Indigenous Sustainable Wisdom: First Nation Know-How for Global Flourishing’s contributors describe ways of being that reflect a worldview that has guided humanity for 99% of human history; they describe the practical traditional wisdom stemming from Nature-based relational cultures that were or are guided by this worldview. Such cultures did not cause the kinds of anti-Nature and de-humanizing or inequitable policies and practices that now pervade our world. Far from romanticizing Indigenous histories, Indigenous Sustainable Wisdom offers facts about how human beings, (...) with our potential for good and evil behaviors, can live in relative harmony again. Contributions cover views from anthropology, psychology, sociology, leadership, native science, native history, native art. (shrink)

'The arrow of time' refers to the curious asymmetry that distinguishes the future from the past. Reversing the Arrow of Time argues that there is an intimate link between the symmetries of 'time itself' and time reversal symmetry in physical theories, which has wide-ranging implications for both physics and its philosophy. This link helps to clarify how we can learn about the symmetries of our world, how to understand the relationship between symmetries and what is real, and how to overcome (...) pervasive illusions about the direction of time. Roberts explains the significance of time reversal in a way that intertwines physics and philosophy, to establish what the arrow of time means and how we can come to know it. This book is both mathematically and philosophically rigorous yet remains accessible to advanced undergraduates in physics and the philosophy of physics. This title is also available as Open Access on Cambridge Core. (shrink)

Many philosophers and scientists have claimed that time has an arrow that points in a special direction. The Roman poet Ovid may have referred to this one-way property of time when he said, “Time itself glides on with constant motion, ever as a flowing river.” However, understanding this arrow is not … Continue reading The Arrow of Time →.

In response to recent work on the aggregation of individual judgments on logically connected propositions into collective judgments, it is often asked whether judgment aggregation is a special case of Arrowian preference aggregation. We argue for the converse claim. After proving two impossibility theorems on judgment aggregation (using "systematicity" and "independence" conditions, respectively), we construct an embedding of preference aggregation into judgment aggregation and prove Arrow’s theorem (stated for strict preferences) as a corollary of our second result. Although we thereby (...) provide a new proof of Arrow’s theorem, our main aim is to identify the analogue of Arrow’s theorem in judgment aggregation, to clarify the relation between judgment and preference aggregation, and to illustrate the generality of the judgment aggregation model. JEL Classi…cation: D70, D71.. (shrink)

Riker (1982) famously argued that Arrow’s impossibility theorem undermined the logical foundations of “populism”, the view that in a democracy, laws and policies ought to express “the will of the people”. In response, his critics have questioned the use of Arrow’s theorem on the grounds that not all configurations of preferences are likely to occur in practice; the critics allege, in particular, that majority preference cycles, whose possibility the theorem exploits, rarely happen. In this essay, I argue that the critics’ (...) rejoinder to Riker misses the mark even if its factual claim about preferences is correct: Arrow’s theorem and related results threaten the populist’s principle of democratic legitimacy even if majority preference cycles never occur. In this particular context, the assumption of an unrestricted domain is justified irrespective of the preferences citizens are likely to have. (shrink)

In a quantum universe with a strong arrow of time, it is standard to postulate that the initial wave function started in a particular macrostate---the special low-entropy macrostate selected by the Past Hypothesis. Moreover, there is an additional postulate about statistical mechanical probabilities according to which the initial wave function is a ''typical'' choice in the macrostate. Together, they support a probabilistic version of the Second Law of Thermodynamics: typical initial wave functions will increase in entropy. Hence, there are two (...) sources of randomness in such a universe: the quantum-mechanical probabilities of the Born rule and the statistical mechanical probabilities of the Statistical Postulate. I propose a new way to understand time's arrow in a quantum universe. It is based on what I call the Thermodynamic Theories of Quantum Mechanics. According to this perspective, there is a natural choice for the initial quantum state of the universe, which is given by not a wave function but by a density matrix. The density matrix plays a microscopic role: it appears in the fundamental dynamical equations of those theories. The density matrix also plays a macroscopic / thermodynamic role: it is exactly the projection operator onto the Past Hypothesis subspace. Thus, given an initial subspace, we obtain a unique choice of the initial density matrix. I call this property "the conditional uniqueness" of the initial quantum state. The conditional uniqueness provides a new and general strategy to eliminate statistical mechanical probabilities in the fundamental physical theories, by which we can reduce the two sources of randomness to only the quantum mechanical one. I also explore the idea of an absolutely unique initial quantum state, in a way that might realize Penrose's idea of a strongly deterministic universe. (shrink)

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)

