Can God create a stone too heavy for him to lift? Can time have a beginning? Which came first, the chicken or the egg? Riddles, paradoxes, conundrums--for millennia the human mind has found such knotty logical problems both perplexing and irresistible. Now Roy Sorensen offers the first narrative history of paradoxes, a fascinating and eye-opening account that extends from the ancient Greeks, through the Middle Ages, the Enlightenment, and into the twentieth century. When Augustine asked what God was doing before (...) He made the world, he was told: "Preparing hell for people who ask questions like that." A Brief History of the Paradox takes a close look at "questions like that" and the philosophers who have asked them, beginning with the folk riddles that inspired Anaximander to erect the first metaphysical system and ending with such thinkers as Lewis Carroll, Ludwig Wittgenstein, and W.V. Quine. Organized chronologically, the book is divided into twenty-four chapters, each of which pairs a philosopher with a major paradox, allowing for extended consideration and putting a human face on the strategies that have been taken toward these puzzles. Readers get to follow the minds of Zeno, Socrates, Aquinas, Ockham, Pascal, Kant, Hegel, and many other major philosophers deep inside the tangles of paradox, looking for, and sometimes finding, a way out. Filled with illuminating anecdotes and vividly written, A Brief History of the Paradox will appeal to anyone who finds trying to answer unanswerable questions a paradoxically pleasant endeavor. (shrink)

In this chapter I articulate the threat that time travel to the past allegedly poses to the free will of the time traveler, and I argue that on the traditional way of thinking about free will, the incompatibilist about time travel and free will wins the day. However, a residual worry about the incompatibilist view points the way toward a novel way of thinking about free will, one that I tentatively explore toward the end of the chapter.

A three-valued propositional logic is presented, within which the three values are read as ?true?, ?false? and ?nonsense?. A three-valued extended functional calculus, unrestricted by the theory of types, is then developed. Within the latter system, Bochvar analyzes the Russell paradox and the Grelling-Weyl paradox, formally demonstrating the meaninglessness of both.

Nobody interested in philosophy need be deterred by Kant's reputation for difficulty from familiarizing himself with his ethics. While the Critique of Pure Reason and his other non-ethical works are very hard to follow, the first two chapters of the Fundamental Principles of the Metaphysic of Morals at least are clear and straightforward and presuppose little previous acquaintance with philosophy. The third chapter is not about ethics as such but about the metaphysical problem of freedom and should be omitted by (...) anyone who is not familiar with Kant's general philosophy, but the first two. (shrink)

The notion of choice and its individualistic underpinnings is fundamentally inconsistent with the collectivist NHS ethosIn both the policy1 and academic2 literatures, the issue of extending patient choice in the UK National Health Service is currently a much discussed issue. From December 2005—for example, general practitioners will be required to offer patients needing elective surgery the choice of five providers at the point of referral.1 Choice is often thought of as an intrinsically good thing; that is, that people value choice (...) in and of itself.3 A probable underlying reason for this belief is that choice is tied in with the notion of individual autonomy, or freedom, a concept that looms large in ethical theories of the good. Beauchamp and Childress—for example, classified respect for …. (shrink)

Given any proposition, is it possible to have rationally acceptable attitudes towards it? Absent reasons to the contrary, one would probably think that this should be possible. In this paper I provide a reason to the contrary. There is a proposition such that, if one has any opinions about it at all, one will have a rationally unacceptable set of propositional attitudes—or if one doesn’t, one will end up being cognitively imperfect in some other manner. The proposition I am concerned (...) with is a self-referential propositional attitude ascription involving the propositional attitude of rejection. Given a basic assumption about what constitutes irrationality, and a few assumptions about the nature of cognitively ideal agents, a paradox results. This paradox is superficially like the Liar, but it is importantly different in that no alethic notions are involved at all. As such, it stands independent of the Liar and is not a ‘revenge’ version of it. After setting out the paradox I discuss possible responses. After considering several I argue that one is best off simply accepting that the paradox shows us something surprising and interesting about rationality: that some cognitive shortfall is unavoidable even for ideal agents. I argue that nothing disastrous follows from accepting this conclusion. (shrink)

