This article is concerned to formulate some open problems in the philosophy of space and time that require methods characteristic of mathematical traditions in the foundations of geometry for their solution. In formulating the problems an effort has been made to fuse the separate traditions of the foundations of physics on the one hand and the foundations of geometry on the other. The first part of the paper deals with two classical problems in the geometry of space, that of (...) giving operationalism an exact foundation in the case of the measurement of spatial relations, and that of providing an adequate theory of approximation and error in a geometrical setting. The second part is concerned with physical space and space-time and deals mainly with topics concerning the axiomatic theory of bodies, the operational foundations of special relativity and the conceptual foundations of elementary physics. (shrink)

The philosophy of information (PI) is a new area of research with its own field of investigation and methodology. This article, based on the Herbert A. Simon Lecture of Computing and Philosophy I gave at Carnegie Mellon University in 2001, analyses the eighteen principal open problems in PI. Section 1 introduces the analysis by outlining Herbert Simon's approach to PI. Section 2 discusses some methodological considerations about what counts as a good philosophical problem. The discussion centers on Hilbert's (...) famous analysis of the central problems in mathematics. The rest of the article is devoted to the eighteen problems. These are organized into five sections: problems in the analysis of the concept of information, in semantics, in the study of intelligence, in the relation between information and nature, and in the investigation of values. (shrink)

The Rovelli relational interpretation of quantum mechanics is based on the assumption that the notion of observer-independent state of a physical system is to be rejected. In RQM the primary target of the theory is the analysis of the whole network of relations that may be established among quantum subsystems, and the shift to a relational perspective is supposed to address in a satisfactory way the general problem of the interpretation of quantum mechanics. Here I discuss two basic issues, (...) that I take to be serious open problems of the interpretation. First, I wish to show—mainly through an analysis of the so-called third person problem—that it is far from clear what a relativization of states to observers exactly achieves and in what sense such an approach really advances our understanding of the peculiar features of quantum phenomena. Second, I argue that the claim, according to which RQM is able to preserve locality, is at best dubious. I conclude that further work needs to be done before RQM may aspire to become a satisfactory interpretational framework for the main foundational issues in quantum mechanics. (shrink)

Mereology deals with the study of the relations between wholes and parts. In this work we will discuss different developments and open problems related to the formulation of a quantum mereology. In particular, we will discuss different advances in the development of formal systems aimed to describe the whole-parts relationship in the context of quantum theory.

Mereology deals with the study of the relations between wholes and parts. In this work we will discuss different developments and open problems related to the formulation of a quantum mereology. In particular, we will discuss different advances in the development of formal systems aimed to describe the whole-parts relationship in the context of quantum theory.

In this short note, which is the final chapter of the volume 60 Years of Connexive Logic, we list ten open problems. Some of these problems are technical and precisely stated, while others are less technical and even speculative. We hope that the list inspires some readers to contribute to the field by tackling one or many of the problems.

Jeremy Fix, in ‘Two Sorts of Constitutivism’ (2021), makes a case for the possibility of contingent essential properties to account for the metaphysical status of constitutive standards of things. In this brief note, I will present an open problem affecting Fix's conception, namely, the explanation of the membership of particulars to a genus, which is necessary to identify particulars subject to standards.

The aim of the present paper is to attack some of the conceptual problems that arise when the framework of mathematical learning theory is applied to the description of the behavior of the firm, in setting prices and production quotas, in a competitive market. The goal is to depict the process by which the firm fixes prices and production quotas as a stochastic learning process. A solution to such problems is proposed which is based on statistical-decision concepts. The conceptualization of (...) the behavior of the firm by means of concepts pertaining to mathematical learning theory gives rise to certain mathematical problems, which are formulated here in rather precise terms. (shrink)

