In recent years, there has been a growing interest in truthmaker semantics as a framework for understanding a range of phenomena in philosophy and linguistics. Despite this interest, there has been limited study of the various logics that arise from the semantics. This paper aims to address this gap by exploring numerous ‘truthmaker logics’ and proving their compactness and decidability. This is in continuation with the inquiry of Fine and Jago (2019), who proved compactness and decidability for a particular kind (...) of truthmaker logic. The key results going into this are (1) ‘standard translations’ into first-order logic; (2) a truthmaker analogue of the finite model property; and (3) a proof showing that truthmaker consequence on semilattices coincides with truthmaker consequence on complete lattices. Finally, the connection with modal logic is examined. Specifically, it is illustrated how endowing truthmaker semantics with classical negation results in modal information logics. (shrink)

We investigate risk attitudes when the underlying domain of payoffs is finite and the payoffs are, in general, not numerical. In such cases, the traditional notions of absolute risk attitudes, that are designed for convex domains of numerical payoffs, are not applicable. We introduce comparative notions of weak and strong risk attitudes that remain applicable. We examine how they are characterized within the rank-dependent utility model, thus including expected utility as a special case. In particular, we characterize strong (...) comparative risk aversion under rank-dependent utility. This is our main result. From this and other findings, we draw two novel conclusions. First, under expected utility, weak and strong comparative risk aversion are characterized by the same condition over finite domains. By contrast, such is not the case under non-expected utility. Second, under expected utility, weak comparative risk aversion is characterized by the same condition when the utility functions have finite range and when they have convex range. By contrast, such is not the case under non-expected utility. Thus, considering comparative risk aversion over finite domains leads to a better understanding of the divide between expected and non-expected utility, more generally, the structural properties of the main models of decision-making under risk. (shrink)

Hyperboolean algebras are Boolean algebras with operators, constructed as algebras of complexes (or, power structures) of Boolean algebras. They provide an algebraic semantics for a modal logic (called here a {\em hyperboolean modal logic}) with a Kripke semantics accordingly based on frames in which the worlds are elements of Boolean algebras and the relations correspond to the Boolean operations. We introduce the hyperboolean modal logic, give a complete axiomatization of it, and show that it lacks the finite model (...) property. The method of axiomatization hinges upon the fact that a "difference" operator is definable in hyperboolean algebras, and makes use of additional non-Hilbert-style rules. Finally, we discuss a number of open questions and directions for further research. (shrink)

We investigate an enrichment of the propositional modal language L with a "universal" modality ■ having semantics x ⊧ ■φ iff ∀y(y ⊧ φ), and a countable set of "names" - a special kind of propositional variables ranging over singleton sets of worlds. The obtained language ℒ $_{c}$ proves to have a great expressive power. It is equivalent with respect to modal definability to another enrichment ℒ(⍯) of ℒ, where ⍯ is an additional modality with the semantics x ⊧ ⍯φ (...) iff Vy(y ≠ x → y ⊧ φ). Model-theoretic characterizations of modal definability in these languages are obtained. Further we consider deductive systems in ℒ $_{c}$ . Strong completeness of the normal ℒ $_{c}$ logics is proved with respect to models in which all worlds are named. Every ℒ $_{c}$ -logic axiomatized by formulae containing only names (but not propositional variables) is proved to be strongly frame-complete. Problems concerning transfer of properties ([in]completeness, filtration, finite model property etc.) from ℒ to ℒ $_{c}$ are discussed. Finally, further perspectives for names in multimodal environment are briefly sketched. (shrink)

We formally introduce a novel, yet ubiquitous, category of norms: norms of instrumentality. Norms of this category describe which actions are obligatory, or prohibited, as instruments for certain purposes. We propose the Logic of Agency and Norms (LAN) that enables reasoning about actions, instrumentality, and normative principles in a multi-agent setting. Leveraging LAN , we formalize norms of instrumentality and compare them to two prevalent norm categories: norms to be and norms to do. Last, we pose principles relating the three (...) categories and evaluate their validity vis-à-vis notions of deliberative acting. On a technical note, the logic will be shown decidable via the finite model property. (shrink)

We investigate a recently devised polyhedral semantics for intermediate logics, in which formulas are interpreted in n-dimensional polyhedra. An intermediate logic is polyhedrally complete if it is complete with respect to some class of polyhedra. The first main result of this paper is a necessary and sufficient condition for the polyhedral completeness of a logic. This condition, which we call the Nerve Criterion, is expressed in terms of Alexandrov’s notion of the nerve of a poset. It affords a purely combinatorial (...) characterisation of polyhedrally complete logics. Using the Nerve Criterion we show, easily, that there are continuum many intermediate logics that are not polyhedrally complete but which have the finite model property. We also provide, at considerable combinatorial labour, a countably infinite class of logics axiomatised by the Jankov–Fine formulas of ‘starlike trees’ all of which are polyhedrally complete. The polyhedral completeness theorem for these ‘starlike logics’ is the second main result of this paper. (shrink)

We introduce and study a variety of modal logics of parallelism, orthogonality, and affine geometries, for which we establish several completeness, decidability and complexity results and state a number of related open, and apparently difficult problems. We also demonstrate that lack of the finite model property of modal logics for sufficiently rich affine or projective geometries (incl. the real affine and projective planes) is a rather common phenomenon.