We argue that a semantics for counterfactual conditionals in terms of comparative overall similarity faces a formal limitation due to Arrow’s impossibility theorem from social choice theory. According to Lewis’s account, the truth-conditions for counterfactual conditionals are given in terms of the comparative overall similarity between possible worlds, which is in turn determined by various aspects of similarity between possible worlds. We argue that a function from aspects of similarity to overall similarity should satisfy certain plausible constraints while Arrow’s impossibility (...) theorem rules out that such a function satisfies all the constraints simultaneously. We argue that a way out of this impasse is to represent aspectual similarity in terms of ranking functions instead of representing it in a purely ordinal fashion. Further, we argue against the claim that the determination of overall similarity by aspects of similarity faces a difficulty in addition to the Arrovian limitation, namely the incommensurability of different aspects of similarity. The phenomena that have been cited as evidence for such incommensurability are best explained by ordinary vagueness. (shrink)

Kenneth Arrow presents Rawls as making a controversial assumption, which he terms “asset egalitarianism”: that all the assets of society, including personal skills, are available for distribution. I distinguish two versions of the assumption and draw attention to difficulties in determining what Arrow’s concern over the assumption is.

We argue that the asymmetry between diverging and converging electromagnetic waves is just one of many asymmetries in observed phenomena that can be explained by a past hypothesis and statistical postulate (together assigning probabilities to different states of matter and field in the early universe). The arrow of electromagnetic radiation is thus absorbed into a broader account of temporal asymmetries in nature. We give an accessible introduction to the problem of explaining the arrow of radiation and compare our preferred strategy (...) for explaining the arrow to three alternatives: (i) modifying the laws of electromagnetism by adding a radiation condition requiring that electromagnetic fields always be attributable to past sources, (ii) removing electromagnetic fields and having particles interact directly with one another through retarded action-at-a-distance, (iii) adopting the Wheeler-Feynman approach and having particles interact directly through half-retarded half-advanced action-at-a-distance. In addition to the asymmetry between diverging and converging waves, we also consider the related asymmetry of radiation reaction. (shrink)

I propose that, in addition to the commonly recognized increase of entropy, two more time arrows influence living beings. The increase of damage reactions, which produce aging and genetic variation, and the decrease of the rate of entropy production involved in natural selection are neglected arrows of time. Although based on the statistical theory of the arrow of time, they are distinguishable from the general arrow of the increase of entropy. Physiology under healthy conditions only obeys the increase of entropy (...) arrow. But aging, death, and evolution are determined by the other time arrows as well. Paradoxes emerge from conflicts among the specific determinisms associated with each arrow. These conflicts, along with uncertainties intrinsic to the low-number statistics of the arrows of damage reactions and decrease of the rate of production of entropy, highlight the limits of determinism at different levels of biology and its dependence on time span and number of organisms. The recognition of the three time arrows opens new perspectives for the problem of compatibility of the flow of time in physics and psychology. (shrink)

Statistical physics cannot explain why a thermodynamic arrow of time exists, unless one postulates very special and unnatural initial conditions. Yet, we argue that statistical physics can explain why the thermodynamic arrow of time is universal, i.e., why the arrow points in the same direction everywhere. Namely, if two subsystems have opposite arrow-directions at a particular time, the interaction between them makes the configuration statistically unstable and causes a decay towards a system with a universal direction of the arrow of (...) time. We present general qualitative arguments for that claim and support them by a detailed analysis of a toy model based on the baker’s map. (shrink)

This paper studies the problem of the arrow of time from the scientific and philosophical perspective. The scientific section (Castagnino) poses the topic according to the instruments of measuring employed in physical theories, specially when they are applied to dynamic chaotic systems in which a temporal asymmetry is shown. From the analysis of “two schools” (epistemological and ontological), the conclusion is favorable to the reality (both ontological and epistemological) of the difference between past and future, with the recourse to Reichenbach’s (...) notion of global system. In the philosophical section (Sanguineti) the content of the scientific part of the article is presented in a qualitative way. The role of some philosophical choices in the scientific field is stressed, taking into account the diversity of a positivistic and realistic view. (shrink)

Time in electromagnetism shares many features with time in other physical theories. But there is one aspect of electromagnetism's relationship with time that has always been controversial, yet has not always attracted the limelight it deserves: the electromagnetic arrow of time. Beginning with a re-analysis of a famous argument between Ritz and Einstein over the origins of the radiation arrow, this chapter frames the debate between modern Einsteinians and neo-Ritzians. It tries to find a clean statement of what the arrow (...) is and then explains how it relates to the cosmological and thermodynamic arrows, representing the most developed and sophisticated attack yet, in either the physics or philosophy literature, on the electromagnetic arrow of time. (shrink)

In this paper, I investigate the relationship between preference and judgment aggregation, using the notion of ranking judgment introduced in List and Pettit. Ranking judgments were introduced in order to state the logical connections between the impossibility theorem of aggregating sets of judgments and Arrow’s theorem. I present a proof of the theorem concerning ranking judgments as a corollary of Arrow’s theorem, extending the translation between preferences and judgments defined in List and Pettit to the conditions on the aggregation procedure.

