Is logic normative for belief? A standard approach to answering this question has been to investigate bridge principles relating claims of logical consequence to norms for belief. Although the question is naturally an epistemic one, bridge principles have typically been investigated in isolation from epistemic debates over the correct norms for belief. In this paper we tackle the question of whether logic is normative for belief by proposing a Kripkean model theory accounting for the interaction between logical, doxastic, (...) epistemic and deontic notions and using this model theory to show which bridge principles are implied by epistemic norms that we have independent reason to accept, for example, the knowledge norm and the truth norm. We propose a preliminary theory of the interaction between logical, doxastic, epistemic and deontic notions that has among its commitments bridge principles expressing how logic is normative for belief. We also show how our framework suggests that logic is exceptionally normative. (shrink)

Is logic normative for belief? A standard approach to answering this question has been to investigate bridge principles relating claims of logical consequence to norms for belief. Although the question is naturally an epistemic one, bridge principles have typically been investigated in isolation from epistemic debates over the correct norms for belief. In this paper we tackle the question of whether logic is normative for belief by proposing a Kripkean model theory accounting for the interaction between logical, doxastic, (...) epistemic and deontic notions and using this model theory to show which bridge principles are implied by epistemic norms that we have independent reason to accept, for example, theknowledge normand thetruth norm. We propose a preliminary theory of the interaction between logical, doxastic, epistemic and deontic notions that has among its commitments bridge principles expressing how logic is normative for belief. We also show how our framework suggests that logic is exceptionally normative. (shrink)

We show that Zilber’s conjecture that complex exponentiation is isomorphic to his pseudo-exponentiation follows from the a priori simpler conjecture that they are elementarily equivalent. An analysis of the first-order types in pseudo-exponentiation leads to a description of the elementary embeddings, and the result that pseudo-exponential fields are precisely the models of their common first-order theory which are atomic over exponential transcendence bases. We also show that the class of all pseudo-exponential fields is an (...) example of a nonfinitary abstract elementary class, answering a question of Kesälä and Baldwin. (shrink)

An exponential $\exp $ on an ordered field $$. The structure $$ is then called an ordered exponential field. A linearly ordered structure $$ is called o-minimal if every parametrically definable subset of M is a finite union of points and open intervals of M.The main subject of this thesis is the algebraic and model theoretic examination of o-minimal exponential fields $$ whose exponential satisfies the differential equation $\exp ' = \exp $ with initial (...) condition $\exp = 1$. This study is mainly motivated by the Transfer Conjecture, which states as follows:Any o-minimal exponential field $$ whose exponential satisfies the differential equation $\exp ' = \exp $ with initial condition $\exp =1$ is elementarily equivalent to $\mathbb {R}_{\exp }$.Here, $\mathbb {R}_{\exp }$ denotes the real exponential field $$, where $\exp $ denotes the standard exponential $x \mapsto \mathrm {e}^x$ on $\mathbb {R}$. Moreover, elementary equivalence means that any first-order sentence in the language $\mathcal {L}_{\exp } = \{+,-,\cdot,0,1, <,\exp \}$ holds for $$ if and only if it holds for $\mathbb {R}_{\exp }$.The Transfer Conjecture, and thus the study of o-minimal exponential fields, is of particular interest in the light of the decidability of $\mathbb {R}_{\exp }$. To the date, it is not known if $\mathbb {R}_{\exp }$ is decidable, i.e., whether there exists a procedure determining for a given first-order $\mathcal {L}_{\exp }$ -sentence whether it is true or false in $\mathbb {R}_{\exp }$. However, under the assumption of Schanuel’s Conjecture—a famous open conjecture from Transcendental Number Theory—a decision procedure for $\mathbb {R}_{\exp }$ exists. Also a positive answer to the Transfer Conjecture would result in the decidability of $\mathbb {R}_{\exp }$. Thus, we study o-minimal exponential fields with regard to the Transfer Conjecture, Schanuel’s Conjecture, and the decidability question of $\mathbb {R}_{\exp }$.Overall, we shed light on the valuation theoretic invariants of o-minimal exponential fields—the residue field and the value group—with additional induced structure. Moreover, we explore elementary substructures and extensions of o-minimal exponential fields to the maximal ends—the smallest elementary substructures being prime models and the maximal elementary extensions being contained in the surreal numbers. Further, we draw connections to models of Peano Arithmetic, integer parts, density in real closure, definable Henselian valuations, and strongly NIP ordered fields.Parts of this thesis were published in [2–5].Abstract prepared by Lothar Sebastian KrappE-mail: [email protected]: https://d-nb.info/1202012558/34. (shrink)

We study the model theory of fields k carrying a henselian valuation with real closed residue field. We give a criteria for elementary equivalence and elementary inclusion of such fields involving the value group of a not necessarily definable valuation. This allows us to translate theories of such fields to theories of ordered abelian groups, and we study the properties of this translation. We also characterize the first-order definable convex subgroups of a given ordered abelian (...) group and prove that the definable real valuation rings of k are in correspondence with the definable convex subgroups of the value group of a certain real valuation of k. (shrink)

