According to terror management theory, humans rely on meaningful and permanence-promising cultural worldviews, like religion, to manage mortality concerns. Prior research indicates that, compared to religious individuals, atheists experience lower levels of meaning in life following reminders of death. The present study investigated whether reminders of death would change atheists’ meaning in life after exposure to normative support for atheism. Atheists were either reminded of death or a control topic and exposed to information portraying atheism as either common or rare, (...) and then asked to rate their perceived meaning in life. Results showed that reminders of death reduced meaning in life among atheists who were told that atheism is common. Results were consistent with the view that atheism reflects the rejection of religious faith rather than a meaningful secular terror managing worldview. Discussion considers implications for maintaining healthy existential wellbeing, identifies limitations, and highlights future research directions. (shrink)

In the context of network-ecological thought, information ethics is perhaps best understood as a transversal reflexive practice, aimed at identifying the stakes attending the creation, consumption, and disposal of infor-mation technologies. To situate itself as well as potential interlocutors, such a thought requires correspondingly complex cartographies, a multidimensional mapping of practices and presuppositions, of individual, collective, institutional actors as well as the conditions of possibility of their mutual engagement. Such cartographies do not assume the existence of the „local“ or the (...) „global“ as a given. Instead, they attend to the way human and non-human actors and the discursive and material practices they are involved in contribute to construction and reconstruction of geocultural formations. Reapproached from within such a „network-ecological“ horizon, information ethics becomes geophilosophy, generating new modalities of intervention in the conflictual dynamics associated with the social-economic life of waste. (shrink)

Various authors have argued that in the future not only will it be technically feasible for human minds to be transferred to other substrates, but this will become, for most humans, the preferred option over the current biological limitations. It has even been claimed that such a scenario is inevitable in order to solve the challenging, but imperative, multi-agent value alignment problem. In all these considerations, it has been overlooked that, in order to create a suitable environment for a particular (...) mind – for example, a personal universe in a computational substrate – numerous other potentially sentient beings will have to be created. These range from non-player characters to subroutines. This article analyzes the additional suffering and mind crimes that these scenarios might entail. We offer a partial solution to reduce the suffering by imposing on the transferred mind the perception of indicators to measure potential suffering in non-player characters. This approach can be seen as implementing literal empathy through enhanced cognition. (shrink)

Die "Gottesfrage" ist anerkanntermaßen eine äußerst komplexe, vieldeutige und obskure Frage. In ausführlicher Auseinandersetzung mit Heidegger, in dessen Schriften eine sehr einflussreiche einseitige und entstellende Interpretation und Kritik der großen metaphysischen Tradition immer wieder präsentiert wird, zeigt Lorenz B. Puntel, dass die Gottesfrage klar, rational und argumentativ, kurz: mit theoretischer Rigorosität, behandelt werden kann. Dies aber setzt einen umfassenden philosophischen Theorierahmen voraus, der die Entfaltung einer systematischen Konzeption des Seins als solchen und im Ganzen ermöglicht und in nuce enthält. (...) Anschließend wird eine solche Konzeption im Grundriss zur Darstellung gebracht. In einem ausführlichen Kapitel werden die Positionen von É. Lévinas und J.-L. Marion, den zwei wohl radikalsten postmodernen Kritikern und Gegnern jeder Form eines positiven Verhältnisses zwischen dem "Sein" und "Gott", eingehend analysiert und deren radikale Unhaltbarkeit demonstriert. (shrink)

