How should we account for the extraordinary regularity in the world? Humeans and Non-Humeans sharply disagree. According to Non-Humeans, the world behaves in an extraordinarily regular way because of certain necessary connections in nature. However, Humeans have thought that Non-Humean views are metaphysically objectionable. In particular, there are two general metaphysical principles that Humeans have found attractive that are incompatible with all existing versions of Non-Humeanism. My goal in this paper is to develop a novel version of Non-Humeanism that is (...) consistent with (and even entails) both of these general metaphysical principles. By endorsing such a view, one can have the explanatory benefits of Non-Humeanism while at the same time avoiding two of the major metaphysical objections towards Non-Humeanism. (shrink)

David Enoch, in Taking Morality Seriously, argues for a broad normative asymmetry between how we should behave when disagreeing about facts and how we should behave when disagreeing due to differing preferences. Enoch claims that moral disputes have the earmarks of a factual dispute rather than a preference dispute and that this makes more plausible a realist understanding of morality. We try to clarify what such claims would have to look like to be compelling and we resist his main (...) conclusions. (shrink)

This is a corrected version of the final proofs. I've fixed a number of typos, and corrected a blunder in chapter 4. In chapter 4 I say that 'this is this' is analytic, and 'this is not this' is antonymous. This is inconsistent with what I say in chapter 5, and not what I actually think. Rather, 'this is this' is taugologous, and 'this is not this' is contradictory. Analyticity and autnonmy are sense properties while tautologousness and contradictoriness are formal (...) logical properties. Heading, ToC and Index updated accordingly. (Oxford will make these corrections in their online version and in future print runs.). (shrink)

We start by presenting three different views that jointly imply that every person has many conscious beings in their immediate vicinity, and that the number greatly varies from person to person. We then present and assess an argument to the conclusion that how confident someone should be in these views should sensitively depend on how massive they happen to be. According to the argument, sometimes irreducibly de se observations can be powerful evidence for or against believing in metaphysical theories.

In the course of daily life we solve problems often enough that there is a special term to characterize the activity and the right to expect a scientific theory to explain its dynamics. The classical view in psychology is that to solve a problem a subject must frame it by creating an internal representation of the problem’s structure, usually called a problem space. This space is an internally generable representation that is mathematically identical to a graph structure with nodes and (...) links. The nodes can be annotated with useful information, and the whole representation can be distributed over internal and external structures such as symbolic notations on paper or diagrams. If the representation is distributed across internal and external structures the subject must be able to keep track of activity in the distributed structure. Problem solving proceeds as the subject works from an initial state in mentally supported space, actively constructing possible solution paths, evaluating them and heuristically choosing the best. Control of this exploratory process is not well understood, as it is not always systematic, but various heuristic search algorithms have been proposed and some experimental support has been provided for them. (shrink)

Open theists deny that God knows future contingents. Most open theists justify this denial by adopting the position that there are no future contingent truths to be known. In this paper we examine some of the arguments put forward for this position in two recent articles in this journal, one by Dale Tuggy and one by Alan Rhoda, Gregory Boyd, and Thomas Belt. The arguments concern time, modality, and the semantics of ‘will’ statements. We explain why we find none of (...) these arguments persuasive. This wide road leads only to destruction. (shrink)

In the first half of this paper, I argue that essential properties are intrinsic and that this permits a modal analysis of essence that is immune the sort of objections raised by Fine. In the second half, I argue that intrinsic properties collectively have a certain structure and that this accounts for some observations about essences: that things are essentially determinate; that things often have properties within a certain range essentially; and that the essential properties of things are their core (...) properties. (shrink)

I argue that according to Socrates in the Phaedo we should not merely evaluate bodily pleasures and desires as worthless or bad, but actively avoid them. We need to avoid them because they change our values and make us believe falsehoods. This change in values and acceptance of falsehoods undermines the soul’s proper activity, making virtue and happiness impossible for us. I situate this account of why we should avoid bodily pleasures within Plato’s project in the Phaedo of providing Pythagorean (...) and Orphic ideas with clearer meanings and better justifications. (shrink)

