Following a long-standing philosophical tradition, impartiality is a distinctive and determining feature of moral judgments, especially in matters of distributive justice. This broad ethical tradition was revived in welfare economics by Vickrey, and above all, Harsanyi, under the form of the so-called Impartial Observer Theorem. The paper offers an analytical reconstruction of this argument and a step-wise philosophical critique of its premisses. It eventually provides a new formal version of the theorem based on subjective probability.

This chapter of the Handbook of Utility Theory aims at covering the connections between utility theory and social ethics. The chapter first discusses the philosophical interpretations of utility functions, then explains how social choice theory uses them to represent interpersonal comparisons of welfare in either utilitarian or non-utilitarian representations of social preferences. The chapter also contains an extensive account of John Harsanyi's formal reconstruction of utilitarianism and its developments in the later literature, especially when society faces uncertainty rather than (...) probabilistic risk. (shrink)

Harsanyi claimed that his Aggregation and Impartial Observer Theorems provide a justification for utilitarianism. This claim has been strongly resisted, notably by Sen and Weymark, who argue that while Harsanyi has perhaps shown that overall good is a linear sum of individuals’ von Neumann-Morgenstern utilities, he has done nothing to establish any con- nection between the notion of von Neumann-Morgenstern utility and that of well-being, and hence that utilitarianism does not follow. The present article defends Harsanyi against the (...) Sen-Weymark cri- tique. I argue that, far from being a term with precise and independent quantitative content whose relationship to von Neumann-Morgenstern utility is then a substantive question, terms such as ‘well-being’ suffer (or suffered) from indeterminacy regarding precisely which quantity they refer to. If so, then (on the issue that this article focuses on) Harsanyi has gone as far towards defending ‘utilitarianism in the original sense’ as could coherently be asked. (shrink)

This is a chapter of a collective volume of Rawls's and Harsanyi's theories of distributive justice. It focuses on Harsanyi's important Social Aggregation Theorem and technically reconstructs it as a theorem in welfarist social choice.

I build on Adam Smith’s account of the impartial spectator in The Theory of Moral Sentiments in order to offer a modest ideal observer theory of moral judgment that is adequate in the following sense: the account specifies the hypothetical conditions that guarantee the authoritativeness of an agent’s (or agents’) responses in constituting the standard in question, and, if an actual agent or an actual community of agents are not under those conditions, their responses are not authoritative in (...) setting this standard. However, in the account that I provide, the hypothetical conditions can themselves be constructed from the psychology and interactions of actual human beings. In other words, facts about the morally appropriate and inappropriate are determined from hypothetical conditions that––while agents in a given society might have yet to attain them––can be constructed from those agents’ shared experiences. Thus, the account offers both an attainable standard of moral judgment and a standard that can transcend the biases of the society which gave rise to it. I also defend the account against three challenges: (a) ideal observer theories do not offer the right kind of motivation to act on the verdicts of the ideal observer; (b) ideal observer theories cannot explain why the idealization in question is well-motivated and not objectionably ad hoc; (c) the standard used in ideal observer theories cannot be defended upon further reflection, because we would need a non-arbitrary, second-order standard to govern our reflection on the first-order standard of moral judgment. (shrink)

Antimicrobial resistance (AMR) is a global public health disaster driven largely by antibiotic use in human health care. Doctors considering whether to prescribe antibiotics face an ethical conflict between upholding individual patient health and advancing public health aims. Existing literature mainly examines whether patients awaiting consultations desire or expect to receive antibiotic prescriptions, but does not report views of the wider public regarding conditions under which doctors should prescribe antibiotics. It also does not explore the ethical significance of public views (...) or their sensitivity to awareness of AMR risks or the standpoint (self-interested or impartial) taken by participants. Methods: An online survey was conducted with a sample of the U.S. public (n = 158). Participants were asked to indicate what relative priority should be given to individual patients and society-at-large from various standpoints and in various contexts, including antibiotic prescription. Results: Of the participants, 50.3% thought that doctors should generally prioritize individual patients over society, whereas 32.0% prioritized society over individual patients. When asked in the context of AMR, 39.2% prioritized individuals whereas 45.5% prioritized society. Participants were significantly less willing to prioritize society over individuals when they themselves were the patient, both in general (p = .001) and in relation to AMR specifically (p = .006). Conclusions: Participants’ attitudes were more oriented to society and sensitive to collective responsibility when informed about the social costs of antibiotic use and when considered from a third-person rather than first-person perspective. That is, as participants came closer to taking the perspective of an informed and impartial “ideal observer,” their support for prioritizing society increased. Our findings suggest that, insofar as antibiotic policies and practices should be informed by attitudes that are impartial and well-informed, there is significant support for prioritizing society. (shrink)

I demonstrate that Bell's theorem is based on circular reasoning and thus a fundamentally flawed argument. It unjustifiably assumes the additivity of expectation values for dispersion-free states of contextual hidden variable theories for non-commuting observables involved in Bell-test experiments, which is tautologous to assuming the bounds of ±2 on the Bell-CHSH sum of expectation values. Its premises thus assume in a different guise the bounds of ±2 it sets out to prove. Once this oversight is ameliorated from Bell's argument (...) by identifying the impediment that leads to it and local realism is implemented correctly, the bounds on the Bell-CHSH sum of expectation values work out to be ±2√2 instead of ±2, thereby mitigating the conclusion of Bell's theorem. Consequently, what is ruled out by any of the Bell-test experiments is not local realism but the linear additivity of expectation values, which does not hold for non-commuting observables in any hidden variable theories to begin with. I also identify similar oversight in the GHZ variant of Bell's theorem, invalidating its claim of having found an inconsistency in the premisses of the argument by EPR for completing quantum mechanics. Conceptually, the oversight in both Bell's theorem and its GHZ variant traces back to the oversight in von Neumann's theorem against hidden variable theories identified by Grete Hermann in the 1930s. (shrink)

Bell’s theorem has fascinated physicists and philosophers since his 1964 paper, which was written in response to the 1935 paper of Einstein, Podolsky, and Rosen. Bell’s theorem and its many extensions have led to the claim that quantum mechanics and by inference nature herself are nonlocal in the sense that a measurement on a system by an observer at one location has an immediate effect on a distant entangled system. Einstein was repulsed by such “spooky action at (...) a distance” and was led to question whether quantum mechanics could provide a complete description of physical reality. In this paper I argue that quantum mechanics does not require spooky action at a distance of any kind and yet it is entirely reasonable to question the assumption that quantum mechanics can provide a complete description of physical reality. The magic of entangled quantum states has little to do with entanglement and everything to do with superposition, a property of all quantum systems and a foundational tenet of quantum mechanics. (shrink)

We present an abstract social aggregation theorem. Society, and each individual, has a preorder that may be interpreted as expressing values or beliefs. The preorders are allowed to violate both completeness and continuity, and the population is allowed to be infinite. The preorders are only assumed to be represented by functions with values in partially ordered vector spaces, and whose product has convex range. This includes all preorders that satisfy strong independence. Any Pareto indifferent social preorder is then shown (...) to be represented by a linear transformation of the representations of the individual preorders. Further Pareto conditions on the social preorder correspond to positivity conditions on the transformation. When all the Pareto conditions hold and the population is finite, the social preorder is represented by a sum of individual preorder representations. We provide two applications. The first yields an extremely general version of Harsanyi's social aggregation theorem. The second generalizes a classic result about linear opinion pooling. (shrink)

This paper is about the role of interpersonal comparisons in Harsanyi's aggregation theorem. Harsanyi interpreted his theorem to show that a broadly utilitarian theory of distribution must be true even if there are no interpersonal comparisons of well-being. How is this possible? The orthodox view is that it is not. Some argue that the interpersonal comparability of well-being is hidden in Harsanyi's premises. Others argue that it is a surprising conclusion of Harsanyi's theorem, which (...) is not presupposed by any one of the premises. I argue instead that Harsanyi was right: his theorem and its weighted-utilitarian conclusion do not require interpersonal comparisons of well-being. The key to making sense of this possibility is to treat Harsanyi's weights as dimensional constants rather than dimensionless numbers. (shrink)

