a paradox to the same mathematician at a later time. -/- The present article considers several set-theoretic argumentations that appeared in the period 1903-1908. The year 1903 saw the publication of B. Russell's Principles of mathematics, [Cambridge Univ. Press, Cambridge, 1903; Jbuch 34, 62]. The year 1908 saw the publication of Russell's article on type theory as well as Ernst Zermelo's two watershed articles on the axiom of choice and the foundations of set theory. The argumentations discussed concern “the largest cardinal", “the largest ordinal", the well-ordering principle, “the well-ordering of the continuum", denumerability of ordinals and denumerability of reals. The article shows that these argumentations were variously classified by various mathematicians and that the surrounding atmosphere was one of confusion and misunderstanding, partly as a result of failure to make or to heed distinctions similar to those made above. The article implies that historians have made the situation worse by not observing or not analysing the nature of the confusion. -/- RECOMMENDATION This well-written and well-documented article exemplifies the fact that clarification of history can be achieved through articulation of distinctions that had not been articulated (or were not being heeded) at the time. The article presupposes extensive knowledge of the history of mathematics, of mathematics itself (especially set theory) and of philosophy. It is therefore not to be recommended for casual reading. AFTERWORD: This review was written at the same time Corcoran was writing his signature “Argumentations and logic”[249] that covers much of the same ground in much more detail. https://www.academia.edu/14089432/Argumentations_and_Logic . (shrink)

This article explores the life and work of Emma Goldman to formulate a radical critique of intimacy. Goldman’s theory of sexual freedom and revolutionary love offers a feminist vision that challenges contemporary debates concerning uses of the language of feminine desire. Goldman appealed to ideals of feminine instinct and feminine desire in order to challenge the conventional meanings attached to femininity in her day. Her views on marriage, love, sexuality and the feminine are analysed alongside her writings on her (...) own personal experience, in order to illuminate the continuing paradoxes feminists face in regard to definitions and experiencesof femininity. (shrink)

We suggest that, far from establishing an inconsistency in the standard theory of the geometrical linear continuum, Zeno’s Paradox of Extension merely establishes an inconsistency between the standard theory of geometrical magnitude and a misguided system of length measurement. We further suggest that our resolution of Zeno’s paradox is superior to Adolf Grünbaum’s now standard resolution based on Lebesgue measure theory.

This article studies the origin and continuity of the identity of the entities inscribed in a distributed ledger. Specifically, it focuses on the differences between the identities of the entities that exist in a distributed ledger and those of the entities that exist outside the ledger but must be represented in the ledger in order to interact with it. It suggests that a distributed ledger that contains representations of entities that exist outside the ledger can yield a continuum of (...) interconnected existing and past identities that is constantly redefined to represent new conceptual entities. This continuum can be understood as a metasortal—or a sortal of sortals—that resembles the mathematical structure of a set of sets. Further, the article presents the dilemma that arises when representing the identities of entities in a distributed ledger, and it draws an analogy between this dilemma and Russell's Paradox. (shrink)

This paper argues that, for Ockham, the parts of the continuum exist in act in the continuum: they are already there before any division of the continuum. Yet, they are infinitely many in that no division of the continuum will exhaust all the existing parts of the continuum taken conjointly. This reading of Ockham takes into account the crucial place of his new concept of the infinite in his analysis of the infinite divisibility of the (...) continuum. Like many of his fellow anti-atomists, Ockham stresses that the concept of a potential infinite seems to contradict Aristotle’s modal logic, in particular the central assumption that there is no potency that will never be realized. Ockham, like other fourteenth-century anti-atomists, tried not only to refute atomism, but also to propose an analysis of the infinite divisibility of the continuum that is not incompatible with their modal logic. (shrink)

