What value should we put on our chances of obtaining a good? This paper argues that, contrary to the widely accepted theory of von Neumann and Morgenstern, the value of a chance of some good G may be a nonlinear function of the value of G. In particular, chances may have diminishing marginal utility, a property that is termed chance uncertainty aversion. The hypothesis that agents are averse to uncertainy about chances explains a pattern of preferences often observed in the (...) Ellsberg paradox. While these preferences have typically been taken to refute Bayesian decision theory, it is shown that chance risk aversion is perfectly compatible with it. (shrink)

I advance a decision principle called the "weak dominance principle" (WDP) based on the interval notion of probability to deal with the Ellsberg type paradox (ETP). Given ETP, I explain three things: (i) Why WDP is a better principle than many principles e.g. Kyburg's principle and Gardenfors and Sahlin's principle, (ii) Why one should not, contrary to many principles, expect a unique solution in ETP, and (iii) What is the relationship between WDP and the principles mentioned above. I prove (...) also that WDP induces a strict partial ordering on the intervals to which it is applied. (shrink)

Experimental results on the Ellsberg paradox typically reveal behavior that is commonly interpreted as ambiguity aversion. The experiments reported in the current paper find the objective probabilities for drawing a red ball that make subjects indifferent between various risky and uncertain Ellsberg bets. They allow us to examine the predictive power of alternative principles of choice under uncertainty, including the objective maximin and Hurwicz criteria, the sure-thing principle, and the principle of insufficient reason. Contrary to our expectations, the principle (...) of insufficient reason performed substantially better than rival theories in our experiment, with ambiguity aversion appearing only as a secondary phenomenon. (shrink)

Ellsberg's (1961) famous paradox shows that decision-makers give events with ‘known’ probabilities a higher weight in their outcome evaluation. In the same article, Ellsberg suggests a preference representation which has intuitive appeal but lacks an axiomatic foundation. Schmeidler (1989) and Gilboa (1987) provide an axiomatisation for expected utility with non-additive probabilities. This paper introduces E-capacities as a representation of beliefs which incorporates objective information about the probability of events. It can be shown that the Choquet integral of an E-capacity (...) is the Ellsberg representation. The paper further explores properties of this representation of beliefs and provides an axiomatisation for them. (shrink)

The promise to keep "secrets of state," once demanded and given, becomes virtually part of one's core identity. In the national security apparatus, one's pride and self-respect is founded in particular in the fact that one has been trusted to keep secrets in general and trusted with these particular secrets. I suggest that there are psycho-social aspects of promises made under these circumstances—bearing on self-image and self-respect, as well as status and acceptance in the larger society— that especially inhibit violating (...) these particular promises. The circumstances I have in mind apply to "secret societies" ranging from the Mafia or associations like the Masons to the CIA, and much more broadly to the Departments of Defense and State and the multitude of corporate contractors that do classified work for the Pentagon and the "intelligence community." Thus what is most feared by most prospective secret-tellers—with good reason— is social isolation, ostracism, exile, if they reveal the secrets of the group. If they are found out, they can expect the loss of friends and relationships, more or less irrevocably, as well as loss of job and career. What would a better secrecy system in a democracy look like? Let's take a moment to be utopian and consider some features it might have or omit, without asking what we could get from this Congress and this president or the next. (shrink)

This paper constructs a simple model of decision-making that accounts for the paradoxes of Ellsberg and Machina. It does so by representing decision makers’ beliefs on the vector space $${\mathbb{R}}\times {\mathbb{R}}$$ R × R and by providing a reasonable decision rule with axiomatic foundations. Moreover, the model allows for a characterization that clearly distinguishes between the two paradoxes. The interesting feature of the paper is that the ‘resolution’ of the paradoxes is along the lines suggested by the eponymous authors themselves. (...) This is to say, the decision rule derived from the axioms corresponds to Ellsberg’s own rule in the narrow set of circumstances that he explored, and the decision rule embodies Machina’s injunction that we treat choice under uncertainty in a similar manner to the way we treat standard consumer theory. That the paper cleaves to the advice of both authors is a little surprising given that it utilizes a two-dimensional vector space that neither author deployed. (shrink)

