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Resolute readings of later Wittgenstein and the challenge of avoiding hierarchies in philosophy
(2011)
This dissertation addresses the question: How did later Wittgenstein aim to achieve his goal of putting forward a way of dissolving philosophical problems which centered on asking ourselves what we mean by our words – yet which did not entail any claims about the essence of language and meaning? This question is discussed with reference to “resolute” readings of Wittgenstein. I discuss the readings of James Conant, Oskari Kuusela, and Martin Gustafsson. I follow Oskari Kuusela’s claim that in order to fully appreciate how later Wittgenstein meant to achieve his goal, we need to clearly see how he aimed to do away with hierarchies in philosophy: Not only is the dissolution of philosophical problems via the method of clarifying the grammar of expressions to be taken as independent from any theses about what meaning must be – but furthermore, it is to be taken as independent from the dissolution of any particular problem via this method. As Kuusela stresses, this also holds for the problems involving rule-following and meaning: the clarification of the grammar of “rule” and “meaning” has no foundational status – it is nothing on which the method of clarifying the grammar of expressions as such were meant to in any way rely on. The lead question of this dissertation then is: What does it mean to come to see that the method of dissolving philosophical problems by asking “How is this word actually used?” does not in any way rely on the results of our having investigated the grammar of the particular concepts “rule” and “meaning”? What is the relation of such results – results such as “To follow a rule, [...], to obey an order, [...] are customs (uses, institutions)” or “The meaning of a word is its use in the language” – to this method? From this vantage point, I concern myself with two aspects of the readings of Gustafsson and Kuusela. In Gustafsson, I concern myself with his idea that the dissolution of philosophical problems in general “relies on” the very agreement which – during the dissolution of the rule-following problem – comes out as a presupposition for our talk of “meaning” in terms of rules. In Kuusela, I concern myself with his idea that Wittgenstein, in adopting a way of philosophical clarification which investigates the actual use of expressions, is following the model of “meaning as use” – which model he had previously introduced in order to perspicuously present an aspect of the actual use of the word “meaning”. This dissertation aims to show how these two aspects of Gustafsson’s and Kuusela’s readings still fail to live up to the vision of Wittgenstein as a philosopher who aimed to do away with any hierarchies in philosophy. I base this conclusion on a detailed analysis of which of the occasions where Wittgenstein invokes the notions of “use” and “application” (as also “agreement”) have to do with the dissolution of a specific problem only, and which have to do with the dissolution of philosophical problems in general. I discuss Wittgenstein’s remarks on rule-following, showing how in the dissolution of the rule-following paradox, notions such as “use”, “application”, and “practice” figure on two distinct logical levels. I then discuss an example of what happens when this distinction is not duly heeded: Gordon Baker and Peter Hacker’s idea that the rule-following remarks have a special significance for his project of dissolving philosophical problems as such. I furnish an argument to the effect that their idea that the clarification of the rules of grammar of the particular expression “following a rule” could answer a question about rules of grammar in general rests on a conflation of the two logical levels on which “use” occurs in the rule-following remarks, and that it leads into a regress. I then show that Gustafsson’s view – despite its decisive advance over Baker and Hacker – contains a version of that same idea, and that it likewise leads into a regress. Finally, I show that Kuusela’s idea of a special significance of the model “meaning as use” for the whole of the method of stating rules for the use of words is open to a regress argument of a similar kind as that he himself advances against Baker and Hacker. I conclude that in order to avoid such a regress, we need to reject the idea that the grammatical remark “The meaning of a word is its use in the language” – because of the occurrence of “use” in it – stood in any special relation to the method of dissolving philosophical problems by describing the use of words. Rather, we need to take this method as independent from this outcome of the investigation of the use of the particular word “meaning”.
