Related papers: Non-Additive Axiologies in Large Worlds
Axiomatizing mathematical structures and theories is an objective of Mathematical Logic. Some axiomatic systems are nowadays mere definitions, such as the axioms of Group Theory; but some systems are much deeper, such as the axioms of…
The Anthropic Principle has been with us since the 1970s. This Principle is advanced to account for the "fine tuning" of the 25 constants of the Standard Model of Particle Physics. Were these constants very different, life could not exist.…
Many annotation tasks in natural language processing are highly subjective in that there can be different valid and justified perspectives on what is a proper label for a given example. This also applies to the judgment of argument quality,…
Many methods to explain black-box models, whether local or global, are additive. In this paper, we study global additive explanations for non-additive models, focusing on four explanation methods: partial dependence, Shapley explanations…
In previous papers on this project a general static logical framework for formalizing and mechanizing set theories of different strength was suggested, and the power of some predicatively acceptable theories in that framework was explored.…
The anthropic principle implies that life can emerge and be sustained only in a narrow range of values of fundamental constants. Here we show that anthropic arguments can set powerful constraints on {\em transient} variations of the…
This study investigates possibility and impossibility results of the repugnant and sadistic conclusions in population ethics and economics. The repugnant conclusion says that an enormous population with very low well-being is socially…
Abductive explanations (AXp's) are widely used for understanding decisions of classifiers. Existing definitions are suitable when features are independent. However, we show that ignoring constraints when they exist between features may lead…
A qualitatively new, much more liberal and efficient organisation of science is proposed and justified, in connection with growing debate about further role and development of fundamental science. Although the key ideas can be explained…
The idea of a multiverse -- an ensemble of universes -- has received increasing attention in cosmology, both as the outcome of the originating process that generated our own universe, and as an explanation for why our universe appears to be…
An elementary rheory of concatenation is introduced and used to establish mutual interpretability of Robinson arithmetic, Minimal Predicative Set Theory, the quantifier-free part of Kirby's finitary set theory, and Adjunctive Set Theory,…
Our understanding about things is conceptual. By stating that we reason about objects, it is in fact not the objects but concepts referring to them that we manipulate. Now, so long just as we acknowledge infinitely extending notions such as…
Social abstract argumentation is a principled way to assign values to conflicting (weighted) arguments. In this note we discuss the important property of the uniqueness of the model.
In this talk we discuss three different issues. First of all, there exist several proposals how to solve cosmological problems by adiabatic expansion of the Universe, without any use of inflation. We explain why these models do not solve…
In many instances in first order logic or computable algebra, classical theorems show that many problems are undecidable for general structures, but become decidable if some rigidity is imposed on the structure. For example, the set of…
Recent results, establishing evidence of intractability for such restrictive utility functions as additively separable, piecewise-linear and concave, under both Fisher and Arrow-Debreu market models, have prompted the question of whether we…
A central theme in set theory is to find universes with extreme, well-understood behaviour. The case we are interested in is assuming GCH and has a strong forcing axiom of higher order than usual. Instead of "for every suitable forcing…
In this paper, we study extensions of valuations over algebraic field extensions without the use of the Axiom of Choice. We show a bijection between the extensions of a valuation and the maximal ideals of the relative integral closure of…
Ecosystems are commonly conceptualized as networks of interacting species. However, partitioning natural diversity of organisms into discrete units is notoriously problematic, and mounting experimental evidence raises the intriguing…
On the largest scales, the universe appears to be almost homogeneous and isotropic, adhering to the cosmological principle. In contrast, on smaller scales inhomogeneities and anisotropy become increasingly prominent, reflecting the origin,…