Often, when one faces a choice between alternative actions, there are reasons both for and against each alternative. On one way of understanding these words, what one “ought to do all things considered (ATC)” is determined by the totality of these reasons. So, these reasons can somehow be “combined” or “aggregated” to yield an ATC verdict on these alternatives. First, various assumptions about this sort of aggregation of reasons are articulated. Then it is shown that these assumptions allow for the (...) proof of a “Reasons Aggregation Theorem” – parallel to John Harsanyi’s 1955 “Social Aggregation Theorem”. All reasons for action are grounded in reason-providing values; and, for every such reason-providing value, there is in principle a way of measuring how strongly this value counts against each alternative. The theorem tells us that the appropriate measure of how much reason ATC there is against each alternative is simply a weighted sum of the strengths with which these values count against that alternative; the agent ought not ATC to perform an action iff there is ATC more reason against it than against some available alternative. (shrink)

[First published in Italian as: “L’irreligione e lo spettatore imparziale nel sistema morale di Adam Smith”, in Rivista di Filosofia 3 (3):375-403 (2005). -/- Translated by E. Lecaldano.] -/- A number of commentators on Smith’s philosophy have observed that the relationship between his moral theory and his theological beliefs is “exceedingly difficult to unravel.” The available evidence, as generally presented, suggests that although Smith was not entirely orthodox by contemporary standards, he has no obvious or significant irreligious commitments or orientation. (...) Contrary to this view of things, this essay argues that behind the veneer of orthodoxy that covers Smith’s discussion in The Theory of the Moral Sentiments there are significant irreligious themes present in his work. -/- . (shrink)

The Buddhist denial of the world seems hard to defend if it is confronted with empirical data. Surveys on subjective life satisfaction consistently report that the majority is satisfied with their lives. Is the desire to escape from the cycle of rebirth a sign of risk-aversion or even irrationality? How would an impartial observer evaluate the world? -/- An impartial view is achieved by interpreting the surveys on life satisfaction as probability distributions for life’s risks and chances. (...) It turns out that there is no indisputable metric for measuring risks and no reliable forecast. Given this uncertainty the denial of the world cannot easily be dismissed as being irrational. (shrink)

In this essay a quantum-dualistic, perspectival and synchronistic interpretation of quantum mechanics is further developed in which the classical world-from-decoherence which is perceived (decoherence) and the perceived world-in-consciousness which is classical (collapse) are not necessarily identified. Thus, Quantum Reality or "{\it unus mundus}" is seen as both i) a physical non-perspectival causal Reality where the quantum-to-classical transition is operated by decoherence, and as ii) a quantum linear superposition of all classical psycho-physical perspectival Realities which are governed by synchronicity as well (...) as causality (corresponding to classical first-person observes who actually populate the world). This interpretation is termed the Nietzsche-Jung-Pauli interpretation and is a re-imagining of the Wigner-von Neumann interpretation which is also consistent with some reading of Bohr's quantum philosophy. (shrink)

We introduce a ranking of multidimensional alternatives, including uncertain prospects as a particular case, when these objects can be given a matrix form. This ranking is separable in terms of rows and columns, and continuous and monotonic in the basic quantities. Owing to the theory of additive separability developed here, we derive very precise numerical representations over a large class of domains (i.e., typically notof the Cartesian product form). We apply these representationsto (1)streams of commodity baskets through time, (2)uncertain social (...) prospects, (3)uncertain individual prospects. Concerning(1), we propose a finite horizon variant of Koopmans’s (1960) axiomatization of infinite discounted utility sums. The main results concern(2). We push the classic comparison between the exanteand expostsocial welfare criteria one step further by avoiding any expected utility assumptions, and as a consequence obtain what appears to be the strongest existing form of Harsanyi’s (1955) Aggregation Theorem. Concerning(3), we derive a subjective probability for Anscombe and Aumann’s (1963) finite case by merely assuming that there are two epistemically independent sources of uncertainty. (shrink)

Garrett Cullity contends that fairness is appropriate impartiality (See Cullity (2004) Chapters 8 and 10 and Cullity (2008)). Cullity deploys his account of fairness as a means of limiting the extreme moral demand to make sacrifices in order to aid others that was posed by Peter Singer in his seminal article ‘Famine, Affluence and Morality’. My paper is founded upon the combination of (1) the observation that the idea that fairness consists in appropriate impartiality is very vague and (2) the (...) fact that psychological studies show the self-serving bias is especially likely to infect one’s judgements when the ideas involved are vague. I argue that Cullity’s solution to extreme moral demandingness is threatened by these findings. I then comment on whether some other theories of fairness are vulnerable to the same objection. (shrink)

Non-commuting quantities and hidden parameters – Wave-corpuscular dualism and hidden parameters – Local or nonlocal hidden parameters – Phase space in quantum mechanics – Weyl, Wigner, and Moyal – Von Neumann’s theorem about the absence of hidden parameters in quantum mechanics and Hermann – Bell’s objection – Quantum-mechanical and mathematical incommeasurability – Kochen – Specker’s idea about their equivalence – The notion of partial algebra – Embeddability of a qubit into a bit – Quantum computer is not Turing machine (...) – Is continuality universal? – Diffeomorphism and velocity – Einstein’s general principle of relativity – „Mach’s principle“ – The Skolemian relativity of the discrete and the continuous – The counterexample in § 6 of their paper – About the classical tautology which is untrue being replaced by the statements about commeasurable quantum-mechanical quantities – Logical hidden parameters – The undecidability of the hypothesis about hidden parameters – Wigner’s work and и Weyl’s previous one – Lie groups, representations, and psi-function – From a qualitative to a quantitative expression of relativity − psi-function, or the discrete by the random – Bartlett’s approach − psi-function as the characteristic function of random quantity – Discrete and/ or continual description – Quantity and its “digitalized projection“ – The idea of „velocity−probability“ – The notion of probability and the light speed postulate – Generalized probability and its physical interpretation – A quantum description of macro-world – The period of the as-sociated de Broglie wave and the length of now – Causality equivalently replaced by chance – The philosophy of quantum information and religion – Einstein’s thesis about “the consubstantiality of inertia ant weight“ – Again about the interpretation of complex velocity – The speed of time – Newton’s law of inertia and Lagrange’s formulation of mechanics – Force and effect – The theory of tachyons and general relativity – Riesz’s representation theorem – The notion of covariant world line – Encoding a world line by psi-function – Spacetime and qubit − psi-function by qubits – About the physical interpretation of both the complex axes of a qubit – The interpretation of the self-adjoint operators components – The world line of an arbitrary quantity – The invariance of the physical laws towards quantum object and apparatus – Hilbert space and that of Minkowski – The relationship between the coefficients of -function and the qubits – World line = psi-function + self-adjoint operator – Reality and description – Does a „curved“ Hilbert space exist? – The axiom of choice, or when is possible a flattening of Hilbert space? – But why not to flatten also pseudo-Riemannian space? – The commutator of conjugate quantities – Relative mass – The strokes of self-movement and its philosophical interpretation – The self-perfection of the universe – The generalization of quantity in quantum physics – An analogy of the Feynman formalism – Feynman and many-world interpretation – The psi-function of various objects – Countable and uncountable basis – Generalized continuum and arithmetization – Field and entanglement – Function as coding – The idea of „curved“ Descartes product – The environment of a function – Another view to the notion of velocity-probability – Reality and description – Hilbert space as a model both of object and description – The notion of holistic logic – Physical quantity as the information about it – Cross-temporal correlations – The forecasting of future – Description in separable and inseparable Hilbert space – „Forces“ or „miracles“ – Velocity or time – The notion of non-finite set – Dasein or Dazeit – The trajectory of the whole – Ontological and onto-theological difference – An analogy of the Feynman and many-world interpretation − psi-function as physical quantity – Things in the world and instances in time – The generation of the physi-cal by mathematical – The generalized notion of observer – Subjective or objective probability – Energy as the change of probability per the unite of time – The generalized principle of least action from a new view-point – The exception of two dimensions and Fermat’s last theorem. (shrink)