This chapter discusses two different issues about the relationship between legal positivism and robust normativity (understood as the most authoritative kind of normativity to which we appeal). First, the chapter argues that, in many contexts when discussing “legal positivism” and “legal antipositivism”, the discussion should be shifted from whether legal facts are ultimately partly grounded in moral facts to whether they are ultimately partly grounded in robustly normative facts. Second, the chapter explores an important difference within the kinds of arguments (...) that legal philosophers give for the (purported) truth of legal positivism. The difference concerns whether (purportedly) robustly normative facts are appealed to as premises in those arguments or not. (A closely connected issue is whether (purportedly) normative facts that bear one or more important connections to robustly normative facts are appealed to in premises to those arguments.) The chapter argues that thinking about this dividing line helps people better situate the positivist/antipositivist dispute, better understand the space of views in legal philosophy, better evaluate those views, and avoid having merely verbal disputes. (shrink)

I offer a novel conception of the nature of wanting. According to it, wanting is lacking something one needs. Lacking is not a normative notion but needing is, and that is how goodness figures in to wanting. What a thing needs derives from what it is to be a good thing of its kind. In people, wanting is connected to both knowledge and the will. A person can know that she wants something and can act on that knowledge. When she (...) does, she is acting in light of that want and her want is a reason why she acted. There is a close connection between wanting and our wills, not just because we can sometimes choose how to get what we need, but because our choices can determine what we want. We can't simply choose to want something, but in deciding how to live our lives, who to be, and what to pursue, we are free to settle what we want, at least within limits. These connections to knowledge and the will make human wanting rich and morally relevant, but they don't transform human wanting into something special. Wanting is everywhere just a matter of lacking something one needs. (shrink)

Humor is unlike other forms of communication because its content is not meant literally. Like acts of play, humor is not intended to be taken at face value. As a consequence, the assumptions and rules that govern normal conversation do not apply. Humor therefore depends upon both the speaker and the audience fully understanding that what was communicated should be treated in this unique way. The play frame refers to this shared understanding about the nature of the communication. Analyzing whether (...) a communication falls within the play frame may help us better understand not only whether the communication can be deemed non-serious or serious, but also whether it can be treated uniquely as merely the speaker’s attempt at play or as a typical instance of literal speech for which the speaker can be deemed ethically responsible. (shrink)

In this paper I offer an account of the normative dimension implicit in D. Bernoulli’s expected utility functions by means of an analysis of the juridical metaphors upon which the concept of mathematical expectation was moulded. Following a suggestion by the late E. Coumet, I show how this concept incorporated a certain standard of justice which was put in question by the St. Petersburg paradox. I contend that Bernoulli would have solved it by introducing an alternative normative criterion rather than (...) a positive model of decision making processes. (shrink)

Computation is a process of making explicit, information that was implicit. In computing 5 as the solution to ∛125, for example, we move from a description that is not explicitly about 5 to one that is. We are drawing out numerical consequences to the description ∛125. We are extracting information implicit in the problem statement. Can we precisely state the difference between information thati s implicit in a state, structure or process and information that is explicit?

In this paper, we present three necessary conditions for morally responsible animal research that we believe people on both sides of this debate can accept. Specifically, we argue that, even if human beings have higher moral status than nonhuman animals, animal research is morally permissible only if it satisfies (a) an expectation of sufficient net benefit, (b) a worthwhile-life condition, and (c) a no unnecessary-harm/qualified-basic-needs condition. We then claim that, whether or not these necessary conditions are jointly sufficient conditions of (...) justified animal research, they are relatively demanding with the consequence that many animal experiments may fail to satisfy them. (shrink)