This paper seeks to question the position of ZF as the dominant system of set theory, and in particular to examine whether there is any philosophical justification for the axiom of foundation. After some historical observations regarding Poincare and Russell, and the notions of circularity and hierarchy, the iterative conception of set is argued to be a semi-constructvist hybrid without philosophical coherence. ZF cannot be justified as necessary to avoid paradoxes, as axiomatizing a coherent notion of set, nor on pragmatic (...) grounds, and should be replaced by a system allowing non-well-founded sets. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:"And Her Substance Would Be Mine":Envy, Hate, and Ontological Evacuation in Josephine Hart's SinA. Samuel Kimball (bio)Envy involuntarily testifies to a lack of being that puts the envious to shame.—René Girard, A Theatre of EnvySin, offspring of snt-ya, "that which is," in Germanic sun(d)jo, "it is true," "the sin is real," and ultimately from es-, "to be," source of am, is, sooth, soothe; of the Sanskrit roots sat- and (...) sant-, "existing, true, virtuous"; of the Latin, esse, "to be," from which is derived such words as essence, presence, absence, and represent; of the Greek roots einei, "to be" as well as ont-, "being," which provides the name for the philosophical study of being itself, ontology.—Adapted from The American Heritage Dictionaryof Indo-European RootsI: Ruth Garton's Envious NarrationThe etymology of sin suggests that the evil it names reveals something fundamental about being, something ruinous and yet unavoidable, something that endangers or even nullifies being and yet is inseparable from it, even essential to it. In Josephine Hart's second novel, Sin, this something is a species of Girardian desire in the form of a monstrous envy, which impels the first-person narrator, Ruth Garton, to a lifelong hatred of her cousin and stepsister, Elizabeth. The focus of Ruth's confessional narrative, envy, drives Ruth to take covert and increasingly virulent revenge against her quasi-sibling in a self-deluding attempt to appropriate not only the objects of Elizabeth's desire but ultimately Elizabeth's desire itself and the apparent ontological fullness that Ruth attributes to it. Over the course of her life, then, Ruth loses the promise [End Page 239] of her name in her ruthless pursuit of her enemy. As she becomes increasingly frustrated in her efforts to destroy her sister's life, Ruth finally turns her hatred of her nemesis against herself as well as the readers to whom she appeals for understanding. If envy heightens Ruth's consciousness to the point where she can perceive that her desire signals her ontological emptiness, nevertheless, it so captures her, so dominates her emotional and cognitive life, that she is unable to find a way to affirm her own—or anyone else's—being in the world. The result is a spectacular narrative record of the cost of recognizing but being unable to resist the mimeticism of desire.1II. The Girardian Dynamic of SinAs Girard has demonstrated, one of the most difficult existential challenges is to understand that desire is mimetically mediated. The result is that we come into our desire only through someone else's and always want something more and other than we think we want. Behind every move to possess a particular object is a largely unrecognized and in principle unsatisfiable desire for absolute satisfaction in the form of ontological completeness, self-sufficiency, intactness. On the one hand, Girard writes, "by the example of his own desire…the model conveys to the subject the supreme desirability of the object" (1977, 146). On the other hand, since to desire mimetically means to come into desire through the other rather than through oneself, by this same example the model conveys to the subject the contingency, the dependency, the secondariness, hence the emptiness of the subject's desire, even the subject's lack of desire, the lack that, paradoxically, constitutes his or her desire. Therefore, to be subjected to the other's want ultimately has the effect of signaling the seeming priority, fullness, and self-origination of this other person's desire. For this reason Girard asserts that "man... desires being, something he himself lacks and which some other person seems to possess" (146).If at first the other person models the desire that the subject lacks, it is in the logic of mimesis that the other will become a rival and, unless the rivalry is somehow interrupted or abrogated, inevitably an enemy to be destroyed. The subject will become locked into a potentially deadly game of trying to obtain the same object that the model desires, so as to experience the satisfactions—ultimately, the sense of being—that the object in question seems to provide... (shrink)

1. The “puzzle” Physical objects are coloured: roses are red, violets are blue, and so forth. In particular, physical objects have fine-grained shades of colour: a certain chip, we can suppose, is true blue (unique, or pure blue). The following sort of scenario is commonplace. The chip looks true blue to John; in the same (ordinary) viewing conditions it looks (slightly) greenish-blue to Jane. Both John and Jane are “normal” perceivers. Now, nothing can be both true blue and greenish-blue; since (...) the chip is true blue, it is not greenish-blue. Hence Jane, unlike John, is misperceiving the chip. Generalizing, the conclusion is that there is widespread misperception of fine-grained shades. According to Tye (2006), and Cohen, Hardin, and McLaughlin (2006), the previous paragraph amounts to a paradox: an apparently unacceptable conclusion has been drawn from apparently acceptable premises via apparently acceptable reasoning. (See also Hawthorne and Kovakovich 2006, 180-1.) Tye swallows the conclusion, aided by a dose of evolutionary speculation. Hardin (1988), on the other hand, rejects the first premise, and denies that physical objects are coloured. Cohen (2004) and McLaughlin (2003) claim that both Jane and John have the colour of the chip right. Our opening paragraph concealed a crucial parameter. In fact, the chip looks greenish-blue-relative-to- circumstances-C to Jane, and true-blue-relative-to-circumstances-C* to John, and the chip has both these relativized colours.1 All this ingenious philosophizing would be in vain, of course, if the conclusion of the opening paragraph were not puzzling or problematic. So, why is it supposed to be? According to Tye, the conclusion is puzzling because John and Jane are both “normal perceivers” (xx). He seems to think that it is (prima facie) plausible to assume.. (shrink)