The problem of multiple-computations discovered by Hilary Putnam presents a deep difficulty for functionalism (of all sorts, computational and causal). We describe in out- line why Putnam’s result, and likewise the more restricted result we call the Multiple- Computations Theorem, are in fact theorems of statistical mechanics. We show why the mere interaction of a computing system with its environment cannot single out a computation as the preferred one amongst the many computations implemented by the system. We explain why (...) nonreductive approaches to solving the multiple- computations problem, and in particular why computational externalism, are dualistic in the sense that they imply that nonphysical facts in the environment of a computing system single out the computation. We discuss certain attempts to dissolve Putnam’s unrestricted result by appealing to systems with certain kinds of input and output states as a special case of computational externalism, and show why this approach is not workable without collapsing to behaviorism. We conclude with some remarks about the nonphysical nature of mainstream approaches to both statistical mechanics and the quantum theory of measurement with respect to the singling out of partitions and observables. (shrink)

We give two social aggregation theorems under conditions of risk, one for constant population cases, the other an extension to variable populations. Intra and interpersonal welfare comparisons are encoded in a single ‘individual preorder’. The theorems give axioms that uniquely determine a social preorder in terms of this individual preorder. The social preorders described by these theorems have features that may be considered characteristic of Harsanyi-style utilitarianism, such as indifference to ex ante and ex post equality. However, the theorems are (...) also consistent with the rejection of all of the expected utility axioms, completeness, continuity, and independence, at both the individual and social levels. In that sense, expected utility is inessential to Harsanyi-style utilitarianism. In fact, the variable population theorem imposes only a mild constraint on the individual preorder, while the constant population theorem imposes no constraint at all. We then derive further results under the assumption of our basic axioms. First, the individual preorder satisfies the main expected utility axiom of strong independence if and only if the social preorder has a vector-valued expected total utility representation, covering Harsanyi’s utilitarian theorem as a special case. Second, stronger utilitarian-friendly assumptions, like Pareto or strong separability, are essentially equivalent to strong independence. Third, if the individual preorder satisfies a ‘local expected utility’ condition popular in non-expected utility theory, then the social preorder has a ‘local expected total utility’ representation. Fourth, a wide range of non-expected utility theories nevertheless lead to social preorders of outcomes that have been seen as canonically egalitarian, such as rank-dependent social preorders. Although our aggregation theorems are stated under conditions of risk, they are valid in more general frameworks for representing uncertainty or ambiguity. (shrink)

The physics literature contains many claims that elementary particles have been observed: such observational claims are, of course, important for the development of existential knowledge. Regarding claimed observations of short-lived unstable particles in particular, the use of the word 'observation' is based on the convention in physics that the observation of a short-lived unstable particle can be claimed when its predicted decay products have been observed with a significance of 5 sigma. This paper, however, shows that this 5 sigma convention (...) is inconsistent with existing concepts of observation by showing that unstable particles with a lifetime of less than 0.01 attosecond are fundamentally unobservable both from the perspective of Fox's recent concepts of direct and indirect observation, and from the perspective of Van Fraassen's notion of observability. This cognitive inaccessibility of parts of the subatomic world has far-reaching implications for physics, not the least of which is that the aforementioned convention is untenable: claims that such short-lived unstable particles have been observed will thus have to be retracted. The main implications are two incompleteness theorems for physics, respectively stating (i) that experiments cannot prove completeness of a physical theory predicting short-lived unstable particles, and (ii) that experiments cannot prove correctness of such a theory|one can at most test its empirical adequacy. On a general note, the conclusion is that the importance of philosophical arguments for particle physics is herewith demonstrated: it is, thus, a widespread misconception that philosophical arguments can be completely avoided. (shrink)

In the present paper, these authors argue on actual reasons why Hilbert’s axiomatic program to unify gravitation theory and electromagnetism failed completely. An outline of plausible resolution of this problem is given here, based on: a) Gödel’s incompleteness theorem, b) Newton’s aether stream model. And in another paper we will present our calculation of receding Moon from Earth based on such a matter creation hypothesis. More experiments and observations are called to verify this new hypothesis, albeit it is inspired (...) from Newton’s theory himself. (shrink)

Risky prospects represent policies that impose different types of risks on multiple people. I present an example from food safety. A utilitarian following Harsanyi's Aggregation Theorem ranks such prospects according to their mean expected utility or the expectation of the social utility. Such a ranking is not sensitive to any of four types of distributional concerns. I develop a model that lets the policy analyst rank prospects relative to the distributional concerns that she considers fitting in the context (...) at hand. I name this model ‘the Distribution View’ posing an alternative to Parfit's Priority View for risky prospects. (shrink)

Epistemic states of uncertainty play important roles in ethical and political theorizing. Theories that appeal to a “veil of ignorance,” for example, analyze fairness or impartiality in terms of certain states of ignorance. It is important, then, to scrutinize proposed conceptions of ignorance and explore promising alternatives in such contexts. Here, I study Lerner’s probabilistic egalitarian theorem in the setting of imprecise probabilities. Lerner’s theorem assumes that a social planner tasked with distributing income to individuals in a population (...) is “completely ignorant” about which utility functions belong to which individuals. Lerner models this ignorance with a certain uniform probability distribution, and shows that, under certain further assumptions, income should be equally distributed. Much of the criticism of the relevance of Lerner’s result centers on the representation of ignorance involved. Imprecise probabilities provide a general framework for reasoning about various forms of uncertainty including, in particular, ignorance. To what extent can Lerner’s conclusion be maintained in this setting? (shrink)

The veil of ignorance argument was used by John C. Harsanyi to defend Utilitarianism and by John Rawls to defend the absolute priority of the worst off. In a recent paper, Lara Buchak revives the veil of ignorance argument, and uses it to defend an intermediate position between Harsanyi's and Rawls' that she calls Relative Prioritarianism. None of these authors explore the implications of allowing that agent's behind the veil are averse to ambiguity. Allowing for aversion to ambiguity---which is (...) both the most commonly observed and a seemingly reasonable attitude to ambiguity---however supports a version of Egalitarianism, whose logical form is quite different from the theories defended by the aforementioned authors. Moreover, it turns out that the veil of ignorance argument neither supports standard Utilitarianism nor Prioritarianism unless we assume that rational people are insensitive to ambiguity. (shrink)

While the philosophers of science discuss the General Relativity, the mathematical physicists do not question it. Therefore, there is a conflict. From the theoretical point view “the question of precisely what Einstein discovered remains unanswered, for we have no consensus over the exact nature of the theory 's foundations. Is this the theory that extends the relativity of motion from inertial motion to accelerated motion, as Einstein contended? Or is it just a theory that treats gravitation geometrically in the spacetime (...) setting?”. “The voices of dissent proclaim that Einstein was mistaken over the fundamental ideas of his own theory and that their basic principles are simply incompatible with this theory. Many newer texts make no mention of the principles Einstein listed as fundamental to his theory; they appear as neither axiom nor theorem. At best, they are recalled as ideas of purely historical importance in the theory's formation. The very name General Relativity is now routinely condemned as a misnomer and its use often zealously avoided in favour of, say , Einstein's theory of gravitation What has complicated an easy resolution of the debate are the alterations of Einstein's own position on the foundations of his theory”, (Norton, 1993). Of other hand from the mathematical point view the “General Relativity had been formulated as a messy set of partial differential equations in a single coordinate system. People were so pleased when they found a solution that they didn't care that it probably had no physical significance” (Hawking and Penrose, 1996). So, during a time, the declaration of quantum theorists:“I take the positivist viewpoint that a physical theory is just a mathematical model and that it is meaningless to ask whether it corresponds to reality. All that one can ask is that its predictions should be in agreement with observation.” (Hawking and Penrose, 1996)seemed to solve the problem, but recently achieved with the help of the tightly and collectively synchronized clocks in orbit frontally contradicts fundamental assumptions of the theory of Relativity. These observations are in disagree from predictions of the theory of Relativity. (Hatch, 2004a, 2004b, 2007). The mathematical model was developed first by Grossmann who presented it, in 1913, as the mathematical part of the Entwurf theory, still referred to a curved Minkowski spacetime. Einstein completed the mathematical model, in 1915, formulated for Riemann ́s spacetimes. In this paper, we present as of General Relativity currently remains only the mathematical model, darkened with the results of Hatch and, course, we conclude that a Einstein ́s gravity theory does not exist. (shrink)