Classical logic is usually interpreted as the logic of propositions. But from Boole's original development up to modern categorical logic, there has always been the alternative interpretation of classical logic as the logic of subsets of any given (nonempty) universe set. Partitions on a universe set are dual to subsets of a universe set in the sense of the reverse-the-arrows category-theoretic duality--which is reflected in the duality between quotient objects and subobjects throughout algebra. Hence the idea arises of a dual (...) logic of partitions. That dual logic is described here. Partition logic is at the same mathematical level as subset logic since models for both are constructed from (partitions on or subsets of) arbitrary unstructured sets with no ordering relations, compatibility or accessibility relations, or topologies on the sets. Just as Boole developed logical finite probability theory as a quantitative treatment of subset logic, applying the analogous mathematical steps to partition logic yields a logical notion of entropy so that information theory can be refounded on partition logic. But the biggest application is that when partition logic and the accompanying logical information theory are "lifted" to complex vector spaces, then the mathematical framework of quantum mechanics is obtained. Partition logic models indefiniteness (i.e., numerical attributes on a set become more definite as the inverse-image partition becomes more refined) while subset logic models the definiteness of classical physics (an entity either definitely has a property or definitely does not). Hence partition logic provides the backstory so the old idea of "objective indefiniteness" in QM can be fleshed out to a full interpretation of quantum mechanics. (shrink)

eSports practice designates a unique set of activities tethered to competitive, virtual environments, or worlds. This correlation between eSports practitioner and virtual world, we argue, is inadequately accounted for solely in terms of something physical or intellectual. Instead, we favor a perspective on eSports practice to be analyzed as a perceptual and embodied phenomenon. In this article, we present the phenomenological approach and focus on the embodied sensations of eSports practitioners as they cope with and perceive within their virtual worlds. (...) By approaching eSports phenomenologically, we uncover ways in which its unique forms of virtual involvement overlap with as well as differentiate themselves from traditional structures of embodiment. (shrink)

In the last few years, a new paradigm of the knowledge of the divinity in Aristotle has emerged, affording the possibility of understanding him as efficient cause. In that case, if God is efficient cause and gives rise to teleology, this must have some existential significance for man. We can ask ourselves therefore whether the knowledge of metaphysics can offer some orientation also for ethics. Yet if this were true, the need would arise to deepen the question of how much (...) the gods love men and what would the nature of their relationship be to natural justice. Given that man is born and lives thanks to the divinity, the conclusion is that two consequences follow: a response of religious thanksgiving is needed but also, that since the will of the divinity desires the good for man, the human search for happiness is the same as the fulfillment of the divine law. All this is explained, to a certain extent, in the context of the friendship between man and the divine. (shrink)

Reductive representationalism is the view that the qualitative properties associated with conscious experience are properties of the objects of the experience, and not of the experience itself. A prima facie problem for this view arises from dreams and hallucinations, in which qualitative properties are experienced but not instantiated in external objects of perception. I argue that representationalist attempts to solve it by appeal to actually uninstantiated properties are guilty of an absurdity akin to that which Ryle accused Descartes of in (...) the latter’s doctrine of immaterial substance. (shrink)

Failure of substitutivity of coreferential terms, one of the hallmarks of referential opacity, is standardly explained in terms of the presence of an expression (such as a verb of propositional attitude, a modal adverb or quotation marks) with opacity-inducing properties. It is thus assumed that any term in a complex expression for which substitutivity fails will be within the scope of an expression of one of these types, and that where there is an expression of one of these types there (...) will be failure of substitutivity for terms within its scope. I shall discuss a series of examples that have been thought to challenge this explanation by exhibiting failure of substitutivity of coreferential terms for positions not within the scope of any of the standard opacity-inducing expressions. If these examples are genuine, then the usual explanations of opacity are either incomplete – because there are sources of opacity other than those standardly identified, or completely mistaken – because the standardly identified expressions are not causes of opacity. I will argue, however, that the examples only exhibit failure of substitutivity of non-coreferential terms, and, hence, do not present a challenge to standard explanations of opacity. (shrink)