In this paper, I develop an original view of the structure of space—called infinitesimal atomism—as a reply to Zeno’s paradox of measure. According to this view, space is composed of ultimate parts with infinitesimal size, where infinitesimals are understood within the framework of Robinson’s nonstandard analysis. Notably, this view satisfies a version of additivity: for every region that has a size, its size is the sum of the sizes of its disjoint parts. In particular, the size of a finite (...) region is the sum of the sizes of its infinitesimal parts. Although this view is a coherent approach to Zeno’s paradox and is preferable to Skyrms’s infinitesimal approach, it faces both the main problem for the standard view and the main problem for finite atomism, leaving it with no clear advantage over these familiar alternatives. (shrink)

What fourth dimension of a four-dimensional space-time continuum. I propose to develop some of the commonly held implications of this view, and to show that they involve a contradiction. Hence whatever time is, it cannot be the thing corresponding to this particular theory.

Putative resolutions of the sorites paradox in which the major premise is declared false or illegitimate, Including max black's treatment in terms of the alleged illegitimacy of vague attributions to borderline cases, Are rejected on semantical grounds. The resort to a non-Bivalent logic of representational "accuracy" with a continuum of accuracy values is shown to resolve the paradox, And the identification of accuracy values as truth values is defended as compatible with the central insight of the correspondence (...) theory of truth and with the practical legitimacy of most applications of ordinary, Bivalent logic to statements involving vague predicates. (shrink)

Edmund Husserl’s engagement with Bertrand Russell’s paradox stands in a continuum of reciprocal reception and discussions about impossible objects in the School of Brentano. Against this broader context, we will focus on Husserl’s discussion of Russell’s paradox in his manuscript A I 35α from 1912. This highly interesting and revealing manuscript has unfortunately remained unpublished, which probably explains the scant attention it has received. I will examine Husserl’s approach in A I 35α by relating it to earlier (...) discussions of relevant topics in his manuscripts and the broader historical context of the School of Brentano and early phenomenology. (shrink)

Alcohol use has been recognized as a challenge in eldercare and social care, and some anticipate that problems related to alcohol use will increase in the future as the current adult generation has high alcohol consumption rates. Accordingly, it is suggested that care workers are at risk of becoming passive bystanders to the destructive lifestyles of vulnerable older adults and even facilitating these lifestyles. In the present paper, we suggest that alcohol exacerbates and underscores inherent difficulties in eldercare, such as (...) finding an appropriate balance between the personal freedom of the older adult and the responsibility of the care worker to provide care. The specific focus in the paper regard the communication and interaction involving values between people in eldercare in cases of problematic alcohol‐related situations to uncover the difficulties. We found it noteworthy that the objectives and perspectives of older adults, care workers, managers and relatives have implications regarding their interactions and communications because their varying experiences involve values that are not necessarily aligned. Sometimes, care workers have no choice but to act against what, in the public sphere and to the other care workers, is ruled out by virtue of their professional ethics. It is suggested that care workers describe and judge situations where alcohol is present paradoxically by virtue of their professional ethics, yet regulate their care to preserve the dignity of older adults, even when they find the situation to be an apparent dilemma. (shrink)

The insights described by Nevin & Grace may be summarized without reference to the Newtonian concepts they suggest. The metaphor to Newtonian mechanics seems dubious in three ways: (1) extensions seem to lead to paradoxes; (2) many well-known phenomena are ignored; (3) the Newtonian concepts seem difficult to reconcile with the larger framework of evolutionary theory.

Pruss uses an example of Lester Dubins to argue against the claim that appealing to hyperreal-valued probabilities saves probabilistic regularity from the objection that in continuum outcome-spaces and with standard probability functions all save countably many possibilities must be assigned probability 0. Dubins’s example seems to show that merely finitely additive standard probability functions allow reasoning to a foregone conclusion, and Pruss argues that hyperreal-valued probability functions are vulnerable to the same charge. However, Pruss’s argument relies on the rule (...) of conditionalisation, but I show that in examples like Dubins’s involving nonconglomerable probabilities, conditionalisation is self-defeating. (shrink)