This volume presents philosophy of science at its best, i.e. as a philosophical questioning informed by current scientific research, which carefully assesses and evaluates its commitments and consequences. As such it represents philosophy simpliciter at its best, for it is concerned with and dares to ask fundamental questions about the nature of the results of the natural sciences, arguably our most reliable sources of knowledge of the world. The contributions collected in this volume make clear that a philosophy that is (...) disconnected from science is sterile and that the practice of science that is disconnected from a philosophical attempt to understand the natural world in its most general features is blind. Throughout the book we are confronted with questions about the nature of species, numbers, space, time, matter, consciousness and so on. Taking seriously these questions, along with other open problems in philosophy of sciences, and keeping the dialogue between science and philosophy wide open, is likely to be our best bet for a deeper understanding of what surrounds us. The book has a further, deeply important merit. Being the result of a post-graduate conference, it brings together not only leading, long established experts in the field but also new, young researchers, who usually find too small a place within the academic environment. Promoting exactly this kind of interaction is an essential step in constructing a new paradigm for an open, collaborative and fruitful scientific community. (shrink)

We discuss some of the relationships between the notion of "mutual stationarity" of Foreman and Magidor and measurability in inner models. The general thrust of these is that very general mutual stationarity properties on small cardinals, such as the ℵns, is a large cardinal property. A number of open problems, theorems, and conjectures are stated.

In his article Open Problems in the Philosophy of Information 1 Luciano Floridi presented a Philosophy of Information research program in the form of eighteen open problems, covering the following fundamental areas: Information definition, information semantics, intelligence/cognition, informational universe/nature and values/ethics. We revisit Floridis program, highlighting some of the major advances, commenting on unsolved problems and rendering the new landscape of the Philosophy of Information emerging at present. As we analyze the progress of PI we try to situate (...) Floridis program in the context of scientific and technological development that have been made last ten years. We emphasize that Philosophy of Information is a huge and vibrant research field, with its origins dating before Open Problems, and its domains extending even outside their scope. In this paper, we have been able only to sketch some of the developments during the past ten years. Our hope is that, even if fragmentary, this review may serve as a contribution to the effort of understanding the present state of the art and the paths of development of Philosophy of Information as seen through the lens of Open Problems. (shrink)

Decentralized autonomous organizations (DAOs) are a new, rapidly-growing class of organizations governed by smart contracts. Here we describe how researchers can contribute to the emerging science of DAOs and other digitally-constituted organizations. From granular privacy primitives to mechanism designs to model laws, we identify high-impact problems in the DAO ecosystem where existing gaps might be tackled through a new data set or by applying tools and ideas from existing research fields such as political science, computer science, economics, law, and organizational (...) science. Our recommendations encompass exciting research questions as well as promising business opportunities. We call on the wider research community to join the global effort to invent the next generation of organizations. (shrink)

Dov Gabbay is a prolific logician just by himself. But beyond that, he is quite good at making other people investigate the many further things he cares about. As a result, King's College London has become a powerful attractor in our field worldwide. Thus, it is a great pleasure to be an organizer for one of its flagship events: the Augustus de Morgan Workshop of 2005. Benedikt Loewe and I proposed the topic of 'interactive logic' for this occasion, with an (...) emphasis on social software – the logical analysis and design of social procedures – and on games, arguably the formal interactive setting par excellence. This choice reflects current research interests in our logic community at ILLC Amsterdam and beyond. In this broad area of interfaces between logic, computer science, and game theory, this paper is my own attempt at playing Dov. I am, perhaps not telling, but at least asking other people to find out for me what I myself cannot. (shrink)

... to discuss the state of epistemology, inspired by new perspectives and possibilities opened by Hintikka's recent papers on the study of epistemic logic, information, rationality, and inquiry as questioning."--Page 4 of cover.

artificial life, each of which is a grand challenge requiring a major advance on a fundamental issue for its solution. Each problem is briefly explained, and, where deemed helpful, some promising paths to its solution are indicated.

