In this work, we investigate the representation of counterfactual conditionals using the vector logic, a matrix-vector formalism for logical functions and truth values. Inside this formalism, the counterfactuals can be transformed in complex matrices preprocessing an implication matrix with one of the square roots of NOT, a complex matrix. This mathematical approach puts in evidence the virtual character of the counterfactuals. This happens because this representation produces a valuation of a counterfactual that is the superposition of the (...) two opposite truth values weighted, respectively, by two complex conjugated coefficients. This result shows that this procedure gives an uncertain evaluation projected on the complex domain. After this basic representation, the judgement of the plausibility of a given counterfactual allows us to shift the decision towards an acceptance or a refusal. This shift is the result of applying for a second time one of the two square roots of NOT. (shrink)

'Overpopulation' is often implicated as a major causative factor of poverty and environmental degradation in the developing world. This review of the population-resource debate focusses on Red, Green and neo-Malthusian ideologies to demonstrate how they have ramified into current economic and development theory. A central hypothesis is that key elements of Marxist analysis, tempered by the best of Green thought, still have much to offer the subject. The contributions of capitalism to 'underdevelopment', and its associated environmental crises, are clarified and (...) reasserted in a contemporary context. The concept of valuation vector is also introduced, and a novel closure of Blaikie's 'Chain of Explanation' is proposed. The Circuit of Capital model thus created is applied to specific case-studies of resource-population conflict so as to overturn the simplistic conventional connection held between population growth and ecological devastation. The model highlights sequential causes of poverty arising from important capital-based factors which might otherwise be overlooked. It can accommodate a variety of Red-Green perspectives and its structural form is suited to the unravelling of complex population-resource pressures in the multi-dimensional space of the modern global political economy. (shrink)

§1. Introduction.The motivation of this work comes from two different directions: infinite abelian groups, and ordered algebraic structures. A challenging problem in both cases is that of classification. In the first case, it is known for example (cf. [KA]) that the classification of abelian torsion groups amounts to that of reducedp-groups by numerical invariants called theUlm invariants(given by Ulm in [U]). Ulm's theorem was later generalized by P. Hill to the class of totally projective groups. As to the second case, (...) let us consider for instance the class of divisible ordered abelian groups. These may be viewed as ordered ℚ-vector spaces. Their theory being unstable, we cannot hope to classify them by numerical invariants. On the other hand, being o-minimal, the theory enjoys several good model theoretic properties (cf. [P-S]), so the search for some reasonable invariants is well motivated. The common denominator of the two cases, as well as of many others, is valuation theory. Indeed given an ordered vector space, one can consider it as a valued vector space, endowed with the natural valuation. Also, the socleG[p] of a reduced abelianp-groupG, endowed with the height functionhG, is a valued vector space over(the prime field of characteristicp) with values in the ordinals (cf. [F]). (shrink)

Values, Valuations, and Axiological Norms in Richard Rorty's Neopragmatism sympathetically discusses Richard Rorty's neopragmatist philosophy. This book brings together a range of interpretations and possibilities on a variety of humanistic topics, including philosophy, literature, culture, film, economics, social issues, politics, and more. Skowroński involves the work of philosophers such as Kant, Dewey, Santayana, and Kołakowski as he delves into various philosophical problems using the lens of Rorty’s neopragmatist thought.

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.

Vector autoregression (VAR) modeling allows probing bidirectional relationships in gender/sex development and may support hypothesis testing following multi-modal data collection. We show VAR in three lights: supporting a hypothesis, rejecting a hypothesis, and opening up new questions. To illustrate these capacities of VAR, we reanalyzed longitudinal data that recorded dyadic mother-infant interactions for 15 boys and 15 girls aged 3 to 11 months of age. We examined monthly counts of 15 infant behaviors and 13 maternal behaviors (Seifert et al., (...) 1994). VAR models demonstrated that infant crawling predicted a subsequently close feedback loop from mothers of boys but a subsequently open ended, branched response from mothers of girls. A different finding showed that boys’ standing independently later predicted significant later increases of four maternal behaviors: rocking/jiggling, lifting, affectionate touching, and stimulation of infant gross-motor activity. In contrast, crawling by girls led mothers to later decrease the same maternal behaviors. Thus, VAR might allow us to identify how mothers respond differently during daily interactions depending on infant gender/sex. The present work intends mainly to showcase the VAR method in the specific context of the empirical study of gender/sex development. (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)