I want to model a finite, fallible cognitive agent who imagines that p in the sense of mentally representing a scenario—a configuration of objects and properties—correctly described by p. I propose to capture imagination, so understood, via variably strict world quantifiers, in a modal framework including both possible and so-called impossible worlds. The latter secure lack of classical logical closure for the relevant mental states, while the variability of strictness captures how the agent imports information from actuality in (...) the imagined non-actual scenarios. Imagination turns out to be highly hyperintensional, but not logically anarchic. Section 1 sets the stage and impossible worlds are quickly introduced in Sect. 2. Section 3 proposes to model imagination via variably strict world quantifiers. Section 4 introduces the formal semantics. Section 5 argues that imagination has a minimal mereological structure validating some logical inferences. Section 6 deals with how imagination under-determines the represented contents. Section 7 proposes additional constraints on the semantics, validating further inferences. Section 8 describes some welcome invalidities. Section 9 examines the effects of importing false beliefs into the imagined scenarios. Finally, Sect. 10 hints at possible developments of the theory in the direction of two-dimensional semantics. (shrink)

Gödel's Philosophical Legacy Kurt Gödel's contributions to philosophy extend beyond his incompleteness theorems. He engaged deeply with the work of other philosophers, including Immanuel Kant and Edmund Husserl, and explored topics such as the nature of time, the structure of the universe, and the relationship between mathematics and reality. Gödel's philosophical writings, though less well-known than his mathematical work, offer rich insights into his views on the nature of existence, the limits of human knowledge, and the interplay between the (...) class='Hi'>finite and the infinite. His work continues to inspire and challenge philosophers, mathematicians, and scientists, inviting them to explore the profound and often enigmatic questions at the heart of human understanding. -/- Kurt Gödel's Broader Contributions to Philosophy Kurt Gödel, while primarily known for his monumental incompleteness theorems, made significant contributions that extended beyond the realm of mathematical logic. His philosophical pursuits deeply engaged with the works of eminent philosophers like Immanuel Kant and Edmund Husserl. Gödel's explorations into the nature of time, the structure of the universe, and the relationship between mathematics and reality reveal a profound and multifaceted intellectual legacy. -/- Engagement with Immanuel Kant Gödel held a deep interest in the philosophy of Immanuel Kant. He admired Kant's critical philosophy, particularly the distinction between the noumenal and phenomenal worlds. Kant posited that human experience is shaped by the mind’s inherent structures, leading to the conclusion that certain aspects of reality (the noumenal world) are fundamentally unknowable. Gödel’s incompleteness theorems echoed this Kantian theme, illustrating the limits of formal systems in capturing the totality of mathematical truth. Gödel believed that mathematical truths exis t independently of human thought, akin to Kant's noumenal realm. This philosophical alignment provided a robust foundation for Gödel's Platonism, which asserted the existence of mathematical objects as real, albeit abstract, entities. -/- Influence of Edmund Husserl Gödel was also profoundly influenced by Edmund Husserl, the founder of phenomenology. Husserl's phenomenology emphasizes the direct investigation and description of phenomena as consciously experienced, without preconceived theories about their causal explanation. Gödel saw Husserl's work as a pathway to bridge the gap between the abstract world of mathematics and concrete human experience. Husserl's ideas about the structures of consciousness and the intentionality of thought resonated with Gödel's views on mathematical intuition. Gödel believed that human minds could access mathematical truths through intuition, a concept that draws on Husserlian phenomenological methods. -/- The Nature of Time and the Universe Gödel's philosophical inquiries extended to the nature of time and the structure of the universe. His collaboration with Albert Einstein at the Institute for Advanced Study led to the development of the "Gödel metric" in 1949. This solution to Einstein's field equations of general relativity described a rotating universe where time travel to the past was theoretically possible. Gödel's model challenged conventional notions of time and causality, suggesting that the universe might have a more intricate structure than previously thought. Gödel's exploration of time was not just a mathematical curiosity but a profound philosophical statement about the nature of reality. He questioned whether time was an objective feature of the universe or a construct of human consciousness. His work hinted at a timeless realm of mathematical truths, aligning with his Platonist view. -/- Mathematics and Reality Gödel's philosophical outlook extended to the broader relationship between mathematics and reality. He believed that mathematics provided a more profound insight into the nature of reality than empirical science. For Gödel, mathematical truths were timeless and unchangeable, existing independently of human cognition. This perspective led Gödel to critique the materialist and mechanistic views that dominated 20th-century science and philosophy. He argued that a purely physicalist interpretation of the universe failed to account for the existence of abstract mathematical objects and the human capacity to understand them. Gödel's philosophy suggested a more integrated view of reality, where both physical and abstract realms coexist and inform each other. -/- Gödel's Exploration of Time Kurt Gödel, one of the most profound logicians of the 20th century, ventured beyond the confines of mathematical logic to explore the nature of time. His inquiries into the concept of time were not merely theoretical musings but were grounded in rigorous mathematical formulations. Gödel's exploration of time challenged conventional views and opened new avenues of thought in both physics and philosophy. -/- Gödel and Einstein Gödel’s interest in the nature of time was significantly influenced by his friendship with Albert Einstein. Both were faculty members at the Institute for Advanced Study in Princeton, where they engaged in deep discussions about the nature of reality, time, and space. Gödel's exploration of time culminated in his solution to Einstein's field equations of general relativity, known as the Gödel metric. -/- The Gödel Metric In 1949, Gödel presented a model of a rotating universe, which became known as the Gödel metric. This solution to the equations of general relativity depicted a universe where time travel to the past was theoretically possible. Gödel’s rotating universe contained closed timelike curves (CTCs), paths in spacetime that loop back on themselves, allowing for the possibility of traveling back in time. The Gödel metric posed a significant philosophical challenge to the conventional understanding of time. If time travel were possible, it would imply that time is not linear and absolute, as commonly perceived, but rather malleable and subject to the geometry of spacetime. This raised profound questions about causality, the nature of temporal succession, and the very structure of reality. -/- Philosophical Implications Gödel’s exploration of time extended beyond the mathematical implications to broader philosophical inquiries: Nature of Time: Gödel questioned whether time was an objective feature of the universe or a construct of human consciousness. His work suggested that our understanding of time as a linear progression from past to present to future might be an illusion, shaped by the limitations of human perception. -/- Causality and Free Will: The existence of closed timelike curves in Gödel’s model raised questions about causality and free will. If one could travel back in time, it would imply that future events could influence the past, potentially leading to paradoxes and challenging the notion of a deterministic universe. -/- Temporal Ontology: Gödel's work contributed to debates in temporal ontology, particularly the debate between presentism (the view that only the present exists) and eternalism (the view that past, present, and future all equally exist). Gödel’s rotating universe model seemed to support eternalism, suggesting a block universe where all points in time are equally real. Philosophy of Science: Gödel’s exploration of time had implications for the philosophy of science, particularly in the context of understanding the limits of scientific theories. His work underscored the importance of considering philosophical questions when developing scientific theories, as they shape our fundamental understanding of concepts like time and space. -/- Legacy Gödel’s exploration of time remains a significant and controversial contribution to both physics and philosophy. His work challenged established notions and encouraged deeper inquiries into the nature of reality. Gödel’s rotating universe model continues to be a topic of interest in theoretical physics and cosmology, inspiring new research into the nature of time and the possibility of time travel. In philosophy, Gödel’s inquiries into time have prompted ongoing debates about the nature of temporal reality, the relationship between mathematics and physical phenomena, and the limits of human understanding. His work exemplifies the intersection of mathematical rigor and philosophical inquiry, demonstrating the profound insights that can emerge from such an interdisciplinary approach. The Temporal Ontology of Kurt Gödel Kurt Gödel's profound contributions to mathematics and logic extend into the realm of temporal ontology—the philosophical study of the nature of time and its properties. Gödel's insights challenge conventional perceptions of time and suggest a more intricate, layered understanding of temporal reality. This essay explores Gödel's contributions to temporal ontology, particularly through his engagement with relativity and his philosophical reflections. -/- Gödel's Rotating Universe One of Gödel’s most notable contributions to temporal ontology comes from his work in cosmology, specifically his solution to Einstein’s field equations of general relativity, known as the Gödel metric. Introduced in 1949, the Gödel metric describes a rotating universe with closed timelike curves (CTCs). These curves imply that, in such a universe, time travel to the past is theoretically possible, presenting a significant challenge to conventional views of linear, unidirectional time. -/- Implica tions for Temporal Ontology Gödel's rotating universe model has profound implications for our understanding of time: Eternalism vs. Presentism: Gödel’s model supports the philosophical stance known as eternalism, which posits that past, present, and future events are equally real. In contrast to presentism, which holds that only the present moment exists, eternalism suggests a "block universe" where time is another dimension like space. Gödel’s rotating universe, with its CTCs, reinforces this view by demonstrating that all points in time could, in principle, be interconnected in a consistent manner. Non-linearity of Time: The possibility of closed timelike curves challenges the idea of time as a linear sequence of events. In Gödel’s universe, time is not merely a straight path from past to future but can loop back on itself, allowing for complex interactions between different temporal moments. This non-linearity has implications for our understanding of causality and the nature of temporal succession. Objective vs. Subjective Time: Gödel’s work invites reflection on the distinction between objective time (the time that exists independently of human perception) and subjective time (the time as experienced by individuals). His model suggests that our subjective experience of a linear flow of time may not correspond to the objective structure of the universe. This raises questions about the relationship between human consciousness and the underlying temporal reality. -/- Gödel and Philosophical Reflections on Time Gödel’s engagement with temporal ontology was not limited to his cosmological work. He also reflected deeply on philosophical questions about the nature of time and reality, drawing on the ideas of other philosophers and integrating them into his own thinking. Kantian Influences: Gödel was influenced by Immanuel Kant’s distinction between the noumenal world (things as they are in themselves) and the phenomenal world (things as they appear to human observers). Gödel’s views on time echoed this distinction, suggesting that our perception of time might be a phenomenon shaped by the limitations of human cognition, while the true nature of time (the noumenal aspect) might be far more complex and non-linear. Husserlian Phenomenology: Gödel’s interest in Edmund Husserl’s phenomenology also informed his views on time. Husserl’s emphasis on the structures of consciousness and the intentionality of thought resonated with Gödel’s belief in the importance of intuition in accessing mathematical truths. Gödel’s reflections on time incorporated a phenomenological perspective, considering how temporal experience is structured by human consciousness. Mathematical Platonism: Gödel’s Platonist views extended to his understanding of time. Just as he believed in the independent existence of mathematical objects, Gödel saw time as an objective entity with a structure that transcends human perception. His work on the Gödel metric can be seen as an attempt to uncover this objective structure, revealing the deeper realities that underlie our experience of time. (shrink)

