Rabern and Rabern (2008) have noted the need to modify `the hardest logic puzzle ever’ as presented in Boolos 1996 in order to avoid trivialization. Their paper ends with a two-question solution to the original puzzle, which does not carry over to the amended puzzle. The purpose of this note is to offer a two-question solution to the latter puzzle, which is, after all, the one with a claim to being the hardest (...) logic puzzle ever. (shrink)

"The Hardest Logic Puzzle Ever" was first described by the late George Boolos in the Spring 1996 issue of the Harvard Review of Philosophy. Although not dissimilar in appearance from many other simpler puzzles involving gods (or tribesmen) who always tell the truth or always lie, this puzzle has several features that make the solution far from trivial. This paper examines the puzzle and describes a simpler solution than that originally proposed by Boolos.

Rabern and Rabern (Analysis 68:105–112 2 ) and Uzquiano (Analysis 70:39–44 4 ) have each presented increasingly harder versions of ‘the hardest logic puzzle ever’ (Boolos The Harvard Review of Philosophy 6:62–65 1 ), and each has provided a two-question solution to his predecessor’s puzzle. But Uzquiano’s puzzle is different from the original and different from Rabern and Rabern’s in at least one important respect: it cannot be solved in less than three questions. In (...) this paper we solve Uzquiano’s puzzle in three questions and show why there is no solution in two. Finally, to cement a tradition, we introduce a puzzle of our own. (shrink)

We present the simplest solution ever to 'the hardest logic puzzle ever'. We then modify the puzzle to make it even harder and give a simple solution to the modified puzzle. The final sections investigate exploding god-heads and a two-question solution to the original puzzle.

In this paper, we first propose a simple formal language to specify types of agents in terms of necessary conditions for their announcements. Based on this language, types of agents are treated as ‘first-class citizens’ and studied extensively in various dynamic epistemic frameworks which are suitable for reasoning about knowledge and agent types via announcements and questions. To demonstrate our approach, we discuss various versions of Smullyan’s Knights and Knaves puzzles, including the Hardest Logic Puzzle Ever (...) (HLPE) proposed by Boolos (in Harv Rev Philos 6:62–65, 1996). In particular, we formalize HLPE and verify a classic solution to it. Moreover, we propose a spectrum of new puzzles based on HLPE by considering subjective (knowledge-based) agent types and relaxing the implicit epistemic assumptions in the original puzzle. The new puzzles are harder than the previously proposed ones in the literature, in the sense that they require deeper epistemic reasoning. Surprisingly, we also show that a version of HLPE in which the agents do not know the others’ types does not have a solution at all. Our formalism paves the way for studying these new puzzles using automatic model checking techniques. (shrink)

Uzquiano (Analysis 70:39–44, 2010 ) showed that the Hardest Logic Puzzle Ever ( HLPE ) [in its amended form due to Rabern and Rabern (Analysis 68:105–112, 2008 )] has a solution in only two questions. Uzquiano concludes his paper by noting that his solution strategy naturally suggests a harder variation of the puzzle which, as he remarks, he does not know how to solve in two questions. Wheeler and Barahona (J Philos Logic, to appear, (...) 2011 ) formulated a three question solution to Uzquiano’s puzzle and gave an information theoretic argument to establish that a two question solution for Uzquiano’s puzzle does not exist. However, their argument crucially relies on a certain conception of what it means to answer self-referential yes–no questions truly and falsely . We propose an alternative such conception which, as we show, allows one to solve Uzquiano’s puzzle in two questions. The solution strategy adopted suggests an even harder variation of Uzquiano’s puzzle which, as we will show, can also be solved in two questions. Just as all previous solutions to versions of HLPE , our solution is presented informally. The second part of the paper investigates the prospects of formally representing solutions to HLPE by exploiting theories of truth. (shrink)

In this paper, we present a framework in which we analyze three riddles about truth that are all (originally) due to Smullyan. We start with the riddle of the yes-no brothers and then the somewhat more complicated riddle of the da-ja brothers is studied. Finally, we study the Hardest Logic Puzzle Ever (HLPE). We present the respective riddles as sets of sentences of quotational languages , which are interpreted by sentence-structures. Using a revision-process the consistency of (...) these sets is established. In our formal framework we observe some interesting dissimilarities between HLPE’ s available solutions that were hidden due to their previous formulation in natural language. Finally, we discuss more recent solutions to HLPE which, by means of self-referential questions , reduce the number of questions that have to be asked in order to solve HLPE . Although the essence of the paper is to introduce a framework that allows us to formalize riddles about truth that do not involve self-reference, we will also shed some formal light on the self-referential solutions to HLPE. (shrink)