In recent years, there has been a heated debate about how to interpret findings that seem to show that humans rapidly and automatically calculate the visual perspectives of others. In the current study, we investigated the question of whether automatic interference effects found in the dot-perspective task (Samson, Apperly, Braithwaite, Andrews, & Bodley Scott, 2010) are the product of domain-specific perspective-taking processes or of domain-general “submentalizing” processes (Heyes, 2014). Previous attempts to address this question have done so by implementing inanimate (...) controls, such as arrows, as stimuli. The rationale for this is that submentalizing processes that respond to directionality should be engaged by such stimuli, whereas domain-specific perspective-taking mechanisms, if they exist, should not. These previous attempts have been limited, however, by the implied intentionality of the stimuli they have used (e.g. arrows), which may have invited participants to imbue them with perspectival agency. Drawing inspiration from “novel entity” paradigms from infant gaze-following research, we designed a version of the dot-perspective task that allowed us to precisely control whether a central stimulus was viewed as animate or inanimate. Across four experiments, we found no evidence that automatic “perspective-taking” effects in the dot-perspective task are modulated by beliefs about the animacy of the central stimulus. Our results also suggest that these effects may be due to the task-switching elements of the dot-perspective paradigm, rather than automatic directional orienting. Together, these results indicate that neither the perspective-taking nor the standard submentalizing interpretations of the dot-perspective task are fully correct. (shrink)

Ismael traces our sense that the past is fixed and the future open to what she calls ‘the practical arrow’ – ‘the sense that we can affect the future but not the past.’ In this piece I draw a sharper distinction than Ismael herself does between agents and mere observers, even self-referential observers; and I use it to argue that Ismael’s explanation of the practical arrow is incomplete. To explain our inability to affect the past we need to appeal to (...) our own temporal orientation as agents, and not merely to the ingredients from physics that allow us to predict the consequences of our actions. [This piece is a commentary on J Ismael’s ‘The Open Universe: Totality, Self-Reference and Time’, to appear in the Australasian Philosophical Review.]. (shrink)

The foundation of irreversible, probabilistic time -- the classical time of conscious observation -- is the reversible and deterministic time of the quantum wave function. The tendency in physics is to regard time in the abstract, a mere parameter devoid of inherent direction, implying that a concept of real time begins with irreversibility. In reality time has no need for irreversibility, and every invocation of time implies becoming or flow. Neither symmetry under time reversal, of which Newton was well aware, (...) nor the absence of an absolute parameter, as in relativity, negates temporal passage. Far from encapsulating time, irreversibility is a secondary property dependent on the emergence of distinct moments from the ceaseless presence charted by the wave function. (shrink)

One of the most difficult problems in the foundations of physics is what gives rise to the arrow of time. Since the fundamental dynamical laws of physics are (essentially) symmetric in time, the explanation for time's arrow must come from elsewhere. A promising explanation introduces a special cosmological initial condition, now called the Past Hypothesis: the universe started in a low-entropy state. Unfortunately, in a universe where there are many copies of us (in the distant ''past'' or the distant ''future''), (...) the Past Hypothesis is not enough; we also need to postulate self-locating (de se) probabilities. However, I show that we can similarly use self-locating probabilities to strengthen its rival---the Fluctuation Hypothesis, leading to in-principle empirical underdetermination and radical epistemological skepticism. The underdetermination is robust in the sense that it is not resolved by the usual appeal to 'empirical coherence' or 'simplicity.' That is a serious problem for the vision of providing a completely scientific explanation of time's arrow. (shrink)

Evolution's Arrow argues that evolution is directional and progressive, and that this has major consequences for humanity. Without resort to teleology, the book demonstrates that evolution moves in the direction of producing cooperative organisations of greater scale and evolvability - evolution has organised molecular processes into cells, cells into organisms, and organisms into societies. The book founds this position on a new theory of the evolution of cooperation. It shows that self-interest at the level of the genes does not prevent (...) cooperation from increasing as evolution unfolds. Evolution progresses by discovering ways to build cooperative organisations out of self-interested individuals. The book also shows that evolution itself has evolved. Evolution has progressively improved the ability of evolutionary mechanisms to discover effective adaptations. And it has produced new and better mechanisms. Evolution's Arrow uses this understanding of the direction of evolution to identify the next great steps in the evolution of life on earth - the steps that humanity must take if we are to continue to be successful in evolutionary terms. A key step for humanity is to increase the scale and evolvability of our societies, eventually forming a unified and cooperative society on the scale of the planet. We must also transform ourselves psychologically to become self-evolving organisms - organisms that are able to escape their biological and cultural past by adapting in whatever directions are necessary to achieve future evolutionary success. (shrink)