In Richard Bradley’s book, Decision Theory with a Human Face, we have selected two themes for discussion. The first is the Bolker-Jeffrey theory of decision, which the book uses throughout as a tool to reorganize the whole field of decision theory, and in particular to evaluate the extent to which expected utility theories may be normatively too demanding. The second theme is the redefinition strategy that can be used to defend EU theories against the Allais and Ellsberg paradoxes, a strategy (...) that the book by and large endorses, and even develops in an original way concerning the Ellsberg paradox. We argue that the BJ theory is too specific to fulfil Bradley’s foundational project and that the redefinition strategy fails in both the Allais and Ellsberg cases. Although we share Bradley’s conclusion that EU theories do not state universal rationality requirements, we reach it not by a comparison with BJ theory, but by a comparison with the non-EU theories that the paradoxes have heuristically suggested. (shrink)

Many books explain what is known about the universe. This book investigates what cannot be known. Rather than exploring the amazing facts that science, mathematics, and reason have revealed to us, this work studies what science, mathematics, and reason tell us cannot be revealed. In The Outer Limits of Reason, Noson Yanofsky considers what cannot be predicted, described, or known, and what will never be understood. He discusses the limitations of computers, physics, logic, and our own thought processes. Yanofsky describes (...) simple tasks that would take computers trillions of centuries to complete and other problems that computers can never solve; perfectly formed English sentences that make no sense; different levels of infinity; the bizarre world of the quantum; the relevance of relativity theory; the causes of chaos theory; math problems that cannot be solved by normal means; and statements that are true but cannot be proven. He explains the limitations of our intuitions about the world -- our ideas about space, time, and motion, and the complex relationship between the knower and the known. Moving from the concrete to the abstract, from problems of everyday language to straightforward philosophical questions to the formalities of physics and mathematics, Yanofsky demonstrates a myriad of unsolvable problems and paradoxes. Exploring the various limitations of our knowledge, he shows that many of these limitations have a similar pattern and that by investigating these patterns, we can better understand the structure and limitations of reason itself. Yanofsky even attempts to look beyond the borders of reason to see what, if anything, is out there. (shrink)

There are three questions associated with Simpson’s Paradox (SP): (i) Why is SP paradoxical? (ii) What conditions generate SP?, and (iii) What should be done about SP? By developing a logic-based account of SP, it is argued that (i) and (ii) must be divorced from (iii). This account shows that (i) and (ii) have nothing to do with causality, which plays a role only in addressing (iii). A counterexample is also presented against the causal account. Finally, the causal and (...) logic-based approaches are compared by means of an experiment to show that SP is not basically causal. (shrink)

G. E. Moore observed that to assert, 'I went to the pictures last Tuesday but I don't believe that I did' would be 'absurd'. Over half a century later, such sayings continue to perplex philosophers. In the definitive treatment of the famous paradox, Green and Williams explain its history and relevance and present new essays by leading thinkers in the area.

There are three distinct questions associated with Simpson's paradox, (i) Why or in what sense is Simpson's paradox a paradox? (ii) What is the proper analysis of the paradox? (iii) How one should proceed when confronted with a typical case of the paradox? We propose a "formar" answer to the first two questions which, among other things, includes deductive proofs for important theorems regarding Simpson's paradox. Our account contrasts sharply with Pearl's causal (and questionable) (...) account of the first two questions. We argue that the "how to proceed question?" does not have a unique response, and that it depends on the context of the problem. We evaluate an objection to our account by comparing ours with Blyth's account of the paradox. Our research on the paradox suggests that the "how to proceed question" needs to be divorced from what makes Simpson's paradox "paradoxical.". (shrink)