An important objection to preference-satisfaction theories of well-being is that they cannot make sense of interpersonal comparisons. A tradition dating back to Harsanyi :434, 1953) attempts to solve this problem by appeal to people’s so-called extended preferences. This paper presents a new problem for the extended preferences program, related to Arrow’s celebrated impossibility theorem. We consider three ways in which the extended-preference theorist might avoid this problem, and recommend that she pursue one: developing aggregation rules that violate Arrow’s Independence (...) of Irrelevant Alternatives condition. (shrink)

The paper addresses Leon Hen.kin's proposition as a " lighthouse", which can elucidate a vast territory of knowledge uniformly: logic, set theory, information theory, and quantum mechanics: Two strategies to infinity are equally relevant for it is as universal and t hus complete as open and thus incomplete. Henkin's, Godel's, Robert Jeroslow's, and Hartley Rogers' proposition are reformulated so that both completeness and incompleteness to be unified and thus reduced as a joint property of infinity and of all infinite sets. (...) However, only Henkin's proposition equivalent to an internal position to infinity is consistent . This can be retraced back to set theory and its axioms, where that of choice is a key. Quantum mechanics is forced to introduce infinity implicitly by Hilbert space, on which is founded its formalism. One can demonstrate that some essential properties of quantum information, entanglement, and quantum computer originate directly from infinity once it is involved in quantum mechanics. Thus, these phenomena can be elucidated as both complete and incomplete, after which choice is the border between them. A special kind of invariance to the axiom of choice shared by quantum mechanics is discussed to be involved that border between the completeness and incompleteness of infinity in a consistent way. The so-called paradox of Albert Einstein, Boris Podolsky, and Nathan Rosen is interpreted entirely in the same terms only of set theory. Quantum computer can demonstrate especially clearly the privilege of the internal position, or " observer'' , or "user" to infinity implied by Henkin's proposition as the only consistent ones as to infinity. An essential area of contemporary knowledge may be synthesized from a single viewpoint. (shrink)

The article is a plea for ethicists to regard probability as one of their most important concerns. It outlines a series of topics of central importance in ethical theory in which probability is implicated, often in a surprisingly deep way, and lists a number of open problems. Topics covered include: interpretations of probability in ethical contexts; the evaluative and normative significance of risk or uncertainty; uses and abuses of expected utility theory; veils of ignorance; Harsanyi’s aggregation theorem; population size (...) problems; equality; fairness; giving priority to the worse off; continuity; incommensurability; nonexpected utility theory; evaluative measurement; aggregation; causal and evidential decision theory; act consequentialism; rule consequentialism; and deontology. (shrink)

Can a group be an orthodox rational agent? This requires the group's aggregate preferences to follow expected utility (static rationality) and to evolve by Bayesian updating (dynamic rationality). Group rationality is possible, but the only preference aggregation rules which achieve it (and are minimally Paretian and continuous) are the linear-geometric rules, which combine individual values linearly and combine individual beliefs geometrically. Linear-geometric preference aggregation contrasts with classic linear-linear preference aggregation, which combines both values and beliefs linearly, but achieves only static (...) rationality. Our characterisation of linear-geometric preference aggregation has two corollaries: a characterisation of linear aggregation of values (Harsanyi's Theorem) and a characterisation of geometric aggregation of beliefs. (shrink)

Extensive measurement is the standard measurement-theoretic approach for constructing a ratio scale. It involves the comparison of objects that can be concatenated in an additively representable way. This paper studies the implications of extensively measurable welfare for social choice theory. We do this in two frameworks: an Arrovian framework with a fixed population and no interpersonal comparisons, and a generalized framework with variable populations and full interpersonal comparability. In each framework we use extensive measurement to introduce novel domain restrictions, independence (...) conditions, and constraints on social evaluation. We prove a welfarism theorem for these domains and characterize the social welfare functions that satisfy the axioms of extensive measurement at both the individual and social levels. The main results are simple axiomatizations of strong dictatorship in the Arrovian framework and classical utilitarianism in the generalized framework. (shrink)

Lewis Carroll, both logician and writer, suggested a logical paradox containing furthermore two connotations (connotations or metaphors are inherent in literature rather than in mathematics or logics). The paradox itself refers to implication demonstrating that an intermediate implication can be always inserted in an implication therefore postponing its ultimate conclusion for the next step and those insertions can be iteratively and indefinitely added ad lib, as if ad infinitum. Both connotations clear up links due to the shared formal structure with (...) other well-known mathematical observations: (1) the paradox of Achilles and the Turtle; (2) the transitivity of the relation of equality. Analogically to (1), one can juxtapose the paradox of the Liar (for Lewis Carroll’s paradox) and that of the arrow (for “Achilles and the Turtle”), i.e. a logical paradox, on the one hand, and an aporia of motion, on the other hand, suggesting a shared formal structure of both, which can be called “ontological”, on which basis “motion” studied by physics and “conclusion” studied by logic can be unified being able to bridge logic and physics philosophically in a Hegelian manner: even more, the bridge can be continued to mathematics in virtue of (2), which forces the equality (for its property of transitivity) of any two quantities to be postponed analogically ad lib and ad infinitum. The paper shows that Hilbert arithmetic underlies naturally Lewis Carroll’s paradox admitting at least three interpretations linked to each other by it: mathematical, physical and logical. Thus, it can be considered as both generalization and solution of his paradox therefore naturally unifying the completeness of quantum mechanics (i.e. the absence of hidden variables) and eventual completeness of mathematics as the same and isomorphic to the completeness of propositional logic in relation to set theory as a first-order logic (in the sense of Gödel (1930)’s completeness theorems). (shrink)

In his essay “The Human Prejudice” Bernard Williams presented a sophisticated defense of the moral relevance of the concept “human being”. Here I offer both an analysis of his essay and a defense of his conclusions against criticisms made by Julian Savulescu and Peter Singer. After a discussion of the structure of Williams’s argument, I focus on several complaints from Savulescu: that Williams underestimates the similarities between speciesism and racism or sexism, that Williams relies on a disputable internalism about reasons (...) to make his case, that Williams ignores the arbitrariness of species membership, and (a complaint also made by Singer) that Williams attacks a straw man in considering only negative utilitarianism when criticizing the idea of an Impartial Observer. I defend Williams against these charges and end with a brief discussion of how his alien invasion example illustrates the fundamentally different philosophical sensibility of Bernard Williams in comparison to critics like Savulescu and Singer. (shrink)

In the Appendix I of his "Remarks on the Foundations of Mathematics", Wittgenstein elaborates a different interpretation of Gödel’s First Incompleteness Theorem, which we have come to refer to as "Gödel’s Theorem" or "Incompleteness Theorem". This nomenclature arises from the recognition that the so-called "Second Incompleteness Theorem" is essentially a corollary of the primary theorem. Wittgenstein aims to reassess Gödel’s conclusion that there exist true formulas not demonstrable within formal systems capable of representing a sufficient (...) amount of arithmetic theory. Gödel’s initial reaction, as well as other commentators, was that Wittgenstein had not understood the proof. Nevertheless, recent commentators view worthy commentaries in wittgensteinian writings: some commentators, such as Juliet Floyd and Hilary Putnam, distinguish between mathematical proof and philosophical prose that surrounds the theorem, making it possible to understand Wittgenstein’s remarks. Ultimately, Wittgenstein’s observations serve as a lens through which Gödel’s theorem can be reconsidered within the realm of non-classical logics, such as paraconsistent logic. (shrink)