The notation and terminology of this paper follow [2], and are dual to those of [6] and [7]. If L is a language in the narrow sense, Cn may be any consequence operation on sets of sentences of L that includes classical sentential logic. Henceforth when we talk of the language L we intend to include reference to some fixed, though unspecified, operation Cn. X is a deductive system if X = Cn(X). Sentences x, z that are logically equivalent with (...) respect to Cn – that is x ∈ Cn({z}) and z ∈ Cn({x}) – are identified. If X and Z are systems we often write X x instead of x ∈ X and Z X instead of X ⊆ Z. If X = Cn({x}) for some sentence x, X is (finitely) axiomatizable. The set theoretical intersection of X and Z has the logical force of disjunction, and is written X ∨ Z; Cn(X ∪ Z), the smallest system to include both X and Z, is written XZ. If K is a family of systems, [K] and [K] may be defined in an analogous way. The logically strongest system S is the set of all sentences of L; the weakest system T is defined as Cn(∅). The autocomplement Z of Z is defined to be the strongest system to complement T, namely the system [{Y : Y ∨ Z = T}]. More generally we may define X − Z as [{Y : X Y ∨ Z}]. In terms of this operation to remainder, Z is identical with T − Z. The class of all deductive systems forms a distributive lattice under the operations of concatenation and ∨; and indeed a Brouverian algebra (a relatively authocomplemented lattice with unit) under concatenation, ∨ – and T. (shrink)

After briefly introducing the topic of reference, which has a long tradition but did not become a major issue until the last century, when language started to occupy center-stage in philosophy, and after mentioning some of the open problems that the semantic revolution promoted by Saul Kripke and others in the late 1960s and early 1970s left us, which are dealt with in the volume, I offer a preview of the papers collected in the latter, explaining how the volume (...) is organized and how the papers relate to one another. (shrink)

This short paper about fuzzy set-based approximate reasoning first emphasizes the three main semantics for fuzzy sets: similarity, preference and uncertainty. The difference between truth-functional many-valued logics of vague or gradual propositions and non fully compositional calculi such as possibilistic logic (which handles uncertainty) or similarity logics is stressed. Then, potentials of fuzzy set-based reasoning methods are briefly outlined for various kinds of approximate reasoning: deductive reasoning about flexible constraints, reasoning under uncertainty and inconsistency, hypothetical reasoning, exception-tolerant plausible reasoning using (...) generic knowledge, interpolative reasoning, and abductive reasoning (under uncertainty). Open problems are listed in the conclusion. (shrink)

The chapter investigates the main open problems in PI. Section 2.1 introduces their analysis. Section 2.2 discusses some methodological considerations about what counts as a good philosophical problem. The discussion centres on Hilbert's famous analysis of the central problems in mathematics. The rest of the chapter is devoted to the presentation of eighteen main problems. These are organized into five areas: problems in the analysis of the concept of _information_, in _semantics_, in the study of _intelligence_, in the (...) relation between information and _nature_ and in the investigation of _values_. Each area is discussed in a specific section. (shrink)

In response to a paper by Harris & Fitelson, Slaney states several open questions concerning possible strategies for proving distributivity in a wide class of positive sentential logics. In this note, I provide answers to all of Slaney's open questions. The result is a better understanding of the class of positive logics in which distributivity holds.

The schematic CERES method has yielded significant results in proof theory, particularly in the analysis of proof schemata and the extraction of Herbrand systems. However, several challenges remain unresolved, leaving promising investigations for further exploration. This chapter outlines current open problems and concrete plans for future development, with particular emphasis on the completeness of schematic CERES, applications to arithmetic systems, and the ongoing extension of the GAPT system.

We revisit a longstanding question about the shortest single axioms for positive implicational logic. Meredith discovered several 17-symbol single axioms and asked whether shorter ones exist. Later work reduced the problem to four candidate formulas of length 15. Using the automated theorem prover Vampire, we compute saturated clause sets that yield countermodels showing that three of these candidates are not single axioms. This demonstrates the effectiveness of saturation-based reasoning for such problems, which have traditionally been studied via finite model (...) searches. (shrink)

The advent of the Web is one of the defining technological events of the twentieth century, yet its impact on the fundamental questions of philosophy has not yet been explored, much less systematized. The Web, as today implemented on the foundations of the Internet, is broadly construed as the space of all items of interest identified by URIs. Originally a space of linked hypertext documents, today the Web is rapidly evolving as a universal platform for data and computation. Even swifter (...) is the Web‐driven transformation of many previously unquestioned philosophical concepts of privacy, belief, intelligence, cognition, and even embodiment in surprising ways. The ensuing essays in this collection hope to explore the philosophical foundation of the World Wide Web and open the debate on whether or not the changes caused by the Web to technology and society warrant the creation of a philosophy of the Web. (shrink)

