Related papers: Non-Additive Axiologies in Large Worlds
Inspired by Raychaudhuri's work, and using the equation named after him as a basic ingredient, a new singularity theorem is proved. Open non-rotating everywhere expanding universes with non-vanishing spatial average of the matter variables…
The standard assumptions that underlie many conceptual and quantitative frameworks do not hold for many complex physical, biological, and social systems. Complex systems science clarifies when and why such assumptions fail and provides…
A quantum theory of the universe consists of a theory of its quantum dynamics and a theory of its quantum state The theory predicts quantum multiverses in the form of decoherent sets of alternative histories describing the evolution of the…
Contrary to an oft-made claim, there can be observational distinctions (say for the expansion of the universe or the cosmological constant) between "single-history" quantum theories and "many-worlds" quantum theories. The distinctions occur…
Shnirel'man's inequality and Shnirel'man's basis theorem are fundamental results about sums of sets of positive integers in additive number theory. It is proved that these results are inherently order-theoretic and extend to partially…
The inflationary scenario is not the only paradigm of early universe cosmology which is consistent with current observations. General criteria will be presented which any successful early universe model must satisfy. Various ways, including…
We describe the non-minimal Standard Model, consisting of minimalistic extensions of the Standard Model, which for all we know is the theory of the universe, able to describe all of the universe from the beginning of time. Extensions…
We suggest to combine the Anthropic Principle with the Many-Worlds Interpretation of Quantum Theory. Realizing the multiplicity of worlds it provides an opportunity of explanation of some important events which are assumed to be extremely…
When utilities are additive, we uncovered in our previous paper (Bogomolnaia et al. "Dividing Goods or Bads under Additive Utilities") many similarities but also surprising differences in the behavior of the familiar Competitive rule (with…
Gravity theories with non-minimally coupled scalar fields are used as characteristic examples in order to demonstrate the challenges, pitfalls and future perspectives of considering alternatives to general relativity. These lecture notes…
Building upon previous research, this paper further explores the topological foundations for maintaining universal rules within ultra-large-scale societies. It finds that in small-scale societies, absolute egalitarianism and the rule of law…
A natural notion of rationality/consistency for aggregating models is that, for all (possibly aggregated) models $A$ and $B$, if the output of model $A$ is $f(A)$ and if the output model $B$ is $f(B)$, then the output of the model obtained…
Non-critical String Cosmologies are offered as an alternative to Standard Big Bang Cosmology. The new features encompassed within the dilaton dependent non-critical terms affect the dynamics of the Universe\'s evolution in an unconventional…
After surveying classical results, we introduce a generalized notion of inference system to support structural recursion on non-well-founded data types. Besides axioms and inference rules with the usual meaning, a generalized inference…
As machine learning and algorithmic decision making systems are increasingly being leveraged in high-stakes human-in-the-loop settings, there is a pressing need to understand the rationale of their predictions. Researchers have responded to…
Inclusion logic is a variant of dependence logic that was shown to have the same expressive power as positive greatest fixed-point logic. Inclusion logic is not axiomatizable in full, but its first-order consequences can be axiomatized. In…
It is explained in detail why the Anthropic Principle (AP) cannot yield any falsifiable predictions, and therefore cannot be a part of science. Cases which have been claimed as successful predictions from the AP are shown to be not that.…
Multiverse scenarios in cosmology assume that other universes exist "beyond" our own universe. They are an exciting challenge both for empirical and theoretical research as well as for philosophy of science. They could be necessary to…
Many of the properties of sectional category, topological complexity and homotopic distance are in fact derived from a small number of basic properties, which, once established, lead to all the others without further recourse to topology.…
I survey physics theories involving parallel universes, arguing that they form a natural four-level hierarchy of multiverses allowing progressively greater diversity. Level I: A generic prediction of inflation is an infinite ergodic…