We provide an introduction to methods and recent results on infinitely generated abelian groups with decidable word problem.

We show that for every computable ordinal of the form β=δ+2n+1>1, where δ is zero or a limit ordinal and n∈ω, there exists a torsion-free abelian group having an X-computable copy if and only if X is nonlowβ.

We study punctual categoricity on a cone and intrinsically punctual functions and obtain complete structural characterizations in terms of model-theoretic notions. As a corollary, we answer a question of Bazhenov, Downey, Kalimullin, and Melnikov by showing that relational structures are not punctually universal. We will also apply this characterisation to derive an algebraic characterisation of relatively punctually categorical mono-unary structures.

We study computable Polish spaces and Polish groups up to homeomorphism. We prove a natural effective analogy of Stone duality, and we also develop an effective definability technique which works up to homeomorphism. As an application, we show that there is a $\Delta ^0_2$ Polish space not homeomorphic to a computable one. We apply our techniques to build, for any computable ordinal $\alpha $, an effectively closed set not homeomorphic to any $0^{}$-computable Polish space; this answers a question of Nies. (...) We also prove analogous results for compact Polish groups and locally path-connected spaces. (shrink)

We prove that for any computable successor ordinal of the form α = δ + 2k there exists computable torsion-free abelian group that is relatively Δα0 -categorical and not Δα−10 -categorical. Equivalently, for any such α there exists a computable TFAG whose initial segments are uniformly described by Σαc infinitary computable formulae up to automorphism, and there is no syntactically simpler family of formulae that would capture these orbits. As far as we know, the problem of finding such optimal examples (...) of Δα0-categorical TFAGs for arbitrarily large α was first raised by Goncharov at least 10 years ago, but it has resisted solution 315–356]). As a byproduct of the proof, we introduce an effective functor that transforms a 0″-computable worthy labeled tree into a computable TFAG. We expect that this techni... (shrink)

We review publications in automated scientific discovery using deep learning, with the aim of shedding light on problems with strong connections to philosophy of science, of physics in particular. We show that core issues of philosophy of science, related, notably, to the nature of scientific theories; the nature of unification; and of causation loom large in scientific deep learning. Therefore, advances in deep learning could, and ideally should, have impact on philosophy of science, and vice versa. We suggest lines of (...) further research, and highlight the role ‘theory-based’ AI could have in future developments of the field. (shrink)

We give a systematic technical exposition of the foundations of the theory of computably compact metric spaces. We discover several new characterizations of computable compactness and apply these characterizations to prove new results in computable analysis and effective topology. We also apply the technique of computable compactness to give new and less combinatorially involved proofs of known results from the literature. Some of these results do not have computable compactness or compact spaces in their statements, and thus these applications are (...) not necessarily direct or expected. (shrink)

We describe punctual categoricity in several natural classes, including binary relational structures and mono-unary functional structures. We prove that every punctually categorical structure in a finite unary language is${\text {PA}}(0')$-categorical, and we show that this upper bound is tight. We also construct an example of a punctually categorical structure whose degree of categoricity is$0''$. We also prove that, with a bit of work, the latter result can be pushed beyond$\Delta ^1_1$, thus showing that punctually categorical structures can possess arbitrarily complex (...) automorphism orbits.As a consequence, it follows that binary relational structures and unary structures are not universal with respect to primitive recursive interpretations; equivalently, in these classes every rich enough interpretation technique must necessarily involve unbounded existential quantification or infinite disjunction. In contrast, it is well-known that both classes are universal for Turing computability. (shrink)

We solve a problem posed by Goncharov and Knight 639–681, 757]). More specifically, we produce an effective Friedberg enumeration of computable equivalence structures, up to isomorphism. We also prove that there exists an effective Friedberg enumeration of all isomorphism types of infinite computable equivalence structures.

Review by: Alexander G. Melnikov The Bulletin of Symbolic Logic, Volume 19, Issue 3, Page 400-401, September 2013.

The survey contains a detailed discussion of methods and results in the new emerging area of online “punctual” structure theory. We also state several open problems.

Computability theory is used to evaluate the complexity of classifying various kinds of Lebesgue spaces and associated isometric isomorphism problems.