We present a novel approach to defining the mathematical constant π through the infinite den- sification of a sweeping net, which approximates a circle as the net becomes infinitely dense. By developing and enhancing notation related to sweeping nets and saddle maps, we establish a rigor- ous framework for expressing π in terms of the densification process using reverse integration. This method, inspired by the concept that numbers ”come from infinity,” leverages a reverse integral approach to model the transition (...) from infinite densification to the finite circle. Our work not only offers a new perspective on the geometric interpretation of π but also provides insights into reverse integration techniques and their applications in mathematical analysis. (shrink)

The electronic and muonic hydrogen energy levels are calculated very accurately [1] in Quantum Electrodynamics (QED) by coupling the Dirac Equation four vector (c ,mc2) current covariantly with the external electromagnetic (EM) field four vector in QED’s Interactive Representation (IR). The c -Non Exclusion Principle(c -NEP) states that, if one accepts c as the electron/muon velocity operator because of the very accurate hydrogen energy levels calculated, the one must also accept the resulting electron/muon internal spatial and time coordinate operators (ISaTCO) (...) derived directly from c without any assumptions. This paper does not change any of the accurate QED calculations of hydrogen’s energy levels, given the simplistic model of the proton used in these calculations [1]. The Proton Radius Puzzle [2, 3] may indicate that new physics is necessary beyond the Standard Model (SM), and this paper describes the bizarre, and very different, situation when the electron and muon are located “inside” the spatially extended proton with their Centers of Charge (CoCs) orbiting the proton at the speed of light in S energy states. The electron/muon center of charge (CoC) is a structureless point that vibrates rapidly in its inseparable, non-random vacuum whose geometry and time structure are defined by the electron/muon ISaTCO discrete geometry. The electron/muon self mass becomes finite in a natural way due to the ISaTCOs cutting off high virtual photon energies in the photon propagator. The Dirac-Maxwell-Wilson (DMW) Equations are derived from the ISaTCO for the EM fields of an electron/muon, and the electron/muon “look” like point particles in far field scattering experiments in the same way the electric field from a sphere with evenly distributed charge “e” “looks” like a point with the same charge in the far field (Gauss Law). The electron’s/muon’s three fluctuating CoC internal spatial coordinate operators have eight possible eigenvalues [4, 5, 6] that fall on a spherical shell centered on the electron’s CoM with radius in the rest frame. The electron/muon internal time operator is discrete, describes the rapid virtual electron/positron pair production and annihilation. The ISaTCO together create a current that produce spin and magnetic moment operators, and the electron and muon no longer have “intrinsic” properties since the ISaTCO kinematics define spin and magnetic moment properties. (shrink)