In this chapter, I argue that the loss of loved ones requires a revised vision of our relationship to past persons. In particular, I argue that relating to deceased loved ones as points on an ordered, forward-moving timeline—on which they grow more distant from us by the moment—has a distorting and damaging effect on our own identity. If we detach ourselves completely from those who sustain important aspects of our identity, this will cause a jagged break in our narrative where (...) a new self must be constructed (whether by us or our circumstances) ex nihilo. On the other hand, if we allow ourselves to drift into the past with the dead—resigning ourselves to existence as an historical object—we will find that we begin to fade away ourselves. Either way, both the self and the beloved are ultimately lost, since both depend on the lost union. To reject both options is a tremendously difficult task that will require rethinking time and our relationship to the past. I argue that we can look to Kierkegaard’s work on maintaining contemporaneity with the historical past, particularly his warnings about how we must not respond to the loss of a beloved. In the last section of the paper, I offer some suggestions for how we might, in a Kierkegaardian spirit, strive to maintain real union with deceased loved ones, thereby rising above the destructive current of time. (shrink)

Some argue that time’s causal arrow is grounded in an underlying thermodynamic asymmetry. Often, this is tied to Humean skepticism that causes produce their effects, in any robust sense of ‘produce’. Conversely, those who advocate stronger notions of natural necessity often reject thermodynamic reductions of time’s causal arrow. Against these traditional pairings, I argue that ‘reduction-plus-production’ is coherent. Reductionists looking to invoke robust production can insist that there are metaphysical constraints on the signs of objects’ velocities in any state, given (...) other—including far later—states’ properties. The Past Hypothesis may thus be a metaphysical condition, not a physical law. (shrink)

Can the second law of thermodynamics explain our mental experience of the direction of time? According to an influential approach, the past hypothesis of universal low entropy also explains how the psychological arrow comes about. We argue that although this approach has many attractive features, it cannot explain the psychological arrow after all. In particular, we show that the past hypothesis is neither necessary nor sufficient to explain the psychological arrow on the basis of current physics. We propose two necessary (...) conditions on the workings of the brain that any account of the psychological arrow of time must satisfy. And we propose a new reductive physical account of the psychological arrow of time compatible with time-symmetric physics, according to which these two conditions are also sufficient. Our proposal has some radical implications, for example, that the psychological arrow of time is fundamental, whereas the temporal direction of entropy increase in the second law of thermodynamics and the past hypothesis is derived from it, rather than the other way around. 1Introduction2A Physical Account of the Psychological Arrow of Time3Necessary Conditions for the Psychological Arrow of Time4The Psychological Arrow of Time via the Second Law of Thermodynamics and the Past Hypothesis5Why the Past Hypothesis Is Insufficient for the Psychological Arrow of Time5.1Stage 1, Version 1: From the past hypothesis to the psychological arrow via typicality5.2Stage 1, Version 2: From the past hypothesis to the psychological arrow via dynamical or causal considerations5.3Stage 2: From entropy gradient in the brain to the psychological arrow of time6Why the Past Hypothesis Is Unnecessary for the Psychological Arrow of Time7A New Reductive Account of the Psychological Arrow of Time. (shrink)

Two of the most difficult problems in the foundations of physics are (1) what gives rise to the arrow of time and (2) what the ontology of quantum mechanics is. They are difficult because the fundamental dynamical laws of physics do not privilege an arrow of time, and the quantum-mechanical wave function describes a high-dimensional reality that is radically different from our ordinary experiences. -/- In this paper, I characterize and elaborate on the ``Wentaculus” theory, a new approach to time’s (...) arrow in a quantum universe that offers a unified solution to both problems. Central to the Wentaculus are (i) Density Matrix Realism, the idea that the quantum state of the universe is objective but can be impure, and (ii) the Initial Projection Hypothesis, a new law of nature that selects a unique initial quantum state. On the Wentaculus, the quantum state of the universe is sufficiently simple to be a law, and the arrow of time can be traced back to an exact boundary condition. It removes the intrinsic vagueness of the Past Hypothesis, eliminates the Statistical Postulate, provides a higher degree of theoretical unity, and contains a natural realization of “strong determinism." I end by responding to four recent objections. In a companion paper, I elaborate on Density Matrix Realism. (shrink)

The aim of this paper is to analyze time-asymmetric quantum mechanics with respect to the problems of irreversibility and of time’s arrow. We begin with arguing that both problems are conceptually different. Then, we show that, contrary to a common opinion, the theory’s ability to describe irreversible quantum processes is not a consequence of the semigroup evolution laws expressing the non-time-reversal invariance of the theory. Finally, we argue that time-asymmetric quantum mechanics, either in Prigogine’s version or in Bohm’s version, does (...) not solve the problem of the arrow of time because it does not supply a substantial and theoretically founded criterion for distinguishing between the two directions of time. (shrink)

