It has been widely discussed whether the existence of other universes than the known universe is a purely metaphysical consideration. This paper argues to the contrary that the existence of other universes is a meaningful hypothesis, which can be tested based on observable data. The paper applies the perspective of observer bias as an approach for assigning probabilities to the mutually excluding hypotheses of universe vs. multiverse, i.e., whether the known universe is the only universe, or just one universe in (...) an ensemble of universes, a so-called multiverse. The basic idea of the paper relies on the following consideration. In a multiverse, the vast majority of observers would live in universes that are more life friendly. Thus, conditional on there being a multiverse, we should expect to find ourselves in a universe with values of the fundamental parameters that provide particularly fertile grounds for life. In contrast, if there is only a single universe, it may well be the case that there is still a few observers even if the parameters are far from ideal for life, and in that case, those observers will find values of the parameters that are not ideal for intelligent life. It may well be the case that, among all parameter configurations that allow life at least somewhere, those that are not ideal for life far outnumber those that are ideal for life. Based on this elementary consideration, the paper proceeds to propose a quantitative framework to determine probabilities for either hypothesis. In particular, it is described how a future ab initio determination of some of the factors in the Drake equation may be used to infer which one of the two hypotheses is the more likely. A quantitative approach to this end is proposed. Expressing these factors of the Drake equation in the context of the two hypotheses, a general likelihood approach is first described. Then, to support intuition, example computations are provided, illustrating how an actual hypothesis test would work in practice. (shrink)

The study of continuous group actions is ubiquitous in mathematics, and perhaps the most general kinds of actions for which we can hope to prove theorems in just ZFC are those where a Polish group acts on a Polish space.For this general class we can find works such as [29] that build on ideas from ergodic theory and examine actions of locally compact groups in both the measure theoretic and topological contexts. On the other hand a text in model theory, (...) such as [12], will typically consider issues bearing on the actions by the symmetric group of all permutations of the integers. More generally [1] shows that the orbit equivalence relations induced by closed subgroups of the infinite symmetric group can be reduced to the isomorphism relation on corresponding classes of countable models.This paper considers a third category formed by the continuous actions of separable Banach spaces on Polish spaces. These examples cannot be subsumed under the two earlier headings, and it is known from [10] that theBorel cardinalitiesof the quotient spaces that arise from such actions are incomparable with the equivalence relations induced by the symmetric group or any locally compact Polish group action.One of the first things to be addressed concerns the complexity of these equivalence relations. This question forappears in [1]. (shrink)

We reformulate, in the context of continuous logic, an oscillation theorem proved by G. Hjorth and give a proof of the theorem in that setting which is similar to, but simpler than, Hjorth's original one. The point of view presented here clarifies the relation between Hjorth's theorem and first-order logic.

Large-scale transnational land acquisition of agricultural land in the global south by rich corporations or countries raises challenging normative questions. In this article, the author critically examines and advocates a human rights approach to these questions. Mutually reinforcing, policies, governance and practice promote equitable and secure land tenure that in turn, strengthens other human rights, such as to employment, livelihood and food. Human rights therefore provide standards for evaluating processes and outcomes of transnational land acquisitions and, thus, for determining whether (...) they are ethically unacceptable land grabs. A variety of recent policy initiatives on the issue have evoked human rights, most centrally through the consultation and negotiation of the Voluntary Guidelines on the Responsible Governance of Tenure of Land, Fisheries and Forests concluded in 2012. However, a case of transnational land appropriation illustrates weak host and investor state enforcement of human rights, leaving the parties to in interaction with local groups in charge of protecting human rights. Generally, we have so far seen limited direct application of human rights by states in their governance of transnational land acquisition. Normative responses to transnational land acquisition—codes of conduct, principles of responsible agricultural investment or voluntary guidelines—do not in themselves secure necessary action and change. Applying human rights approaches one must therefore also analyze the material conditions, power relations and political processes that determine whether and how women and men can secure the human rights accountability of the corporations and governments that promote large-scale, transnational land acquisition in the global south. (shrink)

We prove that if p ≠ q are distinct primes, then the classification problems for p-local and q-local torsion-free abelian groups of rank two are incomparable with respect to Borel reducibility.

The existence of a countable complete theory with exactly $\aleph_1$ many minimal models is independent of $\mathrm{ZFC} + \neg\mathrm{CH}$.

Addresses the concept of truth in Chinese Daoist philosophy and ritual. Through wide-ranging research into Daoist ritual, both in history and as it survives in the present day, shows that the concept of true reality that informs this tradition posits being as a paradox anchored in the inexistent Way"--Provided by publisher.

If some infinitary sentence provides a counterexample to Vaught's Conjecture, then there is an infinitary sentence which also provides a counterexample but has no model of cardinality bigger than ℵ₁.