Ch. 1: Inadequate approaches to the question of God -- 1.1. Initial clarifications -- 1.2 Wholly unsystematic direct approaches -- 1.3. Semi-systematic indirect approaches -- 1.4. A wholly anti-systematic, anti-theoretical, and direct approach: Ludwig Wittgenstein -- 1.5. A characteristic example of a failed critique: Thomas Nagel's objections to God as "last point" -- Ch. 2. Heidegger's thinking of Being: the flawed development of a significant approach -- 2.1. Heidegger's failed and distorting interpretation and critique of the Christian metaphysics of Being (...) -- 2.2. Heidegger's four approaches to "retrieving" the "question of being" -- 2.3. What is unthought in Heidegger's thinking of Being I: Being-as-Ereignis -- 2.4. What is unthought in Heidegger's "thinking of Being" II: Being and being(s)- Ereignis and Ereignete(s) -- 2.5. The "overcoming [Überwinding] of metaphysics" as "transformational recovering [Verwindung]" of metaphysics and "the end of the history of Being" -- 2.6. The status of Heideggerian thinking I: thinking of Being as thinking within Ereignis, thinking that reaches its destination with Ereignis (Denken, das in das Ereignis einkehrt) -- 2.7. The status of Heideggerian thinking II: absolute claim, provisionality, the poverty of language, the language of thinking, the finitude of thinking -- 2.8. Heidegger's thinking and the topic "God" -- 2.9. Heidegger's "thinking": a fundamentally deficient and confused form of thinking -- Ch. 3:The structural-systematic approach to a theory of Being and God -- 3.1. The systematic context: the theoretical framework of the structural-systematic philosophy -- 3.2. The unrestricted universe of discourse as the universal dimension of primordial Being -- 3.3. Explication of the dimension of Being I: theory of Being as such -- 3.4. Explication of the dimension of Being II: theory of Being as a whole -- 3.5. Explication of the relation between absolutely necessary Being and the contingent dimension of Being as key to a conception of absolutely necessary Being as minded (as personal) -- 3.6. Absolutely necessary minded (personal) Being as creator of the world (as absolute creating) -- 3.7. The clarified relation between Being and God and the task of developing an integral theory about God -- Ch. 4: Critical examination of two counterpositions: Emmanuel Levinas and Jean-Luc Marion -- 4.1. Levinas's misguided conception of transcendence "beyond B/being" -- 4.2. Jean-Luc Marion's failed conception of "radical and non-metaphysical transcendence" and of "God without Being". (shrink)

Hendrik Lorenz presents a comprehensive study of Plato's and Aristotle's conceptions of non-rational desire. They see this as something that humans share with animals, and which aims primarily at the pleasures of food, drink, and sex. Lorenz explores the cognitive resources that both philosophers make available for the explanation of such desires, and what they take rationality to add to the motivational structure of human beings. In doing so, he finds conceptions of the mind that are coherent and (...) deeply integrated with both philosophers' views about such topics as the relation between body and soul, or the nature of the virtues. (shrink)

Duality in Logic and Language [draft--do not cite this article] Duality phenomena occur in nearly all mathematically formalized disciplines, such as algebra, geometry, logic and natural language semantics. However, many of these disciplines use the term ‘duality’ in vastly different senses, and while some of these senses are intimately connected to each other, others seem to be entirely … Continue reading Duality in Logic and Language →.

Die "Gottesfrage" ist anerkanntermaßen eine äußerst komplexe, vieldeutige und obskure Frage. In ausführlicher Auseinandersetzung mit Heidegger, in dessen Schriften eine sehr einflussreiche einseitige und entstellende Interpretation und Kritik der großen metaphysischen Tradition immer wieder präsentiert wird, zeigt Lorenz B. Puntel, dass die Gottesfrage klar, rational und argumentativ, kurz: mit theoretischer Rigorosität, behandelt werden kann. Dies aber setzt einen umfassenden philosophischen Theorierahmen voraus, der die Entfaltung einer systematischen Konzeption des Seins als solchen und im Ganzen ermöglicht und in nuce enthält. (...) Anschließend wird eine solche Konzeption im Grundriss zur Darstellung gebracht. In einem ausführlichen Kapitel werden die Positionen von É. Lévinas und J.-L. Marion, den zwei wohl radikalsten postmodernen Kritikern und Gegnern jeder Form eines positiven Verhältnisses zwischen dem "Sein(sdenken)" und (dem Thema) "Gott", eingehend analysiert und deren radikale Unhaltbarkeit demonstriert. (shrink)

The article aims to show that current understandings and developments of “metaphysics,” in both analytic and continental philosophy, fail to do justice both to the metaphysical tradition as a whole and to the potentialities inherent in that tradition’s mode and aim of thinking. The root failure is the failure to recognize that Thomas Aquinas, by distinguishing between ens and esse, reveals that metaphysics must thematize Being (esse) as well as being(s) (ens/entia). To be sure, Aquinas’s understanding of Being solely as (...) actus essendi is fundamentally inadequate, but Being is not even a topic for analytic philosophy, for which metaphysical questions concern only being(s). The article takes seriously Heidegger’s (only partially correct) charge that an “oblivion of Being” pervades metaphysics and, against Heidegger, shows how to conceive of and develop an adequate theory of Being. (shrink)