Valuation is portrayed here as a dynamic and interactive process, not a static notion linked to willingness to pay. Valuation through economic measures can be built upon by creating trusting and legitimising procedures of stakeholder negotiation and mediation. This is a familiar practice in the US, but it is only beginning to be recognised as an environmental management tool in the UK. The introduction of strategic environmental and landuse appraisal plans for shorelines, estuaries, river catchments and rural landscapes, (...) combined with the mobilisation of protest around landuse proposals that are not seemingly justified on the basis of 'need' suggest that a more legitimate participatory form of democracy is required to reveal valuation through consensual negotiation. (shrink)

A central question for psychologists, economists, and philosophers is how human lives should be valued. Whereas egalitarian considerations give rise to models emphasizing that every life should be valued equally, empirical research has demonstrated that valuations of lives depend on a variety of factors that often do not conform to specific normative expectations. Such factors include emotional reactions to the victims and cognitive considerations leading to biased perceptions of lives at risk (e.g., attention, mental imagery, pseudo-inefficacy, and scope neglect). They (...) can lead to a valuation function with decreasing marginal value and sometimes even decreasing absolute value as the number of victims increases. As a result, people spend more money to save an individual while at the same time being insensitive and apathetic to large losses of life, despite endorsing egalitarian norms. In this conceptual paper, we propose a descriptive model highlighting the role of different motivations and the conditions under which cognitions and emotions result in deviations from egalitarian normative valuations of human lives. (shrink)

This paper considers some issues to do with valuational presentations of consequence relations, and the Galois connections between spaces of valuations and spaces of consequence relations. Some of what we present is known, and some even well-known; but much is new. The aim is a systematic overview of a range of results applicable to nonreflexive and nontransitive logics, as well as more familiar logics. We conclude by considering some connectives suggested by this approach.

This paper considers some issues to do with valuational presentations of consequence relations, and the Galois connections between spaces of valuations and spaces of consequence relations. Some of what we present is known, and some even well-known; but much is new. The aim is a systematic overview of a range of results applicable to nonreflexive and nontransitive logics, as well as more familiar logics. We conclude by considering some connectives suggested by this approach.

Support vector machines are being used increasingly in affective science as a data-driven classification method and feature reduction technique. Whereas traditional statistical methods typically compare group averages on selected variables, SVMs use a predictive algorithm to learn multivariate patterns that optimally discriminate between groups. In this review, we provide a framework for understanding the methods of SVM-based analyses and summarize the findings of seminal studies that use SVMs for classification or data reduction in the behavioral and neural study of (...) emotion and affective disorders. We conclude by discussing promising directions and potential applications of SVMs in future research in affective science. (shrink)

In this paper, we present valuation semantics for the Propositional Intuitionistic Calculus (also called Heyting Calculus) and three important subcalculi: the Implicative, the Positive and the Minimal Calculus (also known as Kolmogoroff or Johansson Calculus). Algorithms based in our definitions yields decision methods for these calculi. DOI:10.5007/1808-1711.2010v14n1p125.

Valuations are ubiquitous. We may be for or against genetically modified food; we find some politicians irresponsible; we prefer Beethoven to rock ‘n’ roll or vice versa; some enjoy bird-watching while others find it boring; and we may think that we have to tighten up on green-house gas emissions. Valuing is pervasive and often we are not even aware that we are valuing. However, many of our valuations are ill grounded and rationally defective. They are frequently based on misinformation, sloppy (...) thinking, prejudice, and are biased in many ways as psychological research shows. For this reason there is widespread agreement among phi-losophers that we need an account of substantive valuational rationality, both for the theory of practical reasoning and for ethics as well. My main object in this paper is to outline such an account and to present a principle that allows a non-technical rational criticism of valuations. (shrink)

