14,573 research outputs found
Argument-based Belief in Topological Structures
This paper combines two studies: a topological semantics for epistemic
notions and abstract argumentation theory. In our combined setting, we use a
topological semantics to represent the structure of an agent's collection of
evidence, and we use argumentation theory to single out the relevant sets of
evidence through which a notion of beliefs grounded on arguments is defined. We
discuss the formal properties of this newly defined notion, providing also a
formal language with a matching modality together with a sound and complete
axiom system for it. Despite the fact that our agent can combine her evidence
in a 'rational' way (captured via the topological structure), argument-based
beliefs are not closed under conjunction. This illustrates the difference
between an agent's reasoning abilities (i.e. the way she is able to combine her
available evidence) and the closure properties of her beliefs. We use this
point to argue for why the failure of closure under conjunction of belief
should not bear the burden of the failure of rationality.Comment: In Proceedings TARK 2017, arXiv:1707.0825
Mirror Symmetry and Other Miracles in Superstring Theory
The dominance of string theory in the research landscape of quantum gravity
physics (despite any direct experimental evidence) can, I think, be justified
in a variety of ways. Here I focus on an argument from mathematical fertility,
broadly similar to Hilary Putnam's 'no miracles argument' that, I argue, many
string theorists in fact espouse. String theory leads to many surprising,
useful, and well-confirmed mathematical 'predictions' - here I focus on mirror
symmetry. These predictions are made on the basis of general physical
principles entering into string theory. The success of the mathematical
predictions are then seen as evidence for framework that generated them. I
attempt to defend this argument, but there are nonetheless some serious
objections to be faced. These objections can only be evaded at a high
(philosophical) price.Comment: For submission to a Foundations of Physics special issue on "Forty
Years Of String Theory: Reflecting On the Foundations" (edited by G. `t
Hooft, E. Verlinde, D. Dieks and S. de Haro)
Every hierarchy of beliefs is a type
When modeling game situations of incomplete information one usually considers
the players' hierarchies of beliefs, a source of all sorts of complications.
Hars\'anyi (1967-68)'s idea henceforth referred to as the "Hars\'anyi program"
is that hierarchies of beliefs can be replaced by "types". The types constitute
the "type space". In the purely measurable framework Heifetz and Samet (1998)
formalize the concept of type spaces and prove the existence and the uniqueness
of a universal type space. Meier (2001) shows that the purely measurable
universal type space is complete, i.e., it is a consistent object. With the aim
of adding the finishing touch to these results, we will prove in this paper
that in the purely measurable framework every hierarchy of beliefs can be
represented by a unique element of the complete universal type space.Comment: 19 page
Relational Spacetime Ontology
In the aftermath of the rediscovery of Einsteinâs hole argument by Earman and Norton (1987), we hear that the ontological relational/substantival debate over the status of spacetime seems to have reached stable grounds. Despite Einsteinâs early intention to cast GRâs spacetime as a relational entity Ă la Leibniz-Mach, most philosophers of science feel comfortable with the now standard sophisticated substantivalist (SS) account of spacetime. Furthermore, most philosophers share the impression that although relational accounts of certain highly restricted models of GR are viable, at a deep down level, they require substantival spacetime structures. SS claims that although manifold spacetime points do not enjoy the sort of robust existence provided by primitive identity, it is still natural to be realistic about the existence of spacetime as an independent entity in its own right. It is argued that since the bare manifold lacks the basic spacetime structures âsuch as geometry and inertia- one should count as an independent spacetime the couple manifold +metric (M, g). The metric tensor field of GR encodes inertial and metrical structure so, in a way, it plays the explanatory role that Newtonian absolute space played in classical dynamics. In a nutshell, according to the SS account of spacetime, one should view the metric field of GR as the modern version of a realistically constructed spacetime since it has the properties âor contains the structures- that Newtonian space had. I will try to dismantle the widespread impression that a relational account of full GR is implausible. To do so, I will start by highlighting that when turning back to the original Leibniz-Newton dispute one sees that substantivalism turns out prima facie triumphant since Newton was able to successfully formulate dynamics. However, to give relationalism a fair chance, one can also put forward the following hypothetical questions: What if Leibniz âor some leibnizian- had had a good relational theory? What role would geometry play in this type of theory? Would it be natural to view geometry and inertia as intrinsic properties of substantival space âif not spacetime? Would it still seem natural to interpret the metric field of GR along substantival lines regardless of the fact that it also encodes important material properties such as energy-momentum? After bringing these questions out into the light I will cast some important doubts on the substantival (SS) interpretation of the metric field. Perhaps the metric turns out to be viewed as a relational matter field. Finally, to strengthen the relational account of spacetime I expect to remove the possible remaining interpretative tension by briefly discussing the relevance of two important facts: i) Dynamical variables are usually linked to material objects in physical theories. The metric field of GR is a dynamical object so, I claim, it should be viewed as a matter field. ii) Barbour and Bertotti (BB2, 1982) have provided and alternative formulation of classical dynamics. They provide a âgenuinely relational interpretation of dynamicsâ (Pooley & Brown 2001). Geometry and inertia become âcontra SS- relational structures in BB2
Nontrivial quantum effects in biology: A skeptical physicists' view
Invited contribution to "Quantum Aspects of Life", D. Abbott Ed. (World
Scientific, Singapore, 2007).Comment: 15 pages, minor typographical errors correcte
Resolving the Structure of Black Holes: Philosophizing with a Hammer
We give a broad conceptual review of what we have learned about black holes
and their microstate structure from the study of microstate geometries and
their string theory limits. We draw upon general relativity, supergravity,
string theory and holographic field theory to extract universal ideas and
structural features that we expect to be important in resolving the information
problem and understanding the microstate structure of Schwarzschild and Kerr
black holes. In particular, we emphasize two conceptually and physically
distinct ideas, with different underlying energy scales: a) the transition that
supports the microstate structure and prevents the formation of a horizon and
b) the representation of the detailed microstate structure itself in terms of
fluctuations around the transitioned state. We also show that the supergravity
mechanism that supports microstate geometries becomes, in the string theory
limit, either brane polarization or the excitation of non-Abelian degrees of
freedom. We thus argue that if any mechanism for supporting structure at the
horizon scale is to be given substance within string theory then it must be
some manifestation of microstate geometries.Comment: 32 pages + reference
Computing with Coloured Tangles
We suggest a diagrammatic model of computation based on an axiom of
distributivity. A diagram of a decorated coloured tangle, similar to those that
appear in low dimensional topology, plays the role of a circuit diagram.
Equivalent diagrams represent bisimilar computations. We prove that our model
of computation is Turing complete, and that with bounded resources it can
moreover decide any language in complexity class IP, sometimes with better
performance parameters than corresponding classical protocols.Comment: 36 pages,; Introduction entirely rewritten, Section 4.3 adde
- âŚ