In recent years, a number of authors have started studying Aristotelian diagrams containing metalogical notions, such as tautology, contradiction, satisfiability, contingency, strong and weak interpretations of contrariety, etc. The present paper is a contribution to this line of research, and its main aims are both to extend and to deepen our understanding of metalogical diagrams. As for extensions, we not only study several metalogical decorations of larger and less widely known Aristotelian diagrams, but also consider metalogical decorations of another type (...) of logical diagrams, viz. duality diagrams. At a more fundamental level, we present a unifying perspective which sheds new light on the connections between new and existing metalogical diagrams, as well as between object- and metalogical diagrams. Overall, the paper studies two types of logical diagrams and four kinds of metalogical decorations. (shrink)

For a set M, let \\) denote the set of all finite sequences which can be formed with elements of M, and let \ denote the set of all 2-element subsets of M. Furthermore, for a set A, let Open image in new window denote the cardinality of A. It will be shown that the following statement is consistent with Zermelo–Fraenkel Set Theory \: There exists a set M such that Open image in new window and no function Open image (...) in new window is finite-to-one. (shrink)

This paper studies John Buridan's octagons of opposition for the de re modal propositions and the propositions of unusual construction. Both Buridan himself and the secondary literature have emphasized the strong similarities between these two octagons (as well as a third one, for propositions with oblique terms). In this paper, I argue that the interconnection between both octagons is more subtle than has previously been thought: if we move beyond the Aristotelian relations, and also take Boolean considerations into account, then (...) the strong analogy between Buridan's octagons starts to break down. These differences in Boolean structure can already be discerned within the octagons themselves; on a more abstract level, they lead to these two octagons having different degrees of Boolean complexity (i.e. Boolean closures of different sizes). These results are obtained by means of bitstring analysis, which is one of the key tools from contemporary logical geometry. Finally, I argue that this historical investigation is directly relevant for the theoretical framework of logical geometry, and discuss how it helps us to address certain open questions in this framework. (shrink)

The chapter describes the sharing economy in Germany as a heterogeneous dynamic, combining local trends and histories with economic forms drawing on experiences mainly from across Europe and North America. Increasingly taken into account by policymakers in the regulation of markets and the redesign of innovation governance frameworks, “sharing” as a complex nexus linking the exercise of citizenship to sustainable consumption and informational self-determination in digital societies will continue to drive and frame the creation of value chains. Of particular interest (...) are linkages between sharing economies and the traditions of cooperativism, currently experiencing a renaissance. The latter is key because it shapes the context in which sharing economy initiatives exist and expand—an opening of definitions and narrative of innovation, of value, and of collaborative agency and cooperative management. (shrink)

This paper studies the Lockean thesis from the perspective of contemporary epistemic logic. The Lockean thesis states that belief can be defined as ‘sufficiently high degree of belief’. Its main problem is that it gives rise to a notion of belief which is not closed under conjunction. This problem is typical for classical epistemic logic: it is single-agent and static. I argue that from the perspective of contemporary epistemic logic, the Lockean thesis fares much better. I briefly mention that it (...) can successfully be extended from single-agent to multi-agent settings. More importantly, I show that accepting the Lockean thesis (and a more sophisticated version for conditional beliefs) leads to a significant and unexpected unification in the dynamic behavior of (conditional) belief and high (conditional) probability with respect to public announcements. This constitutes a methodological argument in favor of the Lockean thesis. Furthermore, if one accepts Baltag’s Erlangen program for epistemology, this technical observation has even stronger philosophical implications: because belief and high probability display the same dynamic behavior, it is plausible that they are indeed one and the same epistemic notion. (shrink)