In this paper, I examine Wittgenstein’s conception of reason and rationality through the lens of his conception of reasons. Central in this context, I argue, is the image of the chain, which informs not only his methodology in the form of the chain-method, but also his conception of reasons as linking up immediately, like the links of a chain. I first provide a general sketch of what reasons are on Wittgenstein’s view, arguing that giving reasons consists in making thought and (...) action intelligible by delineating reasoning routes; that something is a reason not in virtue of some intrinsic property, but in virtue of its role; and that citing something as a reason characterises it in terms of the rational relations it stands in according to context-dependent norms. I then argue that on Wittgenstein’s view, we misconceive chains of reasons if we think of them on the model of chains of causes. Chains of reasons are necessarily finite, because they are anchored in and held in place by our reason-giving practices, and it is in virtue of their finitude that chains of reasons can guide, justify and explain. I argue that this liberates us from the expectation that one should be able to give reasons for everything, but that it limits the reach of reasons by tying them to particular reasoning-practices that they cannot themselves justify. I end by comparing and reconciling Wittgenstein’s dichotomy between chains of reasons and chains of causes with seemingly competing construals of the dichotomy, and I clarify its relation to the dichotomy between explanation and justification. (shrink)

Classical logic is usually interpreted as the logic of propositions. But from Boole's original development up to modern categorical logic, there has always been the alternative interpretation of classical logic as the logic of subsets of any given (nonempty) universe set. Partitions on a universe set are dual to subsets of a universe set in the sense of the reverse-the-arrows category-theoretic duality--which is reflected in the duality between quotient objects and subobjects throughout algebra. Hence the idea arises of a dual (...) logic of partitions. That dual logic is described here. Partition logic is at the same mathematical level as subset logic since models for both are constructed from (partitions on or subsets of) arbitrary unstructured sets with no ordering relations, compatibility or accessibility relations, or topologies on the sets. Just as Boole developed logical finite probability theory as a quantitative treatment of subset logic, applying the analogous mathematical steps to partition logic yields a logical notion of entropy so that information theory can be refounded on partition logic. But the biggest application is that when partition logic and the accompanying logical information theory are "lifted" to complex vector spaces, then the mathematical framework of quantum mechanics is obtained. Partition logic models indefiniteness (i.e., numerical attributes on a set become more definite as the inverse-image partition becomes more refined) while subset logic models the definiteness of classical physics (an entity either definitely has a property or definitely does not). Hence partition logic provides the backstory so the old idea of "objective indefiniteness" in QM can be fleshed out to a full interpretation of quantum mechanics. (shrink)

The abstract basis of modern computation is the formal description of a finite state machine, the Universal Turing Machine, based on manipulation of integers and logic symbols. In this contribution to the discourse on the computer-brain analogy, we discuss the extent to which analog computing, as performed by the mammalian brain, is like and unlike the digital computing of Universal Turing Machines. We begin with ordinary reality being a permanent dialog between continuous and discontinuous worlds. So it is with (...) computing, which can be analog or digital, and is often mixed. The theory behind computers is essentially digital, but efficient simulations of phenomena can be performed by analog devices; indeed, any physical calculation requires implementation in the physical world and is therefore analog to some extent, despite being based on abstract logic and arithmetic. The mammalian brain, comprised of neuronal networks, functions as an analog device and has given rise to artificial neural networks that are implemented as digital algorithms but function as analog models would. Analog constructs compute with the implementation of a variety of feedback and feedforward loops. In contrast, digital algorithms allow the implementation of recursive processes that enable them to generate unparalleled emergent properties. We briefly illustrate how the cortical organization of neurons can integrate signals and make predictions analogically. While we conclude that brains are not digital computers, we speculate on the recent implementation of human writing in the brain as a possible digital path that slowly evolves the brain into a genuine (slow) Turing machine. (shrink)

It is well-known that the global structure of every space-time model for relativistic cosmology is observationally underdetermined. In order to alleviate the severity of this underdetermination, it has been proposed that we adopt the Cosmological Principle because the Principle restricts our attention to a distinguished class of space-time models (spatially homogeneous and isotropic models). I argue that, even assuming the Cosmological Principle, the topology of space remains observationally underdetermined. Nonetheless, I argue that we can muster reasons to prefer various (...) topological properties over others. In particular, I favor the adoption of multiply connected universe models on grounds of (i) simplicity, (ii) Machian considerations, and (iii) explanatory power. We are able to appeal to such grounds because multiply connected topologies open up the possibility of finite universe models (consistent with our best data), which in turn avoid thorny issues concerning the postulation of an actually infinite universe. (shrink)

Purpose. The article aims to provide practical recommendations for calculating natural frequencies in axisymmetric shells using finite element methods. It focuses on the need to develop a simplified model that can be used in any modern finite element software package. The study analyzes the impact of the simplified homogeneous model on the deviation and error of natural frequencies compared to real structures. Design / Method / Approach. The research is based on creating a simplified shell geometry (...) by determining parameters such as shell thickness and density. These parameters are derived under the condition of equivalence in the moment of inertia and mass of the cross-sectional element. These parameters can vary along the height of the shell. Findings. The natural frequencies of the experimental shell with complex geometry were calculated and compared with those of the simplified model. The deviations and errors in the calculated frequencies were determined. It was demonstrated that the simplified model allows the calculation of natural frequencies with a deviation of no more than 1% from the experimental model, while significantly reducing computation time and the required computer resources. Theoretical Implications. The research expands the understanding of challenges in calculating the natural frequencies of complex objects using finite element methods under limited computational resources. Practical Implications. Practical recommendations are provided for engineers and designers when performing modeling tasks in the mechanics of deformable solid bodies. Originality / Value. The article presents an original analysis of a real case where a simplified model was implemented to determine the natural harmonics of a liquid rocket engine nozzle, making it a valuable tool for studying complex structures. Research Limitations / Future Research. The study is limited to the analysis of determining the natural frequencies of axisymmetric shells and does not cover all possible geometric features. Future research may focus on developing simplified models based on the equivalence of stiffness and mass parameters. Article Type. Case study, practical article. (shrink)