This Open Access book addresses the age-old problem of infinite regresses in epistemology. How can we ever come to know something if knowing requires having good reasons, and reasons can only be good if they are backed by good reasons in turn? The problem has puzzled philosophers ever since antiquity, giving rise to what is often called Agrippa's Trilemma. The current volume approaches the old problem in a provocative and thoroughly contemporary way. Taking seriously the idea (...) that good reasons are typically probabilistic in character, it develops and defends a new solution that challenges venerable philosophical intuitions and explains why they were mistakenly held. Key to the new solution is the phenomenon of fading foundations, according to which distant reasons are less important than those that are nearby. The phenomenon takes the sting out of Agrippa's Trilemma; moreover, since the theory that describes it is general and abstract, it is readily applicable outside epistemology, notably to debates on infinite regresses in metaphysics. (shrink)

This paper aims to engage with J. L. Schellenberg’s problem of divine hiddenness. While there has been considerable discussion on this topic, few responses incorporate a Muslim perspective. I aim to fill this gap by engaging with the argument from the perspective of a reflective Muslim. To this end, I draw on the tradition of Islamic Theism to critically evaluate the first premise of Schellenberg’s argument, namely: if a perfectly loving God exists, then there exists a God who is (...) always open to a personal relationship with any finite person. There are several reasons to doubt this premise, and drawing on the Quran, I argue that consent may also have a role to play. I contend that finite persons may consent to divine hiddenness, thus allowing God to limit openness to personal relationship. (shrink)

Conceptual Engineering promises to deliver a new (or unduly neglected) way of doing philosophy whereby progress is to be made by assessing and improving our representational devices (words, concepts, meanings). This methodology faces a famous objection. Namely, Strawson’s Objection: ‘To do [Conceptual Engineering] is not to solve the typical philosophical problem, but to change the subject’ (Strawson [1963]. “Carnap’s Views on Conceptual Systems versus Natural Languages in Analytic Philosophy.” In The Philosophy of Rudolf Carnap, edited by Paul Arthur Schilpp, (...) 503–518. La Salle: Open Court). Despite being over sixty years old, this Objection has yet to receive a fully satisfactory treatment – or so it will be argued. In fact, there are really two worries at large here. There is Strawson’s original worry plus a strengthened, deeper problem: even if you are not changing the subject in doing Conceptual Engineering, you are still not solving the original problem. This deeper objection is The Old Problem Problem. The primary goal here is to offer a response to this Problem which, in turn, delivers a new solution to Strawson’s Objection. This then yields a response to a related worry (The New Problem Problem): Conceptual Engineers are just answering questions that weren’t being asked. The aim here is not to defend Conceptual Engineering as such but to gain a better (more pluralist) picture of what this new approach to philosophy does, and does not, involve. (shrink)

The Monty Hall problem is a problem for causal decision theorists. Or so I argue here. My case for this claim is based on a novel "exotic" variant of the original Monty Hall problem, wherein the game-show contestant has foreknowledge of what door the game-show host will open. I argue that the causal decision theorist's treatment of this case is in tension with our knowledge that we should switch when confronted with the original Monty Hall (...) class='Hi'>problem. (shrink)

One hears a great deal about “Russellian physicalism”, “Russellian panpsychism”, and “Russellian monism”. They’re proposed as solutions to the so-called mind–body problem. There is, however, a great deal of unclarity about Russell’s views on this matter. This is partly his own fault. It’s well known that he endorses “neutral monism”, but he’s also prepared to call himself a materialist or physicalist, and at one point claims to nd himself “driven to a position not unlike that of Berkeley without his (...) God”; and, in all this, he claims to have “completely solved” the mind–body problem. This chapter argues that Russell has good reason to make this last claim, and it defends his self-understanding: (1) he is indeed a neutral monist, as he understands the term; (2) he is indeed a materialist and a physicalist, in the original and best senses of these terms; and (3) he is an outright realist about consciousness who takes it that one knows something of the intrinsic nature of the physical simply in having conscious experience. (4) He is also consistently open to the idea that some form of panpsychism is true, while remaining ofcially agnostic. (shrink)