According to Stephen Finlay, ‘A ought to X’ means that X-ing is more conducive to contextually salient ends than relevant alternatives. This in turn is analysed in terms of probability. I show why this theory of ‘ought’ is hard to square with a theory of a reason’s weight which could explain why ‘A ought to X’ logically entails that the balance of reasons favours that A X-es. I develop two theories of weight to illustrate my point. I first look at (...) the prospects of a theory of weight based on expected utility theory. I then suggest a simpler theory. Although neither allows that ‘A ought to X’ logically entails that the balance of reasons favours that A X-es, this price may be accepted. For there remains a strong pragmatic relation between these claims. (shrink)

A common concern with respect to cloning is based on the belief that cloning produces identical individuals. This is a fundamental misunderstanding of what type of identity-relation cloning involves. The concept "identity" is ambiguous, and the statement that cloning produces "identical" individuals is not meaningful unless the notion of identity is clarified. This paper distinguishes between numerical and qualitative; relational and intrinsic; logical and empirical identity, and discusses the empirical individuation of clones in terms of genetics, physiology, perception, cognition and (...) personality. I argue that the only relation of identity cloning involves is qualitative, intrinsic and empirical: genetic indiscernibility , unlikely to include identity under other aspects mentioned. A popular argument against cloning claims our "right" to a "unique identity". This objection either implies (absurdly) the right not to be an identical twin, or assumes (incorrectly) that cloning involves identity other than genetic. Either way, the argument is untenable. (shrink)

How deep is the current diversity in the panoply of theories to define consciousness, and to what extent do these theories share common denominators? Here we first examine to what extent different theories are commensurable (or comparable) along particular dimensions. We posit logical (and, when applicable, empirical) commensurability as a necessary condition for identifying common denominators among different theories. By consequence, dimensions for inclusion in a set of logically and empirically commensurable theories of consciousness can be proposed. Next, we compare (...) a limited subset of neuroscience-based theories in terms of commensurability. This analysis does not yield a denominator that might serve to define a minimally unifying model of consciousness. Theories that seem to be akin by one denominator can be remote by another. We suggest a methodology of comparing different theories via multiple probing questions, allowing to discern overall (dis)similarities between theories. Despite very different background definitions of consciousness, we conclude that, if attention is paid to the search for a common methological approach to brain-consciousness relationships, it should be possible in principle to overcome the current Babylonian confusion of tongues and eventually integrate and merge different theories. (shrink)

The belief that memory is essential to the self is common. Extreme amnesia, e.g., Korsakoff Syndrome, is held to dissolve the afflicted person’s self. This belief is a misconception that rests on a confusion of epistemic with ontological relevance. Epistemically, memory is relevant to the self: a subject’s self-knowledge partly depends on memories of past experiences. However, it is not by virtue of these memories that the subject is a self: ontologically, memory is irrelevant to that status. The fact that (...) an individuals conception of herself as existing through time is wanting does not prevent that individual from being a self at a given point in time. As the past is there whether or not it is remembered, so the self is there whether or not it remembers. If instead we define the self as awareness of being a subject of experience, the self may survive even the most extreme forms of amnesia. Being a self is an important social value, a prerequisite of numerous legal or moral rights. This in itself is questionable, like the social exclusion it may entail. Denying an amnesic person a self is therefore more than a logical mistake: it is a social exclusion that can also be questioned on ethical grounds. (shrink)

The belief that memory is essential to the self is common. Extreme amnesia, e.g., Korsakoff Syndrome, is held to dissolve the afflicted person’s self. This belief is a misconception that rests on a confusion of epistemic with ontological relevance. Epistemically, memory is relevant to the self: a subject’s self-knowledge partly depends on memories of past experiences. However, it is not by virtue of these memories that the subject is a self: ontologically, memory is irrelevant to that status. The fact that (...) an individuals conception of herself as existing through time is wanting does not prevent that individual from being a self at a given point in time. As the past is there whether or not it is remembered, so the self is there whether or not it remembers. If instead we define the self as awareness of being a subject of experience, the self may survive even the most extreme forms of amnesia. Being a self is an important social value, a prerequisite of numerous legal or moral rights. This in itself is questionable, like the social exclusion it may entail. Denying an amnesic person a self is therefore more than a logical mistake: it is a social exclusion that can also be questioned on ethical grounds. (shrink)