In this dissertation we present proof systems for several modal logics. These proof systems are based on analytic (or semantic) tableaux. -/- Modal logics are logics for reasoning about possibility, knowledge, beliefs, preferences, and other modalities. Their semantics are almost always based on Saul Kripke’s possible world semantics. In Kripke semantics, models are represented by relational structures or, equivalently, labeled graphs. Syntactic formulas that express statements about knowledge and other modalities are evaluated in terms of such models. -/- This dissertation (...) focuses on modal logics with dynamic operators for public announcements, belief revision, preference upgrades, and so on. These operators are defined in terms of mathematical operations on Kripke models. Thus, for example, a belief revision operator in the syntax would correspond to a belief revision operation on models. -/- The ‘dynamic’ semantics of dynamic modal logics are a clever way of extending languages without compromising on intuitiveness. We present ‘dynamic’ tableau proof systems for these dynamic semantics, with the express aim to make them conceptually simple, easy to use, modular, and extensible. This we do by reflecting the semantics as closely as possible in the components of our tableau system. For instance, dynamic operations on Kripke models have counterpart dynamic relations between tableaux. -/- Soundness, completeness, and decidability are three of the most important properties that a proof system may have. A proof system is sound if and only if any formula for which a proof exists, is true in every model. A proof system is complete if and only if for any formula that is true in all models, a proof exists. A proof system is decidable if and only if any formula can be proved to be a theorem or not a theorem in a finite number of steps. All proof systems in this dissertation are sound, complete, and decidable. -/- Part of our strategy to create modular tableau systems is to delay concerns over decidability until after soundness and completeness have been established. Decidability is attained through the operations of folding and through operations on ‘tableau cascades’, which are graphs of tableaux. -/- Finally, we provide a proof-of-concept implementation of our dynamic tableau system for public announcement logic in the Clojure programming language. (shrink)

The conventional notion of a formal system is adapted to conform to the sound deductive inference model operating on finite strings. Finite strings stipulated to have the semantic property of Boolean true provide the sound deductive premises. Truth preserving finite string transformation rules provide valid the deductive inference. Conclusions of sound arguments are derived from truth preserving finite string transformations applied to true premises.

The prospects and limitations of defining truth in a finite model in the same language whose truth one is considering are thoroughly examined. It is shown that in contradistinction to Tarski's undefinability theorem for arithmetic, it is in a definite sense possible in this case to define truth in the very language whose truth is in question.

ABSTRACT The main informational components of consciousness are described as Operative Informational System (OIS) assuring the reactive short-time adaptation and Programmed Informational System (PIS), assuring the life maintenance and the species survival, working in an integrated manner with the informed matter IM (body). The defined informational subsystems allow to describe consciousness as a sum of cognition centers defined by Ibelieve, Iknow, Iwant, Ilove, Iam, Icreate and Icreated. The cognition center Ibelieve was defined as related with the anti-entropic field of the (...) bipolar universal matter/antimatter informational system, assisting the life structuring and health and explaining the precognition, psychokinesis, near-death experiences and other "paranormal" phenomena. PIS related activity of the cognition centers was described as the projected data in OIS by two components: (1) personal status as survival needs; (2) the info-consequences on oneself perception and action impulses perceived by Iam, Icreate and Icreated, reflecting together with Iknow, Iwant and Ilove the "normal" (regular) mind properties. (shrink)

We study several perfect set properties of the Baire space which follow from the Ramsey property ω→(ω) ω . In particular we present some independence results which complete the picture of how these perfect set properties relate to each other.

Twenty-first century science faces a dilemma. Two of its well-verified foundation stones - relativity and quantum theory - have proven inconsistent. Resolution of the conflict has resisted improvements in experimental precision leaving some to believe that some fundamental understanding in our world-view may need modification or even radical reform. Employment of the wave-front model of electrodynamics, as a propagation process with a Markov property, may offer just such a clarification.

According to Finite Fine-grainedness (roughly), there is a finite sequence of intuitively small differences between any two welfare levels. The assumption of Finite Fine-grainedness is essential to Gustaf Arrhenius’s favored sixth impossibility theorem in population axiology and plays an important role in the spectrum argument for the (Negative) Repugnant Conclusion. I argue that Theravāda Buddhists will deny Finite Fine-grainedness and consider the space that doing so opens up—and fails to open up—in population axiology. I conclude with (...) a lesson for population axiology that generalizes beyond the Buddhist context: to plausibly deny Finite Fine-grainedness, we must locate a welfare good—such as the good of awakening (bodhi)—with some rather esoteric axiological properties. (shrink)

Kripke models, interpreted realistically, have difficulty making sense of the thesis that there might have existed things that do not in fact exist, since a Kripke model in which this thesis is true requires a model structure in which there are possible worlds with domains that contain things that do not exist. This paper argues that we can use Kripke models as representational devices that allow us to give a realistic interpretation of a modal language. The method of (...) doing this is sketched, with the help of an analogy with a Galilean relativist theory of spatial properties and relations. (shrink)