In this work we study dimensional theoretical properties of some a±ne dynamical systems. By dimensional theoretical properties we mean Hausdor® dimension and box- counting dimension of invariant sets and ergodic measures on theses sets. Especially we are interested in two problems. First we ask whether the Hausdor® and box- counting dimension of invariant sets coincide. Second we ask whether there exists an ergodic measure of full Hausdor® dimension on these invariant sets. If this is not the case we ask the (...) question, whether at least the variational principle for Haus- dor® dimension holds, which means that there is a sequence of ergodic measures such that their Hausdor® dimension approximates the Hausdor® dimension of the invariant set. It seems to be well accepted by experts that these questions are of great importance in developing a dimension theory of dynamical systems (see the book of Pesin about dimension theory of dynamical systems [PE2]). Dimensional theoretical properties of conformal dynamical systems are fairly well understood today. For example there are general theorems about conformal repellers and hyperbolic sets for conformal di®eomorphisms (see chapter 7 of [PE2]). On the other hand the existence of two di®erent rates of expansion or contraction forces problems that are not captured by a general theory this days. At this stage of de- velopment of the dimension theory of dynamical systems it seems natural to study non conformal examples. This is the ¯rst step to understand the mechanisms that determine dimensional theoretical properties of non conformal dynamical systems. A±ne dynamical systems represent simple examples of non conformal systems. They are easy to de¯ne, but studying their dimensional theoretical properties does never- theless provide challenging mathematical problems and exemplify interesting phe- nomena. We consider here a special class of self-a±ne repellers in dimension two, depending on four parameters (see 2.1.). Furthermore we study a class of attractors of piecewise a±ne maps in dimension three depending on four parameters as well. The last object of our work are projections of these maps that are known as gener- alized Baker's transformations (see 2.2.). The contents of our work is the following: In chapter two we give an overview about some main results in the area of di- mension theory of a±ne dynamical systems and de¯ne the systems we study in this work. We will explain, what is known about the dimensional theoretical properties of these systems and describe what our new results are. In chapter three we then apply symbolic dynamics to our systems. We will introduce explicit shift codings 4 and ¯nd representations of all ergodic measures for our systems using these codings. From chapter four to chapter eight we study dimensional theoretical properties, which our systems generally or generically have. In chapter four we will prove a formula for the box-counting dimension of the repellers and the attractors (see the- orem 4.1.). Then in chapter ¯ve we apply general dimensional theoretical results for ergodic measures found by Ledrappier and Young [LY] and Barreira, Schmeling and Pesin [BPS] to our systems. These results relate the dimension of ergodic measures to metric entropy and Lyapunov exponents. Using this approach we will be able to reduce questions about the dimension of ergodic measures in our context to ques- tions about certain overlapping and especially overlapping self-similar measures on the line. These overlapping self-similar measures are studied in chapter six. Our main theorem extends a result of Peres and Solomyak [PS2] concerning the absolute continuity resp. singularity of symmetric self-similar measures to asymmetric ones (see theorem 6.1.3.). In chapter seven we bring our results together. We prove that we generically (in the sense of Lebesgue measure on a part of the parameter space) have the iden- tity of box-counting and Hausdor® dimension for the repellers and the attractors. (see theorem 7.1.1. and corollary 7.1.2.). This result suggest that one can expect that the identity of box-counting dimension and Hausdor® dimension holds at least generically in some natural classes of non conformal dynamical systems. Furthermore we will see in chapter seven that there generically exists an ergodic measure of full Hausdor® dimension for the repellers. On the other hand the vari- ational principle for Hausdor® dimension is not generic for the attractors. It holds only if we assume a certain symmetry (see theorem 7.1.1.). For generalized Baker's transformations we will ¯nd a part of the parameter space where there generically is an ergodic measure of full dimension and a part where the variational principle for Hausdor® dimension does not hold (see theorem 7.1.3.). Roughly speaking the reason why the variational principle does not hold here is, that if there exists both a stable and an unstable direction one can not generically maximize the dimension in the stable and in the unstable direction at the same time. In an other setting this phenomenon was observed before by Manning and McCluskey [MM]. In chapter eight we extend some results of the last section to invariant sets that correspond to special Markov chains instead of full shifts (see theorem 8.1.1.). In the last two chapters of our work we are interested in number theoretical excep- tions to our generic results. The starting point of our considerations in section nine are results of ErdÄos [ER1] and Alexander and Yorke [AY] that establish singularity and a decrease of dimension for in¯nite convolved Bernoulli measures under special conditions. Using a generalized notion of the Garsia entropy ([GA1/2]) we are able 5 to understand the consequences of number theoretical peculiarities in broader class of overlapping measures (see theorem 9.1.1.). In chapter ten we then analyze number theoretical peculiarities in the context of our dynamical systems. We restrict our attention to a symmetric situation where we generically have the existence of a Bernoulli measure of full dimension and the identity of Hausdor® and box-counting dimension for all of our systems. In the ¯rst section of chapter ten we ¯nd parameter values such that the variational principle for Hausdor® dimension does not hold for the attractors and for the Fat Baker's transformations (see theorem 10.1.1.). These are the ¯rst known examples of dynamical systems for which the variational principle for Hausdor® dimension does not hold because of number theoretical peculiarities of parameter values. For the repellers we have been able to show that under certain number theoretical conditions there is at least no Bernoulli measure of full Hausdor® dimension; the question if the variational principle for Hausdor® dimension holds remains open in this situation. In the second section of chapter ten we will show that the identity for Hausdor® and box-counting dimension can drops because there are number theoretical pecu- liarities. In the context of Weierstrass-like functions this phenomenon was observed by Przytycki and Urbanski [PU]. Our theorem extends this result to a larger class of sets, invariant under dynamical systems (see theorem 10.2.1). At the end of this work the reader will ¯nd two appendices, a list of notations and the list of references. In appendix A we introduce the notions of dimension we use in this work and collect some general facts in dimension theory. In appendix B we state the facts about Pisot-Vijayarghavan number, we need in our analysis of number theoretical peculiarities. The list of notations contains general notations and a table with a summary of notations we use to describe the dynamical systems that we study. Acknowledgments I wish to thank my supervisor JÄorg Schmeling for a lot of valuable discussion and all his help. Also thanks to Luis Barreira for his great hospitality in Lisboa and many interesting comments. This work was done while I was supported by "Promotionstipendium gem. NaFÄoG der Freien UniversitÄat Berlin". (shrink)

This paper examines how the concepts of utility, impartiality, and universality worked together to form the foundation of Adam Smith's jurisprudence. It argues that the theory of utility consistent with contemporary rational choice theory is insufficient to account for Smith's use of utility. Smith's jurisprudence relies on the impartial spectator's sympathetic judgment over whether third parties are injured, and not individuals' expected utility associated with individuals' expected gains from rendering judgments over innocence or guilt.

