Hints towards the Emergent Nature of Gravity

A possible way out of the conundrum of quantum gravity is the proposal that general relativity (GR) is not a fundamental theory but emerges from an underlying microscopic description. Despite recent interest in the emergent gravity program within the physics as well as the philosophy community, an assessment of the theoretical evidence for this idea is lacking at the moment. We intend to fill this gap in the literature by discussing the main arguments in favour of the hypothesis that the metric field and its dynamics are emergent. First, we distinguish between microstructure inspired from GR, such as through quantization or discretization, and microstructure that is not directly motivated from GR, such as strings, quantum bits or condensed matter fields. The emergent gravity approach can then be defined as the view that the metric field and its dynamics are derivable from the latter type of microstructure. Subsequently, we assess in how far the following properties of (semi-classical) GR are suggestive of underlying microstructure: (1) the metric's universal coupling to matter fields, (2) perturbative non-renormalizability, (3) black hole thermodynamics, and (4) the holographic principle. In the conclusion we formalize the general structure of the plausibility arguments put forward.Comment: 36 pages, v2: minor additions, references added. Journal version in Studies in History and Philosophy of Modern Physic

Theory blending: extended algorithmic aspects and examples

In Cognitive Science, conceptual blending has been proposed as an important cognitive mechanism that facilitates the creation of new concepts and ideas by constrained combination of available knowledge. It thereby provides a possible theoretical foundation for modeling high-level cognitive faculties such as the ability to understand, learn, and create new concepts and theories. Quite often the development of new mathematical theories and results is based on the combination of previously independent concepts, potentially even originating from distinct subareas of mathematics. Conceptual blending promises to offer a framework for modeling and re-creating this form of mathematical concept invention with computational means. This paper describes a logic-based framework which allows a formal treatment of theory blending (a subform of the general notion of conceptual blending with high relevance for applications in mathematics), discusses an interactive algorithm for blending within the framework, and provides several illustrating worked examples from mathematics

Hypothesis Generation and Pursuit in Scientific Reasoning

This thesis draws a distinction between (i) reasoning about which scientific hypothesis to accept, (ii) reasoning concerned with generating new hypotheses and (iii) reasoning about which hypothesis to pursue. I argue that (ii) and (iii) should be evaluated according to the same normative standard, namely whether the hypotheses generated/selected are pursuit worthy. A consequentialist account of pursuit worthiness is defended, based on C. S. Peirce’s notion of ‘abduction’ and the ‘economy of research’, and developed as a family of formal, decision-theoretic models. This account is then deployed to discuss four more specific topics concerning scientific reasoning. First, I defend an account according to which explanatory reasoning (including the ‘inference to the best explanation’) mainly provides reasons for pursuing hypotheses, and criticise empirical arguments for the view that it also provides reasons for acceptance. Second, I discuss a number of pursuit worthiness accounts of analogical reasoning in science, arguing that, in some cases, analogies allow scientists to transfer an already well-understood modelling framework to a new domain. Third, I discuss the use of analogies within archaeological theorising, arguing that the distinction between using analogies for acceptance, generation and pursuit is implicit in methodological discussions in archaeology. A philosophical analysis of these uses is presented. Fourth, diagnostic reasoning in medicine is analysed from the perspective of Peircean abduction, where the conception of abduction as strategic reasoning is shown to be particularly important

Knowledge data discovery and data mining in a design environment

Designers, in the process of satisfying design requirements, generally encounter difficulties in, firstly, understanding the problem and secondly, finding a solution [Cross 1998]. Often the process of understanding the problem and developing a feasible solution are developed simultaneously by proposing a solution to gauge the extent to which the solution satisfies the specific requirements. Support for future design activities has long been recognised to exist in the form of past design cases, however the varying degrees of similarity and dissimilarity found between previous and current design requirements and solutions has restrained the effectiveness of utilising past design solutions. The knowledge embedded within past designs provides a source of experience with the potential to be utilised in future developments provided that the ability to structure and manipulate that knowledgecan be made a reality. The importance of providing the ability to manipulate past design knowledge, allows the ranging viewpoints experienced by a designer, during a design process, to be reflected and supported. Data Mining systems are gaining acceptance in several domains but to date remain largely unrecognised in terms of the potential to support design activities. It is the focus of this paper to introduce the functionality possessed within the realm of Data Mining tools, and to evaluate the level of support that may be achieved in manipulating and utilising experiential knowledge to satisfy designers' ranging perspectives throughout a product's development

Higher-Order Equational Pattern Anti-Unification

We consider anti-unification for simply typed lambda terms in associative, commutative, and associative-commutative theories and develop a sound and complete algorithm which takes two lambda terms and computes their generalizations in the form of higher-order patterns. The problem is finitary: the minimal complete set of generalizations contains finitely many elements. We define the notion of optimal solution and investigate special fragments of the problem for which the optimal solution can be computed in linear or polynomial time