This article is an effort to understand how the Peirce's Arrow (Logical NOR), as a logical operation, can act within the concept of Ludwig Wittgenstein's language-game, considering that the language game is a satzsystem, i.e., a system of propositions. To accomplish this task, we will cover four steps: (1) understand the possible relationship of the thought of C. S. Peirce with the founding trio of analytic philosophy, namely Frege-RussellWittgenstein, looking for similarities between the logic of Peirce and his students (notably (...) Christine Ladd and O.H. Mitchell) with a New Wittgenstein’s approach, which sees Early Wittgenstein (Tractatus Logico-Philosophicus),Middle Wittgenstein and Last Wittgenstein (Philosophical Investigations) while a coherent way of thinking and not a theoretical break; (2) describe the operation of the Peirce’s Arrow (Logical NOR) as a logical connective; (3)understand the notion of satzsystem (Middle Wittgenstein) and the possibility of applying the concept of language-game (Last Wittgenstein) on it; and (4) understand how the Logical NOR can operate within a satzsystem. The goal here is a search for the logic of the language-game and how the logical ideas of C. S. Peirce can help in this construction. And this construction might be interesting for a better understanding of the analytic philosophy of language. (shrink)

Reductive accounts of the direction of time are often paired with Humean accounts of laws, while non-reductive accounts of time are often paired with anti-Humean accounts of laws. The traditional pairing of views has recently come under question. This paper aims to clarify what sorts of anti-Humean views motivate anti-reductionism about the direction of time. It is argued that those who think (i) that the laws are metaphysically fundamental, and (ii) that the laws contain time-asymmetric contents, should treat the arrow (...) of time as metaphysically fundamental. (shrink)

Methods available for the axiomatization of arbitrary finite-valued logics can be applied to obtain sound and complete intelim rules for all truth-functional connectives of classical logic including the Sheffer stroke and Peirce’s arrow. The restriction to a single conclusion in standard systems of natural deduction requires the introduction of additional rules to make the resulting systems complete; these rules are nevertheless still simple and correspond straightforwardly to the classical absurdity rule. Omitting these rules results in systems for intuitionistic versions of (...) the connectives in question. (shrink)

Particles and photons appear to be total opposites; the former has rest mass which requires space to exist; the latter has kinetic energy which requires time to occur (oscillate). But they do share certain properties (e.g., quantization) that remain invariant when one is transformed (swapped) for the other. This gauge invariance is developed in some detail. The symmetry between particle and photon turns out to be one of inversion. It is the equalities of special relativity that support this inversion and (...) the accompanying invariances: mass transformed to energy; space transformed to time. The great advantage of these symmetries (inversions) is that they provide guidance for an object little understood (the photon) based upon an object well understood (the particle). On this basis, progress can be made in the understanding of some long-standing issues: wave-particle duality, time’s arrow, the constant speed of light and nonlocality. (shrink)

This paper distinguishes between 3 meanings of reversal, all of which are mathematically equivalent in classical mechanics: velocity reversal, retrodiction, and time reversal. It then concludes that in order to have well defined velocities a primitive arrow of time must be included in every time slice. The paper briefly mentions that this arrow cannot come from the Second Law of thermodynamics, but this point is developed in more details elsewhere.

International Studies in the Philosophy of Science, Volume 27, Issue 3, Page 273-293, September 2013.

Contemporary physics, with two Einstein’s theories and with Heisenberg’s principle of indeterminacy are frequently interpreted as a removal of the causality from physics. We argue that this is wrong. There are no indications in physics, either classical or quantum, that physical laws are indeterministic, on the ontological level. On the other hand, both classical and quantum physics are, practically, indeterministic on the epistemic level: there are no means for us to predict the detailed future of the world. Additionally, essentially all (...) physical principles, including the arrow of time and the conservation of energy could be, hypothetically, violated. However, in contrast to Hume’s skepticism, we have no experimental evidence that the causality can be removed or even “hung on” in any case. The text contains some didactical-like issues, as well. (shrink)

If the Past Hypothesis underlies the arrows of time, what is the status of the Past Hypothesis? In this paper, I examine the role of the Past Hypothesis in the Boltzmannian account and defend the view that the Past Hypothesis is a candidate fundamental law of nature. Such a view is known to be compatible with Humeanism about laws, but as I argue it is also supported by a minimal non-Humean "governing'' view. Some worries arise from the non-dynamical and time-dependent (...) character of the Past Hypothesis as a boundary condition, the intrinsic vagueness in its specification, and the nature of the initial probability distribution. I show that these worries do not have much force, and in any case they become less relevant in a new quantum framework for analyzing time's arrows---the Wentaculus. Hence, the view that the Past Hypothesis is a candidate fundamental law should be more widely accepted than it is now. (shrink)