There are three distinct questions associated with Simpson’s paradox. Why or in what sense is Simpson’s paradox a paradox? What is the proper analysis of the paradox? How one should proceed when confronted with a typical case of the paradox? We propose a “formal” answer to the first two questions which, among other things, includes deductive proofs for important theorems regarding Simpson’s paradox. Our account contrasts sharply with Pearl’s causal account of the first two (...) questions. We argue that the “how to proceed question?” does not have a unique response, and that it depends on the context of the problem. We evaluate an objection to our account by comparing ours with Blyth’s account of the paradox. Our research on the paradox suggests that the “how to proceed question” needs to be divorced from what makes Simpson’s paradox “paradoxical.”. (shrink)

A version of nonstandard analysis, Internal Set Theory, has been used to provide a resolution of Zeno's paradoxes of motion. This resolution is inadequate because the application of Internal Set Theory to the paradoxes requires a model of the world that is not in accordance with either experience or intuition. A model of standard mathematics in which the ordinary real numbers are defined in terms of rational intervals does provide a formalism for understanding the paradoxes. This model suggests that in (...) discussing motion, only intervals, rather than instants, of time are meaningful. The approach presented here reconciles resolutions of the paradoxes based on considering a finite number of acts with those based on analysis of the full infinite set Zeno seems to require. The paper concludes with a brief discussion of the classical and quantum mechanics of performing an infinite number of acts in a finite time. (shrink)

There are three questions associated with Simpson’s paradox (SP): (i) Why is SP paradoxical? (ii) What conditions generate SP? and (iii) How to proceed when confronted with SP? An adequate analysis of the paradox starts by distinguishing these three questions. Then, by developing a formal account of SP, and substantiating it with a counterexample to causal accounts, we argue that there are no causal factors at play in answering questions (i) and (ii). Causality enters only in connection with (...) action. (shrink)

Hempel's paradox of the ravens has to do with the question of what constitutes confirmation from a logical point of view; Wason 's selection task has been used extensively to investigate how people go about attempting to confirm or disconfirm conditional claims. This paper presents an argument that the paradox is resolved, and that people's typical performance in the selection task can be explained, by consideration of what constitutes an effective strategy for seeking evidence of the tenability of (...) universal or conditional claims in everyday life. (shrink)

We address the need for a model by considering two competing theories regarding the origin of life: (i) the Metabolism First theory, and (ii) the RNA World theory. We discuss two interrelated points, namely: (i) Models are valuable tools for understanding both the processes and intricacies of origin-of-life issues, and (ii) Insights from models also help us to evaluate the core objection to origin-of-life theories, called “the inefficiency objection”, which is commonly raised by proponents of both the Metabolism First theory (...) and the RNA World theory against each other. We use Simpson’s Paradox (SP) as a tool for challenging this objection. We will use models in various senses, ranging from taking them as representations of reality to treating them as theories/accounts that provide heuristics for probing reality. In this paper, we will frequently use models and theories interchangeably. Additionally, we investigate Conway’s Game of Life and contrast it with our SP-based approach to emergence-of-life issues. Finally, we discuss some of the consequences of our view. A scientific model is testable in three senses: (i) a logical sense, (ii) a nomological sense, and (iii) a current technological sense. The SP-based model is testable in the first two senses but it is not feasible to test it using current technology. (shrink)

The aim of this paper is to distinguish between, and examine, three issues surrounding Humphreys's paradox and interpretation of conditional propensities. The first issue involves the controversy over the interpretation of inverse conditional propensities — conditional propensities in which the conditioned event occurs before the conditioning event. The second issue is the consistency of the dispositional nature of the propensity interpretation and the inversion theorems of the probability calculus, where an inversion theorem is any theorem of probability that makes (...) explicit (or implicit) appeal to a conditional probability and its corresponding inverse conditional probability. The third issue concerns the relationship between the notion of stochastic independence which is supported by the propensity interpretation, and various notions of causal independence. In examining each of these issues, it is argued that the dispositional character of the propensity interpretation provides a consistent and useful interpretation of the probability calculus. (shrink)