This study considers the problem of using approximate way for realizing the neural supervisor for nonlinear multivariable systems. The Nonlinear Autoregressive-Moving Average (NARMA) model is an exact transformation of the input-output behavior of finite-dimensional nonlinear discrete time dynamical organization in a hoodlum of the equilibrium state. However, it is not convenient for intention of adaptive control using neural networks due to its nonlinear dependence on the control input. Hence, quite often, approximate technique are used for realizing the neural (...) supervisor to overcome computational complexity. In this study, we introduce two classes of ideal which are approximations to the NARMA model and which are linear in the control input, namely NARMA-L1 and NARMA-L2. The latter fact substantially simplifies both the theoretical breakdown as well as the practical request of the controller. Extensive imitation studies have shown that the neural controller designed using the proposed approximate models perform very well and in dozens situation even better than an approximate controller designed using the exact NARMA Model. In view of their mathematical tractability as well as their fate in simulation studies, a matter is made in this study that such approximate input-output paragon warrants a detailed study in their own right. (shrink)

A first-order theory T has the Independence Property provided deduction of a statement of type (quantifiers) (P -> (P1 or P2 or .. or Pn)) in T implies that (quantifiers) (P -> Pi) can be deduced in T for some i, 1 <= i <= n). Variants of this property have been noticed for some time in logic programming and in linear programming. We show that a first-order theory has the Independence Property for the class of basic (...) formulas provided it can be axiomatized with Horn sentences. The existence of free models is a useful intermediate result. The independence Property is also a tool to decide that a sentence cannot be deduced. We illustrate this with the case of the classical Caratheodory theorem for Pasch-Peano geometries. (shrink)

There has recently been an explosion of formal models of signalling, which have been developed to learn about different aspects of meaning. This paper discusses whether that success can also be used to provide an original naturalistic theory of meaning in terms of information or some related notion. In particular, it argues that, although these models can teach us a lot about different aspects of content, at the moment they fail to support the idea that meaning just is some kind (...) of information. As an alternative, I suggest a more modest approach to the relationship between informational notions used in models and semantic properties in the natural world. (shrink)

This paper concerns model-checking of fragments and extensions of CTL* on infinite-state Presburger counter systems, where the states are vectors of integers and the transitions are determined by means of relations definable within Presburger arithmetic. In general, reachability properties of counter systems are undecidable, but we have identified a natural class of admissible counter systems (ACS) for which we show that the quantification over paths in CTL* can be simulated by quantification over tuples of natural numbers, eventually allowing translation (...) of the whole Presburger-CTL* into Presburger arithmetic, thereby enabling effective model checking. We provide evidence that our results are close to optimal with respect to the class of counter systems described above. (shrink)

The dynamic viscoelastic properties of Polyvinylacetate with molecular weight 83000g/mol (PVA 83K) were determined by using a Rheometer operated in the dynamic mode and 8 mm parallel plate over a wide range of temperature as a function of frequency. The measurements were performed successively in the parallel plate geometry using 8 mm plate instead of 25 mm. The glass plateau regime is clearly observed because we could measure PVA 83K sample successively under its glass temperature. The rheological properties of polydisperse (...) PVA 83K were completely studied and the experimental data were analyzed using the Winter model. (shrink)

What is the connection between modelling thought and modelling the brain? In a model (as understood here), we strip away from the modelled system some non-essential features and retain some essential ones. What are the essential features of thought that are to be re- tained in the model, and conversely, what are its inessential features, that may be stripped away in the model? According to a prevalent view in contemporary science and philoso- phy, thought is a computation, (...) and therefore its essential features are its computational features. A necessary part of the computational view of thought is the idea that the same computation can be realised by, or implemented in, physically heterogeneous systems, an idea known as “Multiple Realizability” of the computational features or properties by the physical ones. I will describe why the very idea of Multiple Realizability, especially in the case of mental computation, entails mind-body dualism, and explore some implications of this conclusion concerning the question of which are the essential features of thought to be retained in modeling it. (shrink)

New developments in biotechnology radically alter our relationship with our bodies. Body tissues can now be used for commercial purposes, while external objects, such as pacemakers, can become part of the body. Property in the Body: Feminist Perspectives transcends the everyday responses to such developments, suggesting that what we most fear is the feminisation of the body. We fear our bodies are becoming objects of property, turning us into things rather than persons. This book evaluates how well-grounded this (...) fear is, and suggests innovative models of regulating what has been called 'the new Gold Rush' in human tissue. This is an up-to-date and wide-ranging synthesis of market developments in body tissue, bringing together bioethics, feminist theory and lessons from countries that have resisted commercialisation of the body, in a theoretically sophisticated and practically significant approach. (shrink)

This paper shows how the classical finite probability theory (with equiprobable outcomes) can be reinterpreted and recast as the quantum probability calculus of a pedagogical or "toy" model of quantum mechanics over sets (QM/sets). There are two parts. The notion of an "event" is reinterpreted from being an epistemological state of indefiniteness to being an objective state of indefiniteness. And the mathematical framework of finite probability theory is recast as the quantum probability calculus for QM/sets. The point (...) is not to clarify finite probability theory but to elucidate quantum mechanics itself by seeing some of its quantum features in a classical setting. (shrink)

In identifying intrinsic molecular chance and extrinsic adaptive pressures as the only causally relevant factors in the process of evolution, the theoretical perspective of the Modern Synthesis had a major impact on the perceived tenability of an ontology of dispositional properties. However, since the late 1970s, an increasing number of evolutionary biologists have challenged the descriptive and explanatory adequacy of this “chance alone, extrinsic only” understanding of evolutionary change. Because morphological studies of homology, convergence, and teratology have revealed a space (...) of possible forms and phylogenetic trajectories that is considerably more restricted than expected, evo-devo has focused on the causal contribution of intrinsic developmental processes to the course of evolution. Evo-devo’s investigation into the developmental structure of the modality of morphology – including both the possibility and impossibility of organismal form – has led to the utilisation of a number of dispositional concepts that emphasise the tendency of the evolutionary process to change along certain routes. In this sense, and in contrast to the perspective of the Modern Synthesis, evo-devo can be described as a “science of dispositions.” This chapter discusses the recent philosophical literature on dispositional properties in evo-devo, exploring debates about both the metaphysical and epistemological aspects of the central dispositional concepts utilised in contemporary evo-devo and addressing the epistemological question of how dispositional properties challenge existing explanatory models in evolutionary biology. (shrink)