A platitude that took hold with Kuhn is that there can be several equally good ways of balancing theoretical virtues for theory choice. Okasha recently modelled theory choice using technical apparatus from the domain of social choice: famously, Arrow showed that no method of social choice can jointly satisfy four desiderata, and each of the desiderata in social choice has an analogue in theory choice. Okasha suggested that one can avoid the Arrow analogue for theory choice by employing a strategy (...) used by Sen in social choice, namely, to enhance the information made available to the choice algorithms. I argue here that, despite Okasha’s claims to the contrary, the information-enhancing strategy is not compelling in the domain of theory choice. (shrink)

This paper develops and explores a new framework for theorizing about the measurement and aggregation of well-being. It is a qualitative variation on the framework of social welfare functionals developed by Amartya Sen. In Sen’s framework, a social or overall betterness ordering is assigned to each profile of real-valued utility functions. In the qualitative framework developed here, numerical utilities are replaced by the properties they are supposed to represent. This makes it possible to characterize the measurability and interpersonal comparability of (...) well-being directly, without the use of invariance conditions, and to distinguish between real changes in well-being and merely representational changes in the unit of measurement. The qualitative framework is shown to have important implications for a range of issues in axiology and social choice theory, including the characterization of welfarism, axiomatic derivations of utilitarianism, the meaningfulness of prioritarianism, the informational requirements of variable-population ethics, the impossibility theorems of Arrow and others, and the metaphysics of value. (shrink)

According to conciliatory views about the epistemology of disagreement, when epistemic peers have conflicting doxastic attitudes toward a proposition and fully disclose to one another the reasons for their attitudes toward that proposition (and neither has independent reason to believe the other to be mistaken), each peer should always change his attitude toward that proposition to one that is closer to the attitudes of those peers with which there is disagreement. According to pure higher-order evidence views, higher-order evidence for a (...) proposition always suffices to determine the proper rational response to disagreement about that proposition within a group of epistemic peers. Using an analogue of Arrow's Impossibility Theorem, I shall argue that no conciliatory and pure higher-order evidence view about the epistemology of disagreement can provide a true and general answer to the question of what disagreeing epistemic peers should do after fully disclosing to each other the (first-order) reasons for their conflicting doxastic attitudes. (shrink)

Amalgamating evidence of different kinds for the same hypothesis into an overall confirmation is analogous, I argue, to amalgamating individuals’ preferences into a group preference. The latter faces well-known impossibility theorems, most famously “Arrow’s Theorem”. Once the analogy between amalgamating evidence and amalgamating preferences is tight, it is obvious that amalgamating evidence might face a theorem similar to Arrow’s. I prove that this is so, and end by discussing the plausibility of the axioms required for the theorem.

An analogue of Arrow’s theorem has been thought to limit the possibilities for multi-criterial theory choice. Here, an example drawn from Toy Science, a model of theories and choice criteria, suggests that it does not. Arrow’s assumption that domains are unrestricted is inappropriate in connection with theory choice in Toy Science. There are, however, variants of Arrow’s theorem that do not require an unrestricted domain. They require instead that domains are, in a technical sense, ‘rich’. Since there are rich domains (...) in Toy Science, such theorems do constrain theory choice to some extent—certainly in the model and perhaps also in real science. (shrink)

Two of the most difficult problems in the foundations of physics are (1) what gives rise to the arrow of time and (2) what the ontology of quantum mechanics is. I propose a unified 'Humean' solution to the two problems. Humeanism allows us to incorporate the Past Hypothesis and the Statistical Postulate into the best system, which we then use to simplify the quantum state of the universe. This enables us to confer the nomological status to the quantum state in (...) a way that adds no significant complexity to the best system and solves the ''supervenient-kind problem'' facing the original version of the Past Hypothesis. We call the resultant theory the Humean unification. It provides a unified explanation of time asymmetry and quantum entanglement. On this theory, what gives rise to time's arrow is also responsible for quantum phenomena. The new theory has a separable mosaic, a best system that is simple and non-vague, less tension between quantum mechanics and special relativity, and a higher degree of theoretical and dynamical unity. The Humean unification leads to new insights that can be useful to Humeans and non-Humeans alike. (shrink)

In the theory of judgment aggregation, it is known for which agendas of propositions it is possible to aggregate individual judgments into collective ones in accordance with the Arrow-inspired requirements of universal domain, collective rationality, unanimity preservation, non-dictatorship and propositionwise independence. But it is only partially known (e.g., only in the monotonic case) for which agendas it is possible to respect additional requirements, notably non-oligarchy, anonymity, no individual veto power, or implication preservation. We fully characterize the agendas for which there (...) are such possibilities, thereby answering the most salient open questions about propositionwise judgment aggregation. Our results build on earlier results by Nehring and Puppe (2002), Nehring (2006), Dietrich and List (2007a) and Dokow and Holzman (2010a). (shrink)

