The word 'reason' as used today is used ambiguous in its meaning. It may denote either of two mental faculties: a lower reason associated with discursive, linear thinking, and a higher reason associated with direct apprehension of first principles of mathematics and logic, and possibly also of moral and religious truths. These two faculties may be provisionally named Reason (higher reason) and rationality (lower reason). Common language and personal experience supply evidence of these being distinct faculties. So does classical philosophical (...) literature, the locus classicus being Plato's Divided Line analogy. -/- The effect of currently using a single word to denote both faculties not only produces confusion, but has had the effect of decreasing personal and cultural awareness of the higher faculty, Reason. Loss of a sense of Reason has arguably contributed to various psychological, social, moral, and spiritual problems of the modern age. This issue was also a central concern of 19th century Transcendentalists, who reacted to the radical empiricism of Locke. It would be advantageous to adopt consistent terms that make explicit a distinction between higher and lower reason. One possibility is to re-introduce the Greek philosophical terms nous and dianoia for the higher and lower reason, respectively. This discussion has certain parallels with the recent theories of McGilchrist (2009) concerning the increasingly left-brain hemisphere orientation of human culture. (shrink)

Depending on different positions in the debate on scientific realism, there are various accounts of the phenomena of physics. For scientific realists like Bogen and Woodward, phenomena are matters of fact in nature, i.e., the effects explained and predicted by physical theories. For empiricists like van Fraassen, the phenomena of physics are the appearances observed or perceived by sensory experience. Constructivists, however, regard the phenomena of physics as artificial structures generated by experimental and mathematical methods. My paper investigates the historical (...) background of these different meanings of phenomenon in the traditions of physics and philosophy. In particular, I discuss Newton’s account of the phenomena and Bohr’s view of quantum phenomena, their relation to the philosophical discussion, and to data and evidence in current particle physics and quantum optics. (shrink)

This article probes the question of what interpretations of quantum mechanics actually accomplish. In other domains, which are briefly considered, interpretations serve to make alien systematizations intelligible to us. This often involves clarifying the status of their implicit ontology. A survey of interpretations of non-relativistic quantum mechanics supports the evaluation that these interpretations make a contribution to philosophy, but not to physics. Interpretations of quantum field theory are polarized by the divergence between the Lagrangian field theory that led to the (...) Standard Model of Particle physics and the Algebraic quantum field theory, that discounts an ontology of particles. Ruetsche's interpretation, it is argued, offers a potential for loosening the sharp polarization that presently obtains. A brief evaluation focuses on the functional ontology of quantum field theory considered as an effective theory. (shrink)

The Cartan equations defining simple spinors (renamed “pure” by C. Chevalley) are interpreted as equations of motion in compact momentum spaces, in a constructive approach in which at each step the dimensions of spinor space are doubled while those of momentum space increased by two. The construction is possible only in the frame of the geometry of simple or pure spinors, which imposes contraint equations on spinors with more than four components, and then momentum spaces result compact, isomorphic to invariant-mass-spheres (...) imbedded in each other, since the signatures result steadily Lorentzian; starting from dimension four (Minkowski) up to dimension ten with Clifford algebra ℂℓ(1, 9), where the construction naturally ends. The equations of motion met in the construction are most of those traditionally postulated ad hoc: from Weyl equations for neutrinos (and Maxwell's) to Majorana ones, to those for the electroweak model and for the nucleons interacting with the pseudoscalar pion, up to those for the 3 baryon-lepton families, steadily progressing from the description of lower energy phenomena to that of higher ones. The 3 division algebras: complex numbers, quaternions and octonions appear to be strictly correlated with Clifford algebras and then with this spinor-geometrical approach, from which they appear to gradually emerge in the construction, where they play a basic role for the physical interpretation: at the third step complex numbers generate U(1), possible origin of the electric charge and of the existence of charged—neutral fermion pairs, explaining also easily the opposite charges of proton-electron. Another U(1) appears to generate the strong charge at the fourth step. Quaternions generate the signature of space-time at the first step, the SU(2) internal symmetry of isospin and, in the gauge term, the SU(2) L one, of the electroweak model at the third step; they are also at the origin of 3 families; in number equal to that of quaternion imaginary units. At the fifth and last step octonions generate the SU(3) internal symmetry of flavour, with SU(2) isospin subgroup and, in the gauge term, the one of color, correlated with SU(2) L of the electroweak model. These 3 division algebras seem then to be at the origin of charges, families and of the groups of the Standard model. In this approach there seems to be no need of higher dimensional (>4) space-time, here generated by the four Poincaré translations, and dimensional reduction from ℂℓ(1,9) to ℂℓ(1,3) is equivalent to decoupling of the equations of motion. This spinor-geometrical approach is compatible with that based on strings, since these may be expressed bilinearly (as integrals) in terms of Majorana–Weyl simple or pure spinors which are admitted by ℂℓ(1, 9) = R(32). (shrink)