In today’s society, it becomes increasingly important to assess which non-human and non-verbal beings possess consciousness. This review article aims to delineate criteria for consciousness especially in animals, while also taking into account intelligent artifacts. First, we circumscribe what we mean with “consciousness” and describe key features of subjective experience: qualitative richness, situatedness, intentionality and interpretation, integration and the combination of dynamic and stabilizing properties. We argue that consciousness has a biological function, which is to present the subject with a (...) multimodal, situational survey of the surrounding world and body, subserving complex decision-making and goal-directed behavior. This survey reflects the brain’s capacity for internal modeling of external events underlying changes in sensory state. Next, we follow an inside-out approach: how can the features of conscious experience, correlating to mechanisms inside the brain, be logically coupled to externally observable properties? Instead of proposing criteria that would each define a “hard” threshold for consciousness, we outline six indicators: goal-directed behavior and model-based learning; anatomic and physiological substrates for generating integrative multimodal representations; psychometrics and meta-cognition; episodic memory; susceptibility to illusions and multistable perception; and specific visuospatial behaviors. Rather than emphasizing a particular indicator as being decisive, we propose that the consistency amongst these indicators can serve to assess consciousness in particular species. The integration of scores on the various indicators yields an overall, graded criterion for consciousness, somewhat comparable to the Glasgow Coma Scale for unresponsive patients. When considering theoretically derived measures of consciousness, it is argued that their validity should not be assessed on the basis of a single quantifiable measure, but requires cross-examination across multiple pieces of evidence, including the indicators proposed here. Current intelligent machines, including deep learning neural networks and agile robots, are not indicated to be conscious yet. Instead of assessing machine consciousness by a brief Turing-type of test, evidence for it may gradually accumulate when we study machines ethologically and across time, considering multiple behaviors that require flexibility, improvisation, spontaneous problem-solving and the situational conspectus typically associated with conscious experience. (shrink)

BackgroundEthical analyses of disorders of consciousness traditionally focus on residual awareness. Going one step further, this paper explores the potential ethical relevance of the unawareness retained by patients with disorders of consciousness, focusing specifically on the ethical implications of the description of the unconscious provided by recent scientific research.MethodsA conceptual methodology is used, based on the review and analysis of relevant scientific literature on the unconscious and the logical argumentation in favour of the ethical conclusions.ResultsTwo conditions that are generally considered (...) critical components in the ethical discussion of patients with disorders of consciousness might arguably be both conscious and unconscious.ConclusionsThe unconscious, as well as consciousness, should be taken into account in the ethical discussions of patients with disorders of consciousness. (shrink)

Educational leadership has a rich history of epistemological debate. From the ‘Theory Movement’_ _of the 1950-1960s, through to Greenfield’s critique of logical empiricism in the 1970s, the emergence of Bates’ and Foster’s Critical Theory of educational administration in the 1980s, and Evers’ and Lakomski’s naturalistic coherentism from1990 to the present time, debates about ways of knowing, doing, and being in the social world have been central to advancing scholarship. However, since the publication of Evers’ and Lakomski’s work, questions of the (...) epistemological preliminaries of research have become somewhat marginalised. This is not to suggest that such discussions are not taking place, but rather that they have been sporadic and piecemeal. In _New Directions in Educational Leadership Theory_, the contributors sketch possible alternatives for advancing scholarship in educational leadership. The coherence of this volume comes not from the adoption of a single theoretical lens, but rather from its engagement with epistemology, ontology, and methodology. The choice of the plural ‘alternatives’ is deliberate, and its use is to evoke the message that there is more than one way to advance knowledge. The approaches adopted across this collection offer fruitful directions for the field and hopefully will stimulate substantive dialogue and debate in the interest of advancing knowledge. This book was originally published as a special issue of _Educational Philosophy and Theory. _. (shrink)

The two works reprinted in this volume are a unique fusion of logical thought and inimitable whimsy. Written by the 19th-century mathematician who also gave us "Alive in Wonderland", they are among the most entertaining logical works ever written, and contain some of the most thought-provoking puzzles ever devised.