The descriptions and theoretical laws scientists write down when they model a system are often false of any real system. And yet we commonly talk as if there were objects that satisfy the scientists’ assumptions and as if we may learn about their properties. Many attempt to make sense of this by taking the scientists’ descriptions and theoretical laws to define abstract or fictional entities. In this paper, I propose an alternative account of theoretical modelling that draws upon Kendall (...) Walton’s ‘make-believe’ theory of representation in art. I argue that this account allows us to understand theoretical modelling without positing any object of which scientists’ modelling assumptions are true. (shrink)

Concerns over epistemic opacity abound in contemporary debates on Artificial Intelligence (AI). However, it is not always clear to what extent these concerns refer to the same set of problems. We can observe, first, that the terms 'transparency' and 'opacity' are used either in reference to the computational elements of an AI model or to the models to which they pertain. Second, opacity and transparency might either be understood to refer to the properties of AI systems or to the (...) epistemic situation of human agents with respect to these systems. While these diagnoses are independently discussed in the literature, juxtaposing them and exploring possible interrelations will help to get a view of the relevant distinctions between conceptions of opacity and their empirical bearing. In pursuit of this aim, two pertinent conditions affecting computer models in general and contemporary AI in particular are outlined and discussed: opacity as a problem of computational tractability and opacity as a problem of the universality of the computational method. (shrink)

We prove that all extensions of Heyting Arithmetic with a logic that has the finite frame property possess the de Jongh property.

Traditional wisdom dictates that statistical model outputs are estimates, not measurements. Despite this, statistical models are employed as measurement instruments in the social sciences. In this article, I scrutinize the use of a specific model—the logit model—for psychological measurement. Given the adoption of a criterion for measurement that I call comparability, I show that the logit model fails to yield measurements due to properties that follow from its fixed residual variance.

In 'Forever Finite: The Case Against Infinity' (Rond Books, 2023), the author argues that, despite its cultural popularity, infinity is not a logical concept and consequently cannot be a property of anything that exists in the real world. This article summarizes the main points in 'Forever Finite', including its overview of what debunking infinity entails for conceptual thought in philosophy, mathematics, science, cosmology, and theology.

There are alternative models, which are based on the evaluation of certain properties, based on physiology or evolutionary psychology. Classical philosophers have addressed emotions as responses to certain types of events that are related to a subject, causing bodily and behavioral changes. In the last century emotions were neglected, being considered a disturbing factor. Lately, emotions have returned to the attention of philosophers and psychologists, corroborating them with other disciplines such as psychology, neurology, evolutionary biology and even economics. DOI: 10.13140/RG.2.2.28869.06881 (...) . (shrink)

Darwin famously held that his use of the term "chance" in evolutionary theory merely "serves to acknowledge plainly our ignorance of the causes of each particular variation". Is this a tenable view today? Or should we revise our thinking about chance in evolution in light of the more advanced, quantitative models of Neo-Darwinian theory, which make substantial use of statistical reasoning and the concept of probability? Is determinism still a viable metaphysical doctrine about biological reality after the quantum revolution in (...) physics, or dowe have to abandon it in favor of an objective indeterminism? In light of such reflections, what is the relevant interpretation of probability in evolutionary theory? Do biologists use the concept of probability because they are finite cognitive agents or because the evolutionary process is fundamentally probabilistic? In this paper, I will show that we do not yet fully understand the nature of chance in evolution. (shrink)

We prove that all extensions of Heyting Arithmetic with a logic that has the finite frame property possess the de Jongh property.

The central idea is that the cerebral cortex is a model building machine, where regularities in the world serve as templates for the models it builds. First it is shown how this idea can be naturalized, and how the representational contents of our internal models depend upon the evolutionarily endowed design principles of our model building machine. Current neuroscience suggests a powerful form that these design principles may take, allowing our brains to uncover deep structures of the world (...) hidden behind surface sensory stimulation, the individuals, kinds, and properties that form the objects of human perception and thought. It is then shown how this account solves various problems that arose for previous attempts at naturalizing intentionality, and also how it supports rather than undermines folk psychology. As in the parable of the blind men and the elephant, the seemingly unrelated pieces of earlier theories (information, causation, isomorphism, success, and teleology) emerge as different aspects of the evolved model-building mechanism that explains the intentional features of our kind of mind. (shrink)

The objective of this paper is to introduce, into the English scientific-philosophical literature of Genetic Epistemology, a model called the Model of the System of Schemes of Actions and Operations on Symbols and Signs (MoSSAOSS), and summarize its results, so far. MoSSAOSS articulates some of the principal theoretical and experimental results obtained by Piaget and his coworkers, in a systemic, systematic and synthetic view. Here, the term model means a schematic representation of experience, in which the relation (...) of elements can be explored by means of logic and mathematics in order to deduce properties that correspond to direct observable empirical properties, in a sufficiently accurate form. Through explicit definitions and hypotheses, MoSSAOSS intends to reveal, in an abstract and simplified form, the general structure and functioning of the System of Schemes of Actions and Operations on Symbols and Signs. This system makes explicit the necessary elements for the acquisition of knowledge by the epistemic subject (the knower subject), allowing for the explanation of its developmental stages, as well as the attribution of meaning to objects and situations, and to the subject’s actions and operations. Conceived in 1992 and introduced in Portuguese scientific-philosophical literature in 2014, MoSSAOSS has been used in a research program to study the necessary structures for knowledge acquisition, particularly scientific-philosophical knowledge. Its main results are summarized here. (shrink)

In a recent paper, Bird (in: Groff (ed.) Revitalizing causality: Realism about causality in philosophy and social science, 2007 ) has argued that some higher-order properties—which he calls “evolved emergent properties”—can be considered causally efficacious in spite of exclusion arguments. I have previously argued in favour of a similar position. The basic argument is that selection processes do not take physical categorical properties into account. Rather, selection mechanisms are only tuned to what such properties can do, i.e., to their causal (...) powers. This picture seems ultimately untenable in the light of further exclusion problems; but at the same time, it meets our explanatory demands. My purpose is therefore to show that there is a real antinomy with regard to evolved emergent properties. I develop a physicalist exclusion argument and then I go on to consider an argument that seems to establish that evolved emergent properties are causally efficacious, and propose a compatibilist solution. Finally, I very briefly consider what the proposed model may imply for the issue of mental causation. (shrink)