A structure is automatic if its domain, functions, and relations are all regular languages. Using the fact that every automatic structure is decidable, in the literature many decision problems have been solved by giving an automatic presentation of a particular structure. Khoussainov and Nerode asked whether there is some way to tell whether a structure has, or does not have, an automatic presentation. We answer this question by showing that the set of Turing machines that represent automata-presentable structures is ${\rm{\Sigma (...) }}_1^1 $-complete. We also use similar methods to show that there is no reasonable characterisation of the structures with a polynomial-time presentation in the sense of Nerode and Remmel. (shrink)

We investigate what it means for a (Hausdorff, second-countable) topological group to be computable. We compare several potential definitions based on classical notions in the literature. We relate these notions with the well-established definitions of effective presentability for discrete and profinite groups, and compare our results with similar results in computable topology.

We show, for each computable ordinal α and degree $\alpha > {0^{\left( \alpha \right)}}$, the existence of a torsion-free abelian group with proper α th jump degree α.

We study completely decomposable torsion-free abelian groups of the form $\mathcal{G}_S := \oplus_{n \in S} \mathbb{Q}_{p_n}$ for sets $S \subseteq \omega$. We show that $\mathcal{G}_S$has a decidable copy if and only if S is $\Sigma^0_2$and has a computable copy if and only if S is $\Sigma^0_3$.

Some combinations of attitudes--of beliefs, credences, intentions, preferences, hopes, fears, and so on--do not fit together right: they are incoherent. A natural idea is that there are requirements of "structural rationality" that forbid us from being in these incoherent states. Yet a number of surprisingly difficult challenges arise for this idea. These challenges have recently led many philosophers to attempt to minimize or eliminate structural rationality, arguing that it is just a "shadow" of "substantive rationality"--that is, correctly responding to one's (...) reasons. -/- In *Fitting Things Together*, Alex Worsnip pushes back against this trend--defending the view that structural rationality is a genuine kind of rationality, distinct from and irreducible to substantive rationality, and tackling the most important challenges for this view. In so doing, he gives an original positive theory of the nature of coherence and structural rationality that explains how the diverse range of instances of incoherence can be unified under a general account, and how facts about coherence are normatively significant. He also shows how a failure to focus on coherence requirements as a distinctive phenomenon and distinguish them adequately from requirements of substantive rationality has led to confusion and mistakes in several substantive debates in epistemology and ethics. -/- Taken as a whole, Fitting Things Together provides the first sustained defense of the view that structural rationality is a genuine, autonomous, unified, and normatively significant phenomenon. (shrink)

Necessary Existence breaks ground on one of the deepest questions anyone ever asks: why is there anything? Pruss and Rasmussen present an original defence of the hypothesis that there is a necessarily existing being capable of providing an ultimate foundation for the existence of all things.

Jacobi held a position of unparalleled importance in late eighteenth and early nineteenth century intellectual history. This includes his role in bringing about the close of the Enlightenment, his central part in shaping the reception of Kant's philosophy and German idealism, and his influence on the development of Romanticism and existentialism.

This important philosophical reflection on love and sexuality from a broadly Christian perspective is aimed at philosophers, theologians, and educated Christian readers. Alexander R. Pruss focuses on foundational questions on the nature of romantic love and on controversial questions in sexual ethics on the basis of the fundamental idea that romantic love pursues union of two persons as one body. _One Body_ begins with an account, inspired by St. Thomas Aquinas, of the general nature of love as constituted by (...) components of goodwill, appreciation, and unitiveness. Different forms of love, such as parental, collegial, filial, friendly, fraternal, or romantic, Pruss argues, differ primarily not in terms of goodwill or appreciation but in terms of the kind of union that is sought. Pruss examines romantic love as distinguished from other kinds of love by a focus on a particular kind of union, a deep union as one body achieved through the joint biological striving of the sort involved in reproduction. Taking the account of the union that romantic love seeks as a foundation, the book considers the nature of marriage and applies its account to controversial ethical questions, such as the connection between love, sex, and commitment and the moral issues involving contraception, same-sex activity, and reproductive technology. With philosophical rigor and sophistication, Pruss provides carefully argued answers to controversial questions in Christian sexual ethics. "This is a terrific—really quite extraordinary—work of scholarship. It is quite simply the best work on Christian sexual ethics that I have seen. It will become the text that anyone who ventures into the field will have to grapple with—a kind of touchstone. Moreover, it is filled with arguments with which even secular writers on sexual morality will have to engage and come to terms." —_Robert P. George, Princeton University __ "_One Body_ is an excellent piece of philosophical-theological reflection on the nature of sexuality and marriage. This book has the potential to become a standard go-to text for professors and students working on sex ethics issues, whether in philosophy or theology, both for the richness of its arguments, and the scope of its coverage of cases. " — Christopher Tollefsen, University of South Carolina_ "Alexander Pruss here develops sound and humane answers to the whole range of main questions about human sexual and reproductive choices. His principal argument for the key answers is very different from the one I have articulated over the past fifteen years. But his argumentation is at every point attractively direct, careful, energetic in framing and responding to objections, and admirably attentive to realities and the human goods at stake." —_John Finnis, University of Oxford _. (shrink)