Supermassive black holes are a fundamental component of the universe in general and of galaxies in particular. Almost every massive galaxy harbours a supermassive black hole (SMBH) in its center. Furthermore, there is a close connection between the growth of the SMBH and the evolution of its host galaxy, manifested in the relationship between the mass of the black hole and various properties of the galaxy's spheroid component, like its stellar velocity dispersion, luminosity or mass. Understanding this relationship and the growth of SMBHs is essential for our picture of galaxy formation and evolution. In this thesis, I make several contributions to improve our knowledge on the census of SMBHs and on the coevolution of black holes and galaxies. The first route I follow on this road is to obtain a complete census of the black hole population and its properties. Here, I focus particularly on active black holes, observable as Active Galactic Nuclei (AGN) or quasars. These are found in large surveys of the sky. In this thesis, I use one of these surveys, the Hamburg/ESO survey (HES), to study the AGN population in the local volume (z~0). The demographics of AGN are traditionally represented by the AGN luminosity function, the distribution function of AGN at a given luminosity. I determined the local (z<0.3) optical luminosity function of so-called type 1 AGN, based on the broad band B_J magnitudes and AGN broad Halpha emission line luminosities, free of contamination from the host galaxy. I combined this result with fainter data from the Sloan Digital Sky Survey (SDSS) and constructed the best current optical AGN luminosity function at z~0. The comparison of the luminosity function with higher redshifts supports the current notion of 'AGN downsizing', i.e. the space density of the most luminous AGN peaks at higher redshifts and the space density of less luminous AGN peaks at lower redshifts. However, the AGN luminosity function does not reveal the full picture of active black hole demographics. This requires knowledge of the physical quantities, foremost the black hole mass and the accretion rate of the black hole, and the respective distribution functions, the active black hole mass function and the Eddington ratio distribution function. I developed a method for an unbiased estimate of these two distribution functions, employing a maximum likelihood technique and fully account for the selection function. I used this method to determine the active black hole mass function and the Eddington ratio distribution function for the local universe from the HES. I found a wide intrinsic distribution of black hole accretion rates and black hole masses. The comparison of the local active black hole mass function with the local total black hole mass function reveals evidence for 'AGN downsizing', in the sense that in the local universe the most massive black holes are in a less active stage then lower mass black holes. The second route I follow is a study of redshift evolution in the black hole-galaxy relations. While theoretical models can in general explain the existence of these relations, their redshift evolution puts strong constraints on these models. Observational studies on the black hole-galaxy relations naturally suffer from selection effects. These can potentially bias the conclusions inferred from the observations, if they are not taken into account. I investigated the issue of selection effects on type 1 AGN samples in detail and discuss various sources of bias, e.g. an AGN luminosity bias, an active fraction bias and an AGN evolution bias. If the selection function of the observational sample and the underlying distribution functions are known, it is possible to correct for this bias. I present a fitting method to obtain an unbiased estimate of the intrinsic black hole-galaxy relations from samples that are affected by selection effects. Third, I try to improve our census of dormant black holes and the determination of their masses. One of the most important techniques to determine the black hole mass in quiescent galaxies is via stellar dynamical modeling. This method employs photometric and kinematic observations of the galaxy and infers the gravitational potential from the stellar orbits. This method can reveal the presence of the black hole and give its mass, if the sphere of the black hole's gravitational influence is spatially resolved. However, usually the presence of a dark matter halo is ignored in the dynamical modeling, potentially causing a bias on the determined black hole mass. I ran dynamical models for a sample of 12 galaxies, including a dark matter halo. For galaxies for which the black hole's sphere of influence is not well resolved, I found that the black hole mass is systematically underestimated when the dark matter halo is ignored, while there is almost no effect for galaxies with well resolved sphere of influence.