Twisted Logic: Navigating Life's Puzzles, Paradoxes, and Big Questions draws upon an array of popular and novel puzzles and paradoxes to help us understand and navigate our everyday world, as well as engaging with the big questions beyond. It will appeal to all those interested in learning about twisted logic and the ways in which intuition and common sense can sometimes lead us astray. The book is designed for everyone and is accessible to the layman and student alike. (...) No prior mathematical skill or technical knowledge is required. (shrink)

In this thesis I investigate the notion of experience in German Idealist Philosophy. I focus on the exploration of an alternative to the transcendental model notion of experience through Schelling's insight into the notion of logogrif. The structural division of this project into two sections reflects the two theoretical standpoints of this project, namely the logic and the logogrif of experience. The first section - the logic of experience - explores the notion of experience provided in Kant's Critique (...) of Pure Reason, Critique of Judgement and Fichte's Science of Knowledge. I argue that Kant's fundamental question about the possibility of synthetic a priori judgements succeeds in thematising the aporia of cognitive experience but results in a subject-oriented, representational model which radically confines the notion of experience to the constitutive laws of the understanding or to the normative precepts of Reason. Experience is founded upon a sharp division between faith and knowledge, will and logic, desire and reflection, absolute and finitude. Fichte's endeavour to articulate a non-representational account of experience, does not succeed in extricating itself from the representational model, so long as experience is reduced to the ever-producing deeds of the self-positing ego. Despite the serious differences between Kant's and Fichte's notions of experience, both accounts, so long as they unfold from a transcendental standpoint, attempt to resolve experience into conceptual laws or determinations of the ego's absolute will. Experience is transformed into an object of the subject's cognitive or volitional faculties. The paradoxes of man's interaction with the world are intended to be accommodated either by the law-giving spontaneity of the understanding and the Architectonic of Pure Reason or by the overpowerful primordial act of the self-positing ego. This implies the conceptualisation of the self in terms of constant identity-through-time, or sheer self-determination. However, this conceptualisation remains at the normative or prescriptive level, which in turn is projected upon the world. The latter, though appears as the subject's property, essentially remains alien and opaque, confirming the radical limitations of the ego rather than its order-giving authority. Moreover, this notion of experience is ultimately founded upon a radical expulsion of the divine from the world, the de-spiritualisation of the sensual and the de-sensualisation of the spiritual, the sharp juxtaposition between absolute and finitude. This results in a self-defeating subjectivity, whose firm identity and rule-giving authority does not rescue it from its perennial unattainability to 'organise the conditioned' or 'conquer the unconditioned'. In Kant's and Fichte's thought, however, I detect elements that potentially transgress their transcendental account of experience. These are found in Kant's concept of spontaneity and free play between understanding and imagination, and Fichte's concept of productivity. I argue that these elements lose their potential dynamism, so long as they are absorbed by the transcendental demands for the solution of the aporias of logic. However, these elements point to the need for a radical re-conceptualisation of the notion of experience. This is provided by means of Schelling's logogriflic approach, which constitutes the theme of the second section. The second section - the logogrif of experience - attempts to articulate a different approach towards the notion of experience, through an exploration of Schelling's versatile and provocative thought. This section focuses on Schelling's original insight into the notion and act of logogrif, which opens the dialogue between logos and mythos, cosmic becoming and human soul, cosmic imagination and human reflection, faith and knowledge. This section attempts to illuminate Schelling's fascinating philosophical investigations and discoveries that have been rather overlooked, possibly, due to Hegel's overwhelming critique. This section, after a brief critical examination of the Identity Philosophy, attempts to elucidate Schelling's notion of experience through his middle works, Of Human Freedom, Ages of the World, The Deities of Samothrace, which are treated as a self-developing trilogy. Schelling re-addresses the aporias of logic not as part of Reason's self-interrogation but as part of the cosmic paradoxes and living experiences. In this way, Schelling resets the scene of the debate on the conditions of possibility for cognitive experience by putting on the stage the enigmas of the cosmos and life rather than the Tribunal of Reason. Logic itself is conceived as a potency in the cosmic becoming, and consequently can no longer attempt to establish the transcendental conditions for the possibility of cognitive experience. Cosmic becoming, in which man is an active part, is conceived as the process of the movement, the interaction, the transformations and transmutations of multiple potencies. These, far beyond any mechanical conceptualisation, appear as self-moving and yet interdependent, unknown yet familiar, inscrutable and yet manifest powers, describing the mystery of life itself. The latter is depicted as an ever-recurrent act of longing for self-expression as active unity. Experience is conceived as the lived process of a network of living potencies, which may not only resist rational powers but may also puzzle and seize them. In this context, reflection acquires a plastic dimension, as opposed to its rigidity in the representational model of experience. Reflection depicts cosmic longing's self-formation, whose man is part. This self-bending formation partially illuminates the nature of longing, and from this standpoint is the logic of the longing. However, this formation is movable, transmutable and mostly ineffable, and from this standpoint is the logic of a riddle: a logogrif. Logogrif is the transitive term that attempts to describe the transition of experience from its enacted phase to its allusive conceptual utterance, and in this sense the term itself participates in both phases, as both form of thought and form of life. The logogrific approach to experience in turn transposes us as from the realm of pure concepts to the realm of the mystery of life, from pure thought to acts of longing, from the Architectonic of Pure Reason to Cosmic Theurgy. The latter term attempts to grasp the paradox and dynamism of cosmic and non-cosmic becoming by means of multiple, vanishing and ever-recurring, transmutable potencies, or in Schelling's terms 'the magic of insoluble life'. Schelling's logogrific account consists in a powerful voice for the re-enchantment of the world, the introduction into the notion of experience of the imminence of the divine. This is not suggested in terms of the adoption of old religious doctrines but by means of the discovery and re-discovery of the theurgy of life, through the intensification of our artistic mood, the creative expansion of our deeds. This notion of experience allows for the reconsideration of the notion of the self, in terms of a dynamic, conflictual process between conscious and unconscious powers and the critical revaluation of the accounts of subjectivity which reduce it to the sphere of self-consciousness. The thesis concludes with the need for an investigation into the relation between logos and mythos, which only tangentially has been introduced by the present project. In this context it will be possible to re-appraise the potential that the logogrific approach opens for an alternative to both logical and traditional mythological patterns of thinking. (shrink)

