Critics of reliability theories of epistemic justificationoften claim that the `generality problem' is an insurmountabledifficulty for such theories. The generality problem is theproblem of specifying the level of generality at which abelief-forming process is to be described for the purposeof assessing its reliability. This problem is not asintractable as it seems. There are illuminating solutionsto analogous problems in the ethics literature. Reliabilistsought to attend to utilitarian approaches to choices betweeninfinite utility streams; they also ought to attend towelfarist approaches to social (...) choice situations that donot demand full aggregation of individual welfares.These analogies suggest that the traditional `single number'approach to reliability is misguided. I argue that a newapproach – the `vector reliability' approach – is preferable.Vector reliability theories associate target beliefs withreliability vectors – that is, structured collections ofreliability numbers – and construct criteria of epistemicjustification that appeal to these vectors. The bulk of thetheoretical labor involved in a reliability account of epistemicjustification is thus transferred from picking a uniquereliability number to constructing a plausible criterionof epistemic justification. (shrink)
This paper introduces a compositional semantics of locativeprepositional phrases which is based on a vector space ontology.Model-theoretic properties of prepositions like monotonicity andconservativity are defined in this system in a straightforward way.These notions are shown to describe central inferences with spatialexpressions and to account for the grammaticality of prepositionmodification. Model-theoretic constraints on the set of possibleprepositions in natural language are specified, similar to the semanticuniversals of Generalized Quantifier Theory.
This paper consists in an exposition of a proof Newton gave in 1666 of the parallelogram law for compounding velocities, and an examination of its implications for understanding his treatment of motion resulting from a continuously acting force in the Principia. I argue that the “moments” invoked in the fluxional proof of the vector resolution and composition of velocities are “virtual times”, a device allowing Newton to represent motions by the linear displacements produced in such a time; the ratio (...) of velocities at an instant can then be represented by assuming the velocities continue for such a virtual time. By the Method of First and Ultimate Ratios, the first ratio of the velocities is then given by the ratio of such lines, under the presupposition that in the limit they will shrink to zero magnitude. I then argue that the same device is implicit in Newton’s appeal to “moments” or “particles of time” in his proof of Kepler’s Area Law in the “Locke Paper” and in Proposition 1 of Book 1 of the Principia, and that the limiting process involved there is therefore the same as that implicit in the Method of First and Ultimate Ratios. (shrink)
We show that vector space semantics and functional semantics in two-sorted first order logic are equivalent for pregroup grammars. We present an algorithm that translates functional expressions to vector expressions and vice-versa. The semantics is compositional, variable free and invariant under change of order or multiplicity. It includes the semantic vector models of Information Retrieval Systems and has an interior logic admitting a comprehension schema. A sentence is true in the interior logic if and only if the (...) ‘usual’ first order formula translating the sentence holds. The examples include negation, universal quantifiers and relative pronouns. (shrink)
Physicalism is an empirical theory of the mind and its place in nature. So the physicalist must show that current neuroscience does not falsify physicalism, but instead supports it. Current neuroscience shows that a nervous system is what I call a vector function system. I provide a brief outline of the resources that empirical research has made available within the constraints of the vector function approach. Then I argue that these resources are sufficient, indeed apt, for the physicalist (...) enterprise, by offering a vector functional, hence physicalist, theory of the percept--the perceptual experience itself, a paradigm of phenomenally immediate, introspectively accessible consciousness. (shrink)
Vector Space Semantics (VSS) is a branch of model-theoretic semantics that aims to apply logical approaches to meaning to the domain of spatial expressions by adopting vectors as the basic elements of spatial ontology. In this course we will review current work in VSS, giving sufficient introductory background on model-theoretic tools and previous work on spatial expressions.
A compartmental model is described for the spread of Gambian sleeping sickness in a spatially heterogeneous environment in which vector and human populations migrate between two "patches": the village and the plantations. The number of equilibrium points depends on two "summary parameters": gr the proportion removed among human infectives, and R0, the basic reproduction number. The origin is stable for R0 1. Control strategies are assessed by studying the mix of vector control between the two patches that bring (...) R0 below 1. The results demonstrate the importance of vector control in the plantations. For example if 20 percent of flies are in the village and the blood meal rate in the village is 10 percent, then a 20 percent added vector mortality in the village must be combined with a 9 percent added mortality in the plantations in order to bring R0 below 1. The results are quite insentive to the blood meal rate in the village. Optimal strategies (that minimize the total number of flies trapped in both patches) are briefly discussed. (shrink)
Edelman suggests that any shape is encoded by an excitation vector with components corresponding to excitations of corresponding neuronal modules. This results in discrimination of stimuli in a shape space of low dimensionality. Similar vector encoding is present in color vision. Red-green, blue-yellow, bright and dark neurons are modules that represent a number of different color stimuli in color space of low dimensionality. Vector encoding allows effective computation of color differences and color similarities. Such a neuronal (...) class='Hi'>vector-encoding approach has also been applied to the perception of visual movement, line orientation, and stereopsis. (shrink)
Although great progress in neuroanatomy and physiology has occurred lately, we still cannot go directly to those levels to discover the neural mechanisms of higher cognition and consciousness. But we can use neurocomputational methods based on these details to push this project forward. Here we describe vector subtraction as an operation that computes sequential paths through high-dimensional vector spaces. Vector-space interpretations of network activity patterns are a fruitful resource in recent computational neuroscience. Vector subtraction also appears (...) to be implemented neurally in primate frontal eye field activity, which computes dimensions of saccadic eye movements. We use this apparent neural implementation as a model and construct from it a general neurocomputational account of an important type of sequential cognitive and conscious process. We defend the biological plausibility of all components of the general model and show that it yields testable anatomical and physiological predictions. We close by suggesting some interesting consequences for consciousness if our model characterizes correctly the neural mechanisms producing a common type of episode in our conscious streams. (shrink)
Apoptosis proteins have a central role in the development and homeostasis of an organism. These proteins are very important for understanding the mechanism of programmed cell death, and their function is related to their types. According to the classification scheme by Zhou and Doctor (2003), the apoptosis proteins are categorized into the following four types: (1) cytoplasmic protein; (2) plasma membrane-bound protein; (3) mitochondrial inner and outer proteins; (4) other proteins. A powerful learning machine, the Support Vector Machine, is (...) applied for predicting the type of a given apoptosis protein by incorporating the sqrt-amino acid composition effect. High success rates were obtained by the re-substitute test (98/98 = 100 %) and the jackknife test (89/98 = 90.8%). (shrink)
Let $V_\propto$ be a fixed, fully effective, infinite dimensional vector space. Let $\mathscr{L}(V_\propto)$ be the lattice consisting of the recursively enumerable (r.e.) subspaces of $V_\propto$ , under the operations of intersection and weak sum (see § 1 for precise definitions). In this article we examine the algebraic properties of $\mathscr{L}(V_\propto)$ . Early research on recursively enumerable algebraic structures was done by Rabin [14], Frolich and Shepherdson [5], Dekker [3], Hamilton [7], and Guhl [6]. Our results are based upon the (...) more recent work concerning vector spaces of Metakides and Nerode [12], Crossley and Nerode [2], Remmel [15], [16], and Kalantari [8]. In the main theorem below, we extend a result of Lachlan from the lattice E of r.e. sets to $\mathscr{L}(V_\propto)$ . We define hyperhypersimple vector spaces, discuss some of their properties and show if $A, B \in \mathscr{L}(V_\propto)$ , and A is a hyperhypersimple subspace of B then there is a recursive space C such that A + C = B. It will be proven that if $V \in \mathscr{L}(V_\propto)$ and the lattice of superspaces of V is a complemented modular lattice then V is hyperhypersimple. The final section contains a summary of related results concerning maximality and simplicity. (shrink)
Conformal group of Minkowski space-time M is considered as a group of bundle automorphisms of a vector bundle U over M. 4-component spin-vectors (4-spinors) are sections of a subbundle of the tangent bundle over U. Isotropic 4-vectors are images of 4-spinors under projection. This leads to a particularly clear interpretation of the spin properties of Nature.