For \(n\in \omega \), the weak choice principle \(\textrm{RC}_n\) is defined as follows: _For every infinite set_ _X_ _there is an infinite subset_ \(Y\subseteq X\) _with a choice function on_ \([Y]^n:=\{z\subseteq Y:|z|=n\}\). The choice principle \(\textrm{C}_n^-\) states the following: _For every infinite family of_ _n_-_element sets, there is an infinite subfamily_ \({\mathcal {G}}\subseteq {\mathcal {F}}\) _with a choice function._ The choice principles \(\textrm{LOC}_n^-\) and \(\textrm{WOC}_n^-\) are the same as \(\textrm{C}_n^-\), but we assume that the family \({\mathcal {F}}\) is linearly orderable (...) (for \(\textrm{LOC}_n^-\) ) or well-orderable (for \(\textrm{WOC}_n^-\) ). In the first part of this paper, for \(m,n\in \omega \) we will give a full characterization of when the implication \(\textrm{RC}_m\Rightarrow \textrm{WOC}_n^-\) holds in \({\textsf {ZF}}\). We will prove the independence results by using suitable Fraenkel-Mostowski permutation models. In the second part, we will show some generalizations. In particular, we will show that \(\textrm{RC}_5\Rightarrow \textrm{LOC}_5^-\) and that \(\textrm{RC}_6\Rightarrow \textrm{C}_3^-\), answering two open questions from Halbeisen and Tachtsis (Arch Math Logik 59(5):583–606, 2020). Furthermore, we will show that \(\textrm{RC}_6\Rightarrow \textrm{C}_9^-\) and that \(\textrm{RC}_7\Rightarrow \textrm{LOC}_7^-\). (shrink)

For an integer \, Ramsey Choice\ is the weak choice principle “every infinite setxhas an infinite subset y such that\ has a choice function”, and \ is the weak choice principle “every infinite family of n-element sets has an infinite subfamily with a choice function”. In 1995, Montenegro showed that for \, \. However, the question of whether or not \ for \ is still open. In general, for distinct \, not even the status of “\” or “\” is known. (...) In this paper, we provide partial answers to the above open problems and among other results, we establish the following:1.For every integer \, if \ is true for all integers i with \, then \ is true for all integers i with \.2.If \ are any integers such that for some prime p we have \ and \, then in \: \ and \.3.For \, \\\ implies \, and \ implies neither \ nor \ in \.4.For every integer \, \ implies “every infinite linearly orderable family of k-element sets has a partial Kinna–Wagner selection function” and the latter implication is not reversible in \ ). In particular, \ strictly implies “every infinite linearly orderable family of 3-element sets has a partial choice function”.5.The Chain-AntiChain Principle implies neither \ nor \ in \, for every integer \. (shrink)

Martin Heidegger zählt zu den wirkmächtigsten Denkern des 20. Jahrhunderts - zugleich ist er einer der umstrittensten, nicht zuletzt aufgrund seiner Parteinahme für den Nationalsozialismus 1933. Basierend auf neuesten Quellen erzählt Lorenz Jäger das Leben des Philosophen, der den Menschen und sein Dasein in der Welt auf ganz neue Weise gedacht hat - von der katholischen Kindheit in Messkirch und den geistigen Auseinandersetzungen der zwanziger Jahre über den Nationalsozialismus bis weit in die Jahre des Wiederaufbaus hinein. Dabei begegnen uns (...) Lehrer wie Edmund Husserl, dem 1936 die Lehrerlaubnis entzogen wurde, Vertraute wie Karl Jaspers und Hannah Arendt, deren so schwieriges wie intensives Verhältnis zu Heidegger über historische Brüche hinweg anhielt, Intellektuelle und Dichter wie Ernst Jünger und Paul Celan, die ihn in seiner Schwarzwaldhütte besuchten, bis hin zu späten Interpreten wie Lacan und Derrida. Warum Heidegger jede Generation aufs Neue fasziniert und polarisiert, sein Denken auch heute nichts an Bedeutung eingebüsst hat: Auch das zeigt Lorenz Jäger in dieser Biographie, die meisterhaft das Leben Heideggers erzählt - und zugleich ein deutsches Jahrhundert"--Publisher's website. (shrink)

The vision of an internet of things, increasingly considered in the context of the “internet of everything”, calls for an ethics of technology driven less by the philosophical search for the essence of technology than by a transversal curiosity regarding processes of constitution. If growing interest in enhanced and expanded media literacy approaches facilitates ethical reflection, the scope of such reflection is related to the extent of our attention to and awareness of the immanence of our agency, our capacity for (...) relation in machinic assemblages that structure and sustain our communicative existences far beyond the sphere of signification. While the positions from which such reflection occurs are necessarily multiple, we can still respond to the distribution of agency with an aggregation of responsibility and the creation of a commons with greater attention to the vastness of the spatial and temporal scales of our situation. The idea of depletion design is both a concrete set of design strategies and an attempt to establish an experimental institutional object to facilitate and frame such ethico-aesthetic practice, an architecture for commoning that situates and affirms our ethical agency under the conditions of mediation. (shrink)

