Related papers: Non-Additive Axiologies in Large Worlds
We formulate physically-motivated axioms for a physical theory which for systems with a finite number of degrees of freedom uniquely lead to Quantum Mechanics as the only nontrivial consistent theory. Complex numbers and the existence of…
Evaluation is a crucial aspect of human existence and plays a vital role in various fields. However, it is often approached in an empirical and ad-hoc manner, lacking consensus on universal concepts, terminologies, theories, and…
Whether the fate of our species can be forecast from its past has been the topic of considerable controversy. One refutation of the so-called Doomsday Argument is based on the premise that we are more likely to exist in a universe…
A finite-dimensional unital and associative algebra over $\mathbb{R}$, or what we shall call simply "an algebra" in this paper for short, generalities the construction by which we derive the complex numbers by "adjoining an element $i$" to…
This paper takes an axiomatic and calculational view of diversity (or "N-version programming"), where multiple implementations of the same specification are executed in parallel to increase dependability. The central notion is…
Algorithmic predictions are increasingly used to inform the allocations of goods and interventions in the public sphere. In these domains, predictions serve as a means to an end. They provide stakeholders with insights into likelihood of…
Weighted gradual semantics provide an acceptability degree to each argument representing the strength of the argument, computed based on factors including background evidence for the argument, and taking into account interactions between…
These notes are concerned with the existence and the basic properties of the set-theoretic universes for nonstandard analysis, compiled by a beginner in the subject. It assumes a basic background in first-order logic, though the necessary…
Abstraction is a powerful idea widely used in science, to model, reason and explain the behavior of systems in a more tractable search space, by omitting irrelevant details. While notions of abstraction have matured for deterministic…
The topic of diversity is an interesting subject, both as a purely mathematical concept and also for its applications to important real-life situations. Unfortunately, although the meaning of diversity seems intuitively clear, no precise…
Given a set of conflicting arguments, there can exist multiple plausible opinions about which arguments should be accepted, rejected, or deemed undecided. We study the problem of how multiple such judgments can be aggregated. We define the…
Recent work in set theory indicates that there are many different notions of 'set', each captured by a different collection of axioms, as proposed by J. Hamkins in [Ham11]. In this paper we strive to give one class theory that allows for a…
We study situations where a group of voters need to take a collective decision over a number of public issues, with the goal of getting a result that reflects the voters' opinions in a proportional manner. Our focus is on interconnected…
Recently the multitude of vacua in string theory have led some authors to advocate the anthropic principle as a possible resolution for the contrived set of parameters that seem to govern our universe. I suggest that string theories should…
Anthropic arguments in multiverse cosmology and string theory rely on the weak anthropic principle (WAP). We show that the principle, though ultimately a tautology, is nevertheless ambiguous. It can be reformulated in one of two unambiguous…
In this paper we introduce the notion of elementary numerosity as a special function defined on all subsets of a given set X which takes values in a suitable non-Archimedean field, and satisfies the same formal properties of finite…
The locations problem in infinite ethics concerns the relative moral status of different categories of potential bearers of value, the primary examples of which are people and points in time. The challenge is to determine which category of…
We introduce the general notions of an index and a core of a relation. We postulate a limited form of the axiom of choice -- specifically that all partial equivalence relations have an index -- and explore the consequences of adding the…
An axiomatic approach to macroeconomics based on the mathematical structure of thermodynamics is presented. It deduces relations between aggregate properties of an economy, concerning quantities and flows of goods and money, prices and the…
Astrobiology is the field of science devoted to searching for life elsewhere in the Universe. It is inherently interdisciplinary, integrating results from multiple fields of science, and in this respect has strong synergies with 'big…