Categorical logic has shown that modern logic is essentially the logic of subsets (or "subobjects"). Partitions are dual to subsets so there is a dual logic of partitions where a "distinction" [an ordered pair of distinct elements (u,u′) from the universe U ] is dual to an "element". An element being in a subset is analogous to a partition π on U making a distinction, i.e., if u and u′ were in different blocks of π. Subset logic leads to finite (...) probability theory by taking the (Laplacian) probability as the normalized size of each subset-event of a finite universe. The analogous step in the logic of partitions is to assign to a partition the number of distinctions made by a partition normalized by the total number of ordered pairs |U|² from the finite universe. That yields a notion of "logical entropy" for partitions and a "logical information theory." The logical theory directly counts the (normalized) number of distinctions in a partition while Shannon's theory gives the average number of binary partitions needed to make those same distinctions. Thus the logical theory is seen as providing a conceptual underpinning for Shannon's theory based on the logical notion of "distinctions.". (shrink)

Sydney Shoemaker has been arguing for more than a decade for an account of the mind–body problem in which the notion of realization takes centre stage. His aim is to provide a notion of realization that is consistent with the multiple realizability of mental properties or events, and which explains: how the physical grounds the mental; and why the causal work of mental events is not screened off by that of physical events. Shoemaker's proposal consists of individuating properties in terms (...) of causal powers, and defining realization as a relation of inclusion between sets of causal powers. Thus, as the causal powers that define a mental property are a subset of the causal powers that characterize a physical property, it can be said that physical properties realize mental properties. In this paper we examine the physicalist credentials of Shoemaker's mind–body theory in relation to three important issues: the direction of the relation of dependence that the theory is committed to; the possibility of mental properties existing without being anchored by physical properties; and the compatibility of the theory with the causal closure of the physical world. We argue that Shoemaker's theory is problematic in all three respects. After that we consider whether the theory should count as a mind–body theory at all, given that it seems to be committed to a distorted view of mental properties. (shrink)

In this chapter, we argue that it’s possible to lose your faith in God by the actions of other people. In particular, we argue that spiritually violent religious trauma, where religious texts are used to shame a person into thinking themselves unworthy of God’s love, can cause a person to stop engaging in activities that sustain their faith in God, such as engaging in the worship of God. To do this, we provide an analysis of faith, worship, and love on (...) which to have faith in God is to have an attitude of worship to him; to have such an attitude of worship to God is to love him; and to love God is to desire union with him. We apply this analysis particularly to the case of LGBT Christians and their experience in the church today. (shrink)

Philosophical accounts of the nature of belief, at least in the western tradition, are framed in large part by two ideas. One is that believing is a form of representing. The other is that a belief plays a causal role when a person acts on it. The standard picture of belief as a mental entity with representational properties and causal powers merges these two ideas. We are to think of beliefs as things that are true or false and that interact (...) with desires, intentions, and emotions to bring about rational action. Both ideas, I think, are ill-founded. One effect of abandoning them is a further blurring of the distinction between what is inside and what is outside our minds. Another is a shift towards a less mentalistic picture of the roots of rational action. (shrink)

Inspired by recent progress in multi-agent Reinforcement Learning (RL), in this work we examine the collective intelligent behaviour of theoretical universal agents by introducing a weighted mixture operation. Given a weighted set of agents, their weighted mixture is a new agent whose expected total reward in any environment is the corresponding weighted average of the original agents' expected total rewards in that environment. Thus, if RL agent intelligence is quantified in terms of performance across environments, the weighted mixture's intelligence is (...) the weighted average of the original agents' intelligences. This operation enables various interesting new theorems that shed light on the geometry of RL agent intelligence, namely: results about symmetries, convex agent-sets, and local extrema. We also show that any RL agent intelligence measure based on average performance across environments, subject to certain weak technical conditions, is identical (up to a constant factor) to performance within a single environment dependent on said intelligence measure. (shrink)

Kagan argues that human beings who are neither persons nor even potential persons — if their impairment is independent of genetic constitution — are modal persons: individuals who might have been persons. Moreover, he proposes a view according to which both personhood and modal personhood are sufficient for counting more, morally, than nonhuman animals. In response to this proposal, I raise one relatively minor concern about Kagan's reasoning — that he judges too quickly that insentient beings can have interests — (...) before engaging the appeal to modal personhood. I challenge the thesis that modal personhood is relevant to one's moral status, first, by way of analogy to a kicker who misses a field goal though he might have made it; second, by casting doubt on implications for two impaired infants ; and, finally, by examining implications for dogs who would count as modal persons when genetic enhancements are capable of transforming them into persons. (shrink)