The necessary task for philosophy is the development of a metaphysical ontology, i.e., a philosophical theory of everything. The urgency of this task is apparentin, for example, the weakness of proofs for the existence of God. When such “proofs” are not rooted in a comprehensive metaphysical ontology, the principlesapplied, as well as the “God” whose existence has supposedly been proven, are unintelligible. Thus, the explication of Being, from within an adequately articulated framework, should be the central focus of philosophy. The (...) basic conceptual structures required for this task are the three fundamental modalities: necessity, possibility, and contingency. With these tools, we can refute the thesis that everything is contingent and nothing is necessary or absolute. The all-is-contingent thesis has as an implication the assumption of the possibility of absolute nothingness. But this concept both is itself contradictory and has an impossible consequence. Finally, the relation between the absolute dimension of being and persons like us (contingent beings) can be understood by conceiving of the absolute dimension as a personal absolute. From here, we can attempt to interpret the history of the free acts of the personal absolute by studying the history of revealed religions. (shrink)

This paper studies Aumann’s agreeing to disagree theorem from the perspective of dynamic epistemic logic. This was first done by Dégremont and Roy (J Phil Log 41:735–764, 2012) in the qualitative framework of plausibility models. The current paper uses a probabilistic framework, and thus stays closer to Aumann’s original formulation. The paper first introduces enriched probabilistic Kripke frames and models, and various ways of updating them. This framework is then used to prove several agreement theorems, which are natural formalizations of (...) Aumann’s original result. Furthermore, a sound and complete axiomatization of a dynamic agreement logic is provided, in which one of these agreement theorems can be derived syntactically. These technical results are used to show the importance of explicitly representing the dynamics behind the agreement theorem, and lead to a clarification of some conceptual issues surrounding the agreement theorem, in particular concerning the role of common knowledge. The formalization of the agreement theorem thus constitutes a concrete example of the so-called dynamic turn in logic. (shrink)

Several authors have recently studied Aristotelian diagrams for various metatheoretical notions from logic, such as tautology, satisfiability, and the Aristotelian relations themselves. However, all these metalogical Aristotelian diagrams focus on the semantic (model-theoretical) perspective on logical consequence, thus ignoring the complementary, and equally important, syntactic (proof-theoretical) perspective. In this paper, I propose an explanation for this discrepancy, by arguing that the metalogical square of opposition for semantic consequence exhibits a natural analogy to the well-known square of opposition for the categorical (...) statements from syllogistics, but that this analogy breaks down once we move from semantic to syntactic consequence. I then show that despite this difficulty, one can indeed construct metalogical Aristotelian diagrams from a syntactic perspective, which have their own, equally elegant characterization in terms of the categorical statements. Finally, I construct several metalogical Aristotelian diagrams that incorporate both semantic and syntactic consequence (and their interaction), and study how they are influenced by the underlying logical system’s soundness and/or completeness. All of this provides further support for the methodological/heuristic perspective on Aristotelian diagrams, which holds that the main use of these diagrams lies in facilitating analogies and comparisons between prima facie unrelated domains of investigation. (shrink)