Dispositions can combine as vector sums. Recent authors on dispositions, such as George Molnar and Stephen Mumford, have responded to this feature of dispositions by introducing a distinction between effects and contributions to effects, and by identifying disposition-manifestations with the latter. But some have been sceptical of the reality or knowability of component vectors; Jennifer McKitrick (forthcoming) presses these concerns against the conception of manifestations as contributions to effects. In this paper, I aim to respond to McKitrick's arguments and (...) to defend the metaphysical and epistemological propriety of component vectors. My strategy appeals to varying kinematic frames of reference. By transforming to the appropriate non-inertial frame, component acceleration vectors can be transformed into resultant acceleration vectors, and in such frames they become directly observable. Being a component acceleration vector and being a resultant acceleration vector are both frame-dependent properties of properties; they are not to be thought of as intrinsic or fundamental properties of an acceleration vector, but as artefacts of our frame-dependent notation for representing vector quantities. To conclude the paper, I defend the view proposed against two styles of objection. The first objection resurrects scepticism about component vectors as scepticism about fundamental component vectors. The second objection questions the need for reference frames in the explanation by invoking a 'counterfactual' theory of contributions. (shrink)
The authors, on the basis of brief arguments, have dismissed tensor networks as a viable response to Jackendoff's challenges. However, there are reasons to believe that connectionist approaches descended from tensor networks are actually very well suited to answering Jackendoff's challenges. I rebut their arguments for dismissing tensor networks and briefly compare the approaches.
To experience is to undergo a process, to be in a state of receiving input which affords information about our environment. For highly developed beings like ourselves, the inputs determining states of conscious sensory perception are among the most important for our survival. At first glance, these states seem relational, each being a situation wherein a percipient X is passively conscious of something Y--its object, subject-matter, or content--without any apparent effort. Of course, the briefest reflection convinces us that despite a (...) seemingly passive reception of data from without, a good deal of interpretation goes into the making of perceptual judgments, as evidenced by their wide variance in the face of like sensory stimulation. One person looking at the slope of a mountain notices a patch of whitish stones; another sees a flock of sheep grazing. They are distinguished by their different reactions to similar input, whether or not these are best construed as inferences, interpretations, or, simply, differing degrees of attentiveness. (shrink)
We reformulate minimalist grammars as partial functions on term algebras for strings and trees. Using filler/role bindings and tensor product representations, we construct homomorphisms for these data structures into geometric vector spaces. We prove that the structure-building functions as well as simple processors for minimalist languages can be realized by piecewise linear operators in representation space. We also propose harmony, i.e. the distance of an intermediate processing step from the final well-formed state in representation space, as a measure of (...) processing complexity. Finally, we illustrate our findings by means of two particular arithmetic and fractal representations. (shrink)
The paper aims to establish if Grassmann’s notion of an extensive form involved an epistemological change in the understanding of geometry and of mathematical knowledge. Firstly, it will examine if an ontological shift in geometry is determined by the vectorial representation of extended magnitudes. Giving up homogeneity, and considering geometry as an application of extension theory, Grassmann developed a different notion of a geometrical object, based on abstract constraints concerning the construction of forms rather than on the homogeneity conditions required (...) by the modern version of the theory of proportions. Secondly, Grassmann’s conception of mathematical knowledge will be investigated. Parting from the traditional definition of mathematics as a science of magnitudes, Grassmann considered mathematical forms as particulars rather than universals: the classification of the branches of mathematics was thus based on different operational rules, rather than on empirical criteria of abstraction or on the distinction of different species belonging to a common genus. It will be argued that a different notion of generalization is thus involved, and that the knowledge of mathematical forms relies on the understanding of the rules of generation of the forms themselves. Finally, the paper will analyse if Grassmann’s approach in the first edition of the Ausdehnungslehre should be explained in terms of the notion of purity of method, and if it clashes with Grassmann’s later conventionalism. Although in the second edition the features of the operations are chosen by convention, as it is the case for the anti-commutative property of the multiplication, the choice is oriented by our understanding of the resulting forms: a simplification in the algebraic calculus need not correspond to a simplification in the ‘dimensional’ interpretation of the result of the multiplicative operation. (shrink)
This paper presents a new Symmetrical Interpretation (SI) of relativistic quantum mechanics which postulates: quantum mechanics is a theory about complete experiments, not particles; a complete experiment is maximally described by a complex transition amplitude density; and this transition amplitude density never collapses. This SI is compared to the Copenhagen Interpretation (CI) for the analysis of Einstein’s bubble experiment. This SI makes several experimentally testable predictions that differ from the CI, solves one part of the measurement problem, resolves some inconsistencies (...) of the CI, and gives intuitive explanations of some previously mysterious quantum effects. (shrink)
Syndromic surveillance uses new ways of gathering data to identify possible disease outbreaks. Because syndromic surveillance can be implemented to detect patterns before diseases are even identified, it poses novel problems for informed consent, patient privacy and confidentiality, and risks of stigmatization. This paper analyzes these ethical issues from the viewpoint of the patient as victim and vector. It concludes by pointing out that the new International Health Regulations fail to take full account of the ethical challenges raised by (...) syndromic surveillance. (shrink)
A modal accessibility relation is just a transition relation, and so can be represented by a {0, 1} valued transition matrix. Starting from this observation, I first show that the machinery of matrices, over Boolean algebras more general than the two-valued one, is appropriate for investigating multi-modal semantics. Then I show that bisimulations have a rather elegant theory, when expressed in terms of transformations on Boolean vector spaces. The resulting theory is a curious hybrid, fitting between conventional modal semantics (...) and conventional linear algebra. I don’t know where the investigations begun here will ultimately wind up, but in the meantime the approach has a kind of curious charm that others may find appealing. (shrink)
