How should a machine intelligence perform unsupervised structure discovery over streams of sensory input? One approach to this problem is to cast it as an apperception task [1]. Here, the task is to construct an explicit interpretable theory that both explains the sensory sequence and also satisfies a set of unity conditions, designed to ensure that the constituents of the theory are connected in a relational structure. However, the original formulation of the apperception task had one fundamental limitation: it assumed (...) the raw sensory input had already been parsed using a set of discrete categories, so that all the system had to do was receive this already-digested symbolic input, and make sense of it. But what if we don't have access to pre-parsed input? What if our sensory sequence is raw unprocessed information? The central contribution of this paper is a neuro-symbolic framework for distilling interpretable theories out of streams of raw, unprocessed sensory experience. First, we extend the definition of the apperception task to include ambiguous (but still symbolic) input: sequences of sets of disjunctions. Next, we use a neural network to map raw sensory input to disjunctive input. Our binary neural network is encoded as a logic program, so the weights of the network and the rules of the theory can be solved jointly as a single SAT problem. This way, we are able to jointly learn how to perceive (mapping raw sensory information to concepts) and apperceive (combining concepts into declarative rules). (shrink)

The law views with suspicion statistical evidence, even evidence that is probabilistically on a par with direct, individual evidence that the law is in no way suspicious of. But it has proved remarkably hard to either justify this suspicion, or to debunk it. In this paper, we connect the discussion of statistical evidence to broader epistemological discussions of similar phenomena. We highlight Sensitivity – the requirement that a belief be counterfactually sensitive to the truth in a specific way – as (...) a way of epistemically explaining the legal suspicion towards statistical evidence. Still, we do not think of this as a satisfactory vindication of the reluctance to rely on statistical evidence. Knowledge – and Sensitivity, and indeed epistemology in general – are of little, if any, legal value. Instead, we tell an incentive-based story vindicating the suspicion towards statistical evidence. We conclude by showing that the epistemological story and the incentive-based story are closely and interestingly related, and by offering initial thoughts about the role of statistical evidence in morality. (shrink)

The starting point regarding consent has to be that it is both extremely important, and that it is often suspicious. In this article, the author tries to make sense of both of these claims, from a largely liberal perspective, tying consent, predictably, to the value of autonomy and distinguishing between autonomy as sovereignty and autonomy as nonalienation. The author then discusses adaptive preferences, claiming that they suffer from a rationality flaw but that it's not clear that this flaw matters morally (...) or politically. What matters is whether they suffer from an autonomy flaw. To answer this question, the author develops an account of autonomy failure, according to which a preference is nonautonomous if an injustice played an appropriate role in its causal history. The author then discusses the moral implications—and in an initial way, the political ones as well—of proclaiming a preference, or consent based on it, nonautonomous in this way. (shrink)

People are often offended by beliefs, expect apologies for beliefs, apologize for their own beliefs. In many mundane cases, people are morally criticized for their beliefs. Intuitively, then, beliefs seem to sometimes wrong people. Recently, the philosophical literature has picked up on this theme, and has started to discuss it under the heading of doxastic wrongdoing. In this paper we argue that despite the strength of such initial intuitions, at the end of the day they have to be rejected. If (...) it can be ever truthfully asserted that beliefs wrong, this is always derivative – beliefs wrong only in virtue of other things (like evidence-gathering actions) wronging. We distinguish between modest and ambitious doxastic wrongdoing theories (the former deny, while the latter accept, the possibility of a morally wrong yet epistemically permissible belief); we argue that each of these options faces insurmountable problems; and we offer partly debunking explanations of the intuitions purportedly supporting doxastic wrongdoing. (shrink)

Critics have argued that human-controlled avatar interactions fail to facilitate the kinds of expressivity and social understanding afforded by our physical bodies. We identify three claims meant to justify the supposed expressive limits of avatar interactions compared to our physical interactions. First, “The Limited Expressivity Claim”: avatars have a more limited expressive range than our physical bodies. Second, “The Inputted Expressivity Claim”: any expressive avatarial behaviour must be deliberately inputted by the user. Third, “The Decoding Claim”: users must infer or (...) figure out the expressive meaning of human-controlled avatars’ behaviour through cognitively onerous processes. With the aim of critically assessing all three claims, we analyze data collected through observations of and interviews with expert players of the avatar-based video game League of Legends. Focusing on Daniel Stern’s (2010) notion of vitality, we analyze the participants’ descriptions of seeing and interacting with other avatars during performance. Our analysis shows that the informants experience human-based avatarial interactions as qualitatively different than interactions with bots, that the informants see the movements of other players’ avatars as having different expressive styles, and that the informants actively use and manipulate this avatarial expressivity during performance. The results of our analysis, we argue, provide reasons for loosening or resisting the three claims concerning the limits of avatarial expressivity. (shrink)