When people make sense of situations, illustrations, instructions and problems they do more than just think with their heads. They gesture, talk, point, annotate, make notes and so on. What extra do they get from interacting with their environment in this way? To study this fundamental problem, I looked at how people project structure onto geometric drawings, visual proofs, and games like tic tac toe. Two experiments were run to learn more about projection. Projection is a special capacity, similar to (...) perception, but less tied to what is in the environment. Projection, unlike pure imagery, requires external structure to anchor it, but it adds ‘mental’ structure to the external scene much like an augmented reality system adds structure to an outside scene. A person projects when they look at a chessboard and can see where a knight may be moved. Because of the cognitive costs of sustaining and extending projection, humans make some of their projections real. They create structure externally. They move the piece, they talk, point, notate, represent. Much of our interactivity during sense making and problem solving involves a cycle of projecting then creating structure. (shrink)

I argue that Meno’s Paradox targets the type of knowledge that Socrates has been looking for earlier in the dialogue: knowledge grounded in explanatory definitions. Socrates places strict requirements on definitions and thinks we need these definitions to acquire knowledge. Meno’s challenge uses Socrates’ constraints to argue that we can neither propose definitions nor recognize them. To understand Socrates’ response to the challenge, we need to view Meno’s challenge and Socrates’ response as part of a larger disagreement about the value (...) of inquiry. (shrink)

Alexander of Aphrodisias understood the Aristotle´s Unmoved Mover as efficient cause only to the extent that it is the final cause of heaven, which by moving strives to imitate the divine rest. Aquinas seems to agree with him. However his interpretation is original and philosophically more satisfactory: God is the efficient cause of the world, not only as creator, but also as it´s ruler. In this way God is also the final cause.

Been working on this approach for years. Hope to get around to publishing it sometime soon!

Implicit in our everyday attitudes and practices is the assumption that death ordinarily harms a person who dies. A far more contested matter is whether death harms sentient individuals who are not persons, a category that includes many animals and some human beings. On the basis of the deprivation account of the harm of death, I argue that death harms sentient nonpersons. I next consider possible bases for the commonsense judgment that death ordinarily harms persons more than it harms sentient (...) nonpersons. Contrary to what some philosophers believe, it is doubtful that the familiar resources of prudential value theory can vindicate this judgment. I show that the approach that at first glance seems most promising for supporting this judgment – namely, invoking an objective account of well-being – faces substantial challenges, before arguing that McMahan's time-relative interest account supplies the needed theoretical basis. I then go on to extract a significant practical implication of the first thesis, that death ordinarily harms sentient nonpersons: We should find a way to discontinue the routine killing of animal subjects following their use in experiments. (shrink)

After Marx, dissenting economics almost always used 'the labour theory' as a theory of value. This paper develops a modern treatment of the alternative labour theory of property that is essentially the property theoretic application of the juridical principle of responsibility: impute legal responsibility in accordance with who was in fact responsible. To understand descriptively how assets and liabilities are appropriated in normal production, a 'fundamental myth' needs to be cleared away, and then the market mechanism of appropriation can be (...) understood. On the normative side, neoclassical theory represents marginal productivity theory as showing that (a metaphorical version of) the imputation principle is satisfied ('people get what they produce') in competitive enterprises. Since that shows the moral commitment of neoclassical economics to the imputation principle, the labour theory of property is presented here as the actual non-metaphorical application of the imputation principle to property appropriation. The property-theoretic analysis at the firm level shows how the neoclassical (and much heterodox) analysis in terms of 'distributive shares' wholly misframed the basic questions. Finally, the paper shows how the imputation principle (modernised labour theory of property) is systematically violated in the present wage labour system of renting persons. The paper can be seen as taking up the recent challenge posed by Donald Katzner for a dialogue between neoclassical and heterodox microeconomics. (shrink)