We explore a non-classical, universal set theory, based on a purely 'structural' conception of sets. A set is a transfinite process of unfolding of an arbitrary binary structure, with identity of sets given by the observational equivalence between such processes. We formalize these notions using infinitary modal logic, which provides partial descriptions for set structures up to observational equivalence. We describe the comprehension and topological properties of the resulting set-theory, and we use it to give non-classical solutions to classical paradoxes, (...) to prove fixed-point theorems that relate recursion and corecursion, to formalize 'super-large', reflexive categories and 'super-large' circular modes, and to provide 'natural' solutions for domain equations. (shrink)

We use Homer and Sun Tzu as a background to better understand and reformulate confrontation, anger and violence in medicine, contrasting an unproductive ‘love of war’ with a productive ‘art of war’ or ‘art of strategy’. At first glance, it is a paradox that the healing art is not pacific, but riddled with militaristic language and practices. On closer inspection, we find good reasons for this cultural paradox yet regret its presence. Drawing on insights from Homer's The Iliad (...) and The Odyssey, we argue for better understanding of confrontation, anger, bullying, intimidation and violence in medicine in order to change the culture. For example, equating medicine with war is not a given condition of medicine but a convenient metaphor with historical origins and a historical trajectory. Other, non-martial metaphors, such as medicine as collaboration, may be more appropriate in an age of team-based care. Taking lessons from Homer, we suggest three key ways in which cold-hearted confrontation and anger in medicine can be transformed into productive, warm-hearted engagement: the transformation of angry impulse into reflection, moral courage and empathy. Thinking with Homer can offer an aesthetically and morally charged alternative to the current body of literature on topics, such as anger in doctors, and how this may be ‘managed’, without recourse to an instrumental economy where emotions are viewed as commodities, and emotional responses can be ‘trained’ through communication skills courses. (shrink)

Diese Arbeit zeigt, dass die Dualität des mathematischen und dynamischen Erhabenen bei Kant auch dem Zweck der dritten Kritik dient, die Kluft zwischen den Gebieten der Natur und der Freiheit zu schließen. In der Sekundärliteratur zu Kant wird das Erhabene oft als Anhang des Schönen oder aufgrund seiner mehrfachen Dualitäten als Bruch in Kants Ansatz angesehen. Dies geschieht, weil solche Interpretationen die Elemente der Theorie des Erhabenen atomisch und nicht systematisch rekonstruieren. Im Gegensatz dazu wird in dieser Arbeit mittels der (...) Resonanz der teleologischen Behandlung der Vernunft nicht nur die innere Systematik der dritten Kritik gezeigt, sondern auch die von der gesamten kritischen Philosophie. Die Vernunft als Vermögen der Zwecksetzung zu verstehen in ihrem praktischen und theoretischen Gebrauch, ist keine neue Idee oder neuer systematischer Rekonstruktionsversuch der kritischen Philosophie in der Kantforschung. Das eigentlich Neue in dieser Monografie ist, einen Beweis von ihrer teleologischen Einheit aus der ästhetischen Perspektive des paradoxen Gefühls des Erhabenen geleistet zu haben. (shrink)

In 1956, a few writings of Wittgenstein that he didn't publish in his lifetime were revealed to the public. These writings were gathered in the book Remarks on the Foundations of Mathematics (1956). There, we can see that Wittgenstein had some discontentment with the way philosophers, logicians, and mathematicians were thinking about paradoxes, and he even registered a few polemic reasons to not accept Gödel’s incompleteness theorems.

The “theorems” showing the impossibility of ascribing to individual quantum systems a definite value of a set of observables, not necessarily commuting,1–4 are based on the tacit assumption that eachindividual spin component has a discrete dichotomic value. We show explicitly that it is possible to introduce continuous hidden variables for individual spins which avoid these quantum paradoxes without changing any of the observed quantum mechanical results.

A Cabinet of Philosophical Curiosities is a collection of puzzles, paradoxes, riddles, and miscellaneous logic problems. Depending on taste, one can partake of a puzzle, a poem, a proof, or a pun.