Statistical evidence—say, that 95% of your co-workers badmouth each other—can never render resenting your colleague appropriate, in the way that other evidence (say, the testimony of a reliable friend) can. The problem of statistical resentment is to explain why. We put the problem of statistical resentment in several wider contexts: The context of the problem of statistical evidence in legal theory; the epistemological context—with problems like the lottery paradox for knowledge, epistemic impurism and doxastic wrongdoing; and the context of a (...) wider set of examples of responses and attitudes that seem not to be appropriately groundable in statistical evidence. Regrettably, we do not come up with a fully general, fully adequate, fully unified account of all the phenomena discussed. But we give reasons to believe that no such account is forthcoming, and we sketch a somewhat messier account that may be the best that can be had here. (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)

We demonstrate that many philosophers accept the following claim: When an aesthetic object is apprehended correctly, taking pleasure in said object is a reliable sign that the object is aesthetically successful. We undermine this position by showing that what grounds our pleasurable experience is opaque: In many cases, the experienced pleasure is attributable to factors that have little to do with the aesthetic object. The evidence appealed to is a form of Higher-Order Evidence (HOE) and we consider attempts to overcome (...) said evidence. We argue they are unsuccessful. We conclude by considering what this means for our practice of making aesthetic judgements. (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)

Philosophical Issues, Volume 31, Issue 1, Page 85-103, October 2021.

ABSTRACTIn a recent paper, Michael Pardo argues that the epistemic property that is legally relevant is the one called Safety, rather than Sensitivity. In the process, he argues against our Sensitivity-related account of statistical evidence. Here we revisit these issues, partly in order to respond to Pardo, and partly in order to make general claims about legal epistemology. We clarify our account, we show how it adequately deals with counterexamples and other worries, we raise suspicions about Safety's value here, and (...) we revisit our general skepticism about the role that epistemological considerations should play in determining legal policy. (shrink)

Someone acts in a morally worthy way when they deserve credit for doing the morally right thing. But when and why do agents deserve credit for the success involved in doing the right thing? It is tempting to seek an answer to that question by drawing an analogy with creditworthy success in other domains of human agency, especially in sports, arts, and crafts. Accordingly, some authors have recently argued that, just like creditworthy success in, say, chess, playing the piano, or (...) archery, creditworthy moral success is a matter of getting things right by way of manifesting a relevant skill. My main aim in this paper is to bring out an important structural difference between moral creditworthiness and creditworthiness in sports, arts, and craft, undermining attempts to use examples of the latter as a model for understanding the former. As an alternative, I propose an account of morally creditworthy action, according to which such action is a matter of manifesting virtue, not skill—a claim that's based on an important, but underappreciated, difference between the sorts of excellences constituting virtues and skills. The paper thus contributes to a more nuanced picture of normative achievements across different domains of human agency, highlighting largely overlooked structural dissimilarities among them. (shrink)

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)

When an entity ontologically depends on another entity, the former ‘presupposes’ or ‘requires’ the latter in some metaphysical sense. This paper defends a novel view, Dependence Deflationism, according to which ontological dependence is what I call an aggregative cluster concept: a concept which can be understood, but not fully analysed, as a ‘weighted total’ of constructive and modal relations. The view has several benefits: it accounts for clear cases of ontological dependence as well as the source of disagreement in controversial (...) ones; it gives a nice story about the evidential relevance of modal, mereological and set-theoretic facts to ontological dependence; and it makes sense of debates over the relation's formal properties. One important upshot of the deflationary account is that questions of ontological dependence are generally less deep and less interesting than usually thought. (shrink)