Many studies have attempted to assess the relative effects of different vectors of a disease on animal populations. To this end, three measures have been proposed: Vectorial efficiency, Vectorial capacity and recently Vectorial effectiveness (or Vectorial impact). In this study we relate these measures to derive some of their properties emphasising in the vectorial impact for its importance in both, population performance of parasites and the proportion of the prevalence of one parasite due to a given vector. We applied (...) the quantitative expressions advanced in this study to a simple Chilean example with one parasite (Trypanosoma cruzi), two vectors (Triatoma infestans and Mepraia spinolai) and one animal population (humans: Chagas's disease). (shrink)
To assess O'Brien & Opie's connectionist vehicle theory of consciousness, (1) it is not enough to point to the methodological weakness of certain experiments (dichotic listening, etc.). Successful cognitive theories postulating explicit unconscious representations have to be taken into account as well. (2) The distinction between vehicle and process theories cannot be drawn in the way envisaged by the authors because a representation's explicitness depends not only on its structural but also on its processing properties. (3) The stability of an (...) activation vector is not very suitable for implementing the explicitness of a representation. (shrink)
Solomon has made the case, in Social Empicism (2001) for socially naturalized analysis of the dynamics of scientific inquiry that takes seriously two critical insights: that scientific rationality is contingent, disunified, and socially emergent; and that scientific progress is often fostered by factors traditionally regarded as compromising sources of bias. While elements of this framework are widely shared, Solomon intends it to be more resolutely social, more thoroughly naturalizing, and more ambitiously normative than other contextualizing epistemologies currently on offer. Four (...) focal issues are addressed in the commentaries that follow: Solomon's characterization of empirical success as a goal of science (Clough); her distinction between empirical and non-empirical decision vectors and the viability of the multivariate analysis she proposes for assessing epistemic fairness in their distribution (Clough; Richardson); the plausibility of her thesis that normatively appropriate consensus is a (rare) limiting case rather than an intrinsically desirable outcome of inquiry (Oreskes; Richardson); and her conviction that a socially naturalized analysis of science can ground norms of scientific rationality (Longino; Oreskes). (shrink)
Vectors, we will argue, are not just mathematical abstractions. They are also physical properties--universals. What make them distinctive are the rich and varied essences of these universals, and the complex pattern of internal relations which hold amongst them.
Hume thought that if you believed in powers, you believed in necessary connections in nature. He was then able to argue that there were none such because anything could follow anything else. But Hume wrong-footed his opponents. A power does not necessitate its manifestations: rather, it disposes towards them in a way that is less than necessary but more than purely contingent. -/- In this paper a dispositional theory of causation is offered. Causes dispose towards their effects and often produce (...) them. But a set of causes, even though they may succeed in producing an effect, cannot necessitate it since the effect could have been counteracted by some additional power. This would require a separation of our concepts of causal production and causal necessitation. The most conspicuous cases of causation are those where powers accumulate and pass a requisite threshold for an effect to occur. -/- We develop a model for representing powers as constituent vectors within an n-dimensional quality space, where composition of causes appears as vector addition. Even our resultant vector, however, has to be understood as having dispositional force only. This model throws new light on causal modality and cases of prevention, causation by absence and probabilistic causation. (shrink)
We have argued elsewhere that: (A) Natural selection is not a cause of evolution. (B) A resolution-of-forces (or vector addition) model does not provide us with a proper understanding of how natural selection combines with other evolutionary influences. These propositions have come in for criticism recently, and here we clarify and defend them. We do so within the broad framework of our own “hierarchical realization model” of how evolutionary influences combine.
The textbook presentation of quantum mechanics, in a nutshell, is this. The physical state of any isolated system evolves deterministically in accordance with Schrödinger's equation until a "measurement" of some physical magnitude M (e.g. position, energy, spin) is made. Restricting attention to the case where the values of M are discrete, the system's pre-measurement state-vector f is a linear combination, or "superposition", of vectors f1, f2,... that individually represent states that..
There are two versions of the putative connection between consciousness and the measurement problem of quantum mechanics : consciousness as the cause of state vector reduction, and state vector reduction as the physical basis of consciousness. In this article, these controversial ideas are neither accepted uncritically, nor rejected from the outset in the name of some prejudice about objective knowledge. Instead, their origin is sought in our most cherished (but disputable) beliefs about the place of mind and consciousness (...) in the world. It is first pointed out that these common beliefs about mind and consciousness arise from reification of situated first-person experience. Then, situatedness is shown to be a constitutive part of any exhaustive treatment of quantum measurements. It turns out that the alleged connection between consciousness and the measurement problem is a symptom of (i) the ineliminability of our being situated from the end-product of science, and (ii) our difficulty to express correctly this being situated. (shrink)
David Deutsch and others have suggested that the Many-Worlds Interpretation of quantum mechanics is the only interpretation capable of explaining the special efficiency quantum computers seem to enjoy over classical ones. I argue that this view is not tenable. Using a toy algorithm I show that the Many-Worlds Interpretation must crucially use the ontological status of the universal state vector to explain quantum computational efficiency, as opposed to the particular ontology of the MWI, that is, the computational histories of (...) worlds. As such, any other interpretation that treats the state vector as representing real ontological features of a system can explain quantum speedup too. ‡Thanks to Soazig Le Bihan for her critical comments on this paper. †To contact the author, please write to: Department of Philosophy, Liberal Arts 101, University of Montana, Missoula, MT 59812; e-mail: armond.duwell@umontana.edu. (shrink)
It is often said that the Aharonov-Bohm effect shows that the vector potential enjoys more ontological significance than we previously realized. But how can a quantum-mechanical effect teach us something about the interpretation of Maxwell's theory—let alone about the ontological structure of the world—when both theories are false? I present a rational reconstruction of the interpretative repercussions of the Aharonov-Bohm effect, and suggest some morals for our conception of the interpretative enterprise.