Propósito deste ensaio é apresentar uma nova abordagem ao velho problema que é o acesso filosófico ao Deus cristão. Isto acontece dentro do esquema de uma nova metafísica cujo ponto de partida é a capacidade que a mente tem de percepcionar a totalidade do ser, facto este que o artigo apresenta como sendo justamente uma estrutura central do intelecto. Dado que as distinções entre intelecto e mundo, conceitos e realidade, sujeito e objecto, etc., já pressupõem a totalidade do ser dada (...) perceptivamente e nela está baseada, esta totalidade, assim concebida, torna-se mais fundamental que todas aquelas famosas distinções. A tarefa dessa nova metafísica aqui em questão consiste em explicitar uma explicação desta totalidade. No presente artigo, esta explicação é desenvolvida apenas numa direcção, a saber, a explicação no sentido de como proceder da totalidade do ser para o Deus cristão. Neste sentido, uma distinção fundamental é feita entre "o Absoluto" e "Deus ". A filosofia tradicional acreditou frequentemente que a filosofia só poderia explicitar a "determinação" do absoluto como criador do universo finito. O autor do artigo visa justamente demonstrar que outras determinações do Absoluto podem ser filosoficamente alcançadas; mas isto pressupõe que a história da liberdade do Absoluto seja radicalmente tomada em consideração. Ora isto, por sua vez, significa que a história e interpretação da religião - especialmente da religião segundo a tradição judaico-cristã - tem de ser vista como um tópico filosófico verdadeiramente central. Assim compreendido, o Absoluto é apropriadamente designado por "Deus ". Segue-se que uma das consequências desta abordagem é a de que uma vincada distinção entre filosofia tradicional e teologia tradicional cristã deve ser abandonada. /// The purpose of this essay is to present a new approach to the old problem of philosophical access to the Christian God. This is done within the frame of a new metaphysics whose starting point is the mind's perception of the totality of being which is shown to be a central structural feature of the mind as such. Since the distinctions between mind and world, concepts and reality, subject and object, and the like, already presuppose the perceptually given totality of being and are based on it, this totality, so concei-ved, is more fundamental than all those famous distinctions. The task of the envisaged new metaphysics consists in working out an explication of this totality. In this paper this explication is developed only in one direction: the explication in the sense of how to proceed from the totality of being to the Christian God. To this effect, a fundamental distinction is made between "the Absolute" and " God". Traditional philosophy had constantly believed that philosophy could only work out the "determination "of the Absolute as the creator of the finite universe. The paper endeavours to demonstrate that further determinations of the Absolute can be philosophically reached; but this presupposes that the history of the freedom of the Absolute is radically taken into account. And this, in turn, amounts to the claim that the history and interpretation of religion - most especially according to the Judaic-Christian tradition -must be seen as a central philosophical topic. Thus understood, the Absolute is appropriately called " God". One of the consequences of this approach is that the sharp distinction between traditional philosophy and traditional Christian theology should be abandoned. (shrink)

In this paper, we consider certain cardinals in ZF (set theory without AC, the axiom of choice). In ZFC (set theory with AC), given any cardinals C and D, either C ≤ D or D ≤ C. However, in ZF this is no longer so. For a given infinite set A consider $\operatorname{seq}^{1 - 1}(A)$ , the set of all sequences of A without repetition. We compare $|\operatorname{seq}^{1 - 1}(A)|$ , the cardinality of this set, to |P(A)|, the cardinality of (...) the power set of A. What is provable about these two cardinals in ZF? The main result of this paper is that $ZF \vdash \forall A(|\operatorname{seq}^{1 - 1}(A)| \neq|\mathscr{P}(\mathscr{A})|)$ , and we show that this is the best possible result. Furthermore, it is provable in ZF that if B is an infinite set, then $|\operatorname{fin}(B)| <|\mathscr{P}(B)|$ even though the existence for some infinite set B* of a function f from $\operatorname{fin}(B^\ast)$ onto P(B*) is consistent with ZF. (shrink)

The paper attempts to clarify some fundamental aspects of an explanationof the concept of truth which is neither “deflationary” nor “substantive”.The main aspect examined in detail concerns the ontological dimension of truth, the mind/language-world connection traditionally associated with the concept of truth. It is claimed that it does not make sense to defend or reject a relatedness of truth to the ontological dimension so long as the kind of presupposed or envisaged ontology is not made explicit and critically examined. In (...) particular, it is shown that generally an “objectual” ontology is – often only implicitly – presupposed, i.e., an ontology admitting “objects” (substances), properties, relations, sometimes also facts, events, and the like. The paper demonstrates that such an ontology derives from the Principle of Semantic Sentential Compositionality and that this principle should be rejected. It introduces instead the Principle of Semantic Sentential Contextuality (or Context Principle) as the semantic basis of a new ontology, an ontology of “primary states of affairs”. After sketching such an ontology, it is shown that the relatedness of truth to the ontological dimension becomes intelligible. (shrink)