We take it that we can exercise doxastic agency by reasoning and by making judgments. We take it, that is, that we can actively make up our minds by reasoning and judging. On what I call the ‘Standard View’ this is so because judgment can yield belief. It is typical to take it that judgments yield beliefs by causing them. But on the resultant understanding of the Standard View, I argue, it is unclear how judgment could play its role in (...) doxastic agency in the way we take it to. I therefore offer an alternative understanding of how judgment yields belief. Drawing on Ryle I argue that when one comes to believe by judging the event which is one's judging is token identical to the event which is one's coming to believe. This paves the way for version of the Standard View capable of explaining how we can actively make up our minds despite that we cannot believe or come to believe at will. (shrink)

This is a contribution to the symposium on Tim Scanlon’s Being Realistic about Reasons. We have two aims here: First, we ask for more details about Scanlon’s meta-metaphysical view, showing problems with salient clarifications. And second, we raise independent objections to the view – to its explanatory productivity, its distinctness, and the argumentative support it enjoys.

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)

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)

This book concerns the foundations of epistemic modality and hyperintensionality and their applications to the philosophy of mathematics. I examine the nature of epistemic modality, when the modal operator is interpreted as concerning both apriority and conceivability, as well as states of knowledge and belief. The book demonstrates how epistemic modality and hyperintensionality relate to the computational theory of mind; metaphysical modality and hyperintensionality; the types of mathematical modality and hyperintensionality; to the epistemic status of large cardinal axioms, undecidable propositions, (...) and abstraction principles in the philosophy of mathematics; to the modal and hyperintensional profiles of the logic of rational intuition; and to the types of intention, when the latter is interpreted as a hyperintensional mental state. Chapter 2 argues for a novel type of expressivism based on the duality between the categories of coalgebras and algebras, and argues that the duality permits of the reconciliation between modal cognitivism and modal expressivism. I also develop a novel topic-sensitive truthmaker semantics for dynamic epistemic logic, and develop a novel dynamic epistemic two-dimensional hyperintensional semantics. Chapter 3 provides an abstraction principle for epistemic (hyper-)intensions. Chapter 4 advances a topic-sensitive two-dimensional truthmaker semantics, and provides three novel interpretations of the framework along with the epistemic and metasemantic. Chapter 5 applies the fixed points of the modal μ-calculus in order to account for the iteration of epistemic states in a single agent, by contrast to availing of modal axiom 4 (i.e. the KK principle). The fixed point operators in the modal μ-calculus are rendered hyperintensional, which yields the first hyperintensional construal of the modal μ-calculus in the literature and the first application of the calculus to the iteration of epistemic states in a single agent instead of the common knowledge of a group of agents. Chapter 6 advances a solution to the Julius Caesar problem based on Fine's `criterial' identity conditions which incorporate conditions on essentiality and grounding. Chapter 7 provides a ground-theoretic regimentation of the proposals in the metaphysics of consciousness and examines its bearing on the two-dimensional conceivability argument against physicalism. The topic-sensitive epistemic two-dimensional truthmaker semantics developed in chapters 2 and 4 are availed of in order for epistemic states to be a guide to metaphysical states in the hyperintensional setting. Chapters 8-12 provide cases demonstrating how the two-dimensional hyperintensions of hyperintensional, i.e. topic-sensitive epistemic two-dimensional truthmaker, semantics, solve the access problem in the epistemology of mathematics. Chapter 8 examines the interaction between my hyperintensional semantics and the axioms of epistemic set theory, large cardinal axioms, the Epistemic Church-Turing Thesis, the modal axioms governing the modal profile of Ω-logic, Orey sentences such as the Generalized Continuum Hypothesis, and absolute decidability. These results yield inter alia the first hyperintensional Epistemic Church-Turing Thesis and hyperintensional epistemic set theories in the literature. Chapter 9 examines the modal and hyperintensional commitments of abstractionism, in particular necessitism, and epistemic hyperintensionality, epistemic utility theory, and the epistemology of abstraction. I countenance a hyperintensional semantics for novel epistemic abstractionist modalities. I suggest, too, that observational type theory can be applied to first-order abstraction principles in order to make first-order abstraction principles recursively enumerable, i.e. Turing machine computable, and that the truth of the first-order abstraction principle for hyperintensions is grounded in its being possibly recursively enumerable and the machine being physically implementable. Chapter 10 examines the philosophical significance of hyperintensional Ω-logic in set theory and discusses the hyperintensionality of metamathematics. Chapter 11 provides a modal logic for rational intuition and provides a hyperintensional semantics. Chapter 12 avails of modal coalgebras to interpret the defining properties of indefinite extensibility, and avails of hyperintensional epistemic two-dimensional semantics in order to account for the interaction between the interpretational and objective modalities and truthmakers thereof. This yields the first hyperintensional category theory in the literature. I invent a new mathematical trick in which first order structures are treated as categories, and Vopenka's principle can be satisfied because of the elementary embeddings between the categories and generate Vopenka cardinals while bypassing the category of Set in category theory. Chapter 13 examines modal responses to the alethic paradoxes. Chapter 14 examines, finally, the modal and hyperintensional semantics for the different types of intention and the relation of the latter to evidential decision theory. (shrink)