Corvino, Corvino and Schoen, Chruściel and Delay have shown the existence of a large class of asymptotically flat vacuum initial data for Einstein's field equations which are static or stationary in a neighborhood of space-like infinity, yet quite general in the interior. The proof relies on some abstract, non-constructive arguments which makes it difficult to calculate such data numerically by using similar arguments. A quasilinear elliptic system of equations is presented of which we expect that it can be used to construct vacuum initial data which are asymptotically flat, time-reflection symmetric, and asymptotic to static data up to a prescribed order at space-like infinity. A perturbation argument is used to show the existence of solutions. It is valid when the order at which the solutions approach staticity is restricted to a certain range. Difficulties appear when trying to improve this result to show the existence of solutions that are asymptotically static at higher order. The problems arise from the lack of surjectivity of a certain operator. Some tensor decompositions in asymptotically flat manifolds exhibit some of the difficulties encountered above. The Helmholtz decomposition, which plays a role in the preparation of initial data for the Maxwell equations, is discussed as a model problem. A method to circumvent the difficulties that arise when fast decay rates are required is discussed. This is done in a way that opens the possibility to perform numerical computations. The insights from the analysis of the Helmholtz decomposition are applied to the York decomposition, which is related to that part of the quasilinear system which gives rise to the difficulties. For this decomposition analogous results are obtained. It turns out, however, that in this case the presence of symmetries of the underlying metric leads to certain complications. The question, whether the results obtained so far can be used again to show by a perturbation argument the existence of vacuum initial data which approach static solutions at infinity at any given order, thus remains open. The answer requires further analysis and perhaps new methods.
The modeling and evaluation calculus FMC-QE, the Fundamental Modeling Concepts for Quanti-tative Evaluation [1], extends the Fundamental Modeling Concepts (FMC) for performance modeling and prediction. In this new methodology, the hierarchical service requests are in the main focus, because they are the origin of every service provisioning process. Similar to physics, these service requests are a tuple of value and unit, which enables hierarchical service request transformations at the hierarchical borders and therefore the hierarchical modeling. Through reducing the model complexity of the models by decomposing the system in different hierarchical views, the distinction between operational and control states and the calculation of the performance values on the assumption of the steady state, FMC-QE has a scalable applica-bility on complex systems. According to FMC, the system is modeled in a 3-dimensional hierarchical representation space, where system performance parameters are described in three arbitrarily fine-grained hierarchi-cal bipartite diagrams. The hierarchical service request structures are modeled in Entity Relationship Diagrams. The static server structures, divided into logical and real servers, are de-scribed as Block Diagrams. The dynamic behavior and the control structures are specified as Petri Nets, more precisely Colored Time Augmented Petri Nets. From the structures and pa-rameters of the performance model, a hierarchical set of equations is derived. The calculation of the performance values is done on the assumption of stationary processes and is based on fundamental laws of the performance analysis: Little's Law and the Forced Traffic Flow Law. Little's Law is used within the different hierarchical levels (horizontal) and the Forced Traffic Flow Law is the key to the dependencies among the hierarchical levels (vertical). This calculation is suitable for complex models and allows a fast (re-)calculation of different performance scenarios in order to support development and configuration decisions. Within the Research Group Zorn at the Hasso Plattner Institute, the work is embedded in a broader research in the development of FMC-QE. While this work is concentrated on the theoretical background, description and definition of the methodology as well as the extension and validation of the applicability, other topics are in the development of an FMC-QE modeling and evaluation tool and the usage of FMC-QE in the design of an adaptive transport layer in order to fulfill Quality of Service and Service Level Agreements in volatile service based environments. This thesis contains a state-of-the-art, the description of FMC-QE as well as extensions of FMC-QE in representative general models and case studies. In the state-of-the-art part of the thesis in chapter 2, an overview on existing Queueing Theory and Time Augmented Petri Net models and other quantitative modeling and evaluation languages and methodologies is given. Also other hierarchical quantitative modeling frameworks will be considered. The description of FMC-QE in chapter 3 consists of a summary of the foundations of FMC-QE, basic definitions, the graphical notations, the FMC-QE Calculus and the modeling of open queueing networks as an introductory example. The extensions of FMC-QE in chapter 4 consist of the integration of the summation method in order to support the handling of closed networks and the modeling of multiclass and semaphore scenarios. Furthermore, FMC-QE is compared to other performance modeling and evaluation approaches. In the case study part in chapter 5, proof-of-concept examples, like the modeling of a service based search portal, a service based SAP NetWeaver application and the Axis2 Web service framework will be provided. Finally, conclusions are given by a summary of contributions and an outlook on future work in chapter 6. [1] Werner Zorn. FMC-QE - A New Approach in Quantitative Modeling. In Hamid R. Arabnia, editor, Procee-dings of the International Conference on Modeling, Simulation and Visualization Methods (MSV 2007) within WorldComp ’07, pages 280 – 287, Las Vegas, NV, USA, June 2007. CSREA Press. ISBN 1-60132-029-9.