Internalism about a person's good is roughly the view that in order for something to intrinsically enhance a person's well-being, that person must be capable of caring about that thing. I argue in this paper that internalism about a person's good should not be believed. Though many philosophers accept the view, Connie Rosati provides the most comprehensive case in favor of it. Her defense of the view consists mainly in offering five independent arguments to think that at least some form (...) of internalism about one's good is true. But I argue that, on closer inspection, not one of these arguments succeeds. The problems don't end there, however. While Rosati offers good reasons to think that what she calls 'two-tier internalism' would be the best way to formulate the intuition behind internalism about one's good, I argue that two-tier internalism is actually false. In particular, the problem is that no substantive theory of well-being is consistent with two-tier internalism. Accordingly, there is reason to think that even the best version of internalism about one's good is in fact false. Thus, I conclude, the prospects for internalism about a person's good do not look promising. (shrink)

The essence and basic methods of the pure theory -- The state and the law -- Law and its "others" : natural law, morality and social policy -- Constitution and normative hierarchy -- The basic norm and efficacy of the legal system -- The rule of law -- Conclusion -- Index.

Introduction -- What is personal responsibility? -- Ordinary language -- Common conceptions -- What do philosophers mean by responsibility? -- Personally responsible for what? -- What do philosophers think? part I -- Causes -- Capacity -- Control -- Choice versus brute luck -- Second-order attitudes -- Equality of opportunity -- Deservingness -- Reasonableness -- Reciprocity -- Equal shares -- Combining criteria -- What do philosophers think? part II -- Utility -- Self-respect -- Autonomy -- Human flourishing -- Natural duties and (...) special obligations -- A matter of perspectives -- Combining values -- What do politicians think? -- A brief typology -- International comparisons -- Welfare reform -- Healthcare reform -- Rights and responsibilities -- On the responsibilities of politicians -- What do ordinary people think? -- Why ask? -- Attitudes to welfare claimants -- When push comes to shove -- Perceptions and reality -- Further international comparisons -- The trouble with opinion surveys -- Four contemporary issues in focus -- Unemployment -- Health -- Drug abuse -- Personal debt and financial rewards -- So how do we decide? -- Getting the public involved -- Citizens juries -- Answering some potential criticisms. (shrink)

With any structural inference rule A/B, we associate the rule $${(A \lor p)/(B \lor p)}$$, providing that formulas A and B do not contain the variable p. We call the latter rule a join-extension ( $${\lor}$$ -extension, for short) of the former. Obviously, for any intermediate logic with disjunction property, a $${\lor}$$ -extension of any admissible rule is also admissible in this logic. We investigate intermediate logics, in which the $${\lor}$$ -extension of each admissible rule is admissible. We prove that (...) any structural finitary consequence operator (for intermediate logic) can be defined by a set of $${\lor}$$ -extended rules if and only if it can be defined through a set of well-connected Heyting algebras of a corresponding quasivariety. As we exemplify, the latter condition is satisfied for a broad class of algebraizable logics. (shrink)