Vector models of language are based on the contextual aspects of language, the distributions of words and how they co-occur in text. Truth conditional models focus on the logical aspects of language, compositional properties of words and how they compose to form sentences. In the truth conditional approach, the denotation of a sentence determines its truth conditions, which can be taken to be a truth value, a set of possible worlds, a context change potential, or similar. In the (...) class='Hi'>vector models, the degree of co-occurrence of words in context determines how similar the meanings of words are. In this paper, we put these two models together and develop a vector semantics for language based on the simply typed lambda calculus models of natural language. We provide two types of vector semantics: a static one that uses techniques familiar from the truth conditional tradition and a dynamic one based on a form of dynamic interpretation inspired by Heim’s context change potentials. We show how the dynamic model can be applied to entailment between a corpus and a sentence and provide examples. (shrink)

Excerpt from Vector Analysis and the Theory of Relativity One of the most striking effects of the publication of Einstein's papers on generalized relativity and of the discussions which arose in connection with the subsequent astronomical observations was to make students of physics renew their study of mathematics. At first they attempted to learn simply the technique, but soon there was a demand to understand more; real mathematical insight was sought. Unfortunately there were no books available, not even papers. (...) Dr. Murnaghan's little book is a most successful attempt to supply what is a definite need. Every physicist can read it with profit. He will learn the meaning of a vector for the first time. He will learn methods which are available for every field of mathematical physics. He will see which of the processes used by Einstein and others are strictly mathematical and which are physical. Every chapter is illuminating, and the treatment of the subject is that of a student of mathematics and is not developed ad hoc. The extension of surface and line integrals is most interesting for physicists and the discussion of the space relations in a four-dimensional geometry is one most needed. This is specially true concerning the case of point-symmetry which forms the basis of Einstein's formulae for gravitation as applied to the solar system. I feel personally that I owe to this book a great debt. I have read it with care and shall read it again. It has given me a definiteness of understanding which I never had before, and a vision of a field of knowledge which before was remote. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works. (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.

This paper introduces the logic _Q__L__E__T_ _F_, a quantified extension of the logic of evidence and truth _L__E__T_ _F_, together with a corresponding sound and complete first-order non-deterministic valuation semantics. _L__E__T_ _F_ is a paraconsistent and paracomplete sentential logic that extends the logic of first-degree entailment (_FDE_) with a classicality operator ∘ and a non-classicality operator ∙, dual to each other: while ∘_A_ entails that _A_ behaves classically, ∙_A_ follows from _A_’s violating some classically valid inferences. The semantics of (...) _Q__L__E__T_ _F_ combines structures that interpret negated predicates in terms of anti-extensions with first-order non-deterministic valuations, and completeness is obtained through a generalization of Henkin’s method. By providing sound and complete semantics for first-order extensions of _FDE_, _K3_, and _LP_, we show how these tools, which we call here the method of _anti-extensions + valuations_, can be naturally applied to a number of non-classical logics. (shrink)

Is there anything irrational, or self-undermining, about having "inconsistent" attitudes of caring or valuing? In this paper, I argue that, contra suggestions of Harry Frankfurt and Charles Taylor, the answer is "No." Here I focus on "valuations," which are endorsed desires or attitudes. The proper characterization of what I call "valuational inconsistency" I claim, involves not logical form (valuing A and not-A), but rather the co-possibility of what is valued; valuations are inconsistent when there is no possible world in which (...) what is valued can co-exist. Essentially conflicting valuations, I show, are no worse for an agent than contingently conflicting ones, which are common and no threat to rationality or well-being. Partly based on reflections about a conflicted mother, who values staying at home and also having a career, I argue that valuational inconsistency does not render a person unable to act, does not make a person's actions ineffective because of vacillation, does not undermine a person's autonomy, and need not make a person dissatisfied with himself. I defend my characterization of inconsistency as an apt one; I offer some reasons to value inconsistency itself; and I draw out some implications for coherence thinking in moral philosophy. (shrink)

We give a valuation theoretic characterization for a real closed field to be recursively saturated. This builds on work in [9], where the authors gave such a characterization forκ-saturation, for a cardinal$\kappa \ge \aleph _0 $. Our result extends the characterization of Harnik and Ressayre [7] for a divisible ordered abelian group to be recursively saturated.