Moore's paradox pits our intuitions about semantic oddnessagainst the concept of truth-functional consistency. Most solutions tothe problem proceed by explaining away our intuitions. But``consistency'' is a theory-laden concept, having different contours indifferent semantic theories. Truth-functional consistency is appropriateonly if the semantic theory we are using identifies meaning withtruth-conditions. I argue that such a framework is not appropriate whenit comes to analzying epistemic modality. I show that a theory whichaccounts for a wide variety of semantic data about epistemic modals(Update Semantics) (...) buys us a solution to Moore's paradox as a corollary.It turns out that Moorean propositions, when looked at through the lenseof an appropriate semantic theory, are inconsistent after all. (shrink)

My aim in this paper is to suggest a new outlook concerning the nature of Zeno’s paradoxes. The attention is directed towards the three famous paradoxes known as “Dichotomy,” “Achilles and the Tortoise,” and “The Arrow.” An analysis of the paradigmatic proposals for a solution shows that an adequate solution has not yet been reached. An answer is provided instead to the question “How Zeno’s paradoxes emerge in their quality of aporiae?,” that is to say in their quality of impasses, (...) of problem situations without an exit, what is the original meaning of the Greek word “aporia.” It is my claim that this is the correct rational approach for solving these conceptual puzzles. In other words, I am not proposing formal solutions by criticizing and/or altering their premises assuming the continuous or discrete nature of space and time, but I try to draw the philosophical attention to the way we possess the phenomenon of motion as a result of the perception of space-time in human experience. (shrink)

The Condorcet Jury Theorem formalises the “wisdom of crowds”: binary decisions made by majority vote are asymptotically correct as the number of voters tends to infinity. This classical result assumes like-minded, expected utility maximising voters who all share a common prior belief about the right decision. Ellis : 865–895, 2016) shows that when voters have ambiguous prior beliefs—a set of priors—and follow maxmin expected utility, such wisdom requires that voters’ beliefs satisfy a “disjoint posteriors” condition: different private signals lead to (...) posterior sets with disjoint interiors. Both the original theorem and Ellis’s generalisation assume symmetric penalties for wrong decisions. If, as in the jury context, errors attract asymmetric penalties then it is natural to consider voting rules that raise the hurdle for the decision carrying the heavier penalty for error. In a classical model, Feddersen and Pesendorfer :23–35, 1998) have shown that, paradoxically, raising this hurdle may actually increase the likelihood of the more serious error. In particular, crowds are not wise under the unanimity rule: the probability of the more serious error does not vanish as the crowd size tends to infinity. We show that this “Jury Paradox” persists in the presence of ambiguity, whether or not juror beliefs satisfy Ellis’s “disjoint posteriors” condition. We also characterise the strictly mixed equilibria of this model and study their properties. Such equilibria cannot exist in the absence of ambiguity but may exist for arbitrarily large jury size when ambiguity is present. In addition to uninformative strictly mixed equilibria, analogous to those exhibited by Ellis : 865–895, 2016), there may also exist strictly mixed equilibria which are informative about voter signals. (shrink)

As these opening quotes acknowledge, the Prisoner’s Dilemma (PD) represents a core puzzle within the formal mathematics of game theory.3 Its rise in conspicuity is evident figure 2.1 above demonstrating a relatively steady rise in incidences of the phrase’s usage between 1960 to 1995, with a stable presence persisting into the twenty first century. This famous two-person “game,” with a stock narrative cast in terms of two prisoners who each independently must choose whether to remain silent or speak, each advancing (...) self-interest at the expense of the other and thereby achieving a mutually suboptimal outcome, mires any social interaction it is applied to into perplexity. The logic of this game proves the inverse of Adam Smith’s invisible hand: individuals acting on self interest will achieve a mutually suboptimal outcome. However, as this chapter illuminates, the assumptions underlying game theory drive this conclusion. (shrink)