This book is both an introduction to and a research work on Meinongianism. “Meinongianism” is taken here, in accordance with the common philosophical jargon, as a general label for a set of theories of existence – probably the most basic notion of ontology. As an introduction, the book provides the first comprehensive survey and guide to Meinongianism and non-standard theories of existence in all their main forms. As a research work, the book exposes and develops the most up-to-date Meinongian theory (...) (called modal Meinongianism), applies it to specific fields, and discusses its open problems. Part I of the book provides a historical introduction to, and critical discussion of, the dominant philosophical view of existence: the “Kantian-Fregean-Quinean” perspective. Part II is the full-fledged introduction to the Meinongian theories of existence as a real property of individuals: after starting with the so-called naïve Meinongian conception and its problems, it provides a self-contained presentation of the main neo-Meinongian proposals, and a detailed discussion of their strengths and weaknesses. Part III develops a specific neo-Meinongian theory of existence employing a model-theoretic semantic framework. It discusses its application to the ontology and semantics of fictional objects, and its open problems. The methodology of the book follows the most recent trends in analytic ontology. In particular, the meta-ontological point of view is largely privileged. (shrink)

Models treating the simple properties of social groups have a common shortcoming. Typically, they focus on the local properties of group members and the features of the world with which group members interact. I consider economic models of bureaucratic corruption, to show that (a) simple properties of groups are often constituted by the properties of the wider population, and (b) even sophisticated models are commonly inadequate to account for many simple social properties. Adequate models and social policies must treat certain (...) factors that are not local to individual members of the group, even if those factors are not causally connected to those individuals. Key Words: individualism • corruption • supervenience • model • cause. (shrink)

We review some results in the theory of non-relativistic quantum unstable systems. We account for the most important definitions of quantum resonances that we identify with unstable quantum systems. Then, we recall the properties and construction of Gamow states as vectors in some extensions of Hilbert spaces, called Rigged Hilbert Spaces. Gamow states account for the purely exponential decaying part of a resonance; the experimental exponential decay for long periods of time physically characterizes a resonance. We briefly discuss one of (...) the most usual models for resonances: the Friedrichs model. Using an algebraic formalism for states and observables, we show that Gamow states cannot be pure states or mixtures from a standard view point. We discuss some additional properties of Gamow states, such as the possibility of obtaining mean values of certain observables on Gamow states. A modification of the time evolution law for the linear space spanned by Gamow shows that some non-commuting observables on this space become commuting for large values of time. We apply Gamow states for a possible explanation of the Loschmidt echo. (shrink)

The practice of thought experimentation plays a central role in contemporary philosophical methodology. Many philosophers rely on thought experimentation as their primary and even sole procedure for testing theories about the natures of properties and relations. This test procedure involves entertaining hypothetical cases in imaginative thought and then undergoing intuitions about the distribution of properties and relations in them. A theory’s comporting with an intuition is treated as evidence in favour of it; but a clash is treated as evidence against (...) the theory and may even be regarded as falsifying it. -/- The epistemic power of thought experimentation is mysterious. How can experiments carried out within the mind enable us to discover truths about the natures of properties and relations like knowledge, causation, personal identity, reference, meaning, consciousness, beauty, justice, morality, and free will? This epistemological challenge is urgent, but a model of philosophical thought experimentation would seem to be a necessary propaedeutic to any serious discussion of it. An adequate model would make the relevant test procedure explicit, thereby assisting in the identification of points of potential epistemic vulnerability. -/- In this monograph I advance the propaedeutical model-building work already done by Timothy Williamson, Anna-Sara Malmgren, and Jonathan Ichikawa and Benjamin Jarvis. Following the lead of these philosophers, I focus on a single Gettier-style thought experiment and the problem of identifying the real content of the Gettier intuition. My first contribution is to establish the inadequacy of all of the existing models. Each of them, I argue, fails to solve the content problem. It emerges from my discussion, however, that Ichikawa and Jarvis’s truth in fiction approach holds out the prospect of a solution. -/- My second contribution is to develop and defend a new way of implementing the general idea behind the truth in fiction approach. The model I put forward does a better overall job of modelling Gettier-style thought experiments than any of the existing models. It has none of the defects which render those models inadequate and Iam unable to find any major defects peculiar to it. This should make us feel confident that my model is adequate. Moreover, since the Gettier-style thought experiment I focus on is paradigmatic, we should also feel confident that my model will generalise naturally to other philosophical thought experiments. (shrink)

Traditional computers work with finite numbers. Situations where the usage of infinite or infinitesimal quantities is required are studied mainly theoretically. In this paper, a recently introduced computational methodology (that is not related to the non-standard analysis) is used to work with finite, infinite, and infinitesimal numbers numerically. This can be done on a new kind of a computer – the Infinity Computer – able to work with all these types of numbers. The new computational tools both give (...) possibilities to execute computations of a new type and open new horizons for creating new mathematical models where a computational usage of infinite and/or infinitesimal numbers can be useful. A number of numerical examples showing the potential of the new approach and dealing with divergent series, limits, probability theory, linear algebra, and calculation of volumes of objects consisting of parts of different dimensions are given. (shrink)

The concept of shared mental models refers to the shared understanding among team members about how they should behave in different situations. This article aimed to develop a new shared mental model measure, specifically designed for the refereeing context. A cross-sectional study was conducted with three samples: national and regional football referees (n = 133), national football referees and assistant referees and national futsal referees (n = 277), and national futsal referees (n = 60). The proposed version of the (...) Referee Shared Mental Models Measure (RSMMM) has 13 items that are reflected on a single factor structure. The RSMMM presented good validity evidence both based on the internal structure and based on relations to other variables (presenting positive associations with team work engagement, team adaptive performance, and team effectiveness). Such promising psychometric properties point to an optimistic outlook regarding its use to measure shared mental models in futsal and football referee teams. -/- . (shrink)