Retroviral vectors utilize the biochemical processes unique to retroviruses, to transfer genes with high efficiency into a wide variety of cell types in tissue culture and in living animals. With such vectors, the effect of newly introduced genes and the mechanism of gene expression can be studied in cell types so far refractory to other methods of transfer.

National minority women’s defense of nonliberal minority cultures that encompass sexist customs and rules has greatly perplexed liberal theorists. Many attempted to resolve this puzzle by attributing constrained agency to such women and dismissing their defense as unreasonable. This article argues that this liberal assessment of minority women’s position is philosophically indefensible and that the failure of mainstream liberalism to make sense of these women’s response indicates not that these women’s agency is compromised but rather that the liberal conception of (...) agency as autonomy at the heart of the liberal framework has limits in its crosscultural applicability. A conception of agency, valuational agency, that illuminates minority women’s agency is proposed as a more plausible alternative for radically pluralistic societies. -/- . (shrink)

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)

We define and study abstract valuation semantics for logics, an algebraically well-behaved version of valuation semantics. Then, in the context of the behavioral approach to the algebraization of logics, we show, by means of meaningful bridge theorems and application examples, that abstract valuations are suited to play a role similar to the one played by logical matrices in the traditional approach to algebraization.

This paper investigates how people conceive and evaluate nature through language, in a climate change context. With material consisting of 1,200 answers to open-ended questions in nationally representative surveys in Norway, we explore what semantic roles and values the respondents attribute to nature as well as to how they interact with the public debate about climate change. We observe that different conceptions and valuations of nature are tied to different perspectives on the climate change issue: some address the responsibilities of (...) causing climate change, others its consequences, and others yet its potential solutions. The study provides knowledge about the variety of conceptions of nature that can be mobilised by individuals and suggests that policy measures and public communication could benefit by taking this diversity into account. (shrink)

We show that the assertion that every vector space is a projective module implies the axiom of multiple choice and that the reverse implication does not hold in set theory weakened to permit the existence of atoms.

Programming artificial intelligence to make fairness assessments of texts through top-down rules, bottom-up training, or hybrid approaches, has presented the challenge of defining cross-cultural fairness. In this paper a simple method is presented which uses vectors to discover if a verb is unfair or fair. It uses already existing relational social ontologies inherent in Word Embeddings and thus requires no training. The plausibility of the approach rests on two premises. That individuals consider fair acts those that they would be willing (...) to accept if done to themselves. Secondly, that such a construal is ontologically reflected in Word Embeddings, by virtue of their ability to reflect the dimensions of such a perception. These dimensions being: responsibility vs. irresponsibility, gain vs. loss, reward vs. sanction, joy vs. pain, all as a single vector. The paper finds it possible to quantify and qualify a verb as fair or unfair by calculating the cosine similarity of the said verb’s embedding vector against FairVec—which represents the above dimensions. We apply this to Glove and Word2Vec embeddings. Testing on a list of verbs produces an F1 score of 95.7, which is improved to 97.0. Lastly, a demonstration of the method’s applicability to sentence measurement is carried out. (shrink)

Surprisal and Valuation in the Predictive Brain.

We study the algebraic implications of the non-independence property and variants thereof on infinite fields, motivated by the conjecture that all such fields which are neither real closed nor separably closed admit a henselian valuation. Our results mainly focus on Hahn fields and build up on Will Johnson’s “The canonical topology on dp-minimal fields” :1850007, 2018).

