Knowledge, Belief, and the A Priori

The notion of the a priori underwent several changes\ud since the time it came into existence in the Middle Ages.\ud Originally it had been used to mark a certain form of\ud argument, an argument that proceeds from what is prior to\ud what is later, from cause to effect: demonstratio procedens\ud ex causis ad effectum = demonstratio a priori. But this\ud changed with Kant, for whom it meant not a form of\ud argument but rather some special kind of knowledge (or\ud elements thereof), namely knowledge that (a) is independent\ud of particular experiences and (b) that makes experience\ud in general (Erfahrung überhaupt) possible. Tied up\ud with consciousness and the transcendental unity of\ud apperception, Kant"s understanding of the a priori was in\ud the spirit of his transcendental philosophy. But this\ud understanding changed again with the rise of analytic\ud philosophy, in which we still find the first characteristic but\ud not the second anymore. The idea of Erfahrung überhaupt\ud was given up, partly because one naturally wondered what\ud exactly this notion of experience in general, or experience\ud universally conceived, should be. Where should we get it\ud from, if not by way of abstraction and generalization from\ud individual cases of experience? And would this not make it\ud an empirical concept, so that the whole project of asking\ud for the conditions of its possibility would not lead us to the\ud kind of certainty, necessity and universality we expect from\ud a priori knowledge? There would be no guarantee that in\ud the future we would not make discoveries that would give\ud us new kinds of experiences or that would show us our\ud experiences in a new light. Thus, we would have to admit\ud that these experiences did not satisfy the conditions of\ud experience we had set up originally. The a priori conditions\ud would have to be revised

Local FEM Analysis of Composite Beams and Plates: Free-Edge effect and Incompatible Kinematics Coupling

The use of composite laminated structures helped in the last two decades to reduce overall weight of transportation structures. As a consequence the energy needed to power those transportation means is reduced and hence fuel and monetary resources are economized and emissions are reduced. Especially the aerospace sector has a high need of a favourable weight to power ratio. Orthotropic laminated structures are able to provide a higher stiffness combined with a lower density compared to monolithic isotropic materials used in the past. It seems hence, that they are perfect for the use in even a wider spectrum of applications. However through the assembly of differently layers, it is more difficult to model and predict the structures mechanical response to outer loadings. In the recent past different computational methods were developed. Most of them under the scope of being capable to deliver very detailed results of the global behaviour of the structure but also of the interaction between the different layers of the laminate. As a major drawback, a detailed result comes with high computational costs. Hence a need for a good compromise between costs and accuracy has to be found. This benefits especially from the fact that stress concentrations in composites occur mainly in local domains of the structure. The use of detailed models only in those local domains of interest seems therefore straightforward. Examples for such local domains with stress concentrations are laminates with free edges. At the interface between two layers with different elastic properties the stresses have singular behaviour in the immediate vicinity of the free edge, assuming linear elastic material behaviour. This is due to the material discontinuity and the resulting mismatch of the elastic properties at the interface of the layers, the condition of traction-free edges and the equilibrium between the layers. Therefore they are critical to promote delamination. An adequate analysis method for this would be the use of a full three-dimensional analysis model. However it’s computational cost is significant. Composites are often rather thin planar structures, allowing the use of reduced dimensional models, which are also more attractive through their reduced computational cost. Therefore different reduced models with their appropriate hypotheses in the thickness direction are under consideration in this work. Via different thickness expansion functions suitable kinematical theories, are expressed. The Carrera’s Unified Formulation (CUF) is used to have a common base to build the models with the different kinematical theories. The CUF allowing not only purely displacement based models using the Principle of Virtual Displacements (PVD), but also mixed stress and displacement based models with the Reissner’s Mixed Variational Theorem (RMVT). In the first part of this work, the reduced dimensional modelling approaches are compared. Two main class are presented: Equivalent Single Layer (ESL) models treating the layered structure like one homogenous plate of equal mechanical properties, and the Layer Wise approach, treating each layer independently. Subsequently their capabilities to capture the appearing singularities are compared. In order to have a comparable measurement of those singularities, the obtained stress distributions will be expressed via a power law function, which has a priori a singular behaviour. Only two parameters fully describe therefore the singular stress components in the vicinity of the free edge. With the help of these two parameters not only the different models capabilities will be compared, but also the free edge effect itself will be measured and compared for different symmetrical laminates and the case of extensional and uniform bending load. The results for all laminates under both load cases confirm the before stated need for rather complex models in the vicinity of the free edge. However far from the free edges, in the composite plates centre, no significant difference can be noted for rather simple models. The second part of this work is therefore dedicated to the coupling of kinematically incompatible models. The use of costly expensive complex models is restricted to local domains of interest, while economic simple models will model the global domain. The Extended Variational Formulation (XVF) is identified as the most suitable way to couple the kinematically heterogenous but dimensional homogenous models. As it uses a configuration with one common interface without domain overlap, the additional efforts for establishing the coupling are limited. Further the XVF offers the possibility to adapt the conditions imposed at the interface using a single scalar parameter. It will be shown that for the homogenous dimensional problem under consideration only two different conditions can be imposed by this parameter. One matching the strong conditions imposed by the classical Multi Point Constrains (MPC) and a second one providing a weak condition. The last one is shown to provide the possibility to reduce further the domain using the complex kinematical model, without the loss of local precision. As this is the first application of the XVF towards composite structures, the need for a new coupling operator was identified. A new form is proposed, tested and its robustness will be evaluated