This paper critically engages Philip Mirowki's essay, "The scientific dimensions of social knowledge and their distant echoes in 20th-century American philosophy of science." It argues that although the cold war context of anti-democratic elitism best suited for making decisions about engaging in nuclear war may seem to be politically and ideologically motivated, in fact we need to carefully consider the arguments underlying the new rational choice based political philosophies of the post-WWII era typified by Arrow's impossibility theorem. A distrust (...) of democratic decision-making principles may be developed by social scientists whose leanings may be toward the left or right side of the spectrum of political practices. (shrink)

The brain is composed of electrically excitable neuronal networks regulated by the activity of voltage-gated ion channels. Further portraying the molecular composition of the brain, however, will not reveal anything remotely reminiscent of a feeling, a sensation or a conscious experience. In classical physics, addressing the mind–brain problem is a formidable task because no physical mechanism is able to explain how the brain generates the unobservable, inner psychological world of conscious experiences and how in turn those conscious experiences steer the (...) underlying brain processes toward desired behavior. Yet, this setback does not establish that consciousness is non-physical. Modern quantum physics affirms the interplay between two types of physical entities in Hilbert space: unobservable quantum states, which are vectors describing what exists in the physical world, and quantum observables, which are operators describing what can be observed in quantum measurements. Quantum no-go theorems further provide a framework for studying quantum brain dynamics, which has to be governed by a physically admissible Hamiltonian. Comprising consciousness of unobservable quantum information integrated in quantum brain states explains the origin of the inner privacy of conscious experiences and revisits the dynamic timescale of conscious processes to picosecond conformational transitions of neural biomolecules. The observable brain is then an objective construction created from classical bits of information, which are bound by Holevo’s theorem, and obtained through the measurement of quantum brain observables. Thus, quantum information theory clarifies the distinction between the unobservable mind and the observable brain, and supports a solid physical foundation for consciousness research. (shrink)

We need modal imagination in order to extend our conception of reality - and, in particular, of human beings - beyond our immediate experience in the indexical present; and we need to do this in order to preserve the significance of human interaction. To make this leap of imagination successfully is to achieve not only insight but also an impartial perspective on our own and others' inner states. This perspective is a necessary condition of experiencing compassion for others. This (...) is the primary thesis I will try to defend in this discussion. (shrink)

Under the independence and competence assumptions of Condorcet’s classical jury model, the probability of a correct majority decision converges to certainty as the jury size increases, a seemingly unrealistic result. Using Bayesian networks, we argue that the model’s independence assumption requires that the state of the world (guilty or not guilty) is the latest common cause of all jurors’ votes. But often – arguably in all courtroom cases and in many expert panels – the latest such common cause is a (...) shared ‘body of evidence’ observed by the jurors. In the corresponding Bayesian network, the votes are direct descendants not of the state of the world, but of the body of evidence, which in turn is a direct descendant of the state of the world. We develop a model of jury decisions based on this Bayesian network. Our model permits the possibility of misleading evidence, even for a maximally competent observer, which cannot easily be accommodated in the classical model. We prove that (i) the probability of a correct majority verdict converges to the probability that the body of evidence is not misleading, a value typically below 1; (ii) depending on the required threshold of ‘no reasonable doubt’, it may be impossible, even in an arbitrarily large jury, to establish guilt of a defendant ‘beyond any reasonable doubt’. (shrink)

A resolution to the Russell Paradox is presented that is similar to Russell's “theory of types” method but is instead based on the definition of why a thing exists as described in previous work by this author. In that work, it was proposed that a thing exists if it is a grouping tying "stuff" together into a new unit whole. In tying stuff together, this grouping defines what is contained within the new existent entity. A corollary is that a thing, (...) such as a set, does not exist until after the stuff is tied together, or said another way, until what is contained within is completely defined. A second corollary is that after a grouping defining what is contained within is present and the thing exists, if one then alters what is tied together (e.g., alters what is contained within), the first existent entity is destroyed and a different existent entity is created. A third corollary is that a thing exists only where and when its grouping exists. Based on this, the Russell Paradox's set R of all sets that aren't members of themselves does not even exist until after the list of the elements it contains (e.g. the list of all sets that aren't members of themselves) is defined. Once this list of elements is completely defined, R then springs into existence. Therefore, because it doesn't exist until after its list of elements is defined, R obviously can't be in this list of elements and, thus, cannot be a member of itself; so, the paradox is resolved. This same type of reasoning is then applied to Godel's first Incompleteness Theorem. Briefly, while writing a Godel Sentence, one makes reference to a future, not yet completed and not yet existent sentence, G, that claims its unprovability. However, only once the sentence is finished does it become a new unit whole and existent entity called sentence G. If one then goes back in and replaces the reference to the future sentence with the future sentence itself, a totally different sentence, G1, is created. This new sentence G1 does not assert its unprovability. An objection might be that all the possibly infinite number of possible G-type sentences or their corresponding Godel numbers already exist somehow, so one doesn't have to worry about references to future sentences and springing into existence. But, if so, where do they exist? If they exist in a Platonic realm, where is this realm? If they exist pre-formed in the mind, this would seem to require a possibly infinite-sized brain to hold all these sentences. This is not the case. What does exist in the mind is the system for creating G-type sentences and their corresponding numbers. This mental system for making a G-type sentence is not the same as the G-type sentence itself just as an assembly line is not the same as a finished car. In conclusion, a new resolution of the Russell Paradox and some issues with proofs of Godel's First Incompleteness Theorem are described. (shrink)

The paper discusses Hilbert mathematics, a kind of Pythagorean mathematics, to which the physical world is a particular case. The parameter of the “distance between finiteness and infinity” is crucial. Any nonzero finite value of it features the particular case in the frameworks of Hilbert mathematics where the physical world appears “ex nihilo” by virtue of an only mathematical necessity or quantum information conservation physically. One does not need the mythical Big Bang which serves to concentrate all the violations of (...) energy conservation in a “safe”, maximally remote point in the alleged “beginning of the universe”. On the contrary, an omnipresent and omnitemporal medium obeying quantum information conservation rather than energy conservation permanently generates action and thus the physical world. The utilization of that creation “ex nihilo” is accessible to humankind, at least theoretically, as long as one observes the physical laws, which admit it in their new and wider generalization. One can oppose Hilbert mathematics to Gödel mathematics, which can be identified as all the standard mathematics until now featureable by the Gödel dichotomy of arithmetic to set theory: and then, “dialectic”, “intuitionistic”, and “Gödelian” mathematics within the former, according to a negative, positive, or zero value of the distance between finiteness and infinity. A mapping of Hilbert mathematics into pseudo-Riemannian space corresponds, therefore allowing for gravitation to be interpreted purely mathematically and ontologically in a Pythagorean sense. Information and quantum information can be involved in the foundations of mathematics and linked to the axiom of choice or alternatively, to the field of all rational numbers, from which the pair of both dual and anti-isometric Peano arithmetics featuring Hilbert arithmetic are immediately inferable. Noether’s theorems (1918) imply quantum information conservation as the maximally possible generalization of the pair of the conservation of a physical quantity and the corresponding Lie group of its conjugate. Hilbert mathematics can be interpreted from their viewpoint also after an algebraic generalization of them. Following the ideas of Noether’s theorem (1918), locality and nonlocality can be realized both physically and mathematically. The “light phase of the universe” can be linked to the gap of mathematics and physics in the Cartesian organization of cognition in Modernity and then opposed to its “dark phase”, in which physics and mathematics are merged. All physical quantities can be deduced from only mathematical premises by the mediation of the most fundamental physical constants such as the speed of light in a vacuum, the Planck and gravitational constants once they have been interpreted by the relation of locality and nonlocality. (shrink)