Does it have to be trees? : Data-driven dependency parsing with incomplete and noisy training data
(2011)
We present a novel approach to training data-driven dependency parsers on incomplete annotations. Our parsers are simple modifications of two well-known dependency parsers, the transition-based Malt parser and the graph-based MST parser. While previous work on parsing with incomplete data has typically couched the task in frameworks of unsupervised or semi-supervised machine learning, we essentially treat it as a supervised problem. In particular, we propose what we call agnostic parsers which hide all fragmentation in the training data from their supervised components. We present experimental results with training data that was obtained by means of annotation projection. Annotation projection is a resource-lean technique which allows us to transfer annotations from one language to another within a parallel corpus. However, the output tends to be noisy and incomplete due to cross-lingual non-parallelism and error-prone word alignments. This makes the projected annotations a suitable test bed for our fragment parsers. Our results show that (i) dependency parsers trained on large amounts of projected annotations achieve higher accuracy than the direct projections, and that (ii) our agnostic fragment parsers perform roughly on a par with the original parsers which are trained only on strictly filtered, complete trees. Finally, (iii) when our fragment parsers are trained on artificially fragmented but otherwise gold standard dependencies, the performance loss is moderate even with up to 50% of all edges removed.
Rainfall, snow-, and glacial melt throughout the Himalaya control river discharge, which is vital for maintaining agriculture, drinking water and hydropower generation. However, the spatiotemporal contribution of these discharge components to Himalayan rivers is not well understood, mainly because of the scarcity of ground-based observations. Consequently, there is also little known about the triggers and sources of peak sediment flux events, which account for extensive hydropower reservoir filling and turbine abrasion. We therefore lack basic information on the distribution of water resources and controls of erosion processes. In this thesis, I employ various methods to assess and quantify general characteristics of and links between precipitation, river discharge, and sediment flux in the Sutlej Valley. First, I analyze daily precipitation data (1998-2007) from 80 weather stations in the western Himalaya, to decipher the distribution of rain- and snowfall. Rainfall magnitude frequency analyses indicate that 40% of the summer rainfall budget is attributed to monsoonal rainstorms, which show higher variability in the orogenic interior than in frontal regions. Combined analysis of rainstorms and sediment flux data of a major Sutlej River tributary indicate that monsoonal rainfall has a first order control on erosion processes in the orogenic interior, despite the dominance of snowfall in this region. Second, I examine the contribution of rainfall, snow and glacial melt to river discharge in the Sutlej Valley (s55,000 km2), based on a distributed hydrological model, which covers the period 2000-2008. To achieve high spatial and daily resolution despite limited ground-based observations the hydrological model is forced by daily remote sensing data, which I adjusted and calibrated with ground station data. The calibration shows that the Tropical Rainfall Measuring Mission (TRMM) 3B42 rainfall product systematically overestimates rainfall in semi-arid and arid regions, increasing with aridity. The model results indicate that snowmelt-derived discharge (74%) is most important during the pre-monsoon season (April to June) whereas rainfall (56%) and glacial melt (17%) dominate the monsoon season (July-September). Therefore, climate change most likely causes a reduction in river discharge during the pre-monsoon season, which especially affects the orogenic interior. Third, I investigate the controls on suspended sediment flux in different parts of the Sutlej catchments, based on daily gauging data from the past decade. In conjunction with meteorological data, earthquake records, and rock strength measurements I find that rainstorms are the most frequent trigger of high-discharge events with peaks in suspended sediment concentrations (SSC) that account for the bulk of the suspended sediment flux. The suspended sediment flux increases downstream, mainly due to increases in runoff. Pronounced erosion along the Himalayan Front occurs throughout the monsoon season, whereas efficient erosion of the orogenic interior is confined to single extreme events. The results of this thesis highlight the importance of snow and glacially derived melt waters in the western Himalaya, where extensive regions receive only limited amounts of monsoonal rainfall. These regions are therefore particularly susceptible to global warming with major implications on the hydrological cycle. However, the sediment discharge data show that infrequent monsoonal rainstorms that pass the orographic barrier of the Higher Himalaya are still the primary trigger of the highest-impact erosion events, despite being subordinate to snow and glacially–derived discharge. These findings may help to predict peak sediment flux events and could underpin the strategic development of preventative measures for hydropower infrastructures.