It is argued that seemingly “merely technical” issues about the existence and uniqueness of self-adjoint extensions of symmetric operators in quantum mechanics have interesting implications for foundations problems in classical and quantum physics. For example, pursuing these technical issues reveals a sense in which quantum mechanics can cure some of the forms of indeterminism that crop up in classical mechanics; and at the same time it reveals the possibility of a form of indeterminism in quantum mechanics that is quite distinct (...) from the indeterminism of state vector collapse. More generally, the examples considered indicate that the classical–quantum correspondence is more intricate and delicate than is generally appreciated. The aim of the article is to give a series of examples that reveal why the technical issues about self-adjointness are relevant to the philosophy of science and that help to make the issues accessible to philosophers of science. (shrink)
Copenhagen interpretation of quantum mechanics deals with these problems is reviewed. A new interpretation of the formalism of quantum mechanics, the transactional interpretation, is presented. The basic element of this interpretation is the transaction describing a quantum event as an exchange of advanced and retarded waves, as implied by the work of Wheeler and Feynman, Dirac, and others. The transactional interpretation is explicitly nonlocal and thereby consistent with recent tests of the Bell inequality, yet is relativistically invariant and fully causal. (...) A detailed comparison of the transactional and Copenhagen interpretations is made in the context of well-known quantum-mechanical Gedankenexperimenre and "paradoxes." The transactional interpretation permits quantum-mechanical wave functions to be interpreted as real waves physically present in space rather than as "mathematical representations of knowledge" as in the Copenhagen interpretation. The transactional interpretation is shown to provide insight into the complex character of the quantum-mechanical state vector and the mechanism associated with its "collapse." It also leads in a natural way to justification of the Heisenberg uncertainty principle and the Born probability law (P = ii iij*), basic elements of the Copenhagen interpretation. (shrink)
This paper expounds the relations between continuous symmetries and conserved quantities, i.e. Noether's ``first theorem'', in both the Lagrangian and Hamiltonian frameworks for classical mechanics. This illustrates one of mechanics' grand themes: exploiting a symmetry so as to reduce the number of variables needed to treat a problem. I emphasise that, for both frameworks, the theorem is underpinned by the idea of cyclic coordinates; and that the Hamiltonian theorem is more powerful. The Lagrangian theorem's main ``ingredient'', apart from cyclic coordinates, (...) is the rectification of vector fields afforded by the local existence and uniqueness of solutions to ordinary differential equations. For the Hamiltonian theorem, the main extra ingredients are the asymmetry of the Poisson bracket, and the fact that a vector field generates canonical transformations iff it is Hamiltonian. (shrink)
Suppose libertarians could prove that durable, unqualified private property rights could be created through 'original acquisition' of unowned resources in a state of nature. Such a proof would cast serious doubt on the legitimacy of the modern state. It could also render the approach to property rights that I favour irrelevant. I argue here that none of the familiar Lockean-libertarian arguments for a strong natural right to acquisition succeed, and that any successful argument for grounding a right to acquire would (...) have to use my favoured approach to property rights - the 'vector-sum' approach. I conclude with some doubts about original acquisition theory and natural property rights. (shrink)
Vector-based models of word meaning have become increasingly popular in cognitive science. The appeal of these models lies in their ability to represent meaning simply by using distributional information under the assumption that words occurring within similar contexts are semantically similar. Despite their widespread use, vector-based models are typically directed at representing words in isolation, and methods for constructing representations for phrases or sentences have received little attention in the literature. This is in marked contrast to experimental evidence (...) (e.g., in sentential priming) suggesting that semantic similarity is more complex than simply a relation between isolated words. This article proposes a framework for representing the meaning of word combinations in vector space. Central to our approach is vector composition, which we operationalize in terms of additive and multiplicative functions. Under this framework, we introduce a wide range of composition models that we evaluate empirically on a phrase similarity task. (shrink)
Given that the mind is the brain, as materialists insist, those who would understand the mind must understand the brain. Assuming that arrays of neural firing frequencies are highly salient aspects of brain information processing (the vector functional account), four hurdles to an understanding of the brain are identified and inspected: indeterminacy, micro-specificity, chaos, and openness.