A recent case in the Northern Territory of Australia has raised the issues of intra-racial rape and the legal recognition of traditional marriages between Indigenous people. The defendant in the Jamilmira case was charged with statutory rape of a 15-year-old girl. He argued that the girl’s status as his promised wife should lead to mitigation of his sentence. Members of the Northern Territory judiciary and others in the community were divided in their response to his claim. Ultimately the case led (...) to reform of the law in relation to the recognition of traditional marriage, a response which outraged some members of the Indigenous community. In this article I examine the various representations of culture and individuals that were utilised by ‘the law’ and how these representations informed the legal response. In the process I question the limits of my own role as a ‘white middle-class feminist’ in the context of explorations of law and culture. Is there a space to become involved in these debates without being complicit in fostering racism and prejudice and without reverting to stereotypes and cultural arrogance? (shrink)

This dissertation is centrally concerned with exploring obituaries as repositories of values. Obituaries are a publicly-available natural language source that are variably written for members of communities that are wide (nation- level) and narrow (city-level, or at the level of specific groups therein). Because they are explicitly summative, limited in size, and written for consumption by a public audience, obituaries may be expected to express concisely the aspects of their subjects’ lives that the authors (often family members living in the (...) same communities) found most salient or worthy of featuring. 140,599 obituaries nested in 832 newspapers from across the USA were scraped with permission from Legacy.com, an obituaries publisher. Obituaries were coded for the age at death and gender (female/male) of the deceased using automated algorithms. For each publishing newspaper, county-level median income, educational achievement (operationalized as percent of the population with a Bachelor’s degree or higher), and race and ethnicity were averaged across counties, weighting by population size. A Neo4J graph database was constructed using WordNet and the University of South Florida Free Association Norms datasets. Each word in each obituary inthe corpus was lemmatized. The shortest path through the WordNet graph from each lemma to 30 Schwartz value prototype words published by Bardi, Calogero, and Mullen (2008) was then recorded. From these path lengths, a new measure, “word-by-hop,” was calculated for each Schwartz value to reflect the relative lexical distance between each obituary and that Schwartz value. Of the Schwartz values, Power, Conformity, and Security were most indicated in the corpus, while Universalism, Hedonism, and Stimulation were least indicated. A series of seven two-level regression models suggested that, across Schwartz values, newspaper community accounted for the greatest amount of word-by-hop variability in the corpus. The best-fitting model indicated a small, negative effect of female status across Schwartz values. Unexpectedly, Hedonism and Conformity, which had conceptually opposite prototype words, were highly correlated, possibly indicating that obituary authors “compensate” for describing the deceased in a hedonistic way by concurrently emphasizing restraint. Future research could usefully further expand word-by-hop and incorporate individual-level covariates that match the newspaper-level covariates used here. (shrink)