Liberal-contractarian philosophies of justice see the unjust systems of slavery and autocracy in the past as being based on coercion—whereas the social order in modern democratic market societies is based on consent and contract. However, the ‘best’ case for slavery and autocracy in the past were consent-based contractarian arguments. Hence, our first task is to recover those ‘forgotten’ apologia for slavery and autocracy. To counter those consent-based arguments, the historical anti-slavery and democratic movements developed a theory of inalienable rights. Our (...) second task is to recover that theory and to consider several other applications of the theory. Finally, the liberal theories of justice expounded by John Rawls and by Robert Nozick are briefly examined from this perspective. (shrink)

The proposal I offer attempts to remedy the inadequacies of exclusive focus on well-being for moral purposes. The proposal is this: We should allow the agent to decide for herself where she wants to throw the weight that is her due in moral reflection, with the proviso that she understands the way that her weight will be aggregated with others in reaching a moral outcome. I will call this the "autonomy principle." The autonomy principle, I claim, provides the consequentialist's best (...) prospect for taking people into account morally in a way that they endorse. (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)

Aristotle presents a formal logic in the Prior Analytics in which the premises and conclusions are never conditionals. In this paper I argue that he did not simply overlook conditionals, nor does their absence reflect a metaphysical prejudice on his part. Instead, he thinks that arguments with conditionals cannot be syllogisms because of the way he understands the explanatory requirement in the definition of a syllogism: the requirement that the conclusion follow because of the premises. The key passage is Prior (...) Analytics I.32, 47a22–40, where Aristotle considers an argument with conditionals that we would consider valid, but which he denies is a syllogism. I argue that Aristotle thinks that to meet the explanatory requirement a syllogism must draw its conclusion through the way its terms are predicated of one another. Because arguments with conditionals do not, in general, draw their conclusions through predications, he did not include them in his logic. (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)

This is a précis of my book "Know-how as Competence. A Rylean Responsibilist Account".

The new logic of partitions is dual to the usual Boolean logic of subsets (usually presented only in the special case of the logic of propositions) in the sense that partitions and subsets are category-theoretic duals. The new information measure of logical entropy is the normalized quantitative version of partitions. The new approach to interpreting quantum mechanics (QM) is showing that the mathematics (not the physics) of QM is the linearized Hilbert space version of the mathematics of partitions. Or, putting (...) it the other way around, the math of partitions is a skeletal version of the math of QM. The key concepts throughout this progression from logic, to logical information, to quantum theory are distinctions versus indistinctions, definiteness versus indefiniteness, or distinguishability versus indistinguishability. The distinctions of a partition are the ordered pairs of elements from the underlying set that are in different blocks of the partition and logical entropy is defined (initially) as the normalized number of distinctions. The cognate notions of definiteness and distinguishability run throughout the math of QM, e.g., in the key non-classical notion of superposition (= ontic indefiniteness) and in the Feynman rules for adding amplitudes (indistinguishable alternatives) versus adding probabilities (distinguishable alternatives). (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)

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)

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)

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)

I argue that the technique Socrates describes in the Meno at 86e-87c allows him to make progress without definitions, even while accepting that definitions are necessary for knowledge. Some contend that the technique involves provisionally accepting a claim. I argue, instead, that it provides a secure biconditional that one can use to reduce the question one cares care about to a new question that one thinks will be easier to answer.