Heterodox Academy requires its members to pledge their support for its three ideals: open inquiry, viewpoint diversity, and constructive disagreement. Given the history of loyalty oaths in academia, it is surprising that a society that bills itself the way Heterodox Academy does would require one. And there is a more serious problem. “Constructive Disagreement”, as Heterodox Academy understands and advocates for it, is inconsistent with open inquiry and viewpoint diversity.

Open theism argues that traditional responses to the problem of evil fail to provide comfort amidst suffering because of their notion of metaphysical determinism and over-dependence on Greek philosophy. Open theists argue that the best solution to the problem of evil lies in our understanding of the nature of God’s power, which has been relinquished due to his love, the open nature of creation, and the creatures’ inherent powers. This study argues that the open-theistic (...) notion of divine power is reductionistic because it does not consider coercive power as part of divine power. Further, the open theistic logic-of-love defence propagates a loveless God who respects his covenant with the beloved more than the beloved. Finally, the study argues that the open theists’ notions of divine omniscience and divine power are not viable; they raised many questions and objections and, therefore, created room for despair rather than comfort in adversity. (shrink)

Journal of Mathematical Logic, Volume 22, Issue 03, December 2022. In this paper, we show that there exist (continuum many) varieties of bi-Heyting algebras that are not generated by their complete members. It follows that there exist (continuum many) extensions of the Heyting–Brouwer logic [math] that are topologically incomplete. This result provides further insight into the long-standing open problem of Kuznetsov by yielding a negative solution of the reformulation of the problem from extensions of [math] to extensions (...) of [math]. (shrink)

The Problem of Universals is one of the oldest problems of metaphysics. And still, there is no agreement, neither about its nor about its. What is the most adequate formulation of the problem? And what kind of explanation does it require? My aim in this paper is to offer an overview of these two basic questions in the contemporary debate. I will present the four most important formulations (section 1), discuss their connections (section 2) and how the three (...) most prominent are related to these formulations (section 3). We will see that, despite the long history of the problem, in recent years new formulations and approaches have been proposed which may open up original perspectives on its solution. (shrink)

This essay aims at reviewing one of the major difficulties affecting the standard formulation of quantum mechanics, that is, the well-known measurement problem. As it will be explained, the latter originates as a consequence of the quantum theory's postulates. Referring to this, we analyze in particular the conceptual issues implied by the projection (or collapse) rule. After having presented the measurement problem, we then illustrate three possible solutions offered by major interpretations of/alternatives to quantum theory: Bohmian mechanics, Ghirardi–Rimini–Weber (...) theories, and the many-worlds interpretation. As the reader will see, these theoretical frameworks solve this issue by virtue of their unambiguous ontologies and consistent dynamical laws. Finally, a synopsis of the open debates and future perspectives concerning the measurement problem in relativistic contexts concludes the paper. (shrink)

In this article, an attempt is made to introduce a systematization of the loosely connected group of authors called Bildungstheorie. This ought to not only be of significance for German-speaking educational science, for the concept of Bildung is also increasingly used internationally for the formulation and development of pedagogical issues. It is proposed that the concept of complexity could be suitable for bringing attention to common presuppositions in the theoretical dealing with the problem of Bildung. The thesis is that (...) Bildung in theories of Bildung is described from various perspectives as complex, meaning it is an open and uncertain interplay of components irreducibly associated with planning and governance problems. As this thesis is corroborated by means of selected positions within Bildungstheorie, evidence is provided that complexity in educational science—differently than it may seem at first glance—is not for the first time today a theme of importance. Rather, it is demonstrated that a nascent discipline-specific complexity research can be linked to already existing traditions. (shrink)