Epistemologists have addressed a variety of modal epistemic standings, such as sensitivity, safety, risk, and epistemic virtue. These concepts mark out the ways that beliefs can fail to track the truth, articulate the conditions needed for knowledge, and indicate ways to become a better epistemic agent. However, it is our contention that current ways of carving up epistemic modality ignore the complexities that emerge when individuals are embedded within a community and listening to a variety of sources, some of whom (...) are intentionally engaged in deception or bullshit. In this context we want our beliefs to be secure. In this paper we translate the epistemic modal standing of safety into a framework appropriate for social epistemology and argue for the importance of epistemic network-security and belief-security to be added to this framework. We discuss the virtues that are salient for promoting network-security and the vices that undermine it. In particular, we highlight monitoring, adjusting, and restructuring virtues and vices. Importantly, each of these vices can be other-regarding or self-regarding. For example, one tempting way of dealing with insecurity within a network is to completely cut oneself off from biased sources. However, we argue that this is a self-regarding restructuring vice because it closes oneself off from opportunities for epistemic growth. By contrast, an other-regarding restructuring vice would be to cut off others from hearing from sources of information that would make their network more secure. (shrink)

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 reports a Contingent Valuation application to estimate the non-market costs and benefits of hydro scheme developments in an Icelandic wilderness area. A deliberative group -based approach, called Market Stall, is compared to a control group consisting of conventional in-person interviews, in order to investigate flaws of Contingent Valuation, such as poor validity and protest responses. Perceived property rights suggested the use of willingness-to-accept in compensation for wilderness loss and willingness-to-pay for hydro scheme benefits. The study is (...) novel as it applies participant behaviour observation to gain insights into the shortcomings of conventional data collection modes. Main drawbacks with in-person interviews were found to be low motivation, standardised information and time pressure which hindered individuals from carefully considering their preferences. Market Stall performed better in the study: welfare estimates were more easily explained by socio-economic variables, the non-response rate was lower, and respondents were more engaged. Our research findings also suggest that participant behaviour can be used to supplement conventional validity tests. (shrink)

This paper reports a Contingent Valuation application to estimate the non-market costs and benefits of hydro scheme developments in an Icelandic wilderness area. A deliberative group-based approach, called Market Stall, is compared to a control group consisting of conventional in-person interviews, in order to investigate flaws of Contingent Valuation, such as poor validity and protest responses. Perceived property rights suggested the use of willingness-to-accept in compensation for wilderness loss and willingness-to-pay for hydro scheme benefits. The study is novel (...) as it applies participant behaviour observation to gain insights into the shortcomings of conventional data collection modes. Main drawbacks with in-person interviews were found to be low motivation, standardised information and time pressure which hindered individuals from carefully considering their preferences. Market Stall performed better in the study: welfare estimates were more easily explained by socio-economic variables, the non-response rate was lower, and respondents were more engaged. Our research findings also suggest that participant behaviour can be used to supplement conventional validity tests. (shrink)

Economics takes an individualistic approach to human behaviour. This is reflected in the use of 'contingent valuation' surveys to conduct cost benefit analysis for economic policy evaluation. An individual's valuation of a policy is assumed to be unaffected by the burdens it places on others. We report a survey experiment to test this supposition in the context of climate change policy. Willingness to pay for climate change mitigation was higher when richer individuals were to bear higher costs than (...) when, as is usual, no explicit information was provided about cost distribution. This result is inconsistent with the usual interpretation of contingent valuation data. It also suggests that the data may be biased indicators of policy acceptance. Additional survey questions suggest that a collective mode of reasoning is common. (shrink)

Vector logic is a mathematical model of the propositional calculus in which the logical variables are represented by vectors and the logical operations by matrices. In this framework, many tautologies of classical logic are intrinsic identities between operators and, consequently, they are valid beyond the bivalued domain. The operators can be expressed as Kronecker polynomials. These polynomials allow us to show that many important tautologies of classical logic are generated from basic operators via the operations called Type I and (...) Type II products. Finally, it is described a matrix version of the Fredkin gate that extends its properties to the many-valued domain, and it is proved that the filtered Fredkin operators are second degree Kronecker polynomials that cannot be generated by Type I or Type II products. (shrink)

