Related papers: Contextual completeness and a classification schem…
Quantum mechanics is a fundamentally probabilistic theory (at least so far as the empirical predictions are concerned). It follows that, if one wants to properly understand quantum mechanics, it is essential to clearly understand the…
The idea of monotonicity (or positive-definiteness in the linear case) is shown to be the central theme of the solution theories associated with problems of mathematical physics. A "grand unified" setting is surveyed covering a…
The process of canonical quantization is redefined so that the classical and quantum theories coexist when \hbar>0, just as they do in the real world. This analysis not only supports conventional procedures, it also reveals new quantization…
When we test a theory using data, it is common to focus on correctness: do the predictions of the theory match what we see in the data? But we also care about completeness: how much of the predictable variation in the data is captured by…
In glaring contrast to its indisputable century-old experimental success, the ultimate objects and meaning of quantum physics remain a matter of vigorous debate among physicists and philosophers of science. This article attempts to shed new…
The long lasting discussion on the completeness of quantum theory (QT) has not yet come to an end. The discussion is impeded by the lack of a clear understanding of what makes up the contents of a theory of physics in general and of QT…
I argue that, contrary to the standard view, one cannot understand the structure and nature of our knowledge in physics without an analysis of the way that observers (and, more generally, measuring instruments and experimental arrangements)…
We survey a variety of cosmological problems where the issue of generality has arisen. This is aimed at providing a wider context for many claims and deductions made when philosophers of science choose cosmological problems for…
Every quantum physical system can be considered the ''shadow'' of a special kind of classical system. The system proposed here is classical mainly because each observable function has a well precise value on each state of the system: an…
Results of measurements give legitimacy to a physical theory. What if acquiring these results in the first place necessitates what the same theory considers to be an interaction? In this note, we assume that theories account for…
We propose a taxonomy for quantum algorithms grounded in the fundamental symmetries, both continuous and discrete, underlying quantum state spaces, oracles, and circuit dynamics. By organizing algorithms according to their symmetry groups…
Quantum theory describes our universe incredibly successfully. To our classically-inclined brains, however, it is a bizarre description that requires a re-imagining of what fundamental reality, or "ontology", could look like. This thesis…
Automated theorem proving, or more broadly automated reasoning, aims at using computer programs to automatically prove or disprove mathematical theorems and logical statements. It takes on an essential role across a vast array of…
We attempt a justification of a generalisation of the consistent histories programme using a notion of probability that is valid for all complete sets of history propositions. This consists of introducing Cox's axioms of probability theory…
Process theories combine a graphical language for compositional reasoning with an underlying categorical semantics. They have been successfully applied to fields such as quantum computation, natural language processing, linear dynamical…
A formal theory of experimentation will be presented. Such a theory presents the necessary & sufficient conditions a world must satisfy in order to admit the use of the scientific method.
In this paper we introduce a general framework for defining the depth of a sequence with respect to a class of observers. We show that our general framework captures all depth notions introduced in complexity theory so far. We review most…
Formal definitions of quantities, quantity spaces, dimensions and dimension groups are introduced. Based on these concepts, a theoretical framework and a practical algorithm for dimensional analysis are developed, and examples of…
We define an algorithm to be the set of programs that implement or express that algorithm. The set of all programs is partitioned into equivalence classes. Two programs are equivalent if they are essentially the same program. The set of…
"Clarithmetic" is a generic name for formal number theories similar to Peano arithmetic, but based on computability logic (see http://www.cis.upenn.edu/~giorgi/cl.html) instead of the more traditional classical or intuitionistic logics.…