On Wittgenstein on Certainty

In the preface to On Certainty Anscombe and von Wright say that in 1949 Malcolm suggested to Wittgenstein to think again about Moore’s “Defense of Common Sense” (1925) and “Proof of an External World” (1939). Malcolm himself had written on the issue in “Defending Common Sense” (1949). In the preface to the Philosophical Investigations Wittgenstein quotes Nestroy saying that there is usually very little progress in philosophy. But I think some progress has been made from Moore and Malcolm to Wittgenstein regarding skepticism. There is more awareness of practice and perspective and this opens the discussion in novel ways. But it also gives rise to new problems, in particular of morality and relativity

How Pictorial is Chinese? And Does it Matter?

It has often been said that the Chinese script is pictorial or ideographic, and that this is one of the reasons why Chinese tend to think more analogically than logically, and why in the past the natural sciences developed to a lesser degree in China than in the West. These are strong claims. They have often been oversimplified and exaggerated, but I think there is something to be said for them. Here I will focus on the first question. I will argue that Chinese characters still have semantic features that create image-like qualities in a wider sense: not mere resemblances between sign and object, but family resemblances in semantic fields. The fact that Chinese is an isolating and monosyllabic language is essential in this

"Bedeutungserlebnis" and "Lebensgefühl" in Kant and Wittgenstein: Responsibility and the Future

This essay is about the inner and the outer in Wittgenstein, in particular his notion of “meaning experience”. Wittgenstein reminds us that we should not think of the inner, psychological the way we think about the outer, physical world. Again and again he keeps returning to certain views about the soul and our mental states. I think that it is not only therapy he has in mind. I will contrast certain aesthetic and ethical aspects of his thoughts with views from Kant

Aesthetics and Morality in Kant and Confucius. A Second Step

In the framework of his transcendental philosophy, Kant strictly separates morality from aesthetics. The pleasure in the good and the pleasure in the beautiful are two different kinds of pleasure (Arten des Wohlgefallens). As a consequence, a moral act as such cannot be beautiful. It is only in a second step that Kant indicates possible connections, in his comments on aesthetic ideas, symbolism, the sensus communis, and education in general. In Confucius on the other hand we do not find such a radical separation between beauty and morality. Ritual is a source of both. Moral acts can be beautiful. One might wonder whether Confucius missed a point, or whether Kant overdid the separation. Or is it that their conceptions are so fundamentally different that they cannot easily be translated and identified across different philosophical traditions

Where after all are the Meanings? A Defense of Internalism. Searle versus Putnam

There has been recent dispute between Putnam and Searle over whether meanings are “in the head”. Putnam makes use of Twin-Earth thought experiments to show that our mental states alone cannot determine what we refer to (and thus “mean”) and that we rely also on external factors, which are not “in the head”. This suggests to me that we in some way mean more than we actually know. Searle on the other hand makes use of what he calls “Intentional contents”, “conditions of satisfaction”, and “self-referentiality”, to show that meanings can be said to be in the head. It seems to me that an internalist account as we find it in Husserl or Searle is closer to what is going on when we mean something

Chinese Ways of Words

According to the so-called Sapir-Whorf hypothesis, a language influences the mind of its user. This is more or less trivial, but the problems are in the details. It is difficult to make precise what those influences are, be it in general philosophical or in particular empirical-cultural terms. I will give an account of what I take to be basic aesthetic and grammatical features of the Chinese language compared with what we find in Western languages such as Latin or greek. Then I will indicate what I take to be cultural differences and discuss whether these might be the result of differences in language structure

Does Thought Happen in the Brain?

What is the nature of thought? Is thought linguistic and some kind of silent speech? Or is it pre-linguistic and some kind of association of ideas and images in the mind? Does it happen in the brain? I will focus on the last question, but also say something about the other two. I will present a simple thought experiment to show that thought must somehow happen in the brain. But then I will soften the impression this might give by pointing out what is needed to read those thoughts. Simply put, ontologically thought is in the brain, epistemologically it is not