El principio de correspondencia y el punto de vista de la complementariedad constituyen los sucesivos ejes alrededor de los cuales gira la interpretación de Bohr de la teoría cuántica. En este trabajo sostenemos que el concepto kantiano de analogía resulta un hilo conductor que permite comprender satisfactoriamente tal desarrollo histórico del pensamiento de Bohr. Mostraremos que el principio de correspondencia guía la búsqueda de analogías en la experiencia, mientras que desde el punto de vista de la complementariedad Bohr establece analogías (...) simbólicas. The principle of correspondence and, later, the viewpoint of complementarity are the axes around which Bohr´s interpretation of quantum theory rotates. In this paper we claim that the Kantian notion of analogy enables a satisfactory understanding of such historical development of Bohr's thought. We shall show that the principle of correspondence guides the search for analogies in experience, while from the viewpoint of complementarity Bohr establishes symbolic analogies. (shrink)

We use tools of mathematical logic to analyse the notion of a path on a complex algebraic variety, and are led to formulate a “rigidity” property of fundamental groups specific to algebraic varieties, as well as to define a bona fide topology closely related to etale topology. These appear as criteria for ℵ1-categoricity, or rather stability and homogeneity, of the formal countable language we propose to describe homotopy classes of paths on a variety, or equivalently, its universal covering space.Technically, for (...) a variety A defined over a finite field extension of the field Q of rational numbers, we introduce a countable language L describing the universal covering space of A, or, equivalently, homotopy classes of paths in A. Under some assumptions on A source we show that the universal covering space of A is an analytic Zariski structure [26]), and present an Lω1ω)-sentence axiomatising the class containing the structure and that is stable and homogeneous over elementary submodels. The “rigidity” condition on fundamental groups says that projection of the fundamental group of a variety is the fundamental group of the projection, up to finite index and under some irreducibility assumptions, and is used to prove that the projection of an irreducible closed set is closed in the analytic Zariski structure.In particular, we define an analytic Zariski structure on the universal covering space of an Abelian variety defined over a finite extension of the field Q of rational numbers. (shrink)

Understanding a sentence and integrating it into the discourse depends upon the identification of its focus, which, in spoken German, is marked by accentuation. In the case of written language, which lacks explicit cues to accent, readers have to draw on other kinds of information to determine the focus. We study the joint or interactive effects of two kinds of information that have no direct representation in print but have each been shown to be influential in the reader’s text comprehension: (...) i. the (low-level) rhythmic-prosodic structure that is based on the distribution of lexically stressed syllables, and ii. the (high-level) discourse context that is grounded in the memory of previous linguistic content. Systematically manipulating these factors, we examine the way readers resolve a syntactic ambiguity involving the scopally ambiguous focus operator auch (engl. `too') in both oral (Experiment 1) and silent reading (Experiment 2). The results of both experiments attest that discourse context and local linguistic rhythm conspire to guide the syntactic and, concomitantly, the focus-structural analysis of ambiguous sentences. We argue that reading comprehension requires the (implicit) assignment of accents according to the focus structure and that, by establishing a prominence profile, the implicit prosodic rhythm directly affects accent assignment. (shrink)

Dual trends are colliding in U.S. courts. The first trend is a tidal wave of cases requiring courts to engage the domestic laws of foreign legal systems; globalization is the principal driver of this escalation. The second trend is a profound and ever-increasing skepticism of our ability to understand foreign law; the literature of pluralism and postmodernism has illuminated the uniquely local, language-dependent, and culturally embedded nature of law. Courts cope with this dissonance by finding some way to avoid the (...) application of foreign law. However, these outcomes are problematic because parties are denied access to court or have their rights and responsibilities determined pursuant to the incorrect law. This Article offers an exposition of lexical meaning to explain the source of these oppositional trends and to illuminate possible solutions. Legal words and ideas transcend geographic, social, and cultural boundaries. For this reason, the words of another legal system look familiar and, thus, appear knowable to an outsider. Yet autonomous national legal systems tend to tailor the meanings of these shared words for idiosyncratic purposes. Thus, ironically even paradoxically the more commonly a word is used, the less predictable is its meaning. This differentiation of meanings makes actual knowledge of the foreign law difficult to achieve. As a framework for examining this phenomenon, this Article demonstrates that the common meaning of a word is a limited resource. The common meaning of a word erodes when legal systems assign a new meaning to a shared word. Idiosyncratic meanings are useful and generative, but they also introduce an important negative externality because the common meaning of a word is essentially the starting point for measuring the meaning of that word in a foreign system. The more robust the common meaning, the lower the measurement costs. The prototypical solutions to common-pool problems privatization and regulation are infeasible here. Moreover, ubiquitous efforts to unify, approximate, or harmonize laws tend to exacerbate the problem rather than help solve it. We could drop the pretense that we are able to understand foreign law and eliminate the demand for it. Alternatively, if the doctrines are going to presume familiarity with foreign law, we must address the supply side and ensure that courts are, in fact, better able to understand the idiosyncracies of foreign law. (shrink)