In a quantum universe with a strong arrow of time, we postulate a low-entropy boundary condition to account for the temporal asymmetry. In this paper, I show that the Past Hypothesis also contains enough information to simplify the quantum ontology and define a unique initial condition in such a world. First, I introduce Density Matrix Realism, the thesis that the quantum universe is described by a fundamental density matrix that represents something objective. This stands in sharp contrast to Wave Function (...) Realism, the thesis that the quantum universe is described by a wave function that represents something objective. Second, I suggest that the Past Hypothesis is sufficient to determine a unique and simple density matrix. This is achieved by what I call the Initial Projection Hypothesis: the initial density matrix of the universe is the normalized projection onto the special low-dimensional Hilbert space. Third, because the initial quantum state is unique and simple, we have a strong case for the \emph{Nomological Thesis}: the initial quantum state of the universe is on a par with laws of nature. This new package of ideas has several interesting implications, including on the harmony between statistical mechanics and quantum mechanics, the dynamic unity of the universe and the subsystems, and the alleged conflict between Humean supervenience and quantum entanglement. (shrink)

If there are fundamental laws of nature, can they fail to be exact? In this paper, I consider the possibility that some fundamental laws are vague. I call this phenomenon 'fundamental nomic vagueness.' I characterize fundamental nomic vagueness as the existence of borderline lawful worlds and the presence of several other accompanying features. Under certain assumptions, such vagueness prevents the fundamental physical theory from being completely expressible in the mathematical language. Moreover, I suggest that such vagueness can be regarded as (...) 'vagueness in the world.' For a case study, we turn to the Past Hypothesis, a postulate that (partially) explains the direction of time in our world. We have reasons to take it seriously as a candidate fundamental law of nature. Yet it is vague: it admits borderline (nomologically) possible worlds. An exact version would lead to an untraceable arbitrariness absent in any other fundamental laws. However, the dilemma between fundamental nomic vagueness and untraceable arbitrariness is dissolved in a new quantum theory of time's arrow. (shrink)

Suppose that the members of a group each hold a rational set of judgments on some interconnected questions, and imagine that the group itself has to form a collective, rational set of judgments on those questions. How should it go about dealing with this task? We argue that the question raised is subject to a difficulty that has recently been noticed in discussion of the doctrinal paradox in jurisprudence. And we show that there is a general impossibility theorem that that (...) difficulty illustrates. Our paper describes this impossibility result and provides an exploration of its significance. The result naturally invites comparison with Kenneth Arrow's famous theorem (Arrow, 1963 and 1984; Sen, 1970) and we elaborate that comparison in a companion paper (List and Pettit, 2002). The paper is in four sections. The first section documents the need for various groups to aggregate its members' judgments; the second presents the discursive paradox; the third gives an informal statement of the more general impossibility result; the formal proof is presented in an appendix. The fourth section, finally, discusses some escape routes from that impossibility. (shrink)

Juries, committees and experts panels commonly appraise things of one kind or another on the basis of grades awarded by several people. When everybody's grading thresholds are known to be the same, the results sometimes can be counted on to reflect the graders’ opinion. Otherwise, they often cannot. Under certain conditions, Arrow's ‘impossibility’ theorem entails that judgements reached by aggregating grades do not reliably track any collective sense of better and worse at all. These claims are made by adapting the (...) Arrow–Sen framework for social choice to study grading in groups. (shrink)

Two radically different views about time are possible. According to the first, the universe is three dimensional. It has a past and a future, but that does not mean it is spread out in time as it is spread out in the three dimensions of space. This view requires that there is an unambiguous, absolute, cosmic-wide "now" at each instant. According to the second view about time, the universe is four dimensional. It is spread out in both space and time (...) - in space-time in short. Special and general relativity rule out the first view. There is, according to relativity theory, no such thing as an unambiguous, absolute cosmic-wide "now" at each instant. However, we have every reason to hold that both special and general relativity are false. Not only does the historical record tell us that physics advances from one false theory to another. Furthermore, elsewhere I have shown that we must interpret physics as having established physicalism - in so far as physics can ever establish anything theoretical. Physicalism, here, is to be interpreted as the thesis that the universe is such that some unified "theory of everything" is true. Granted physicalism, it follows immediately that any physical theory that is about a restricted range of phenomena only, cannot be true, whatever its empirical success may be. It follows that both special and general relativity are false. This does not mean of course that the implication of these two theories that there is no unambiguous cosmic-wide "now" at each instant is false. It still may be the case that the first view of time, indicated at the outset, is false. Are there grounds for holding that an unambiguous cosmic-wide "now" does exist, despite special and general relativity, both of which imply that it does not exist? There are such grounds. Elsewhere I have argued that, in order to solve the quantum wave/particle problem and make sense of the quantum domain we need to interpret quantum theory as a fundamentally probabilistic theory, a theory which specifies how quantum entities - electrons, photons, atoms - interact with one another probabilistically. It is conceivable that this is correct, and the ultimate laws of the universe are probabilistic in character. If so, probabilistic transitions could define unambiguous, absolute cosmic-wide "nows" at each instant. It is entirely unsurprising that special and general relativity have nothing to say about the matter. Both theories are pre-quantum mechanical, classical theories, and general relativity in particular is deterministic. The universe may indeed be three dimensional, with a past and a future, but not spread out in four dimensional space-time, despite the fact that relativity theories appear to rule this out. These considerations, finally, have implications for views about the arrow of time and free will. (shrink)