Programming artificial intelligence to make fairness assessments of texts through top-down rules, bottom-up training, or hybrid approaches, has presented the challenge of defining cross-cultural fairness. In this paper a simple method is presented which uses vectors to discover if a verb is unfair or fair. It uses already existing relational social ontologies inherent in Word Embeddings and thus requires no training. The plausibility of the approach rests on two premises. That individuals consider fair acts those that they would be willing (...) to accept if done to themselves. Secondly, that such a construal is ontologically reflected in Word Embeddings, by virtue of their ability to reflect the dimensions of such a perception. These dimensions being: responsibility vs. irresponsibility, gain vs. loss, reward vs. sanction, joy vs. pain, all as a single vector. The paper finds it possible to quantify and qualify a verb as fair or unfair by calculating the cosine similarity of the said verb’s embedding vector against FairVec—which represents the above dimensions. We apply this to Glove and Word2Vec embeddings. Testing on a list of verbs produces an F1 score of 95.7, which is improved to 97.0. Lastly, a demonstration of the method’s applicability to sentence measurement is carried out. (shrink)

Elementary particles are considered as local oscillators under the influence of zeropoint fields. Such oscillatory behavior of the particles leads to the deviations in their path of motion. The oscillations of the particle in general may be considered as complex rotations in complex vector space. The local particle harmonic oscillator is analyzed in the complex vector formalism considering the algebra of complex vectors. The particle spin is viewed as zeropoint angular momentum represented by a bivector. It has been (...) shown that the particle spin plays an important role in the kinematical intrinsic or local motion of the particle. From the complex vector formalism of harmonic oscillator, for the first time, a relation between mass $m$ and bivector spin $S$ has been derived in the form $\varvec{\sigma }_3 mc^2{\mathcal {J}}_{\pm } =\lambda \Omega _{\mathbf{s}} \cdot \mathrm{{S}} {\mathcal {J}}_{\pm }$ . Where, $\Omega _{s}$ is the angular velocity bivector of complex rotations, $c$ is the velocity of light. The unit vector $\varvec{\sigma }_3$ acts as an operator on the idempotents ${\mathcal {J}}_{+}$ and ${\mathcal {J}}_{-}$ to give the eigen values $\lambda =\pm 1.$ The constant $\lambda $ represents two fold nature of the equation corresponding to particle and antiparticle states. Further the above relation shows that the mass of the particle may be interpreted as a local spatial complex rotation in the rest frame. This gives an insight into the nature of fundamental particles. When a particle is observed from an arbitrary frame of reference, it has been shown that the spatial complex rotation dictates the relativistic particle motion. The mathematical structure of complex vectors in space and spacetime is developed. (shrink)

Neuron diagrams are heavily employed in academic discussions of causation. Stephen Mumford and Rani Lill Anjum, however, offer an alternative approach employing vector diagrams, which this paper attempts to develop further. I identify three ways in which dispositionalists have taken the activities of powers to be related: stimulation, mutual manifestation, and contribution combination. While Mumford and Anjum do provide resources for representing contribution combination, which might be sufficient for their particular brand of dispositionalism, I argue that those resources are (...) not flexible enough to further accommodate either stimulation or mutual manifestation. Representational tools are provided to address these limitations, improving the general value of the vector model for dispositionalist approaches to causation. (shrink)

In this paper, the author revisits “the emotive theory of value” and argues that values are not entities but nothing other than “linguistic fictions”. Accordingly, valuations—i.e., valuing actions—can be defined as approving or disapproving attitudes of a subject to some object. In this perspective, values cannot be true or false: What we can do is just compare them with regard to strength. As a consequence, value judgments are to be understood as sentences which are used either to say that a (...) subject s values an object o positively or negatively, or to express (evince) a valuation. The author then shows some relations between normative and evaluative discourses. First, he claims that norms as well as valuations are not true or false. Second, he argues that both may be explained or justified, even if the former are usually justified teleologically whereas the latter are explained referring back to the subject's background and life‐style. Third, he notes that a legal order originates from the fact that valuations “crystallize” into norms. Finally, the author examines some further questions related to his analysis. In particular, he argues that the different realms of values, e.g., morals, aesthetics, politics, etc., do not correspond to different evaluative attitudes, but to different phenomena and diverse spheres of human life. (shrink)