What is the ethical impact of artificial intelligence assistants on human lives, and specifically how much do they threaten our individual autonomy? Recently, as part of forming an ethical framework for thinking about the impact of AI assistants on our lives, John Danaher claims that if the external automaticity generated by the use of AI assistants threatens our autonomy and is therefore ethically problematic, then the internal automaticity we already live with should be viewed in the same way. He takes (...) advantage of this paradox of internal automaticity to downplay the threats of external automaticity to our autonomy. We respond in this paper by challenging the legitimacy of the paradox. While Danaher assumes that internal and external automaticity are roughly equivalent, we argue that there are reasons why we should accept a large degree of internal automaticity, that it is actually essential to our sense of autonomy, and as such it is ethically good; however, the same does not go for external automaticity. Therefore, the similarity between the two is not as powerful as the paradox presumes. In conclusion, we make practical recommendations for how to better manage the integration of AI assistants into society. (shrink)

Contents: 1. Life 2. Humanism and Alienation 3. Towards a Science of History 4. Scientific Socialism 5. Labour, Value and Exploitation: I. Theoretical 6. Labour, Value and Exploitation: II. Historical 7. The State, Democracy and Revolution 8. Marx and Philosophy 9. Paradoxes in Marx’s Thought? 10. Marx Today.

A Brief History of the Paradox is the first narrative history of paradoxes. Sorenson draws us deep inside the tangles of riddles, paradoxes and conundrums by answering the questions which are seemingly unanswerable. Can God create a stone too heavy for him to lift? Can time have a beginning? Which came first, the chicken or the egg? Filled with illuminating anecdotes, A Brief History of the Paradox is vividly written and will appeal to anyone who finds trying to (...) answer unanswerable questions a paradoxically pleasant endeavour. (shrink)

A group of thirteen essays, most of them being either meta-philosophical or metaphysical. The latter group can be seen as applying the theme Wisdom plays so often in the former group and in his previous works: the comparison of one type of statement with another, leading to discoveries which resolve philosophical paradoxes but which can, if misused, engender new ones. Of special interest: "Religious Belief" and "The Metamorphosis of Metaphysics." The price of this volume is unfortunate, as is the printing (...) job.—A. E. J. (shrink)

In this rigorous investigation into the logic of truth Anil Gupta and Nuel Belnap explain how the concept of truth works in both ordinary and pathological..

The Cable Guy is coming. You have to be home in order for him to install your new cable service, but to your chagrin he cannot tell you exactly when he will come. He will definitely come between 8.a.m. and 4 p.m. tomorrow, but you have no more information than that. I offer to keep you company while you wait. To make things more interesting, we decide now to bet on the Cable Guy’s arrival time. We subdivide the relevant part (...) of the day into two 4-hour long intervals, ‘morning’: (8, 12], and ‘afternoon’: (12, 4). You nominate an interval on which you will bet. If he arrives during your interval, you win and I will pay you $10; otherwise, I win and you will pay me $10. Notice that we stipulate that if he arrives exactly on the stroke of noon, then (8, 12] is the winning interval, since it is closed on the right; but we agree that this event has probability 0 (we have a very precise clock!). At first you think: obviously there is no reason to favour one interval over the other. Your probability distribution of his arrival time is uniform over the 8 a.m. – 4 p.m. period, and thus assigns probability 1/2 to each of the two 4-hour periods at issue. Whichever period you nominate, then, your expected utility is the same. The two choices are equally rational. But then you reason as follows. Suppose that you choose the morning interval. Then there will certainly be a period during which you will regard the other interval as.. (shrink)

The nature and consequences of readers’ affective engagement with literature has, in recent years, captured the attention of experimental psychologists and philosophers alike. Psychological studies have focused principally on the causal mechanisms explaining our affective interactions with fictions, prescinding from questions concerning their rational justifiability. Transportation Theory, for instance, has sought to map out the mechanisms the reader tracks the narrative experientially, mirroring its descriptions through first-personal perceptual imaginings, affective and motor responses and even evaluative beliefs. Analytical philosophers, by contrast, (...) have largely focussed on the problems fiction poses for traditional theories of rationality (as in the ‘Paradox of Fiction), challenging fiction’s wider epistemic value. The result has been a theoretical impasse in which the power of fiction to affectively ‘transport’ a reader is at once often lauded (by psychologists) as a privileged route to interpersonal understanding, and condemned (by philosophers) as an abdication of the authority of reason. This chapter surveys some of the central claims on both sides, tracing the source of the debate to competing conceptions of rationality. (shrink)

We explore the developmental paradox of false belief understanding. This paradox follows from the claim that young infants already have an understanding of false belief, despite the fact that they consistently fail the elicited-response false belief task. First, we argue that recent proposals to solve this paradox are unsatisfactory because they (i) try to give a full explanation of false belief understanding in terms of a single system, (ii) fail to provide psychological concepts that are sufficiently fine-grained (...) to capture the cognitive requirements for the various manifestations of false belief understanding, and (iii) ignore questions about system interaction. Second, we present a dual-system solution to the developmental paradox of false belief understanding that combines a layered model of perspective taking with an inhibition-selection-representation mechanism that operates on different levels. We discuss recent experimental findings that shed light on the interaction between these two systems, and suggest a number of directions for future research. (shrink)