The article aims to contribute to the sociological theory of the welfare state by addressing a fundamental puzzle of social policy, namely, the weakness of its claim to be a rational effort of society dealing with problems of social integration. Drawing on the work of Franz-Xaver Kaufmann, I distinguish between the cultural or ideational side of the welfare state and the social engineering or outcome side, arguing to take the rhetoric and symbolism of social policy more seriously. The integration (...) of society is more due to the communicative action of social policy than to its organizational quality. As early as the axial age civilizations, symbolism and ideology emerged as an autonomous field of social conflict and societal union. Taking ancient Israel as an example, I argue that societal integration may take place even in the absence of strong institutional correlates of social politics. This can help to explain why the welfare state in modern society is compatible with ever-increasing economic and social inequality. (shrink)

What I want to talk about here is a puzzle for historians of philosophy who, like me, have spent a fair amount of time studying the history of mediaeval logic and semantic theory. I don’t know how to solve it, but in various forms it has come up repeatedly in my own work and in the work of colleagues I have talked with about it. I would like to share it with you now.

Three-time New York Times bestselling author Dan Ariely teams up with legendary The New Yorker cartoonist William Haefeli to present an expanded, illustrated collection of his immensely popularWall Street Journal advice column, “Ask Ariely”. Behavioral economist Dan Ariely revolutionized the way we think about ourselves, our minds, and our actions in his books Predictably Irrational, The Upside of Irrationality, and The Honest Truth about Dishonesty. Ariely applies this scientific analysis of the human condition in his “Ask Ariely” Q & A (...) column in the Wall Street Journal, in which he responds to readers who write in with personal conundrums ranging from the serious to the curious: What can you do to stay calm when you’re playing the volatile stock market? What’s the best way to get someone to stop smoking? How can you maximize the return on your investment at an all-you-can-eat buffet? Is it possible to put a price on the human soul? Can you ever rationally justify spending thousands of dollars on a Rolex? In Ask Ariely, a broad variety of economic, ethical, and emotional dilemmas are explored and addressed through text and images. Using their trademark insight and wit, Ariely and Haefeli help us reflect on how we can reason our way through external and internal challenges. Readers will laugh, learn, and most importantly gain a new perspective on how to deal with the inevitable problems that plague our daily life. (shrink)

An entertaining series of logic problems and puzzles of increasing difficulty, and all relating important mathematical and logical concepts, includes mind-benders, paradoxes, metapuzzles, number exercises, and a mathematical novel.

Seventy-five fun puzzles to help improve mathematical and thinking skills. Decipher various clues by adding, subtracting, multiplying, dividing, reading carefully, and using powers of reason. Transfer the information onto grids that are provided, and find the solution to a given set of circumstances. "...the book is a delightful collection of problem situations that teachers and students will enjoy using..."--Mathematics.

A solitaire version of the classic paper and pencil game! A grid shows an "ocean," in which a flotilla of vessels--that you have to find--is concealed. Most of the puzzles have helpful hints revealing the contents of a few squares, and indicate how many squares in the corresponding rows and columns that contain ships. Sample puzzles show strategies for eliminating possibilities and clueing into likely arrangements. Puzzles are ranked according to difficulty.

In this entertaining and challenging collection of logic puzzles, Raymond Smullyan-author of Forever Undecided-continues to delight and astonish us with his gift for making available, in the thoroughly pleasurable form of puzzles, some of the most important mathematical thinking of our time.