TWENTIETH-CENTURY ETHICS. AFTER NIETZSCHE -/- Preface This book tells the story of twentieth-century ethics or, in more detail, it reconstructs the history of a discussion on the foundations of ethics which had a start with Nietzsche and Sidgwick, the leading proponents of late-nineteenth-century moral scepticism. During the first half of the century, the prevailing trends tended to exclude the possibility of normative ethics. On the Continent, the trend was to transform ethics into a philosophy of existence whose self-appointed task was (...) that of describing the human condition as consisting of choices, as unavoidable as arbitrary, without any attempt at providing criteria for making such choices. In the Anglo-Saxon countries, the heir of ethics was a philosophy of morality, that is, an analysis of the language of morality that intended to clarify valuations without trying to justify them. 1958 was the year of the normative turn that led to the Rehabilitation of practical philosophy, a turn followed by decades of controversies between distinct kinds of normative ethics: utilitarian, Kantian, virtue ethics. While the controversy was raging, a quiet revolution took place, that of applied ethics which surprisingly dissolved the controversy's very subject matter by providing methods for making convergence possible on intermediate principles even when no agreement was available about first principles. The normative turn and the revolution of applied ethics have led us, at the turn of the century, to a goal that was quite far from the starting point. Instead of scepticism and relativism that was the fashion at the beginning of the century, at the beginning of the third millennium impartial and universal moral arguments seem to hold the spot being supported, if not by a final rational foundation, at least by reasonableness, the most precious legacy of the Enlightenment. -/- ● TABLE OF CONTENTS -/- ● I Anglo-Saxon philosophy: naturalism 1. Dewey beyond evolutionism and utilitarianism 2. Dewey and anti-essentialist moral epistemology 3. Dewey and naturalist moral ontology 4. Dewey and normative ethics of conduct and function 5. Perry and semantic naturalism -/- ● II Anglo-Saxon philosophy: ideal utilitarianism and neo-intuitionism 1. Moore's critique of utilitarian empiricism 2. Moore on the naturalistic fallacy 3. Moore on the nature of intrinsic value 4. Moore on ideal utilitarianism 5. Prichard on the priority of the right over the good 6. Ross's coherentist moral epistemology 7. Ross's moral ontology: realism, pluralism, and non-naturalism 8. Ross's normative ethics of prima facie duties -/- The chapter reconstructs the background of ideas, concerns and intentions out of which Moore's early essays, the preliminary version, and then the final version of Principia Ethica originated. It stresses the role of religious concerns, as well as that of the Idealist legacy. It argues that PE is more a patchwork of somewhat diverging contributions than a unitary work, not to say the paradigm of a new school in Ethics. -/- ●III Anglo-Saxon philosophy: non-cognitivism 1. The Scandinavian School, the Vienna circle and proto-emotivism 2. Wittgenstein and the ineffability of ethics 3. Russell's and Ayer's radical emotivism 4. Stevenson and moderate emotivism 5. Stevenson and the pragmatics of moral language 6. Stevenson and the methods for solving ethical disagreement 7. Hare and prescriptivism The chapter reconstructs first the discussion after Moore. The naturalistic-fallacy argument was widely accepted but twisted to prove instead that the intuitive character of the definition of 'good', its non-cognitive meaning, in a first phase identified with 'emotive' meaning. Alfred Julius Ayer is indicated as a typical proponent of such non-cognitivist meta-ethics. More detailed discussion is dedicated to Bertrand Russell's ethics, a more nuanced and sophisticated doctrine, arguing that non-cognitivism does not condemn morality to arbitrariness and that the project of rational normative ethics is still possible, heading finally to the justification of a kind of non-hedonist utilitarianism. Stevenson's theory, another moderate version of emotivism is discussed at some length, showing how the author comes close to the discovery of the role of a pragmatic dimension of language as a basis for ethical argument. A section reconstructs the discussion from the Forties about Hume's law, mentioning Karl Popper's argument and Richard Hare's early non-cognitivist but non-emotivist doctrine named prescriptivism. -/- ●IV Anglo-Saxon philosophy: critics of non-cognitivism 1. Neo-naturalism and its objections to the naturalistic fallacy argument 2. Objections to Hume's law 3. Clarence Lewis and the pragmatic contradiction 4. Toulmin and the good reasons approach 5. Baier and moral reasons 5. Baier, social moralities and the absolute morality 6. Baier and the moral point of view 7. Baier and the contents of absolute ethics -/- ● V Continental philosophy: the philosophy of values 1. Max Weber and the polytheism of values 2. Phenomenology against psychologism and rationalism 3. Reinach and the theory of social acts 4. Scheler and the material ethics of values 5. Hartmann and the ontology of values 6. Plessner, Gehlen and the Philosophische Anthropologie -/- The chapter illustrates first the idea of phenomenology and the Husserl's project of a phenomenological ethic as illustrated in his 1908-1914 lectures. The key idea is dismissing psychology and trying to ground a new science of the apriori of action, within which a more restricted field of inquiry will be the science of right actions. Then the chapter illustrates the criticism of modern moral philosophy conducted in the 1920 lectures, where the main target is naturalism, understood in the Kantian meaning of primacy of common sense. The third point illustrate is Adolph Reinach's theory of social acts as a key the grounding of norms, a view that sketches the ideas 'discovered' later by Clarence I. Lewis, John Searle, Karl-Otto Apel and Jürgen Habermas. A final section discusses Nicolai Hartman, who always refused to define himself a phenomenologist and yet developed a more articulated and detailed theory of 'values' – with surprising affinities with George E. Moore - than philosophers such as Max Scheler, who claimed to be Husserl's legitimate heirs. -/- ● VI Continental philosophy: the critics of the philosophy of values 1. Freud, the Superego and Civilization 2. Heidegger on original ethos against ethics 3. Sartre and de Beauvoir on authenticity and ambiguity 4. Adorno and Horkheimer on emancipation and immoralism -/- ●VII Post-liberal theologians and religious thinkers 1. Barth on the autonomy of faith from ethics 2. Developments of Reformed moral theology after Barth 3. Bonhoeffer on the concrete divine command and ethics of penultimate realities 4. Developments of Reformed and Catholic moral theology after world war II 5. Baeck and the transformation of liberal Judaism 6. Rosenzweig against liberal Judaism 7. Buber and religion as the vital lymph of morality 8. Heschel and Judaism as a science of actions -/- The chapter examines the main protagonists of Christian theology and Jewish religious thinking in the twentieth century. It stresses how the main dilemmas of contemporary philosophical ethics lie at the root of the various path of inquiry taken by these thinkers. -/- ● VIII Normative ethics: neo-Utilitarianism 1. The discussion on act and rule utilitarianism 2. Hare on two-tiered preference utilitarianism 3. Harsanyi, Gauthier and rational choice ethics 4. Parfit, utilitarianism and the idea of a person 5. Brandt and indirect conscience utilitarianism -/- The chapter addresses the issue of the complex process of self-transformation Utilitarianism underwent after Sidgwick's and Moore's fatal criticism and the unexpected Phoenix-like process of rebirth of a doctrine refuted. Two examples give the reader a glimpse at this uproarious process. The first is Roy Harrod Wittgensteinian transformation of utilitarianism in pure normative ethics depurated from hedonism as well as from whatsoever theory of the good. This transformation results in preference utilitarianism combined with a 'Kantian' version of rule utilitarianism. The second is Richard Hare's two-level preference utilitarianism, where act utilitarianism plays the function of the eventual rational justification of moral judgments and rule-utilitarianism that of an action-guiding practical device. -/- ● IX Normative ethics: neo-Aristotelianism and virtue ethics 1. Hannah Arendt, action and judgement 2. Hans-Georg Gadamer and phronesis 3. Alasdair MacIntyre on practices, virtues, and traditions 5. Stuart Hampshire on deliberation 6. Bernard Williams and moral complexity 7. Feminist ethics -/- Sect 1 reconstructs the post-war rediscovery of ethics by many German thinkers and its culmination in the Sixties in the movement named 'Rehabilitation of practical philosophy' is described. Heidegger's most brilliant disciples were the promoters of this Rehabilitation. Hans-Georg Gadamer is a paradigmatic example. His reading of Aristotle's lesson I reconstructed, starting with Heidegger's lesson but then subtly subverting its outcome thanks to the recovery of the significant role of the notion of phronesis. Sect 3 discusses the three theses defended by Anscombe in 'Modern Moral Philosophy'. It argues that: a) her answer to the question "why should I be moral?" requires a solution of the problem of theodicy, and ignores any attempts to save the moral point of view without recourse to divine retribution; b) her notion of divine law is an odd one more neo-Augustinian than Biblical or Scholastic; c) her image of Kantian ethics and intuitionism is the impoverished image manufactured by consequentialist opponents for polemical purposes and that she seems strangely accept it; d) the difficulty of identifying the "relevant descriptions" of acts is not an argument in favour of an ethics of virtue and against consequentialism or Kantian ethics, and indeed the role of judgment in the latter is a response to the difficulties raised by the case of judgment concerning future action. The chapter gives a short look at further developments in the neo-naturalist current trough a reconstruction of Philippa Foot's and Peter Geach's critiques to the naturalist-fallacy argument and Alasdair MacIntyre's grand reconstruction of the origins and allegedly inevitable failure of the Enlightenment project of an autonomous ethic. -/- ● X Normative ethics: Kantian and rights-based ethics 1. Dialogical constructivism 2. Apel, Habermas and discourse ethics 3. Gewirth and rights-based ethics 4. Nagel on agent-relative reasons 5. Donagan and persons as ends in themselves Parallel to the neo-Aristotelian trend, there was in the Rehabilitation of practical philosophy a Kantian current. This current started with the discovery of the pragmatic dimension of language carried out by Charles Peirce and the Oxford linguistic philosophy. On this basis, Karl-Otto Apel singled out as the decisive proponent of the linguistic and Kantian turn in German-speaking ethics, worked out the performative-contradiction argument while claiming that this was able to provide a new rational and universal basis for normative ethics. The chapter offers an examination of his argument in some detail, followed by a more cursory reconstruction of Jürgen Habermas's elaboration on Apel's theory. -/- ● XI The applied ethics renaissance 1. Elisabeth Anscombe on the atom bomb 2. From medical ethics to bioethics 3. Rawls and public ethics 3. Nozick, Dworkin and further developments of public ethics 5. Sen and the revival of economic ethics -/- The chapter presents the revolution of applied ethics while stressing its methodological novelty, exemplified primarily by Beauchamp and Childress principles approach and then by Jonsen and Toulmin's new casuistry. The chapter argues that Rawls's distinction between a "political" and a "metaphysical" approach to the theory of justice, one central part of ethical theory, is a formulation of the same basic idea at the root of both the principles approach and the new casuistry, both discussed in the following chapter. The idea is that it is possible to reach an agreement concerning positive moral judgments even though the discussion is still open – and in Rawls' view never will be close – on the essential criteria for judgment. -/- ● XII Fin-de-siècle metaethics 1. Deontic logics 2. Anti-realism 3. External realism 4. Internal realism 5. Kantian constructivism -/- The chapter illustrates the fresh start of meta-ethical discussion in the Eighties and Nineties and the resulting new alignments: metaphysical naturalism, internal realism, anti-realism, and constructivism. (shrink)