A structure is a triple A = (A, {Ri: i ∈ I}, {ej: j ∈ J}), where A, the domain or universe of A, is a nonempty set, {Ri: i ∈ I} is an indexed family of relations on A and {ej: j ∈ J}) is an indexed set of elements —the designated elements of A. For each i ∈ I there is then a natural number λ(i) —the degree of Ri —such that Ri is a λ(i)-place relation on A, (...) i.e., Ri ⊆ Aλ(i). This λ may be regarded as a function from I to the set ω of natural numbers; the pair (λ, J) is called the type of A. Structures of the same type are said to be similar. Note that since an n-place operation f: An → A can be regarded as an (n+1)-place relation on A, algebraic structures containing operations such as groups, rings, vector spaces, etc. may be construed as structures in the above sense. (shrink)
Rovelli’s RQM is first characterized by contrast with both Everett’s and Bohr’s interpretations of quantum mechanics. Then, it is shown that a basic difficulty arises from the choice of formulating RQM in a naturalistic framework. Even though, according to Rovelli’s interpretation, statements about the world only make sense relative to certain naturalized observers described by means of quantum mechanics, this very meta-statement seems to make sense relative to a sort of super-observer which does not partake of the naturalized status of (...) ordinary observers. The difficulty is solved by substituting functional reference frames for physical (or naturalized) observers throughout. Instead of being relative to physical observers, statements about the state vector of physical systems are here relative to well-defined projects of probabilistic prediction which may be embodied by several physical observers. (shrink)
The attractive feature of the Everett approach is its admirable spirit of approaching the quantum puzzle with a Zen-like "beginner’s mind" in order to try to envision what the pure formalism might be saying about quantum reality, even if that journey leads to a strange place. It is argued that the transactional interpretation of quantum mechanics (TI), appropriately interpreted, shares the same motivation and achieves much more, with far fewer conceptual perplexities, by taking into account heretofore overlooked features of the (...) quantum formalism itself (i.e. advanced states). In particular, TI does not need to talk about brain states, consciousness, or observers (rational or otherwise). In its possibilist variant (“PTI”), it shares the realist virtues of treating state vector branches as genuine dynamical entities, without having to explain how or why all of their associated outcomes actually happen (they don’t), how to account for a plenitude of counterpart observers in some coherent notion of trans-temporal identity of the bifurcating observers (observers don’t bifurcate in TI), nor how the certainty of all outcomes could be consistent with any coherent theory of probability, let alone the Born probability (the Born probability emerges naturally in TI). In short, TI is precisely the one-world interpretation Kent is looking for in his (2010). (shrink)
For nearly six decades, the conscious observer has played a central and essential rôle in quantum measurement theory. I outline some difficulties which the traditional account of measurement presents for material theories of mind before introducing a new development which promises to exorcise the ghost of consciousness from physics and relieve the cognitive scientist of the burden of explaining why certain material structures reduce wavefunctions by virtue of being conscious while others do not. The interactive decoherence of complex quantum systems (...) reveals that the oddities and complexities of linear superposition and state vector reduction are irrelevant to computational aspects of the philosophy of mind and that many conclusions in related fields are ill founded. (shrink)
In this book, Mumford and Anjum advance a theory of causation based on a metaphysics of powers. The book is for the most part lucidly written, and contains some interesting contributions: in particular on the (lack of) necessary connection between cause and effect and on the perceivability of the causal relation. I do, however, have reservations about some of the book’s central theses: in particular, that cause and effect are simultaneous, and that causes can fruitfully be represented as vectors.
Evolutionary ethics (EE) is a branch of philosophy that arouses both fascination and deep suspicion. It claims that Darwinian mechanisms and evolutionary data on animal sociality are relevant to ethical reflection. This field of study is often misunderstood and rarely fails to conjure up images of Social Darwinism as a vector for nasty ideologies and policies. However, it is worth resisting the temptation to reduce EE to Social Darwinism and developing an objective analysis of whether it is appropriate to (...) adopt an evolutionary approach in ethics. The purpose of this article is to ‘dedemonise’ EE while exploring its limits. I shall begin by presenting two ways of integrating a Darwinian way of thinking into the context of social and political sciences : Social Darwinism and what one could label ‘Pro-social Darwinism’. Next I will point out some of the fundamental errors on which Social Darwinism is grounded; this will help in understanding why contemporary evolutionary ethicists cannot possibly hold the views defended by this theory (unless they are inclined to intellectual dishonesty). On the contrary, EE seems more akin to a Pro-social Darwinian approach, except for the fact that it restricts its reflections to theoretical ethics. The second part of the paper (sections 3 to 7) provides a clear and detailed picture of EE as well as an analysis of its relevance at the different levels of ethics (descriptive, meta-, normative and practical). Special focus will be given to questions relating to the genesis of morals and the delicate shift from facts to norms. (shrink)
These are notes designed to bring the beginning student of the philosophy of quantum mechanics 'up to scratch' on the mathematical background needed to understand elementary finite-dimensional quantum theory. There are just three chapters: Ch. 1 'Vector Spaces'; Ch. 2 'Inner Product Spaces'; and Ch. 3 'Operators on Finite-Dimensional Complex Inner Product Spaces'. The notes are entirely self-contained and presuppose knowledge of only high school level algebra.
Bayesian Coherence Theory of Justification or, for short, Bayesian Coherentism, is characterized by two theses, viz. (i) that our degree of confidence in the content of a set of propositions is positively affected by the coherence of the set, and (ii) that coherence can be characterized in probabilistic terms. There has been a longstanding question of how to construct a measure of coherence. We will show that Bayesian Coherentism cannot rest on a single measure of coherence, but requires a (...) class='Hi'>vector whose components exhaustively characterize the coherence properties of the set. Our degree of confidence in the content of the information set is a function of the reliability of the sources and the components of the coherence vector. The components of this coherence vector are weakly but not strongly separable, which blocks the construction of a single coherence measure. (shrink)
Two hundred years ago, Friedrich Schleiermacher took critical issue with Immanuel Kant's intellectual notion of intuition as applied to human nature (Wellmon 2006). He found it necessary to modify—"hermeneutically," as he said—Kant's notion of anthropology by enabling it to include as human the new and strange human tribes Captain Cook found in the Pacific South Seas. A similar hermeneutic move is necessary if physics is to include the local contextual empirical syntheses of relativity and quantum physics. In this hermeneutical revision (...) the synthesis is formed around the notion of a Hilbert Vector Space as the universal grammar of physics, adding to it the dynamic of the Schrödinger equation, and representing empirical "observables" by projection operators that map the subspaces of definite measurable values. Among the set of observable projection operators, some pairs share the same subspace, commute with one another, and share a common laboratory setting. Other pairs do not share this property and are described as being mutually complementary. Complementary symmetries introduce into the discursive language of physics the commonsense notion of contextuality. The new synthesis, proposed by Eugene Wigner, John von Neumann, and (in his own way) Paul Dirac, brought physics into the community of common language and established it as a work of general human achievement. 1. (shrink)
I dispute that consciousness is generated by core circuitry in the forebrain, with predominance of motor areas, as Cotterillproposes in Enchanted Looms and other theorists do also. Ipropose instead that conscious contents are the momentary modeof action of the integrated cortical field, expressed as a point vector ( dominant focus ), to which, in varying degree, allsectors of the network contribute. Consciousness is the brain''saccess to its own activity space, and is identical with the moment''sdominant mode of activity. The (...) dominant focus is generally weightedtoward enactively encoded percepts. Anticipation and preparation,perception and action, inextricably interdigitate. I also dispute the view of Cotterill and others that consciousnesshas unique agency, which bestowed adaptive advantage when the brain evolved. Being identical with the activity of the network,consciousness can have no additional agency, and it can offerno adaptive advantages beyond those that characterize the network. (shrink)
I defend the interpretation of the Aharonov-Bohm effect originally advanced by Aharonov and Bohm, i.e., that it is caused by an interaction between the electron and the vector potential. The defense depends on taking the fiber bundle formulation of electrodynamics literally, or almost literally.