Puzzles of logic involve knights, knaves, gods, demons, and mortals, and Inspector Craig conducts a summer-long adventure in combinatory logic, basic to computer science and artificial intelligence.

This piece is intended to explicate - by providing a precising definition of - the common cinematic figure which I term “the failure of the cinematic imagination,“ while presenting a logical puzzle and its solution within a simple Gricean framework. -/- It should be noted that this is neither fully accurate nor fully precise, because of the audience; one should examine the remaining articles in the issue to understand what I mean.

Puzzle-solving, like several other everyday activities, appears in a more sophisticated and ramified form in the realm of natural science. Improving on Thomas Kuhn's rudimentary account of puzzles in science, this paper formulates logical and functional criteria for the occurrence of scientific puzzles, and examines the two-fold nature of their solutions. Then, with the aid of erotetic logic, puzzle-posing questions are identified, their presuppositional relations to scientific theory and explanations are explored, and a new tool for history (...) of science research is developed. (shrink)

This book is a collage of ideas designed for eighth through twelfth grade students and their parents to have better relationships with one another and with the entire school community, to help and support their communities in different ways, and to appreciate the value of the experiences offered within and outside their communities.

In this paper, I will present a puzzle for logical analyses, such as Russell’s analysis of definite descriptions and Recanati’s analysis of ‘that’-clauses. I will argue that together with Kripke’s disquotational principles connecting sincere assent and belief such non-trivial logical analyses lead to contradictions. Following this, I will compare the puzzle about logical analysis with Frege’s puzzle about belief ascriptions. We will see that although the two puzzles do have similarities, the solutions to Frege’s puzzle cannot (...) be applied mutatis mutandis to the puzzle about logical analysis. Hence, to say it with Kripke, the main thesis of this paper is that the puzzle is a puzzle. A complete solution to the puzzle promises a better understanding of both logical analyses and belief ascriptions. (shrink)

Paradox Lost covers ten of philosophy’s most fascinating paradoxes, in which seemingly compelling reasoning leads to absurd conclusions. The following paradoxes are included: The Liar Paradox, in which a sentence says of itself that it is false. Is the sentence true or false? The Sorites Paradox, in which we imagine removing grains of sand one at a time from a heap of sand. Is there a particular grain whose removal converts the heap to a non-heap? The Puzzle of the (...) Self-Torturer, in which a series of seemingly rational choices has us accepting a life of excruciating pain, in exchange for millions of dollars. Newcomb’s Problem, in which we seemingly maximize our expected profit by taking an unknown sum of money, rather than taking the same sum plus $1000. The Surprise Quiz Paradox, in which a professor finds that it is impossible to give a surprise quiz on any particular day of the week... but also that if this is so, then a surprise quiz can be given on any day. The Two Envelope Paradox, in which we are asked to choose between two indistinguishable envelopes, and it is seemingly shown that each envelope is preferable to the other. The Ravens Paradox, in which observing a purple shoe provides evidence that all ravens are black. The Shooting Room Paradox, in which a deadly game kills 90% of all who play, yet each individual’s survival turns on the flip of a fair coin. Each paradox is clearly described, common mistakes are explored, and a clear, logical solution offered. Paradox Lost will appeal to professional philosophers, students of philosophy, and all who love intellectual puzzles. (shrink)

A number of philosophers maintain that the destruction of an embryo in the first 2 weeks after fertilization is not morally problematic as it is metaphysically impossible for any human organism to then have existed. We contend that the typical adult human organism was once a zygote so there is no metaphysical shortcut to justify early abortion. We show that five arguments against human organisms ever having been zygotes fail. All of the arguments have to do with one variant (...) or another of the zygote or early embryo dividing. They do not provide any reason to believe that since some adult organisms are not identical to zygotes due to earlier divisions, none could have been. (shrink)