The purpose of this paper is to show that the mathematics of quantum mechanics is the mathematics of set partitions linearized to vector spaces, particularly in Hilbert spaces. That is, the math of QM is the Hilbert space version of the math to describe objective indefiniteness that at the set level is the math of partitions. The key analytical concepts are definiteness versus indefiniteness, distinctions versus indistinctions, and distinguishability versus indistinguishability. The key machinery to go from indefinite to more definite (...) states is the partition join operation at the set level that prefigures at the quantum level projective measurement as well as the formation of maximally-definite state descriptions by Dirac’s Complete Sets of Commuting Operators. This development is measured quantitatively by logical entropy at the set level and by quantum logical entropy at the quantum level. This follow-the-math approach supports the Literal Interpretation of QM—as advocated by Abner Shimony among others which sees a reality of objective indefiniteness that is quite different from the common sense and classical view of reality as being “definite all the way down”. (shrink)

Logical information theory is the quantitative version of the logic of partitions just as logical probability theory is the quantitative version of the dual Boolean logic of subsets. The resulting notion of information is about distinctions, differences and distinguishability and is formalized using the distinctions of a partition. All the definitions of simple, joint, conditional and mutual entropy of Shannon information theory are derived by a uniform transformation from the corresponding definitions at the logical level. The purpose of this paper (...) is to give the direct generalization to quantum logical information theory that similarly focuses on the pairs of eigenstates distinguished by an observable, i.e., qudits of an observable. The fundamental theorem for quantum logical entropy and measurement establishes a direct quantitative connection between the increase in quantum logical entropy due to a projective measurement and the eigenstates that are distinguished by the measurement. Both the classical and quantum versions of logical entropy have simple interpretations as “two-draw” probabilities for distinctions. The conclusion is that quantum logical entropy is the simple and natural notion of information for quantum information theory focusing on the distinguishing of quantum states. (shrink)

Die Übernahme des KI-Unternehmens DeepMind durch Google für rund eine halbe Milliarde US-Dollar signalisierte vor einem Jahr, dass von der KI-Forschung vielversprechende Ergebnisse erwartet werden. Spätestens seit bekannte Wissenschaftler wie Stephen Hawking und Unternehmer wie Elon Musk oder Bill Gates davor warnen, dass künstliche Intelligenz eine Bedrohung für die Menschheit darstellt, schlägt das KI-Thema hohe Wellen. Die Stiftung für Effektiven Altruismus (EAS, vormals GBS Schweiz) hat mit der Unterstützung von Experten/innen aus Informatik und KI ein umfassendes Diskussionspapier zu den Chancen (...) und Risiken der künstlichen Intelligenz verfasst und geht darin auf aktuelle, mittel- und langfristige Herausforderungen im Bereich der KI-Entwicklung ein. (shrink)

A complementary strategy can be defined as any organizing activity which recruits external elements to reduce cognitive loads. Typical organizing activities include pointing, arranging the position and orientation of nearby objects, writing things down, manipulating counters, rulers or other artifacts that can encode the state of a process or simplify perception. To illustrate the idea of a complementary strategy, a simple experiment was performed in which subjects were asked to determine the dollar value of collections of coins. In the no-hands (...) condition, subjects were not allowed to touch the coin images or to move their hands in any way. In the hands condition, they were allowed to use their hands and fingers however they liked. Significant improvements in time and number of errors were observed when S's used their hands over when they did not. To explain these facts, a brief account of some commonly observed complementary strategies is presented, and an account of their potential benefits to perception, memory and attention. (shrink)

We argue that genuine modal realism can be extended, rather than modified, so as to allow for the possibility of nothing concrete, a possibility we term ‘metaphysical nihilism’. The issue should be important to the genuine modal realist because, not only is metaphysical nihilism itself intuitively plausible, but also it is supported by an argument with pre-theoretically credible premises, namely, the subtraction argument. Given the soundness of the subtraction argument, we show that there are two ways that the genuine modal (...) realist can accommodate metaphysical nihilism: (i) by allowing for worlds containing only spatiotemporal points and (ii) by allowing for a world containing nothing but the null individual. On methodological grounds, we argue that the genuine modal realist should reject the former way but embrace the latter way. (shrink)