Classical and quantum field theory provide not only realistic examples of extant notions of empirical equivalence, but also new notions of empirical equivalence, both modal and occurrent. A simple but modern gravitational case goes back to the 1890s, but there has been apparently total neglect of the simplest relativistic analog, with the result that an erroneous claim has taken root that Special Relativity could not have accommodated gravity even if there were no bending of light. The fairly recent acceptance of (...) nonzero neutrino masses shows that widely neglected possibilities for nonzero particle masses have sometimes been vindicated. In the electromagnetic case, there is permanent underdetermination at the classical and quantum levels between Maxwell's theory and the one-parameter family of Proca's electromagnetisms with massive photons, which approximate Maxwell's theory in the limit of zero photon mass. While Yang–Mills theories display similar approximate equivalence classically, quantization typically breaks this equivalence. A possible exception, including unified electroweak theory, might permit a mass term for the photons but not the Yang–Mills vector bosons. Underdetermination between massive and massless (Einstein) gravity even at the classical level is subject to contemporary controversy. (shrink)
Like those famous nations divided by a single tongue, my paper (this volume) and Professor P.M. Churchland's deep and engaging reply offer different spins on a common heritage. The common heritage is, of course, a connectionist vision of the inner neural economy- a vision which depicts that economy in terms of supra-sentential state spaces, vector-to-vector transformations, and the kinds of skillful pattern-recognition routine we share with the bulk of terrestrial intelligent life-forms. That which divides us is, as ever, (...) much harder to isolate and name. Clearly, it has something to do with the role of moral talk and exchange, and something to do with the conception of morality itself (and, correlatively, with the conception of moral progress). Most of this Reply will be devoted to clarifying the nature of the disputed territory. First, though (as a prophylactic against misunderstanding) I shall rehearse some points of agreement concerning moral talk and progress. (shrink)
The formalism of abstracted quantum mechanics is applied in a model of the generalized Liar Paradox. Here, the Liar Paradox, a consistently testable configuration of logical truth properties, is considered a dynamic conceptual entity in the cognitive sphere (Aerts, Broekaert, & Smets, [Foundations of Science 1999, 4, 115–132; International Journal of Theoretical Physics, 2000, 38, 3231–3239]; Aerts and colleagues[Dialogue in Psychology, 1999, 10; Proceedings of Fundamental Approachs to Consciousness, Tokyo ’99; Mind in Interaction]. Basically, the intrinsic contextuality of the truth-value (...) of the Liar Paradox is appropriately covered by the abstracted quantum mechanical approach. The formal details of the model are explicited here for the generalized case. We prove the possibility of constructing a quantum model of the m-sentence generalizations of the Liar Paradox. This includes (i) the truth–falsehood state of the m-Liar Paradox can be represented by an embedded 2m-dimensional quantum vector in a (2m) m -dimensional complex Hilbert space, with cognitive interactions corresponding to projections, (ii) the construction of a continuous ‘time’ dynamics is possible: typical truth and falsehood value oscillations are described by Schrödinger evolution, (iii) Kirchoff and von Neumann axioms are satisfied by introduction of ‘truth-value by inference’ projectors, (iv) time invariance of unmeasured state. (shrink)
The past decade has witnessed the emergence of a novel stance on semantic representation, and its relationship to context sensitivity. Connectionist-minded philosophers, including Clark and van Gelder, have espoused the merits of viewing hidden-layer, context-sensitive representations as possessing semantic content, where this content is partially revealed via the representations'' position in vector space. In recent work, Bodén and Niklasson have incorporated a variant of this view of semantics within their conception of semantic systematicity. Moreover, Bodén and Niklasson contend that (...) they have produced experimental results which not only satisfy a kind of context-based, semantic systematicity, but which, to the degree that reality permits, effectively deals with challenges posed by Fodor and Pylyshyn (1988), and Hadley (1994a). The latter challenge involved well-defined criteria for strong semantic systematicity. This paper examines the relevant claims and experiments of Bodén and Niklasson. It is argued that their case fatally involves two fallacies of equivocation; one concerning ''semantic content'' and the other concerning ''novel test sentences''. In addition, it is argued that their ultimate construal of context sensitive semantics contains serious confusions. These confusions are also found in certain publications dealing with "latent semantic analysis". Thus, criticisms presented here have relevance beyond the work of Bodén and Niklasson. (shrink)
This paper forms part of a wider campaign: to deny pointillisme, the doctrine that a physical theory's fundamental quantities are defined at points of space or of spacetime, and represent intrinsic properties of such points or point-sized objects located there; so that properties of spatial or spatiotemporal regions and their material contents are determined by the point-by-point facts. More specifically, this paper argues against pointillisme about the concept of velocity in classical mechanics; especially against proposals by Tooley, Robinson and Lewis. (...) A companion paper argues against pointillisme about (chrono)-geometry, as proposed by Bricker. To avoid technicalities, I conduct the argument almost entirely in the context of "Newtonian" ideas about space and time, and the classical mechanics of point-particles, i.e. extensionless particles moving in a void. But both the debate and my arguments carry over to relativistic physics. Introduction The wider campaign 2.1 Connecting physics and metaphysics 2.1.1 Avoiding controversy about the intrinsic–extrinsic distinction 2.1.2 Distinction from three mathematical distinctions 2.2 Classical mechanics is not pointilliste, and can be perdurantist 2.2.1 Two versions of pointillisme 2.2.2 Two common claims 2.2.3 My contrary claims 2.3 In more detail... 2.3.1 Four violations of pointillisme 2.3.2 For perdurantism Velocity as intrinsic? 3.1 Can properties represented by vectors be intrinsic to a point? 3.2 Orthodox velocity is extrinsic but local 3.2.1 A question and a debate 3.2.2 The verdict 3.3 Against intrinsic velocity 3.3.1 A common view—and a common problem 3.3.2 Tooley's proposal and his arguments 3.3.3 Tooley's further discussion "Shadow velocities": Lewis and Robinson 4.1 The proposal 4.2 Criticism: the vector field remains unspecified 4.3 Avoiding the presupposition of persistence, using Hilbert's symbol 4.4 Comparison with Robinson and Lewis. (shrink)