The East African Plateau provides a spectacular example of geodynamic plateau uplift, active continental rifting, and associated climatic forcing. It is an integral part of the East African Rift System and has an average elevation of approximately 1,000 m. Its location coincides with a negative Bouguer gravity anomaly with a semi-circular shape, closely related to a mantle plume, which influences the Cenozoic crustal development since its impingement in Eocene-Oligocene time. The uplift of the East African Plateau, preceding volcanism, and rifting formed an important orographic barrier and tectonically controlled environment, which is profoundly influenced by climate driven processes. Its location within the equatorial realm supports recently proposed hypotheses, that topographic changes in this region must be considered as the dominant forcing factor influencing atmospheric circulation patterns and rainfall distribution. The uplift of this region has therefore often been associated with fundamental climatic and environmental changes in East Africa and adjacent regions. While the far-reaching influence of the plateau uplift is widely accepted, the timing and the magnitude of the uplift are ambiguous and are still subject to ongoing discussion. This dilemma stems from the lack of datable, geomorphically meaningful reference horizons that could record surface uplift. In order to quantify the amount of plateau uplift and to find evidence for the existence of significant relief along the East African Plateau prior to rifting, I analyzed and modeled one of the longest terrestrial lava flows; the 300-km-long Yatta phonolite flow in Kenya. This lava flow is 13.5 Ma old and originated in the region that now corresponds to the eastern rift shoulders. The phonolitic flow utilized an old riverbed that once drained the eastern flank of the plateau. Due to differential erosion this lava flow now forms a positive relief above the parallel-flowing Athi River, which is mimicking the course of the paleo-river. My approach is a lava-flow modeling, based on an improved composition and temperature dependent method to parameterize the flow of an arbitrary lava in a rectangular-shaped channel. The essential growth pattern is described by a one-dimensional model, in which Newtonian rheological flow advance is governed by the development of viscosity and/or velocity in the internal parts of the lava-flow front. Comparing assessments of different magma compositions reveal that length-dominated, channelized lava flows are characterized by high effusion rates, rapid emplacement under approximately isothermal conditions, and laminar flow. By integrating the Yatta lava flow dimensions and the covered paleo-topography (slope angle) into the model, I was able to determine the pre-rift topography of the East African Plateau. The modeling results yield a pre-rift slope of at least 0.2°, suggesting that the lava flow must have originated at a minimum elevation of 1,400 m. Hence, high topography in the region of the present-day Kenya Rift must have existed by at least 13.5 Ma. This inferred mid-Miocene uplift coincides with the two-step expansion of grasslands, as well as important radiation and speciation events in tropical Africa. Accordingly, the combination of my results regarding the Yatta lava flow emplacement history, its location, and its morphologic character, validates it as a suitable “paleo-tiltmeter” and has thus to be considered as an important topographic and volcanic feature for the topographic evolution in East Africa.