Modern categorical logic as well as the Kripke and topological models of intuitionistic logic suggest that the interpretation of ordinary “propositional” logic should in general be the logic of subsets of a given universe set. Partitions on a set are dual to subsets of a set in the sense of the category-theoretic duality of epimorphisms and monomorphisms—which is reflected in the duality between quotient objects and subobjects throughout algebra. If “propositional” logic is thus seen as the logic of subsets of (...) a universe set, then the question naturally arises of a dual logic of partitions on a universe set. This paper is an introduction to that logic of partitions dual to classical subset logic. The paper goes from basic concepts up through the correctness and completeness theorems for a tableau system of partition logic. (shrink)

This paper shows how the classical finite probability theory (with equiprobable outcomes) can be reinterpreted and recast as the quantum probability calculus of a pedagogical or toy model of quantum mechanics over sets (QM/sets). There have been several previous attempts to develop a quantum-like model with the base field of ℂ replaced by ℤ₂. Since there are no inner products on vector spaces over finite fields, the problem is to define the Dirac brackets and the probability calculus. The previous attempts (...) all required the brackets to take values in ℤ₂. But the usual QM brackets <ψ|ϕ> give the "overlap" between states ψ and ϕ, so for subsets S,T⊆U, the natural definition is <S|T>=|S∩T| (taking values in the natural numbers). This allows QM/sets to be developed with a full probability calculus that turns out to be a non-commutative extension of classical Laplace-Boole finite probability theory. The pedagogical model is illustrated by giving simple treatments of the indeterminacy principle, the double-slit experiment, Bell's Theorem, and identical particles in QM/Sets. A more technical appendix explains the mathematics behind carrying some vector space structures between QM over ℂ and QM/Sets over ℤ₂. (shrink)

Did Donald Davidson agree with G.E.M. Anscombe that action requires a distinctive form of agential awareness? The answer is No, at least according to the standard interpretation of Davidson’s account of action. A careful study of Davidson’s early writings, however, reveals a much more subtle conception of the role of agential belief in action. While the role of the general belief in Davidson’s theory is familiar and has been much discussed, virtually no attention has been paid to the singular belief. (...) This essay makes a start on remedying this neglect. I begin, in section 1, by examining Davidson’s claim that for a desire or belief to rationalize and cause an action it must have a suitable generality. It must, he says, be ‘logically independent’ of the action itself. While he was clear about this requirement in the case of the desire that forms part of a person’s primary reason, I show in section 2 that his early treatment of belief confuses general and singular beliefs. This confusion reflects his failure clearly to distinguish the two roles belief can play in his account of action: as rationalizing cause and as agential awareness. Somewhat surprisingly, though, after he carefully drew the distinction and announced that intentional action requires practical knowledge, he pretty much ignored it. This may explain why some have assumed that Davidson parted ways with Anscombe on this. But a careful study of their writings shows that in fact they held remarkably similar views on the nature and need for practical knowledge. (shrink)

The logical basis for information theory is the newly developed logic of partitions that is dual to the usual Boolean logic of subsets. The key concept is a "distinction" of a partition, an ordered pair of elements in distinct blocks of the partition. The logical concept of entropy based on partition logic is the normalized counting measure of the set of distinctions of a partition on a finite set--just as the usual logical notion of probability based on the Boolean logic (...) of subsets is the normalized counting measure of the subsets (events). Thus logical entropy is a measure on the set of ordered pairs, and all the compound notions of entropy (join entropy, conditional entropy, and mutual information) arise in the usual way from the measure (e.g., the inclusion-exclusion principle)--just like the corresponding notions of probability. The usual Shannon entropy of a partition is developed by replacing the normalized count of distinctions (dits) by the average number of binary partitions (bits) necessary to make all the distinctions of the partition. (shrink)

This is a précis of my book for an author-meets-critics session forthcoming in Inquiry. The commenters are Daniel Drucker, Miriam Schleifer McCormick, and Mark Richard.