The issue is obscured by the fact that the word `space' can be used in four different ways. It can be used, first, as a term of pure mathematics, as when mathematicians talk of an `n-dimensional phase-space', an `n-dimensional vector-space', a `three-dimensional projective space' or a `twodimensional Riemannian space'. In this sense the word `space' means the totality of the abstract entities-the `points'-implicitly defined by the axioms. There is no doubt that there exist, iii this sense, non-Euclidean spaces, because (...) all that is claimed by such an assertion is that sets of non-Euclidean axioms constitute possible implicit definitions of abstract entities, that is to say that some sets of non-Euclidean axioms are consistent. If Kant or any other philosopher had denied this, he would have been wrong; but Kant himself took care not to deny it, 2 and there is little reason to suppose that any philosopher concerned about space has been using the word in this, the pure mathematician's, sense. (shrink)
The basis of a rigorous formal axiomatization of quantum mechanics is constructed, built upon Dirac's bra–ket notation. The system is three-sorted, with separate variables for scalars, vectors and operators. First-order quantification over all three types of variable is permitted. Economy in the axioms is effected by, e.g., assigning a single logical function * to transform (i) a scalar into its complex conjugate, (ii) a ket vector into a bra and a bra into a ket, (iii) an operator into its (...) adjoint. The system is accompanied by a formal semantics. Further papers will deal with vector subspaces and projection operators, operators with continuous spectra, tensor products, observables, and quantum mechanical probabilities. (shrink)
A rigorous extension of the full Lorentz group is found which is parameterized by interframe velocities v(t) and which reduces to Special Relativity for acceleration-free cases and to Galilean relativity for low velocity cases. Full group properties are exhibited. Four-momentum is defined and particle masses are shown to be invariants. Four-force is introduced and pseudoforces are shown to enter the equations of particle dynamics. Maxwell's equations are shown to take on pseudocurrent terms in accelerating frames. A four-vector Green function (...) solution to the modified Maxwell equations is presented. Finally, a discussion is offered concerning philosophical questions such as the operational definition of time. (shrink)
Prologue: Stormclouds : London, April 1900 -- Quantum of action: The most strenuous work of my life : Berlin, December 1900 ; Annus Mirabilis : Bern, March 1905 ; A little bit of reality : Manchester, April 1913 ; la Comédie Française : Paris, September 1923 ; A strangely beautiful interior : Helgoland, June 1925 ; The self-rotating electron : Leiden, November 1925 ; A late erotic outburst : Swiss Alps, Christmas 1925 -- Quantum interpretation: Ghost field : Oxford, August (...) 1926 ; All this damned quantum jumping : Copenhagen, October 1926 ; The uncertainty principle : Copenhagen, February 1927 ; The 'Kopenhagener geist' : Copenhagen, June 1927 ; There is no quantum world : Lake Como, September 1927 -- Quantum debate: The debate commences : Brussels, October 1927 ; An absolute wonder : Cambridge, Christmas 1927 ; The photon box : Brussels, October 1930 ; A bolt from the blue : Princeton, May 1935 ; The paradox of Schrödinger's cat : Oxford, August 1935 -- Interlude: The first war of physics : Christmas 1938-August 1945 -- Quantum fields: Shelter Island : Long Island, June 1947 ; Pictorial semi-vision thing : New York, January 1949 ; A beautiful idea : Princeton, February 1954 ; Some strangeness in the proportion : Rochester, August 1960 ; Three quarks for Muster Mark! : New York, March 1963 ; The 'God particle' : Cambridge, Massachusetts, Autumn 1967 -- Quantum particles: Deep inelastic scattering : Stanford, August 1968 ; Of charm and weak neutral currents : Harvard, February 1970 ; The magic of colour : Princeton/Harvard, April 1973 ; The November revolution : Long Island/Stanford, November 1974 ; Intermediate vector bosons : Geneva, January/June 1983 ; The standard model : Geneva, September 2003 -- Quantum reality: Hidden variable : Princeton, Spring 1951 ; Bertlmann's socks : Boston, September 1964 ; The Aspect experiments : Paris, September 1982 ; The quantum eraser : Baltimore, January 1999 ; Lab cats : Stony Brook/Delft, July 2000 ; The persistent illusion : Vienna, December 2006 -- Quantum cosmology: The wavefunction of the universe : Princeton, July 1966 ; Hawking radiation : Oxford, February 1974 ; The first superstring revolution : Aspen, August 1984 ; Quanta of space and time : Santa Barbara, February 1986 ; Crisis? What crisis? : Durham, Summer 1994 -- A quantum of solace? : Geneva, March 2010. (shrink)
A possible relation between Derrida's deconstruction of metaphysics and connectionism is explored by considering diff rance in neural nets terms. First diff rance , as the crossing of Saussurian difference and Freudian deferral, is modeled and then the fuller 'sheaf of diff rance is taken up. The metaphysically conceived brain has two versions: in the traditional computational version the brain processes information like a computer and in the connectionist version the brain computes input vector to output vector transformations (...) non-symbolically. The 'deconstructed brain' neither processes information nor computes functions but is spontaneously economical. (shrink)
Our aim in this paper is to take quite seriously Heinz Post's claim that the non-individuality and the indiscernibility of quantum objects should be introduced right at the start, and not made a posteriori by introducing symmetry conditions. Using a different mathematical framework, namely, quasi-set theory, we avoid working within a label-tensor-product-vector-space-formalism, to use Redhead and Teller's words, and get a more intuitive way of dealing with the formalism of quantum mechanics, although the underlying logic should be modified. Thus, (...) this paper can be regarded as a tentative to follow and enlarge Heinsenberg's suggestion that new phenomena require the formation of a new ``closed" (that is, axiomatic) theory, coping also with the physical theory's underlying logic and mathematics. (shrink)
Model simplicity in curve fitting is the fewness of parameters estimated. I use a vector model of least squares estimation to show that degrees of freedom, the difference between the number of observed parameters fit by the model and the number of explanatory parameters estimated, are the number of potential dimensions in which data are free to differ from a model and indicate the disconfirmability of the model. Though often thought to control for parameter estimation, the AIC and similar (...) indices do not do so for all model applications, while goodness of fit indices like chi-square, which explicitly take into account degrees of freedom, do. Hypothesis testing with prespecified values for parameters is based on a metaphoric regulative subject/object schema taken from object perception and has as its goal the accumulation of objective knowledge. (shrink)