Essentialism as applied to individuals is the claim that for at least some individuals there are properties that those individuals possess essentially. What it is to possess a property essentially is a matter of debate. To possess a property essentially is often taken to be akin to possessing a property necessarily, but stronger, although this is not a feature of Aristotle’s essentialism, according to which essential properties are those thing could not lose without ceasing to exist. Kit Fine (1994) takes (...) essential properties to be those that an object has in virtue of its identity, while other essentialists refer (as Fine also does) to the nature of an object as the source of its essential properties. It is sometimes important to distinguish the essential properties of a thing and the ‘full’ essence of a thing. The latter is the set of the essential properties of a thing, when that set necessarily suffices to determine the thing’s identity. One might hold that something has essential properties without agreeing that it has an identity-determining essence. Essentialism was largely in abeyance during the first two thirds of the twentieth century thanks to the domination of analytic philosophy by anti-metaphysical logical empiricism and the linguistic turn. The rehabilitation of essentialism owes much to the development of a formal apparatus for the understanding of modality more generally, thanks to C. I. Lewis, Ruth Barcan Marcus, and Saul Kripke. Kripke’s discussion of essentialism both about individuals and also about about natural kinds brought essentialism to wider philosophical prominence. Natural kind essentialism, which finds its modern genesis also in the work of Hilary Putnam, claims that natural kinds have essential properties: to say that possession of property P is is part of the essence of the kind K implies that, necessarily, every member or sample of the kind K possesses P. Essentialism about individuals has been linked to thinking about natural kinds by the contentious claim that one of the essential properties of any entity is that it belongs to the natural kind (or kinds) it actually belongs to. In this chapter I shall first outline certain claims and arguments concerning essentialism concerning individuals (Section 2).. (shrink)

Mental causation is notoriously threatened by the causal exclusion argument. A prominent strategy to save mental causation from causal exclusion consists in subscribing to an interventionist account of causation. This move has, however, recently been challenged by several authors. In this paper, we do two things: We (i) develop what we consider to be the strongest version of the interventionist causal exclusion argument currently on the market and (ii) propose a new way how it can in principle be overcome. In (...) particular, we propose to replace strict supervenience in the assumption that the mental supervenes on the physical by probabilistic supervenience and show how this move has the potential to license the inference to mental causation. Finally, we argue that probabilistic supervenience captures some of the most important intuitions that strict supervenience captures and discuss possible objections to weakening strict supervenience in the way we suggest. (shrink)

Can philosophy be a source of hope? Today it is common to believe that the answer is no - that providing hope, if it is possible at all, belongs either to the predictive sciences or to religion. In this exciting and simulating book, however, Alexander Douglas argues that the philosophy of Spinoza can offer something akin to religious hope. Douglas shows how Spinoza is able, without appealing to belief in any traditional afterlife or supernatural grace, to develop a profound (...) and original theory of how humans can escape from the conditions of death and sin. Douglas argues that this theory of escape, which Spinoza calls beatitude, is the centrepiece of his entire philosophy, though scholars have often downplayed or ignored it. One reason for this scholarly neglect might be the difficulty of understanding Spinoza's theory, which departs from the standard doctrines and methods of Western philosophy. Douglas's interpretation therefore seeks inspiration beyond the Western tradition, drawing especially on the classical Daoist text Zhuangzi and its commentaries. Here, Douglas argues, surprising resonances with Spinoza's core ideas can be found, leading to a new way of understanding his strange yet compelling theory of beatitude. (shrink)

International regulation of autonomous weapon systems (AWS) is increasingly conceived as an exercise in risk management. This requires a shared approach for assessing the risks of AWS. This paper presents a structured approach to risk assessment and regulation for AWS, adapting a qualitative framework inspired by the Intergovernmental Panel on Climate Change (IPCC). It examines the interactions among key risk factors—determinants, drivers, and types—to evaluate the risk magnitude of AWS and establish risk tolerance thresholds through a risk matrix informed by (...) background knowledge of event likelihood and severity. Further, it proposes a methodology to assess community risk appetite, emphasizing that such assessments and resulting tolerance levels should be determined through deliberation in a multistakeholder forum. The paper highlights the complexities of applying risk-based regulations to AWS internationally, particularly the challenge of defining a global community for risk assessment and regulatory legitimization. (shrink)

Scotland has played an immense role in European high culture through the centuries, and among its cultural links none have been greater than those with France. This book shows that the links with France stretch back deep into the Middle Ages, and continue without a break into the 18th century, the Age of Enlightenment.