A theory of property needs to give an account of the whole life-cycle of a property right: how it is initiated, transferred, and terminated. Economics has focused on the transfers in the market and has almost completely neglected the question of the initiation and termination of property in normal production and consumption (not in some original state or in the transition from common to private property). The institutional mechanism for the normal initiation and termination of property is an invisible-hand function (...) of the market, the market mechanism of appropriation. Does this mechanism satisfy an appropriate normative principle? The standard normative juridical principle is to assign or impute legal responsibility according to de facto responsibility. It is given a historical tag of being "Lockean" but the basis is contemporary jurisprudence, not historical exegesis. Then the fundamental theorem of the property mechanism is proven which shows that if "Hume's conditions" (no transfers without consent and all contracts fulfilled) are satisfied, then the market automatically satisfies the Lockean responsibility principle, i.e., "Hume implies Locke." As a major application, the results in their contrapositive form, "Not Locke implies Not Hume," are applied to a market economy based on the employment contract. It is shown the production based on the employment contract violates the Lockean principle (all who work in an employment enterprise are de facto responsible for the positive and negative results) and thus Hume's conditions must also be violated in the marketplace (de facto responsible human action cannot be transferred from one person to another—as is readily recognized when and employer and employee together commit a crime). (shrink)

Anaxagoras’ “nous” has a cosmological value. Additionally, it has inspired interesting reflections in order to understand metaphysically the intellect. The question we want to answer is twofold. On one hand, we will inquire whether or not Anaxagoras has understood correctly the nature of the intellect. On the other hand, we will discern if our author has understood the peculiarity of consciousness. The answer to these questions will probably be negative. Notwithstanding that, it will be possible to ask whether or not (...) Anaxagoras was able to detect at least the basic elements for a metaphysics of the intellect and, consequently, for an ontology of consciousness. (shrink)

Since the pioneering work of Birkhoff and von Neumann, quantum logic has been interpreted as the logic of (closed) subspaces of a Hilbert space. There is a progression from the usual Boolean logic of subsets to the "quantum logic" of subspaces of a general vector space--which is then specialized to the closed subspaces of a Hilbert space. But there is a "dual" progression. The notion of a partition (or quotient set or equivalence relation) is dual (in a category-theoretic sense) to (...) the notion of a subset. Hence the Boolean logic of subsets has a dual logic of partitions. Then the dual progression is from that logic of partitions to the quantum logic of direct-sum decompositions (i.e., the vector space version of a set partition) of a general vector space--which can then be specialized to the direct-sum decompositions of a Hilbert space. This allows the logic to express measurement by any self-adjoint operators rather than just the projection operators associated with subspaces. In this introductory paper, the focus is on the quantum logic of direct-sum decompositions of a finite-dimensional vector space (including such a Hilbert space). The primary special case examined is finite vector spaces over ℤ₂ where the pedagogical model of quantum mechanics over sets (QM/Sets) is formulated. In the Appendix, the combinatorics of direct-sum decompositions of finite vector spaces over GF(q) is analyzed with computations for the case of QM/Sets where q=2. (shrink)

El presente trabajo nació como una reflexión posterior a la traducción del libro de Stanley Cavell Contesting Tears: The Hollywood Melodrama of the Unknown Woman. La reflexión era necesaria habida cuenta de las dudas suscitadas por la traducción del título del libro. Para ser más exacto, la reflexión giraba en torno a las lágrimas que forman parte de la primera parte del título, las lágrimas vertidas por las mujeres desconocidas que protagonizan los melodramas analizados en el libro. En mi opinión, (...) llegar a entender la razón y la naturaleza de esas lágrimas es clave para comprender lo que Cavell nos viene contando desde hace cinco décadas. Por ello, lo que sigue intenta reunir mis propios comentarios sobre la obra de Cavell en general, con la justificación de la traducción final del título: Más allá de las lágrimas. (shrink)