This paper systematically examines the epistemological pursuit of truth in Bayesian artificial intelligence (AI), arguing that truth convergence is a conditional outcome rather than an inherent property of the algorithm. Bayesian reasoning guarantees formal convergence mathematically, but its alignment with reality depends on prior openness, evidence authenticity, independence, information richness, feedback mechanisms, and institutional support. The study analyzes the limitations of Bayesian convergence theorems, the learnability in open Bayesianism, AI failure modes in modern information ecologies, and design principles and (...) ethical constraints. It emphasizes that truth convergence is not merely an algorithmic property, but a civilizational, collective, and ecological achievement. By implementing non-dogmatic priors, independent evidence channels, explicit modeling of evidence correlations, feedback loop corrections, and institutionalized epistemic humility, AI can pursue truth conditionally. Ultimately, Bayesian AI is both a tool for formal reasoning and a litmus test of civilizational epistemic capacity, providing actionable guidance for modern scientific rationality, ethical practice, and societal institutions. (shrink)

Here I examine the charge that the indeterminism required by event-causal accounts is at best superfluous; if free will is incompatible with determinism, then, it is said, no event-causal libertarian account adequately characterizes free will. The distinction between broad incompatibilism and merely narrow incompatibilism is brought to bear. If the latter thesis is correct, then an event-causal account can secure all that is needed for free will. However, if broad incompatibilism is correct, then no event-causal account is adequate, though such (...) views can still secure some things of value that cannot exist given determinism, such as distinctive types of difference-making and attributability, and the truth of the presumption of open alternatives that we commonly make while deliberating. (shrink)

Let 1 n. We show that the class NrnCAβ of n-dimensional neat reducts of β-dimensional cylindric algebras is not closed under forming elementary subalgebras. This solves a long-standing open problem of Tarski and his co-authors Andréka, Henkin, Monk and Németi. The proof uses genuine model-theoretic arguments.

Recently, many philosophers and psychologists have claimed that the explanation that grounds both passivity phenomena in the cognitive domain and passivity phenomena that occur with respect to overt actions is, along broad lines, the same. Furthermore, they claim that the best account we have of such phenomena in both scenarios is the “comparator” account. However, there are reasons to doubt whether the comparator model can be exported from the realm of overt actions to the cognitive domain in general. There is (...) a lingering worry concerning such explanations of thought insertion: the "What is compared to what?" problem. Here I examine two ways to tackle this problem. First: thought insertion consists of the misattribution of strings of inner speech which are not attenuated (thought insertion is thus another name for auditory verbal hallucinations). Second: thought insertion is misattributed inner speech which exhibits the same phenomenological characteristics as normal inner speech. After explaining the types of problem that each of these potential solutions faces, I conclude with a set of open questions that the comparator theorist has to tackle. (shrink)

In his insightful book, Trust in a Polarized Age, Kevin Vallier (2021) convincingly shows that the legitimacy and sustainability of liberal democratic institutions are dependent upon the maintenance of social and institutional trust. This insight, I believe, has value beyond the illustrious halls of post-Rawlsian, post-Gausian thought. Indeed, while I remain skeptical towards some of the premises of public reason liberalism, I am convinced that any liberal democratic political philosopher who takes the trust literature seriously and who has made their (...) (pragmatic or principled) peace with redistribution has good reasons to sympathize with the general outlines of the institutional palette that emerges out of his book. In this article, I will take for granted Vallier’s assumption that the erosion of social and institutional trust is a serious problem. This motivates investigating the trust-bearing attributes of the redistributive welfare state and the “principle of social insurance” that underpins it. I reconstruct and critically analyse Vallier’s case for a liberal democratic welfare state. I show that he makes a convincing public reason argument for universal social insurance but proceeds too hastily to exclude the principle of unconditionality from consideration. The rest of my paper consists of defending this claim by presenting two kinds of arguments— empirical and theoretical—that I think public reason liberals like Vallier, according to their own commitments, should be motivated to incorporate into their comprehensive discussion of the public justifications for and against basic income. They will show that Universal Basic Income (UBI), although it remains contentious, has some features that could appeal to a diverse citizenry, and thus tilt the balance of public reason judgments towards UBI. (shrink)