Geoffrey Rose’s prevention paradox points to a tension between two prima facie plausible moral principles: that we should save the greater number and that weshould save the most at risk. This paper argues that a novel moral theory, ex-ante contractualism, captures our intuitions in many prevention paradox cases, regardless of our interpretation of probability claims. However, it goes on to show that it might be impossible to square ex-ante contractualism with all of our moral intuitions. It concludes that (...) even if ex-ante contractualism cannot furnish an entire ethics of risk, it does identify important considerations for any such theory. (shrink)

Book Information The Paradox of Self-Consciousness. By José Luis Bermúdez. Bradford/MIT. Cambridge, MA. 1998. Pp. xv + 338. $US30.00.

Subjects classified visible 2-digit numbers as larger or smaller than 55. Target numbers were preceded by masked 2-digit primes that were either congruent (same relation to 55) or incongruent. Experiments 1 and 2 showed prime congruency effects for stimuli never included in the set of classified visible targets, indicating subliminal priming based on long-term semantic memory. Experiments 2 and 3 went further to demonstrate paradoxical unconscious priming effects resulting from task context. For example, after repeated practice classifying 73 as larger (...) than 55, the novel masked prime 37 paradoxically facilitated the “larger” response. In these experiments task context could induce subjects to unconsciously process only the leftmost masked prime digit, only the rightmost digit, or both independently. Across 3 experiments, subliminal priming was governed by both task context and long-term semantic memory. (shrink)

Shoemaker argues that a satisfactory resolution of Moore's paradox requires a _self-intimation thesis that posits a "constitutive relation between belief and believing that one believes." He claims that such a thesis is needed to explain the crucial fact that the assent conditions for '_P' entail those for '_I believe that P'. This paper argues for an alternative resolution of Moore's paradox that provides for an adequate explanation of the crucial fact without relying on the kind of necessary connection (...) between first and second-order beliefs that is posited by Shoemaker's self-intimation thesis. (shrink)

Determinist thought with its sui generis view on life, nature and being as a whole is a point of view that could be observed in many different cultures and beliefs. It was thanks to Greek thought that it ceased to be a cultural element and transformed into a systematic cosmology. Schools such as Leucippos, then Democritos and Stoa attempted to integrate the determinist philosophy into ontology and cosmology. In the course of time, physics and metaphysics-based determinism approaches were introduced, and (...) a wide spectrum has emerged from genetics to behaviorism, from culture to psychology, from atomism to divinity. Determinism, whether physical or metaphysical origin, ignores freedom of will and deny agency competence over human behavior. Due to this feature, it is opposed by ethical theories, legal philosophies and religions. When the arguments for determinism are possible to disprove logically and philosophically, this is not so easy when the claims base themselves on scientific base. As the logical consequence of this novel fact, it is important to question the epistemological value of scientific knowledge and critically analyze the data of experiments and clinical studies in terms of methodology when answering any hypothesis such as neuro-biological, neuro-psychological, or neuro-theological argumentations. On the other hand, it is necessary to reach alternative experiments on the same subject or to show that it is possible to interpret them in different ways, as in the example of the Libet experiment. The neurobiological determinism based on biological reductionism, emerged as the result of ignoring the ontological difference of the mind, equating the mind with the brain, or defining mentality as an epiphenomenon of the brain. The main divergence stems from the acceptance of materialist philosophy. Paradigms that reduce existence only to matter do not take the metaphysical possibilities into account. In this case, although the problems called qualia or subjective experience stand there unresolved, the claim is preserved. Although many new developments such as the discovery of the entropy law, the big bang theory, and quantum physics have shaken the materialist philosophy, modern science resists an epistemological revision. However, with the current epistemology, it does not seem possible to grasp both the universe and the being as a whole. This is the most important reason why every attempt to understand the nature and spiritual side of human beings fails despite numerous experiments on the brain. However, the human brain is an organ that seems sophisticated and its secrets cannot be easily solved. Since there is not enough information about the brain, there is not enough evidence to claim that the brain, and therefore the mind, are part of the deterministic universe. Increasing brain researches since the last quarter of the twentieth century has revealed that genes, neurons and particularly brain chemistry claim much greater role than expected in human behavior. These results have been instrumentalized by some researchers for a radical claim that free will is an illusion, while by others it has led to the acceptance of will as less important over actions than was thought. Both ideas adopted a model of biological determinism in which freedom of will was ignored. Hypotheses based on controversial interpretations of various experiments raised concerns about religious, moral, and legal responsibility. Although man cannot be thought of as a non-free being from the point of view of common sense, the smog screen over the truth would not be lifted unless the scientific data in question had a correct interpretation. At first glance, it seems unreasonable to discuss universal determinism in the quantum universe. Nevertheless, the claim that strong causality prevails in the material world, including consciousness, remains in place. Therefore, firstly criticizing determinism and then examining biological determinism will help to fix the conceptual framework. This article aims to explain why genetics and neurobiology, while acknowledging their importance in the realization of behavior, can’t completely abolish moral agency. Some hypotheses attribute consciousness and free will to the physico-shimic structure of the brain, the random activity of neurons, or the ability to automatically transform inputs into outputs with the advantage of genetic information. This is the most sensitive and important point of being human; it attacks free will. Paradoxically, while global civilization of our time promises infinite freedom to human beings the science of the same age tries to prove that it is not free. (shrink)