Valuation consists in a positive or negative response by a subject S to an entity X. Any positive or negative response has a structure that involves a cognitive and a non-cognitive component, as well as a reason relationship between these. This structure is shown to be present in the explicit value judgement 'Hans is a kraut', and then also pointed out in the reflex-like feeding behaviour of a frog, where S treats X as providing an affordance. The conclusion is (...) that valuation need not involve mental states. The article ends with a discussion of the elusive question: what makes a response positive or negative? (shrink)

This paper uses the notion of Galois-connection to examine the relation between valuation-spaces and logics. Every valuation-space gives rise to a logic, and every logic gives rise to a valuation space, where the resulting pair of functions form a Galois-connection, and the composite functions are closure-operators. A valuation-space (resp., logic) is said to be complete precisely if it is Galois-closed. Two theorems are proven. A logic is complete if and only if it is reflexive and transitive. (...) A valuation-space is complete if and only if it is closed under formation of super-valuations. (shrink)

We study the theory of K-vector spaces with a predicate for the union X of an infinite family of independent subspaces. We show that if K is infinite then the theory is complete and admits quantifier elimination in the language of K-vector spaces with predicates for the n-fold sums of X with itself. If K is finite this is no longer true, but we still have that a natural completion is near-model-complete.

In this paper I provide an ontology for the co‐variant vectors, contra‐variant vectors and tensors that are familiar from General Relativity. This ontology is developed in response to a problem that Timothy Maudlin uses to argue against universals in the interpretation of physics. The problem is that if vector quantities are universals then there should be a way of identifying the same vector quantity at two different places, but there is no absolute identification of vector quantities, merely (...) a path‐relative one.My solution to the problem is to use the mathematical characterization of vectors as differential operators on scalar fields. On the proposed hypothesis a scalar field is a conjunctive state of affairs, and vector and tensor fields are relations instantiated by scalar fields. (shrink)

From a metaphysical point of view, it is important clearly to see the ontological difference between what is studied in mathematics and mathematical physics, respectively. In this respect, the paper is concerned with the vectors of classical physics. Vectors have both a scalar magnitude and a direction, and it is argued that neither conventionalism nor wholesale anti‐conventionalism holds true of either of these components of classical physical vectors. A quantification of a physical dimension requires the discovery of ontological order relations (...) among all the determinate properties of this dimension, as well as a conventional definition that connects the number one and mathematical unit vectors to determinate spatiotemporal physical entities. One might say that mathematics deals with numbers and vectors, but mathematical physics with scalar quantities and vector quantities, respectively. The International System of Units distinguishes between basic and derived scalar quantities; if a similar distinction should be introduced for the vector quantities of classical physics, then duration in directed time ought to be chosen as the basic vector quantity. The metaphysics of physical vectors is intimately connected with the metaphysics of time. From a philosophical‐historical point of view, the paper revives W. E. Johnson's distinction ‘determinates‐determinables’ and Hans Reichenbach's notion of ‘coordinative definition’. (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)

The paper contains a discussion on two kinds of coincidence experiments. First, a standard two-photon coincidence experiment is considered and it is shown that its outcomes are incompatible with any classical radiation theory because of the role of the state vector reduction phenomenon in such an experiment. In the second part of the paper a proposed new kind of photon coincidence experiment is discussed. The classical and quantum predictions for the outcomes of this experiment differ dramatically and therefore the (...) experiment should constitute a new limitation to the classical radiation theories. The proposed experiment should also yield information about the kinematics of the reduction of the state vector process. (shrink)

A standard way of representing causation is with neuron diagrams. This has become popular since the influential work of David Lewis. But it should not be assumed that such representations are metaphysically neutral and amenable to any theory of causation. On the contrary, this way of representing causation already makes several Humean assumptions about what causation is, and which suit Lewis’s programme of Humean Supervenience. An alternative of a vector diagram is better suited for a powers ontology. Causation should (...) be understood as connecting property types and tokens where there are dispositions towards some properties rather than others. Such a model illustrates how an effect is typically polygenous: caused by many powers acting with each other, and sometimes against each other. It models causation as a tendency towards an effect which can be counteracted. The model can represent cases of causal complexity, interference, over-determination and causation of absence (equilibrium). (shrink)