Several current theories have essences as primary drivers of inductive potential: e.g., people infer dogs share properties because they share essences. We investigated the possibility that people take occupational roles as having robust inductive potential because of a different source: their position in stable social institutions. In Studies 1–4, participants learned a novel property about a target, and then decided whether two new individuals had the property (one with the same occupation, one without). Participants used occupational roles to robustly generalize (...) rights and obligations, functional behaviors, personality traits, and skills. In Studies 5–6, we contrasted occupational roles (via label) with race/gender (via visual face cues). Participants reliably favored occupational roles over race/gender for generalizing rights and obligations, functional behaviors, personality traits, and skills (they favored race/gender for inferring leisure behaviors and physiological properties). Occupational roles supported inferences to the same extent as animal categories (Studies 4 and 6). In Study 7, we examined why members of occupational roles share properties. Participants did not attribute the inductive potential of occupational roles to essences, they attributed it to social institutions. In combination, these seven studies demonstrate that any theory of inductive potential must pluralistically allow for both essences and social institutions to form the basis of inductive potential. (shrink)

Writing in the cosmopolitan metropolis of Baghdad, Alfarabi (870-950) is unique in the history of premodern political philosophy for his extensive discussion of the nation, or Umma in Arabic. The term Umma may be traced back to the Qur'ān and signifies, then and now, both the Islamic religious community as a whole and the various ethnic nations of which that community is composed, such as the Turks, Persians, and Arabs. Examining Alfarabi's political writings as well as parts of his logical (...) commentaries, his book on music, and other treatises, Alexander Orwin contends that the connections and tensions between ethnic and religious Ummas explored by Alfarabi in his time persist today in the ongoing political and cultural disputes among the various nationalities within Islam. According to Orwin, Alfarabi strove to recast the Islamic Umma as a community in both a religious and cultural sense, encompassing art and poetry as well as law and piety. By proposing to acknowledge and accommodate diverse Ummas rather than ignoring or suppressing them, Alfarabi anticipated the contemporary concept of "Islamic civilization," which emphasizes culture at least as much as religion. Enlisting language experts, jurists, theologians, artists, and rulers in his philosophic enterprise, Alfarabi argued for a new Umma that would be less rigid and more creative than the Muslim community as it has often been understood, and therefore less inclined to force disparate ethnic and religious communities into a single mold. Redefining the Muslim Community demonstrates how Alfarabi's judicious combination of cultural pluralism, religious flexibility, and political prudence could provide a blueprint for reducing communal strife in a region that continues to be plagued by it today. (shrink)

Das Bild vom glaubwürdigen Wissenschaftler? vom Universalgelehrten der Renaissance zu modernen Laborspezialist*innen - ist ein kulturelles Konstrukt, das die Ansprüche seiner Zeit widerspiegelt. Wie es entsteht, wird im Galvanismusdiskurs um 1800 deutlich.Dieser Band beschäftigt sich mit den Fragen: Wer gilt um 1800 als Naturwissenschaftler? Wie findet man als junger Forscher Aufnahme in die wissenschaftliche Gemeinschaft? Und worin manifestieren sich die wissenschaftskulturellen Unterschiede in Deutschland und Großbritannien zu Beginn des 19. Jahrhunderts? Anhand der frühen Publikationen der jungen aufstrebenden Naturforscher Alexander (...) von Humboldt, Johann Wilhelm Ritter und Christian Heinrich Pfaff sowie ihrer britischen Kollegen untersucht der Autor die Konstruktion vom modernen Naturwissenschaftler durch die wissenschaftliche Gemeinschaft. (shrink)

The posterior cortex, hippocampus, and prefrontal cortex in the Leabra architecture are specialized in terms of various neural parameters, and thus are predilections for learning and processing, but domain-general in terms of cognitive functions such as face recognition. Also, these areas are not encapsulated and violate Fodorian criteria for modularity. Anderson's terminology obscures these important points, but we applaud his overall message.

Lazarus Revived shows how two thought experiments provide the foundation for arguments for the existence of conscious life after death. The theories of pluriverses and the Big Bang are examined and a substitute equation for E=MC² is presented.