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)

Zetetic norms govern our acts of inquiry. Epistemic norms govern our beliefs and acts of belief formation. Recently, Jane Friedman (2020) has defended that we should think of these norms as conforming a single normative domain: epistemology should take a zetetic turn. Though this unification project implies a substantive re-elaboration of our traditional epistemic norms, Friedman argues that the reasons supporting the turn are robust enough to warrant its revisionary implications. In this paper, I suggest we should read Friedman’s proposal (...) as a dilemma. Either we believe the zetetic turn is well-motivated and undertake the task of looking for the proper revision of our traditional epistemic norms, or we take the revisionary implications of the turn to be unacceptable, in which case our challenge is to show why a zetetic epistemology is not a well-motivated project after all. After presenting this dilemma, I make a case for endorsing its second horn by presenting a two-pronged argument against Friedman’s project. First, I show that the revisionary implications of the zetetic turn are more far-reaching than expected. Second, I defend that the most persuasive reasons for endorsing the turn are not strong enough to support it. Taken together, these considerations speak against accepting the zetetic turn and the revisionary implications that come with it. (shrink)

An experiment was performed to test the hypothesis that people sometimes take physical actions to make themselves more effective problem solvers. The task was to generate all possible words that could be formed from seven Scrabble letters. In one condition, participants could use their hands to manipulate the letters, and in another condition, they could not. Results show that more words were generated with physical manipulation than without. However, an interaction was obtained between the physical manipulation conditions and the specific (...) letter sets chosen, indicating that physical manipulation helps more for generating words in some circumstances than in others. Overall, our findings can be explained in terms of an interactive search process in which external, physical activity effectively complements internal, cognitive activity. Within this framework, the interaction can be explained in terms of the relative difficulty of generating words from the letters given in the different sets. (shrink)

This paper argues that the problematic of rule following in Wittgenstein's Philosophical Investigations and Heidegger's analysis of anxiety in Being and Time have analogous structures. Working through these analogies helps our interpretation of both of these authors. Contrasting sceptical and anti-sceptical readings of Wittgenstein helps us to resolve an interpretive puzzle about what an authentic response to anxiety looks like for Heidegger. And considering the importance of anxiety to Heidegger's conception of authenticity allows us to locate in Wittgenstein's later philosophy (...) a covert appeal to something resembling Heideggerian authenticity. (shrink)

“The Ethics of Infection Challenges in Primates,” by Anne Barnhill, Steven Joffe, and Franklin Miller, is an exceptionally timely contribution to the literature on animal research ethics. Animal research has long been both a source of high hopes and a cause for moral concern. When it comes to infection challenge studies with nonhuman primates, neither the hope—to save thousands of human lives from such diseases as Ebola and Marburg—nor the concern—the conviction that primates deserve especially strong protections—could be much higher. (...) Coming just a few years after the National Institutes of Health adopted the Institute of Medicine's recommendations regarding chimpanzees, Barnhill and colleagues attempt to nudge the clarification and specification—one might say the evolution—of NHP research ethics and regulation. They assert that NHP challenge studies “are not justified by marginal gains in human safety or by efficacy gains that are unlikely to translate directly into saving human lives or preventing morbidity.” How, in turn, is their standard—which, although stringent, does permit causing NHPs to suffer and die for human benefit—to be justified? (shrink)

This paper examines whether Socrates provides his interlocutors with good reasons to seek knowledge of what virtue is, reasons that they are in a position to appreciate. I argue that in the Laches he does provide such reasons, but they are not the reasons that are most commonly identified as Socratic. Socrates thinks his interlocutors should be motivated not by the idea that virtue is knowledge nor by the idea that knowledge is good for its own sake, but rather by (...) the idea that knowledge is needed to recognize what to aim at. His argument reaches the potentially life-altering conclusion that we should all seek knowledge of what virtue is. It is powerful precisely because it relies on uncontroversial premises that his interlocutors could be expected to accept. In laying out this argument, I distinguish different ways in which someone could count as a teacher of virtue. At the end of the article, I situate the argument within the debate about whether virtue is teachable. (shrink)

Self-verifying judgments like _I exist_ seem rational, and self-defeating ones like _It will rain, but I don’t believe it will rain_ seem irrational_._ But one’s evidence might support a self-defeating judgment, and fail to support a self-verifying one. This paper explains how it can be rational to defy one’s evidence if judgment is construed as a mental performance or act, akin to inner assertion. The explanation comes at significant cost, however. Instead of causing or constituting beliefs, judgments turn out to (...) be mere epiphenomena, and self-verification and self-defeat lack the broader philosophical import often claimed for them. (shrink)

This paper responds to comments and criticisms by Stefan Brandt and Eva-Maria Jung, directed at the book "Know-how as Competence. A Rylean Responsibilist Account".