Logic in Action/Doron Avital Nothing is more difficult, and therefore more precious, than to be able to decide (Napoleon Bonaparte) Introduction -/- This book was born on the battlefield and in nights of secretive special operations all around the Middle East, as well as in the corridors and lecture halls of Western Academia best schools. As a young boy, I was always mesmerized by stories of great men and women of action at fateful cross-roads of decision-making. Then, like as (...) today, I felt the full weight of the moment of truth as it confronts the individual, the man or woman of action, with the imminent necessity to decide. Alongside, as I was climbing up the ladder of education, I found myself just as well captivated by the great intellectual stories of our times, in particular 20th century analytic philosophy and, at its core, the machinery of modern logic. How do then the cool contemplative modes of the philosophical and analytic outlooks, that are better fitting of the philosopher's armchair at the fireplace, hang together with the heat of the battlefield or the angst of the ticking clock of time left to the completion of a daring special operation? Growing up I was pondering exactly that. Not accidently, and in fact as consequence, I have chosen a course in life that challenged me to visit the poles of both theory and practice. I set myself on a mission to unravel the tension between the contemplative inquiry, supposedly theoretical, aiming at the logical structure of things, and the uncompromising test of life and action. The puzzle of the gap between theory and practice has become ever since the guiding question of my life. -/- Not long ago, I met two friends, Avner Shor, a veteran combat soldier of the special forces unit I eventually commanded, and Aviram Halevi, a fellow officer with whom I served. Why will we not put into writing the ideas that guided us during our years of military action, we wondered. At that time, I used to deliver the keynote lectures to the senior officers' course of Israel central intelligence organization, the Mossad. For this I already had to put some of these ideas in writing. Avner was quick to introduce me with a notable publisher and even helped me write the first chapter. With Aviram I sat to many meetings, where he would challenge me with key questions, and we followed them with memories of operations and battles, aiming to draw the required lessons. This served me well when I finally sat down to write the first draft of the book. The result was more extensive than me and my friends had expected. I had to add a particularly long chapter dealing with the story of modern philosophy and logic. This was required, I felt, as no decision-making process lives in an intellectual vacuum. Knowingly or subconsciously, the intellectual climate of the time guides us for better or worse with the decisions we finally take. The initial draft was naturally cumbersome and inaccessible. But here I had the privilege of meeting a particularly talented editor, Rami Rothholtz. I found in Rami both an editor and a critical reader. As an infantry combat soldier at youth and now a senior journalist and editor, Rami insisted on simplifying and refining my ideas. Had it not been for his work, this book would have been literally unreadable. *** I opened my book with a brief description of a single night of a special operation deep at the Lebanon Bekaa valley, far away from Israel northern border. The mission was to kidnap a senior terror leader known to be holding in captivity an Israeli pilot. This was also the last special operation I commanded in my military career. A single special operation night, but what had to precede it? For sure, many months of intense and skillful preparations. What is Planning? This is the question with which I open up chapter (2) of the book. I confront in this chapter two approaches to planning. The first is the one I saw as a mission to myself to cultivate in my many years of military service. The second is the one I saw as representing a deep-rooted fallacy that holds a firm grip on today's conventional wisdom about planning. To further examine the logic of the competing models, I was required in chapter (3) to analyze the concept of "The Standard". I argue that the false model of planning has its roots in an attitude of an uncompromising adherence to the power of literal obedience to standards and rules. The standard, or what is outlined by a rule as prescribing a future course of action, is seen as an answer to the fundamental tension between theory (planning) and practice (execution). I argue in contrast that the standard does not produce an answer but rather what I call: "A Well-Defined Question". In essence, it is a meticulously-well-planned invitation to exercise a fresh judgment. A judgement that has as an anchor the default answer that the standard produces but is open to extension as it confronts the new frame of reference of the test of reality. In chapter (4), I present a new tool for planning and execution: "The Polygon of Risks" or "The Polygon of Execution". The Polygon is a geometric illustration of the underlying tension that exists between all dimensions of the operational project. The construction and conceptualization of the trade-offs that exist between the various dimensions - segments of the polygon - is the first topic on the planner's agenda. I position the concepts of "Daring" and "Taking Proactive and Well-Informed Risks" as necessary logical constituents of the polygon and show how in contrast the false model of planning is responsible for an operational culture that is risk-averse. It encourages, in fact, the piling up of false securities at the segments' level that eventually lead to the collapse of the polygon. The necessary trade-offs relationships that exist between the segments of the polygon express the fundamental tension between partnership and competition: partnership in a joint goal and competition over resources, both material and abstract. When this tension is not managed well, that is, when the players' local optimizations overshadow the global optimization required for the success of the project, the execution polygon collapses. In this scenario, we may find the setting of the bar of "High Standards" in a players' spheres of responsibility to conceal a hidden agenda of personal insurances taken against a possible failure. Once the overall risk is not mitigated by way of collaborative joint executional dialogue, the process