This paper explores the interplay between logic-sensitivity and bitstring semantics in the square of opposition. Bitstring semantics is a combinatorial technique for representing the formulas that appear in a logical diagram, while logic-sensitivity entails that such a diagram may depend, not only on the formulas involved, but also on the logic with respect to which they are interpreted. These two topics have already been studied extensively in logical geometry, and are thus well-understood by themselves. However, the precise details of their (...) interplay turn out to be far more complicated. In particular, the paper describes an elegant and natural interaction between bitstrings and logic-sensitivity, which makes perfect sense when bitstrings are viewed as purely combinatorial entities. However, when we view bitstrings as semantically meaningful entities (which is actually the standard perspective, cf. the term ‘bitstring semantics’!), this interaction does not seem to have a full and equally natural counterpart. The paper describes some attempts to address this situation, but all of them are ultimately found wanting. For now, it thus remains an open problem to capture this interaction between bitstrings and logic-sensitivity from a semantic (rather than merely a combinatorial) perspective. (shrink)

Este manuscrito inédito corresponde al capítulo final del libro _Latin America replies to Transhumanism. __A Symposium on Sorgner’s We have always been cyborgs _a publicarse el año 2024 por la editorial Trivent. Budapest, Hungria. Agradecemos a Stefan L. Sorgner y Teodora C. Artimon por los permisos de publicación. Las referencias a los autores mencionados corresponden a otros capítulos de este mismo libro. Traducción de Nicolás Rojas Cortés y Camilo Vergara Ramírez.

If we assume the axiom of choice, then every two cardinal numbers are comparable, In the absence of the axiom of choice, this is no longer so. For a few cardinalities related to an arbitrary infinite set, we will give all the possible relationships between them, where possible means that the relationship is consistent with the axioms of set theory. Further we investigate the relationships between some other cardinal numbers in specific permutation models and give some results provable without using (...) the axiom of choice. (shrink)

The aim of this paper is to initiate a systematic exploration of the model theory of epistemic plausibility models (EPMs). There are two subtly different definitions in the literature: one by van Benthem and one by Baltag and Smets. Because van Benthem's notion is the most general, most of the paper is dedicated to this notion. We focus on the notion of bisimulation, and show that the most natural generalization of bisimulation to van Benthem-type EPMs fails. We then introduce parametrized (...) bisimulations, and prove various bisimulationimplies- equivalence theorems, a Hennessy-Milner theorem, and several (un)definability results. We discuss the problems arising from the fact that these bisimulations are syntax-dependent (and thus not fully structural), and we present and compare two different ways of coping with this issue: adding a modality to the language, and putting extra constraints on the models. We argue that the most successful solution involves restricting to uniform and locally connected (van Benthem-type) EPMs: for this subclass the intuitively most natural notion of bisimulation and the technically sound notion coincide. Such EPMs turn out to correspond exactly with Baltag/Smets-type EPMs, which can be interpreted as constituting a methodological argument, favoring Baltag and Smets's definition of EPM over that of van Benthem. (shrink)

In this article we give a forcing characterization for the Ramsey property of Σ 1 2 -sets of reals. This research was motivated by the well-known forcing characterizations for Lebesgue measurability and the Baire property of Σ 1 2 -sets of reals. Further we will show the relationship between higher degrees of forcing absoluteness and the Ramsey property of projective sets of reals.

The Sure-Thing Principle famously appears in Savage’s axiomatization of Subjective Expected Utility. Yet Savage introduces it only as an informal, overarching dominance condition motivating his separability postulate P2 and his state-independence postulate P3. Once these axioms are introduced, by and large, he does not discuss the principle any more. In this note, we pick up the analysis of the Sure-Thing Principle where Savage left it. In particular, we show that each of P2 and P3 is equivalent to a dominance condition; (...) that they strengthen in different directions a common, basic dominance axiom; and that they can be explicitly combined in a unified dominance condition that is a candidate formal statement for the Sure-Thing Principle. Based on elementary proofs, our results shed light on some of the most fundamental properties of rational choice under uncertainty. In particular they imply, as corollaries, potential simplifications for Savage’s and the Anscombe- Aumann axiomatizations of Subjective Expected Utility. Most surprisingly perhaps, they reveal that in Savage’s axiomatization, P3 can be weakened to a natural strengthening of so-called Obvious Dominance. (shrink)