We consider an approach to some philosophical problems that I call the Method of Conceptual Articulation: to recognize that a question may lack any determinate answer, and to re-engineer concepts so that the question acquires a definite answer in such a way as to serve the epistemic motivations behind the question. As a case study we examine “Galileo’s Paradox”, that the perfect square numbers seem to be at once as numerous as the whole numbers, by one-to-one correspondence, and yet (...) less numerous, being a proper subset. I argue that Cantor resolved this paradox by a method at least close to that proposed—not by discovering the true nature of cardinal number, but by articulating several useful and appealing extensions of number to the infinite. Galileo was right to suggest that the concept of relative size did not apply to the infinite, for the concept he possessed did not. Nor was Bolzano simply wrong to reject Hume’s Principle (that one-to-one correspondence implies equal number) in the infinitary case, in favor of Euclid’s Common Notion 5 (that the whole is greater than the part), for the concept of cardinal number (in the sense of “number of elements”) was not clearly defined for infinite collections. Order extension theorems now suggest that a theory of cardinality upholding Euclid’s principle instead of Hume’s is possible. Cantor’s refinements of number are not the only ones possible, and they appear to have been shaped by motivations and fruitfulness, for they evolved in discernible stages correlated with emerging applications and results. Galileo, Bolzano, and Cantor shared interests in the particulate analysis of the continuum and in physical applications. Cantor’s concepts proved fruitful for those pursuits. Finally, Gödel was mistaken to claim that Cantor’s concept of cardinality is forced on us; though Gödel gives an intuitively compelling argument, he ignores the fact that Euclid’s Common Notion is also intuitively compelling, and we are therefore forced to make a choice. The success of Cantor’s concept of cardinality lies not in its truth (for concepts are not true or false), nor its uniqueness (for it is not the only extension of number possible), but in its intuitive appeal, and most of all, its usefulness to the understanding. (shrink)

Various real and imagined criminal law cases rest on “naked statistical evidence”. That is, they rest more or less entirely on a probability for guilt/liability derived from a single statistical model. The intuition is that there is something missing in these cases, high as the probability for guilt/liability may be, such that the relevant standard for legal proof is not met. Here we contribute to the considerable debate about how this intuition is best explained and what it teaches us about (...) evidential reasoning in the legal setting. We part ways with the recent scholarship, however. Unlike most others, our diagnosis is not that there is an important qualitative property that some evidence or bodies of evidence have, and that naked statistical evidence, most strikingly, lacks. Rather, we see cases resting on naked statistical evidence as lying at the extreme of a continuum of cases that are vulnerable to challenge due to “meta-uncertainty” about the underlying model. (shrink)

A daring marriage of philosophical theory and practical politics, this collection is the first of Gianni Vattimo's many books to combine his intellectual pursuits with his public and political life. Vattimo is a paradoxical figure, at once a believing Christian and a vociferous critic of the Catholic Church, an outspoken liberal but not a former communist, and a recognized authority on Nietzsche and Heidegger as well as a prominent public intellectual and member of the European parliament. Building on his (...) unique position as a philosopher and politician, Vattimo takes on some of the most pressing questions of our time: Is it still possible, long after Nietzsche proclaimed the death of God, to talk of moral imperatives, individual rights, or political freedom? Are these values still relevant in today's world? Tackling these crucial issues, Gianni Vattimo argues that nihilism is not the absence of meaning but a recognition of a plurality of meanings; it is not the end of civilization but the beginning of new social paradigms. Commonly associated with the pessimistic belief that all of existence is meaningless, nihilism, as a philosophical principle, is far less sensational--it is the ethical doctrine that there are no moral absolutes or infallible natural laws, that "truth" is inescapably subjective. Because the conditions for equality and liberty are not "naturally" given, society must actively create these ideals or it will inevitably fall prey to irrationality, prejudice, and oppression. Vattimo contends that the infighting, timidity, and confusion that have overtaken contemporary liberal thought and politics are the products a prolonged and indulgent mourning over the loss of the transcendental father figure--any institution or power structure that defines truth, knowledge, and reality. Until humanity overcomes its need for external authority--whether it be organized religion, the nation-state, or free-market capitalism--emancipation will remain unattainable. Collecting fourteen of Vattimo's most influential essays on ethics, politics, and law, _Nihilism and Emancipation_ is a provocative reevaluation of meaning, values, and the idea of freedom in Western culture. (shrink)

