Related papers: Higher-Order Platonism and Multiversism
Taking symmetric extensions can be considered as a generalisation of forcing, which produces a richer multiverse of models with and without the axiom of choice. We can study the structure of this multiverse using modal logic. In particular,…
Nominal Logic is a version of first-order logic with equality, name-binding, renaming via name-swapping and freshness of names. Contrarily to higher-order logic, bindable names, called atoms, and instantiable variables are considered as…
The quantum theory of ur objects postulates that all existing physical objects and their properties are constructed from fundamental objects called ur objects being described by an element of a two dimensional complex Hilbert space. This…
We analyze the applications of general relativity in relativistic astrophysics in order to solve the problem of describing the geometric and physical properties of the interior and exterior gravitational and electromagnetic fields of…
I survey physics theories involving parallel universes, which form a natural four-level hierarchy of multiverses allowing progressively greater diversity. Level I: A generic prediction of inflation is an infinite ergodic universe, which…
We recover the rays in the tensor product of Hilbert spaces within a larger class of so called `states of compoundness', structured as a complete lattice with the `state of separation' as its top element. At the base of the construction…
From a logical point of view, Stone duality for Boolean algebras relates theories in classical propositional logic and their collections of models. The theories can be seen as presentations of Boolean algebras, and the collections of models…
The new orthodoxy of quantum mechanics (QM) based on the decoherence approach requires many-worlds as an essential ingredient for logical consistency, and one may wonder what status to give to all these "other worlds". Here we advocate that…
The General Formal Ontology (GFO) is a top-level ontology that is designed to formally describe different domains of reality. Most recent advancements within GFO have been made in defining its modules of space and material objects, defining…
In the jet bundle description of Field Theories (multisymplectic models, in particular), there are several choices for the multimomentum bundle where the covariant Hamiltonian formalism takes place. As a consequence, several proposals for…
In this paper I argue that the fundamental aspect of our notion of time is that it defines an order relation, be it a total order relation between configurations of the world or just a partial order relation between events. This position is…
The construction of an ontology of scientific knowledge objects, presented here, is part of the development of an approach oriented towards the visualization of scientific knowledge. It is motivated by the fact that the concepts that are…
A number of recent papers treated the representation theory of partially ordered sets in unitary spaces with the so called orthoscalar relation. Such theory generalizes the classical theory which studies the representations of partially…
A choice of first-order variables for the characteristic problem of the linearized Einstein equations is found which casts the system into manifestly well-posed form. The concept of well-posedness for characteristic problems invoked is that…
According to scientific realism, science gives us an approximately true description of what the world is like. But what does it mean? In this chapter, we focus on the ontological and metaphysical aspects of this discussion. That is, we are…
In this work we analyze systems described by Lagrangians with higher order derivatives in the context of the Hamilton-Jacobi formalism for first order actions. Two different approaches are studied here: the first one is analogous to the…
There are several astrophysical configurations where one is interested only in the long-term dynamical evolution. Although the first-order version of this approximation is usually sufficient in applications, second-order corrections may be…
This article grew out of the theoretical part of my Master's thesis at the Faculty of Mathematics and Information Science at Ruprecht-Karls-Universit\"at Heidelberg under the supervision of PD Dr. Andreas Ott. Following the work of G.…
Despite the success of modern physics in formulating mathematical theories that can predict the outcome of quantum-scale experiments, the physical interpretations of these theories remain controversial. In this manuscript, we propose a new…
Recent critiques of the semantic conception of scientific theories suggest that a theory is not best formulated as a collection of models satisfying some set of kinematical or dynamical conditions. Thus it has been argued that additional…