§0. Preface. There has been an expectation that the endgame of the more tenacious problems raised by the Los Angeles ‘cabal’ school of descriptive set theory in the 1970's should ultimately be played out with the use of inner model theory. Questions phrased in the language of descriptive set theory, where both the conclusions and the assumptions are couched in terms that only mention simply definable sets of reals, and which have proved resistant to purely descriptive set theoretic arguments, may (...) at last find their solution through the connection between determinacy and large cardinals.Perhaps the most striking example was given by [24], where the core model theory was used to analyze the structure of HOD and then show that all regular cardinals below ΘL are measurable. John Steel's analysis also settled a number of structural questions regarding HODL, such as GCH.Another illustration is provided by [21]. There an application of large cardinals and inner model theory is used to generalize the Harrington-Martin theorem that determinacy implies )determinacy.However, it is harder to find examples of theorems regarding the structure of the projective sets whose only known proof from determinacy assumptions uses the link between determinacy and large cardinals. We may equivalently ask whether there are second order statements of number theory that cannot be proved under PD–the axiom of projective determinacy–without appealing to the large cardinal consequences of the PD, such as the existence of certain kinds of inner models that contain given types of large cardinals. (shrink)

We announce two new dichotomy theorems for Borel equivalence relations, and present the results in context by giving an overview of related recent developments.§1. Introduction. For X a Polish space and E a Borel equivalence relation on X, a classification of X up to E-equivalence consists of finding a set of invariants I and a map c : X → I such that xEy ⇔ c = c. To be of any value we would expect I and c to be (...) “explicit” or “definable”. The theory of Borel equivalence relations investigates the nature of possible invariants and provides a hierarchy of notions of classification.The following partial ordering is fundamental in organizing this study. Given equivalence relations E and F on X and Y, resp., we say that E can be Borel reduced to F, in symbolsif there is a Borel map f : X → Y with xEy ⇔ fFf. Then if is an embedding of X/E into Y/F, which is “Borel”.Intuitively, E ≤BF might be interpreted in any one of the following ways: The classi.cation problem for E is simpler than that of F: any invariants for F work as well for E. One can classify E by using as invariants F-equivalence classes. The quotient space X/E has “Borel cardinality” less than or equal to that of Y/F, in the sense that there is a “Borel” embedding of X/E into Y/F. (shrink)

We propose the FoodSmart City framework as a transdisciplinary avenue to promote sustainable seafood consumption. We argue that a change in human seafood consumption towards eating at lower trophic levels may be helped by discovering forgotten cultural practices and tapping into locally-sourced marine resources. We set out a framework of knowledge exchange and production between academia, businesses, and civil society to promote and assist healthy and ecologically sustainable living using digital tools and intangible cultural heritage while engaging with innovative chefs (...) and educationalists. The framework targets Dublin City, Ireland, but may potentially be replicated in other contexts. (shrink)

Kant’s critique/doctrine distinction tracks the difference between a canon for the understanding’s proper use and an organon for its dialectical misuse. The latter reflects the dogmatic use of reason to attain a doctrine of knowledge with no antecedent critique. In the 1790s, Fichte collapses Kant’s distinction and redefines dogmatism. He argues that deriving a canon is essentially dialectical and thus yields an organon: critical idealism is properly a doctrine of science or Wissenschaftslehre. Criticism is furthermore said to refute dogmatism, by (...) which Fichte means Spinozism. Schelling repudiates Fichte’s position in his Philosophical Letters by reviving Kant’s distinction. First, ‘critique’ for Schelling names a canon that is valid for all systems—including Spinozism—and thus favours none—not even the Wissenschaftslehre. Second, Schelling coins ‘dogmaticism’ to refer to what Kant calls ‘dogmatism’: reason’s uncritical claim to doctrine. Hence, he says all systems—even Fichte’s—are susceptible to the ‘enthusiasm’ of mistaking themselves for doctrines or ‘objects of knowledge’, instead of subjectively valid ‘objects of freedom’. I reconstruct Schelling’s argument for reviving Kant’s distinction, while noting two consequences for German idealism. First, if criticism favours no system, a system’s origin cannot be an act of knowledge, e.g., intellectual intuition, but only an act of endorsement. Second, if dogmaticism entails enthusiasm, a system’s goal cannot be absolute knowledge, but only infinite striving. Hence, by retrieving Schelling’s notion of dogmaticism, we can both gain a better understanding of the Letters and register the impact of a core Kantian distinction on the German idealist project. (shrink)

If there is a good $\Delta^1_3$ wellordering of the reals, then there is a $\Pi^1_1$ wellfounded relation for which the comparison relation is not projective.

Disintegration and mechanisation.--Sacrifice and atonement.--Communion and the community.--The life-mass and the death-mass.--Life's clair-obscure.

This paper presents an interpretation of Husserl''s phenomenological epoché or bracketing ( Einklammerung), which makes it possible to compare his position with philosophical programs developed within the framework of modern analytical philosophy. At the same time it asks in what sense Husserl''s phenomenology is a form of idealism or exceeds the traditional discussion of idealism versus realism.