This article argues that the Phaedo is written as a new sort of story of how a hero faces death; this story provides an alternative to existing tragedy, as understood by Plato. The opening of the Phaedo makes clear that two features that Plato closely associates with tragedy, pity and lamentation, are inappropriate responses to Socrates’ impending death, and that tuchē (chance) did not affect his happiness. This is the first step in the dialogue’s sustained engagement with tragedy. Tragedy for (...) Plato falls under the category of stories about heroes and gods. Plato wrote the Phaedo so that we would see Socrates as a philosophical hero, a replacement for traditional heroes such as Theseus or Heracles. I argue that in fact the Phaedo meets every requirement in Republic Books 2–3 for how to tell stories about heroes and gods and so belongs to the same broad category as tragedy. Within this framework, it tells its new story of how the true hero faces death. (shrink)

There is a fault line running through classical liberalism as to whether or not democratic self-governance is a necessary part of a liberal social order. The democratic and non-democratic strains of classical liberalism are both present today—particularly in America. Many contemporary libertarians and neo-Austrian economists represent the non-democratic strain in their promotion of non-democratic sovereign city-states (startup cities or charter cities). We will take the late James M. Buchanan as a representative of the democratic strain of classical liberalism. Since the (...) fundamental norm of classical liberalism is consent, we must start with the intellectual history of the voluntary slavery contract, the coverture marriage contract, and the voluntary non-democratic constitution (or pactum subjectionis). Next we recover the theory of inalienable rights that descends from the Reformation doctrine of the inalienability of conscience through the Enlightenment (e.g., Spinoza and Hutcheson) in the abolitionist and democratic movements. Consent-based governments divide into those based on the subjects' alienation of power to a sovereign and those based on the citizens' delegation of power to representatives. Inalienable rights theory rules out that alienation in favor of delegation, so the citizens remain the ultimate principals and the form of government is democratic. Thus the argument concludes in agreement with Buchanan that the classical liberal endorsement of sovereign individuals acting in the marketplace generalizes to the joint action of individuals as the principals in their own organizations. (shrink)

Volume 20, Issue 3, March 2020, Page 71-73.

I suggest that the social justice issues raised by Internet regulation can be exposed and examined by using a methodology adapted from that described by John Rawls in 'A Theory of Justice'. Rawls' theory uses the hypothetical scenario of people deliberating about the justice of social institutions from the 'original position' as a method of removing bias in decision-making about justice. The original position imposes a 'veil of ignorance' that hides the particular circumstances of individuals from them so that they (...) will not be influenced by self-interest. I adapt Rawls' methodology by introducing an abstract description of information technology to those deliberating about justice from within the original position. This abstract description focuses on computing devices that users can use to access information and information networks that information devices use to communicate. The abstractness of this description prevents the particular characteristics of the Internet and the computing devices in use from influencing the decisions about the just use and regulation of information technology and networks. From this abstract position, the principles of justice that the participants accept for the rest of society will also apply to the computing devices people use to communicate, and to Internet regulation. (shrink)

We present data and argument to show that in Tetris—a real-time interactive video game—certain cognitive and perceptual problems are more quickly, easily, and reliably solved by performing actions in the world rather than by performing computational actions in the head alone. We have found that some translations and rotations are best understood as being used to implement a plan, or to implement a reaction. To substantiate our position we have implemented a computational laboratory that lets us record keystrokes and game (...) situations, as well as allows us to dynamically create situations. Using the data of over 30 subjects playing 6 games, tachistoscopic tests of some of these subjects, and results from our own successful efforts at building expert systems to play Tetris, we show why knowing how to use one’s environment to enhance speed and robustness are important components in skilled play. (shrink)