Suggests that contemporary marriage is at the heart of a serious cultural paradox that renders it strongly valued, but rather brittle. Scientific and therapeutic approaches to this dilemma have had limited success in resolving this problem because professionals have accepted and promoted the popular aspiration of personal fulfillment through marriage, which may have engendered the fragility of marriage. The author provides a brief hermeneutic account designed to make the incoherence of contemporary marriage more intelligible, and (...) to clarify the moral dimension of psychology. Marital research illustrates how a hermeneutic perspective can guide a specific research domain in becoming more responsive to the essential social and ethical concerns that animate it. Suggestions for how researchers can explore why marriage is so central to modern life are offered. 2012 APA, all rights reserved). (shrink)

This paper shows an analysis of some found solutions for the famous aporia of the race between Achilles and the Tortoise. As an introduction, we present the mechanical solution, to establish that it is not in the field of matters of fact where you can resolve a purely rational problem like the one raised by Zeno of Elea. And so, the main part of the article is dedicated to the mathematical solutions, which face the problem under the point of view (...) of the single, mathematical reason. There are two mathematical solutions for Zeno’s paradox. First, we attend to that which we denominate “classical” (because it is the most habitually used by mathematicians), which is based on the calculus of addiction of terms of a geometrical series in progressive decrease. The second considered solution is the one that was proposed by Russell, based upon the theory of the transfinite numbers. The analysis we have made gets us to discover that no one of those solutions can save itself from falling into logical contradictions, therefore it seems that Zeno’s problem is an authentic aporia, which, after so much time, continues challenging human intelligence. As the article’s conclusion, we suggest that the cause of the impossibility of solving Zeno’s problem is the very notion of mathematical continuum, because this notion infringes the logic of facts. (shrink)

The paradox of mass voting is not, generally speaking, matched by a paradoxical mass attempt to be politically well informed. As Converse underscored, most people are grossly politically ignorant—just as they would be if, as rational‐ignorance theory holds, they realized that their votes don't matter. Yet many millions of them contradict the theory by voting. This contradiction, and the illogical reasons people offer for voting, suggest that the logic of collective action does not come naturally to people. To equate (...) public ignorance with “rational ignorance,” then, attributes too much theoretical self‐consciousness to people. Even if their ignorance is not based on a grasp of the collective‐action problem, however, people's political ignorance is “rational”: but it is less a matter of calculating the low benefit likely to flow from one vote in a sea of millions, than of encountering the much higher cost of being well informed as compared to voting. As the high cost of becoming well informed appears likely to grow, it may be advisable to move off of the political agenda issues that have no clear continuum toward which a mostly ignorant median voter may gravitate. (shrink)

This chapter contains sections titled: Reference and Literary Language The Second Inheritance: Revealing the World through Metaphor and Paradox Initiation into the World: Appreciating the Adequacy of Words The Continuum between Philosophy and Literature Conclusion.

Hermeneutical scholars doubt whether many past authors really existed. They are only a sort of construction built with the passing of time. Indeed, Zeno of Elea, for instance, was real, and historians attempted to establish what he wrote and intended to say. Our most important source for Zeno is Aristotle. Zeno’s paradoxes deeply influenced the latter’s Physics. Is Aristotle’s physics relevant to us? Yes, because philosophical problems are too complex not to be considered in their historical development as well. In (...) reading Zeno and Aristotle, we can see physical problems from a completely different perspective and learn a lot. In other terms, the historical Zeno is disorienting for us. On the other hand, Zeno’s historical legacy is extremely interesting for us. Indeed, we will see how Zeno’s and Aristotle’s reflections on continuum, extension, and movement could contribute to a better understanding of these notions in the contemporary debate. (shrink)