that leads to a collapse of the polygon is literally unstoppable. *** In chapter (5), I discuss "(Fateful) Decisions". I examine the way in which we should translate the polygon into sequential critical decisions on the timeline. The execution polygon is not a rigid scaffolding but a dynamic conceptual illustration of the -/- project. It will need now to be converted into successive decision junctions. We will find the content of a decision and its timing on the timeline to be inseparable. The right decision is the one that is taken at the right time. The moment of decision is in fact the last moment of deliberation, the first moment available for action, i.e. the first possible "Can" is also the latest possible "Must". Deciding too soon is analog to the "Jumping of the Gun". The decision maker is forcing a pre-conceived answer to a state of affairs not ripe for an answer, e.g. the target in the shooting range is not yet erected. Late to decide and the decision maker may envision what he or she should have done but reality is no longer available for them to harness it right, e.g. consider a tennis player's frustration when reviewing a too-late-to-react move in the video replay. I review in this chapter many fateful decisions, both historical, from Napoleon's Waterloo, to a Bridge Too Far of WWII, to the failed rescue attempt of American hostages at the time of the Iranian Revolution, as well as fateful decisions I had to take in the course of my military life, both in combat and in special operations, and show the sense in which they all answer to our analysis. The theme of chapter (6) is "The Moment of Truth". This is the moment when everything is on the line and from which there is no turning back. I discuss the formative repetitive structure of the schooling and simulation phase and contrast it with the "One Shot, One Opportunity" nature of the moment of truth. This is extremely helpful when we analyze the logical structure of failures as unwarranted repetitions of past lessons. The schooling curriculum indeed consists of important abstractions drawn from lessons of the past. However, it is when we project them in a fashion that is literal or mechanical that we cross path with the possibility of a failure. The paradox of education is that what we must repeat in school and simulation must be extended and not repeated in real life. What is required of us so we do not fall into the fallacy of repetition in face of the moment of truth is the core subject of the discussion of this chapter. In chapter (7), I took a lengthy philosophical detour surveying the intellectual drama of modern logic, and in general, the story of 20th century analytic philosophy. Readers who choose to bypass the somehow demanding narrative of this drama can do so and still keep the argumentative thread of the book. However, even by way of skipping the more technical parts, I would still urge the readers to delve into the discussion in this chapter as I believe this would grant them a deeper understanding of the overall conceptual framework. I explore here the work of two key figures: the logician Kurt Gödel and the philosopher Ludwig Wittgenstein, both were crowned in 2000 by TIME Magazine, as the leading Logician and Philosopher, respectively, of the 20th Century. I review the fascinating logical result of Gödel's Incompleteness Theorem and examine its relevance as setting a theoretical limit to the power of formalization. This amazing logical result - a result that shakes the logical foundations of 20th century thought in as much as the discovery of irrational numbers shook the foundations of the Pythagorean program of the ancient Greeks - bears significantly on the question of action and the blind trust we place in the power of formalization in the form of protocols and rules. It is here that Wittgenstein's philosophy enters in full force. We follow Wittgenstein as he dismantles our conception of rules as if there were "Railroads to Infinite", i.e. as prescribing for us in-advance their proper employments in all possible -/- future eventualities. Instead we propose that the dilemma of action demands of us an extension of rules rather than a mechanical or blind repetition of their literal imperative. In turn, this extension can serve as a new lesson added to the curriculum of school and simulation. The theme of chapter (8), the concluding chapter, is Strategy, Logic, and Ethics. The chapter comes to place the ethical dilemma in the conceptual map we presented in the book. I discuss here the tension between strategy as a process of setting goals and deriving backward as it were the steps that are necessary for achieving these goals, to the inescapable dictation of the ethical imperative. This unavoidable tension is particularly important against the backdrop of contemporary culture that is guided by a vision of personal success and achievement that may threaten our ability to do what is right. Most of all, I am troubled in this chapter, with the role logic may play, first as a liberating force enabling a change that is tuned to the ethical imperative, and second, as a force designed to justify on logical grounds, as it were, the existing power structure. It is in this junction that brave individuals will be called to challenge the governing logic of the zeitgeist - logic that operates now as an oppressive force that serves the vested interest of beneficials of the existing order. When success is favored over doing what is right, as we must admit is the prevailing cultural mood of our times, that the words of Emanuel Kant carry their full weight: "Do the Right thing and leave the Consequences to God". For this we need heroes and heroines that challenge the time by bearing the full weight of responsibility that comes with the doing of what is Right. *** This book was written more than anything from the perspective of the heroes and heroines of action. Sometimes they may be missing the exact words or the full insight into the solid logical complexity that stands between them and the doing of what is right. They feel what is right to do on the battlefield of life, whether in real battle, in political or economic life or whether in the life of creativity and the quest of the intellect. They do need, in analogy, proper logical and intellectual artillery. I hope they will find the logical cannons they require as they travel through the pages of this book. The rest is in their hands at the Moment of Truth. -/- Doron Avital, Tel Aviv 2011 -/- . (shrink)