The paper discusses the sense in which the changes undergone by normative economics in the twentieth century can be said to be progressive. A simple criterion is proposed to decide whether a sequence of normative theories is progressive. This criterion is put to use on the historical transition from the new welfare economics to social choice theory. The paper reconstructs this classic case, and eventually concludes that the latter theory was progressive compared with the former. It also briefly comments on (...) the recent developments in normative economics and their connection with the previous two stages. (Published Online April 18 2006) Footnotes1 This paper suspersedes an earlier one entitled “Is There Progress in Normative Economics?” (Mongin 2002). I thank the organizers of the Fourth ESHET Conference (Graz 2000) for the opportunity they gave me to lecture on this topic. Thanks are also due to J. Alexander, K. Arrow, A. Bird, R. Bradley, M. Dascal, W. Gaertner, N. Gravel, D. Hausman, B. Hill, C. Howson, N. McClennen, A. Trannoy, J. Weymark, J. Worrall, two annonymous referees of this journal, and especially the editor M. Fleurbaey, for helpful comments. The editor's suggestions contributed to determine the final orientation of the paper. The author is grateful to the LSE and the Lachmann Foundation for their support at the time when he was writing the initial version. (shrink)

Maxwell’s Demon is a thought experiment devised by J. C. Maxwell in 1867 in order to show that the Second Law of thermodynamics is not universal, since it has a counter-example. Since the Second Law is taken by many to provide an arrow of time, the threat to its universality threatens the account of temporal directionality as well. Various attempts to “exorcise” the Demon, by proving that it is impossible for one reason or another, have been made throughout the years, (...) but none of them were successful. We have shown (in a number of publications) by a general state-space argument that Maxwell’s Demon is compatible with classical mechanics, and that the most recent solutions, based on Landauer’s thesis, are not general. In this paper we demonstrate that Maxwell’s Demon is also compatible with quantum mechanics. We do so by analyzing a particular (but highly idealized) experimental setup and proving that it violates the Second Law. Our discussion is in the framework of standard quantum mechanics; we give two separate arguments in the framework of quantum mechanics with and without the projection postulate. We address in our analysis the connection between measurement and erasure interactions and we show how these notions are applicable in the microscopic quantum mechanical structure. We discuss what might be the quantum mechanical counterpart of the classical notion of “macrostates”, thus explaining why our Quantum Demon setup works not only at the micro level but also at the macro level, properly understood. One implication of our analysis is that the Second Law cannot provide a universal lawlike basis for an account of the arrow of time; this account has to be sought elsewhere. (shrink)

(This is for the Cambridge Handbook of Analytic Philosophy, edited by Marcus Rossberg) In this handbook entry, I survey the different ways in which formal mathematical methods have been applied to philosophical questions throughout the history of analytic philosophy. I consider: formalization in symbolic logic, with examples such as Aquinas’ third way and Anselm’s ontological argument; Bayesian confirmation theory, with examples such as the fine-tuning argument for God and the paradox of the ravens; foundations of mathematics, with examples such as (...) Hilbert’s programme and Gödel’s incompleteness theorems; social choice theory, with examples such as Condorcet’s paradox and Arrow’s theorem; ‘how possibly’ results, with examples such as Condorcet’s jury theorem and recent work on intersectionality theory; and the application of advanced mathematics in philosophy, with examples such as accuracy-first epistemology. (shrink)

The second law of thermodynamics is traditionally interpreted as a coarse-grained result of classical mechanics. Recently its relation with quantum mechanical processes such as decoherence and measurement has been revealed in literature. In this paper we will formulate the second law and the associated time irreversibility following Everett’s idea: systems entangled with an object getting to know the branch in which they live. Accounting for this self-locating knowledge, we get two forms of entropy: objective entropy measuring the uncertainty of the (...) state of the object alone, and subjective entropy measuring the information carried by the self-locating knowledge. By showing that the summation of the two forms of entropy is a conserved and perspective-free quantity, we interpret the second law as a statement of irreversibility in knowledge acquisition. This essentially derives the thermodynamic arrow of time from the subjective arrow of time, and provides a unified explanation for varieties of the second law, as well as the past hypothesis. (shrink)