G. E. Moore famously observed that to assert ‘I went to the pictures last Tuesday but I do not believe that I did’ would be ‘absurd’. Moore calls it a ‘paradox’ that this absurdity persists despite the fact that what I say about myself might be true. Krista Lawlor and John Perry have proposed an explanation of the absurdity that confines itself to semantic notions while eschewing pragmatic ones. We argue that this explanation faces four objections. We give a (...) better explanation of the absurdity both in assertion and in belief that avoids our four objections. (shrink)

Einstein, in his “Zur Elektrodynamik bewegter Körper”, gave a physical (operational) meaning to “time” of a remote event in describing “motion” by introducing the concept of “synchronous stationary clocks located at different places”. But with regard to “place” in describing motion, he assumed without analysis the concept of a system of co-ordinates.In the present paper, we propose a way of giving physical (operational) meaning to the concepts of “place” and “co-ordinate system”, and show how the observer can define both the (...) place and time of a remote event. Following Einstein, we consider another system “in uniform motion of translation relatively to the former”. Without assuming “the properties of homogeneity which we attribute to space and time”, we show that the definitions of space and time in the two systems are linearly related. We deduce some novel consequences of our approach regarding faster-than-light observers and particles, “one-way” and “two-way” velocities of light, symmetry, the “group property” of inertial reference frames, length contraction and time dilatation, and the “twin paradox”. Finally, we point out a flaw in Einstein’s argument in the “Electrodynamical Part” of his paper and show that the Lorentz force formula and Einstein’s formula for transformation of field quantities are mutually consistent. We show that for faster-than-light bodies, a simple modification of Planck’s formula for mass suffices. (Except for the reference to Planck’s formula, we restrict ourselves to Physics of 1905.). (shrink)