The universality, invariance, and elegance of principles governing the universe may be reflected in principles of the minds that have evolved in that universe – provided that the mental principles are formulated with respect to the abstract spaces appropriate for the representation of biologically significant objects and their properties. (1) Positions and motions of objects conserve their shapes in the geometrically fullest and simplest way when represented as points and connecting geodesic paths in the six-dimensional manifold jointly determined by the (...) Euclidean group of three-dimensional space and the symmetry group of each object. (2) Colors of objects attain constancy when represented as points in a three-dimensional vector space in which each variation in natural illumination is canceled by application of its inverse from the three-dimensional linear group of terrestrial transformations of the invariant solar source. (3) Kinds of objects support optimal generalization and categorization when represented, in an evolutionarily-shaped space of possible objects, as connected regions with associated weights determined by Bayesian revision of maximum-entropy priors. Key Words: apparent motion; Bayesian inference; cognition; color constancy; generalization; mental rotation; perception; psychological laws; psychological space; universal laws. (shrink)
Order of information plays a crucial role in the process of updating beliefs across time. In fact, the presence of order effects makes a classical or Bayesian approach to inference difficult. As a result, the existing models of inference, such as the belief-adjustment model, merely provide an ad hoc explanation for these effects. We postulate a quantum inference model for order effects based on the axiomatic principles of quantum probability theory. The quantum inference model explains order effects by transforming a (...) state vector with different sequences of operators for different orderings of information. We demonstrate this process by fitting the quantum model to data collected in a medical diagnostic task and a jury decision-making task. To further test the quantum inference model, a new jury decision-making experiment is developed. Using the results of this experiment, we compare the quantum inference model with two versions of the belief-adjustment model, the adding model and the averaging model. We show that both the quantum model and the adding model provide good fits to the data. To distinguish the quantum model from the adding model, we develop a new experiment involving extreme evidence. The results from this new experiment suggest that the adding model faces limitations when accounting for tasks involving extreme evidence, whereas the quantum inference model does not. Ultimately, we argue that the quantum model provides a more coherent account for order effects that was not possible before. (shrink)
We consider an isolated, macroscopic quantum system. Let H be a microcanonical “energy shell,” i.e., a subspace of the system’s Hilbert space spanned by the (finitely) many energy eigenstates with energies between E and E + δE. The thermal equilibrium macro-state at energy E corresponds to a subspace Heq of H such that dim Heq/ dim H is close to 1. We say that a system with state vector ψ H is in thermal equilibrium if ψ is “close” to (...) Heq. We show that for “typical” Hamiltonians with given eigenvalues, all initial state vectors ψ0 evolve in such a way that ψt is in thermal equilibrium for most times t. This result is closely related to von Neumann’s quantum ergodic theorem of 1929. (shrink)
In this paper I discuss how Bohm's interpretation models spin measurements and how the two ways in which spin is a contextual property pertains to the Kochen-Specker theorem. I then present locality principles from which a Bell Inequality can be derived, and I identify which of the locality principles Bohm's interpretation violates at which times. I also present reasons why the spin vector should not be attributed to the Bohmian particles.
At the global as well as local scales, some of the geometry of types of neuron arbors—both dendrites and axons—appears to be self-organizing: Their morphogenesis behaves like flowing water, that is, fluid dynamically; waterflow in branching networks in turn acts like a tree composed of cords under tension, that is, vector mechanically. Branch diameters and angles and junction sites conform significantly to this model. The result is that such neuron tree samples globally minimize their total volume—rather than, for example, (...) surface area or branch length. In addition, the arbors perform well at generating the cheapest topology interconnecting their terminals: their large-scale layouts are among the best of all such possible connecting patterns, approaching 5% of optimum. This model also applies comparably to arterial and river networks. S1063-651X 99 16205-6.. (shrink)
According to D. Lewis, fundamental physical quantities such as mass are families of perfectly natural properties. The best theory of naturalness, however, is nominalistic. But the nominalistic Lewisian has to account for the unity of the particular masses in terms of fundamental ordering and congruence relations among individuals. Such a first-order relational theory can do without perfectly natural mass qualities, without making the having of a particular mass extrinsic. This strictly relational account can be applied to fundamental vectorial quantities (...) such as the field strengths, too. So conceived, vector fields are compatible with Lewis' hypothesis of Humean Supervenience. Even the denier of real possible worlds should seek to retain the advantages of this first-order, strictly relational theory. German D. Lewis zufolge sind physikalische Grundgrößen wie die Masse Familien von perfekt natürlichen Eigenschaften. Die beste Theorie der Natürlichkeit ist jedoch die nominalistische. Der nominalistische Lewisianer muss aber den Familienzusammenhalt der einzelnen Massequalitäten durch fundamentale Ordnungs- und Kongruenzbeziehungen zwischen den Masseträgern erklären. Eine solche erststufig-relationale Theorie kann auf perfekt natürliche Massequalitäten verzichten, ohne das Haben einer Masse zu einer extrinsischen Eigenschaft zu machen. Diese strikt relationale Theorie ist auch auf fundamentale Vektorgrößen wie die Feldstärken anwendbar. Derart konzipierte Vektorfelder sind mit Lewis' Hypothese der Hume'schen Supervenienz vereinbar. Die Vorteile dieser erststufigen, strikt relationalen Theorie sollte auch der Gegner des modalen Realismus zu erhalten suchen. (shrink)
The measurement of force is based on a formal law of additivity, which characterizes the effects of two or more configurations on the equilibrium of a material point. The representing vectors (resultant forces) are additive over configurations. The existence of a tight interrelation between the force vector and the geometric space, in which motion is described, depends on observations of partial (directional) equilibria; an axiomatization of this interrelation yields a proof of part two of Newton's second law of motion. (...) The present results (which were derived from a curious and deep isomorphism between force measurement and trichromatic color measurement) yield a kind of subunit, which needs to be incorporated into more complete axiomatizations of mechanics that would fulfill the Mach-Kirchhoff program. (shrink)