According to John Cassian, God bestows his supernatural grace only upon men who transcend Christian legalism and take up Christ’s consilium perfectionis. God’s grace is merited by men who strive to perfection. In so doing, they place themselves sub gratia Christi. For Cassian, the true Christian community is composed solely of ascetics who have set themselves apart from ordinary Christians in order to attain the highest good to which human nature must aspire – theperennial contemplation of God. As Cassian has (...) it, it is the main concern of the ascetic bishop to convey to ordinary Christians the call to perfection. (shrink)

A certain class of geometric objects is considered against the background of a classical gauge field associated with an arbitrary structural Lie group. It is assumed that the components of these objects depend on the gauge potentials and their first derivatives, and also on certain gauge-dependent parameters whose properties are suggested by the interaction of an isotopic spin particle with a classical Yang-Mills field. It is shown that the necessary and sufficient conditions for the invariance of the given objects under (...) a finite gauge transformation are embodied in a set of three relations involving the derivatives of their components. As a special case these so-called invariance identities indicate that there cannot exist a gauge-invariant Lagrangian that depends on the gauge potentials, the interaction parameters, and the4-velocity components of a test particle. However, the requirement that the equations of motion that result from such a Lagrangian be gauge-invariant, uniquely determines the structure of these equations. (shrink)

In this paper I reflect on the nature of mathematical beauty, and examine the connections between mathematics and the arts. I employ Plutarch’s distinction between the intelligible and the sensible, to compare the beauty of mathematics with the beauties of music, poetry and painting. While the beauty of mathematics is almost exclusively intelligible, and the beauties of these arts primarily sensible, it is pointed out that the latter share with mathematics a certain kind of intelligible beauty. The paper also contains (...) reflections on the formal beauty and timelessness of mathematics, beauty as richness flowing from simplicity, form and content in mathematics, and mathematics and fiction. It concludes with some remarks on the question of why mathematical beauty is so little appreciated by non-mathematicians. (shrink)

RESUMEN Se estudia el vínculo entre literatura y derecho en el pensamiento de Jacques Derrida. Se indican algunos recorridos de lectura y se dilucida lo que se entiende por literatura como institución, y su vínculo y alcances en relación con el plagio y con el derecho a decirlo todo en literatura. ABSTRACT The paper examines the connection between literature and law in the thought of Jacques Derrida. On the basis of certain readings, it explains literature as an institution, as well (...) as its relation and significance with respect to plagiarism and the right to say anything in literature. (shrink)

In this paper, we use the differential forms of three-dimensional Euclidean space to realize a Clifford algebra which is isomorphic to the algebra of the Pauli matrices or the complex quaternions. This is an associative vector-antisymmetric tensor algebra with division: We provide the algebraic inverse of an eight-component spinor field which is the sum of a scalar + vector + pseudovector + pseudoscalar. A surface of singularities is defined naturally by the inverse of an eight-component spinor and corresponds to a (...) generalized Minkowski “double” light cone in the parameter space. A general description of finite spatial rotations, which utilizes the Baker-Campbell-Hausdorff formula, generalizes the usual infinitesimal treatments of the rotation group. We derive an explicit expression for the angle corresponding to two successive finite rotations in any direction. We also discuss Lorentz transformations and duality rotations of the electromagnetic field and exhibit a relationship between the algebraic inverse and a duality rotated field. Using a combined transformation, one can always transform an arbitrary electromagnetic field (E≠0) into a pure electric field, but never into a pure magnetic field. (shrink)