Welfarism is the view that individual welfare is the only thing that matters. One important contribution of social choice theory has been to provide a precise formulation and axiomatic characterization of welfarism using Amartya Sen's framework of social welfare functionals. This paper is motivated by the observation that the standard formalization of welfarism is too restrictive, since a welfarist social planner need not be committed to maximizing a preference ordering or any other binary relation over alternatives. We therefore provide a (...) characterization of welfarism in a more general choice-functional setting and show that welfarism, so understood, carries no commitment to rationalizability. This characterization is compatible with welfare values having any structure whatsoever. It also sheds light on different formulations of anonymity, revealing only some of these to be fundamental requirements of impartiality. (shrink)

Two strategies to infinity are equally relevant for it is as universal and thus complete as open and thus incomplete. Quantum mechanics is forced to introduce infinity implicitly by Hilbert space, on which is founded its formalism. One can demonstrate that essential properties of quantum information, entanglement, and quantum computer originate directly from infinity once it is involved in quantum mechanics. Thus, thеse phenomena can be elucidated as both complete and incomplete, after which choice is the border between them. A (...) special kind of invariance to the axiom of choice shared by quantum mechanics is discussed to be involved that border between the completeness and incompleteness of infinity in a consistent way. The so-called paradox of Albert Einstein, Boris Podolsky, and Nathan Rosen is interpreted entirely in the same terms only of set theory. Quantum computer can demonstrate especially clearly the privilege of the internal position, or “observer”, or “user” to infinity implied by Henkin’s proposition as the only consistent ones as to infinity. (shrink)

We provide a new interpretation of Zeno’s Paradox of Measure that begins by giving a substantive account, drawn from Aristotle’s text, of the fact that points lack magnitude. The main elements of this account are (1) the Axiom of Archimedes which states that there are no infinitesimal magnitudes, and (2) the principle that all assignments of magnitude, or lack thereof, must be grounded in the magnitude of line segments, the primary objects to which the notion of linear magnitude applies. Armed (...) with this account, we are ineluctably driven to introduce a highly constructive notion of (outer) measure based exclusively on the total magnitude of potentially infinite collections of line segments. The Paradox of Measure then consists in the proof that every finite or potentially infinite collection of points lacks magnitude with respect to this notion of measure. We observe that the Paradox of Measure, thus understood, troubled analysts into the 1880’s, despite their knowledge that the linear continuum is uncountable. The Paradox was ultimately resolved by Borel in his thesis of 1893, as a corollary to his celebrated result that every countable open cover of a closed line segment has a finite sub-cover, a result he later called the “First Fundamental Theorem of Measure Theory.” This achievement of Borel has not been sufficiently appreciated. We conclude with a metamathematical analysis of the resolution of the paradox made possible by recent results in reverse mathematics. (shrink)

Can we design a perfect democratic decision procedure? Condorcet famously observed that majority rule, our paradigmatic democratic procedure, has some desirable properties, but sometimes produces inconsistent outcomes. Revisiting Condorcet’s insights in light of recent work on the aggregation of judgments, I show that there is a conflict between three initially plausible requirements of democracy: “robustness to pluralism”, “basic majoritarianism”, and “collective rationality”. For all but the simplest collective decision problems, no decision procedure meets these three requirements at once; at most (...) two can be met together. This “democratic trilemma” raises the question of which requirement to give up. Since different answers correspond to different views about what matters most in a democracy, the trilemma suggests a map of the “logical space” in which different conceptions of democracy are located. It also sharpens our thinking about other impossibility problems of social choice and how to avoid them, by capturing a core structure many of these problems have in common. More broadly, it raises the idea of “cartography of logical space” in relation to contested political concepts. (shrink)

It is a remarkable fact that all processes occurring in the observable universe are irre- versible, whereas the equations through which the fundamental laws of physics are formu- lated are invariant under time reversal. The emergence of irreversibility from the funda- mental laws has been a topic of consideration by physicists, astronomers and philosophers since Boltzmann's formulation of his famous \H" theorem. In this paper we shall discuss some aspects of this problem and its connection with the dynamics of (...) space-time, within the framework of modern cosmology. We conclude that the existence of cosmological horizons allows a coupling of the global state of the universe with the local events deter- mined through electromagnetic processes. (shrink)

In classical American pragmatism, fallibilism refers to the conception of truth as an ongoing process of improving human knowledge that is nevertheless susceptible to error. This paper traces appearances of fallibilism in Jewish thought in general, and particularly in the halakhic thought of Eliezer Berkovits. Berkovits recognizes the human condition’s persistent mutability, which he sees as characterizing the ongoing effort to interpret and apply halakhah in shifting historical and social contexts as Torat Ḥayyim. In the conclusion of the article, broader (...) questions and observations are raised regarding Jewish tradition, fallibility, and modernity, and the interaction between Judaism and pragmatism in the history of ideas. (shrink)

In this paper I examine Bernard Williams’ claim that an appealing conception of love can come into conflict with impartial morality. First, I explain how Williams’ claim can survive one strategy to head off the possibility of conflict. I then examine J.D.Velleman’s Kantian conception of love as another possible way to reject Williams’ claim. I argue, however, that Velleman’s attempt to transcend love’s partiality in his account of love produces an unappealing and unconvincing ideal. This is made particularly clear, (...) I suggest, by the analysis that Velleman is forced to give of the kind of case that generated Williams’ observations in the first place. Thus Velleman’s account should be rejected. (shrink)