The historian of philosophy often encounters arguments that are enthymematic: they have conclusions that follow from their explicit premises only by the addition of "tacit" or "suppressed" premises. It is a standard practice of interpretation to supply these missing premises, even where the enthymeme is "real," that is, where there is no other context in which the philosopher in question asserts the missing premises. To do so is to follow a principle of charity: other things being equal, one interpretation is (...) better than another just to the extent that the one produces a better argument than the other. We show that this principle leads to paradoxical conclusions, including the following: there is no objectively correct interpretation of any real enthymeme found in the text of a major philosopher; an interpreter will not regard a real enthymeme of a major philosopher as adequately interpreted until he has found a way of reading it that makes it into a good argument; every classical philosopher is infallible and omniscient; major philosophers never disagree. These conclusions are preposterous, but there are indications that they are in fact being reached, as we show by means of a case study of recent scholarship on Plato's Third Man Argument. To avoid the overinterpretation and anachronism that result from the unrestrained use of the principle of charity, one must employ a counterbalancing principle of parsimony: to seek the simplest explanation for the text under discussion. We study the role of the principle of parsimony by means of a mathematical case study, involving the suppressed premises in Euclid's Elements. Here the principle of parsimony plays a larger role than it does in the interpretation of philosophical texts, leading to a sharper distinction between Euclid's geometry and Euclidean geometry than we find between Plato and Platonism. We conclude by comparing two models of interpretation, which we call prospective and retrospective. Although the prospective model of interpretation leads to Platonism rather than to Plato, we argue that it still has a place in Platonic scholarship. (shrink)

In _On Paradox_ literary and legal scholar Elizabeth S. Anker contends that faith in the logic of paradox has been the cornerstone of left intellectualism since the second half of the twentieth century. She attributes the ubiquity of paradox in the humanities to its appeal as an incisive tool for exposing and dismantling hierarchies. Tracing the ascent of paradox in theories of modernity, in rights discourse, in the history of literary criticism and the linguistic turn, and in (...) the transformation of the liberal arts in higher education, Anker suggests that paradox not only generates the very exclusions it critiques but also creates a disempowering haze of indecision. She shows that reasoning through paradox has become deeply problematic: it engrains a startling homogeneity of thought while undercutting the commitment to social justice that remains a guiding imperative of theory. Rather than calling for a wholesale abandonment of such reasoning, Anker argues for an expanded, diversified theory toolkit that can help theorists escape the seductions and traps of paradox. (shrink)

The very idea of informative analysis gives rise to a well-known paradox. Yet a parallel puzzle, herein called the paradox of synonymy, arises for statements which do not express analyses. The paradox of synonymy has a straightforward metalinguistic solution: certain words are referring to themselves. Likewise, the paradox of analysis can be solved by recognizing that certain expressions in an analysis statement are referring to their own semantic structures.

We report on the simultaneous determination of complementary wave and particle aspects of light in a double-slit type “welcher-weg” experiment beyond the limitations set by Bohr’s Principle of Complementarity. Applying classical logic, we verify the presence of sharp interference in the single photon regime, while reliably maintaining the information about the particular pinhole through which each individual photon had passed. This experiment poses interesting questions on the validity of Complementarity in cases where measurements techniques that avoid Heisenberg’s uncertainty principle and (...) quantum entanglement are employed. We further argue that the application of classical concepts of waves and particles as embodied in Complementarity leads to a logical inconsistency in the interpretation of this experiment. (shrink)

A realist separable hidden variables theory in conformity with Einstein's principle of causality is developed in this paper to explain the Einstein-Podolsky-Rosen paradox, and the experimental results (including those in Aspect's four polarizers experiment) obtained so far with a view to test the non-separability of quantum mechanics.

Sorensen provides a panoramic view of paradoxes of theoretical and practical rationality. These puzzles are organized as apparent counterexamples to attractive principles such as the principle of charity, the transitivity of preferences, and the principle that we should maximize expected utility. The following paradoxes are discussed: fearing fictions, the surprise test paradox, Pascal’s Wager, Pollock’s Ever Better wine, Newcomb’s problem, the iterated prisoner’s dilemma, Kavka’s paradoxes of deterrence, backward inductions, the bottle imp, the preface paradox, Moore’s problem, Buridan’s (...) ass, Condorcet’s paradox of cyclical majorities, the St. Petersburg paradox, weakness of will, the Ellsberg paradox, Allais’s paradox, and Peter Cave’s puzzle of self-fulfilling beliefs. (shrink)