This Thesis puts its focus on the physics of neutron stars and its description with methods of numerical relativity. In the first step, a new numerical framework the Whisky2D code will be developed, which solves the relativistic equations of hydrodynamics in axisymmetry. Therefore we consider an improved formulation of the conserved form of these equations. The second part will use the new code to investigate the critical behaviour of two colliding neutron stars. Considering the analogy to phase transitions in statistical physics, we will investigate the evolution of the entropy of the neutron stars during the whole process. A better understanding of the evolution of thermodynamical quantities, like the entropy in critical process, should provide deeper understanding of thermodynamics in relativity. More specifically, we have written the Whisky2D code, which solves the general-relativistic hydrodynamics equations in a flux-conservative form and in cylindrical coordinates. This of course brings in 1/r singular terms, where r is the radial cylindrical coordinate, which must be dealt with appropriately. In the above-referenced works, the flux operator is expanded and the 1/r terms, not containing derivatives, are moved to the right-hand-side of the equation (the source term), so that the left hand side assumes a form identical to the one of the three-dimensional (3D) Cartesian formulation. We call this the standard formulation. Another possibility is not to split the flux operator and to redefine the conserved variables, via a multiplication by r. We call this the new formulation. The new equations are solved with the same methods as in the Cartesian case. From a mathematical point of view, one would not expect differences between the two ways of writing the differential operator, but, of course, a difference is present at the numerical level. Our tests show that the new formulation yields results with a global truncation error which is one or more orders of magnitude smaller than those of alternative and commonly used formulations. The second part of the Thesis uses the new code for investigations of critical phenomena in general relativity. In particular, we consider the head-on-collision of two neutron stars in a region of the parameter space where two final states a new stable neutron star or a black hole, lay close to each other. In 1993, Choptuik considered one-parameter families of solutions, S[P], of the Einstein-Klein-Gordon equations for a massless scalar field in spherical symmetry, such that for every P > P⋆, S[P] contains a black hole and for every P < P⋆, S[P] is a solution not containing singularities. He studied numerically the behavior of S[P] as P → P⋆ and found that the critical solution, S[P⋆], is universal, in the sense that it is approached by all nearly-critical solutions regardless of the particular family of initial data considered. All these phenomena have the common property that, as P approaches P⋆, S[P] approaches a universal solution S[P⋆] and that all the physical quantities of S[P] depend only on |P − P⋆|. The first study of critical phenomena concerning the head-on collision of NSs was carried out by Jin and Suen in 2007. In particular, they considered a series of families of equal-mass NSs, modeled with an ideal-gas EOS, boosted towards each other and varied the mass of the stars, their separation, velocity and the polytropic index in the EOS. In this way they could observe a critical phenomenon of type I near the threshold of black-hole formation, with the putative solution being a nonlinearly oscillating star. In a successive work, they performed similar simulations but considering the head-on collision of Gaussian distributions of matter. Also in this case they found the appearance of type-I critical behaviour, but also performed a perturbative analysis of the initial distributions of matter and of the merged object. Because of the considerable difference found in the eigenfrequencies in the two cases, they concluded that the critical solution does not represent a system near equilibrium and in particular not a perturbed Tolmann-Oppenheimer-Volkoff (TOV) solution. In this Thesis we study the dynamics of the head-on collision of two equal-mass NSs using a setup which is as similar as possible to the one considered above. While we confirm that the merged object exhibits a type-I critical behaviour, we also argue against the conclusion that the critical solution cannot be described in terms of equilibrium solution. Indeed, we show that, in analogy with what is found in, the critical solution is effectively a perturbed unstable solution of the TOV equations. Our analysis also considers fine-structure of the scaling relation of type-I critical phenomena and we show that it exhibits oscillations in a similar way to the one studied in the context of scalar-field critical collapse.