A number of philosophers :171–187, 2011; Arnold 2011, in Ethics Politics XV:101–138, 2013) have argued that agent-based, evolutionary game theory models of the evolution of cooperation fail to provide satisfying explanations of cooperation because they are too disconnected from actual biology. I show how these criticisms can be answered by employing modeling approaches from the situated cognition research program that allow for more biologically detailed models. Using cases drawn from recent situated cognition modeling research, I show how agent-based models (...) of the evolution of cooperation can become more empirically-informed and relevant to explaining the evolution of cooperation in real populations. I argue that because situated cognition models allow for more detailed representations of not just agents’ brains but bodies and environments as well, they can be informed by a much wider breadth of empirical research than traditional agent-based models. Moreover, because the simulated bodies of these agents exhibit particular behaviors, they can be more readily compared to the behaviors of actual organisms. I conclude that employing situated cognition approaches to modeling the evolution of cooperation is a more promising way to investigate the evolution of cooperation than more traditional agent-based evolutionary game theory models. (shrink)

Assuming “Schanuel's Condition” for a certain class of exponential fields, Sturm's technique for polynomials in real closed fields can be extended to more complicated exponential terms in the corresponding exponential field. Hence for this class of terms the exact number of zeros can be calculated. These results give deeper insights into the model theory of exponential fields. MSC: 03C65, 03C60, 12L12.

Model theorists have been studying analytic functions since the late 1970s. Highlights include the seminal work of Denef and van den Dries on the theory of the p-adics with restricted analytic functions, Wilkie's proof of o-minimality of the theory of the reals with the exponential function, and the formulation of Zilber's conjecture for the complex exponential. My goal in this talk is to survey these main developments and to reflect on today's open problems, in particular (...) for theories of valued fields. (shrink)

Religious therapeutics is the term I use to designate relations between health and spirituality, and medicine and religion. Dimensions of religious therapeutics include religious meanings that inform medical theory, religious means of healing, health as part of religious life, and religion as a remedy for human suffering. Classical Yoga is analyzed to establish an initial matrix of religious therapeutics with 5 branches: philosophical foundations, soteriology, value theory, physical practice, and cultivation of consciousness. Through comparative criticism of classical Yoga, (...) the study presents a heuristic of religious therapeutics: a model for interpreting relations among healing and liberative functions in world religions. ;Body and health are of instrumental but not ultimate value in classical Yoga: the body is used to transcend itself for attainment of Yoga's soteriological goal, realization of self as pure consciousness. Yoga's Samkhya-based metaphysics contains an unreconciled dualism, and while practice of Yoga is paradigmatic of mind/body holism, Yoga prescribes realization of a spiritual self, independent of material and psychological nature. The study rehabilitates the body in respect of the compatibility of embodiedness with religiousness. ;Other Indian and world traditions suggest dimensions of religious therapeutics both resonant with classical Yoga and lacking from it. India's Ayurvedic medicine represents the sixth branch of religious therapeutics: medical therapeutics. I distill from Ayurvedic and Western sources a set of determinants of health: biological, medical/psychological, cultural, and metaphysical. Significant determinants of health are wholeness, self-identity, and freedom; these are incorporated in discussion of the complementary functions of medicine and religion, grounding the claim that in classical Yoga, liberation is healing in an ultimate sense. ;Tantric yogas utilize material nature for human spiritual progress, and unlike classical Yoga, esteem nature, body/mind, the feminine, and relationality. Tantra provides another branch of religious therapeutics: aesthetic therapeutics. The study anticipates elements of health/medicine in western religions, Buddhism, and Lakota religious philosophy. Sacred speech and song are explored to demonstrate comparative inquiry into religious therapeutics; some Native American Indian and Hindu applications of sacred language are considered. Finally, the model of religious therapeutics is supplemented with community, embracing ecological, social, and religious relationality and communication. (shrink)

In the present paper some tools are given to state the exact number of roots for some simple classes of exponential terms . The result were obtained by generalizing Sturm's technique for real closed fields. Moreover for arbitrary non-zero terms t certain estimations concerning the location of roots of t are given. MSC: 03C65, 03C60, 12L12.

In this paper we set out the basic model theory of differential fields of characteristic 0, which have finitely many commuting derivations. We give axioms for the theory of differentially closed differential fields with m derivations and show that this theory is ω-stable, model complete, and quantifier-eliminable, and that it admits elimination of imaginaries. We give a characterization of forking and compute the rank of this theory to be ω m + 1.

The differential field of transseries extends the field of real Laurent series and occurs in various contexts: asymptotic expansions, analytic vector fields, and o-minimal structures, to name a few. We give an overview of the algebraic and model-theoretic aspects of this differential field and report on our efforts to understand its elementary theory.

Generalizing and unifying the known theorems for difference and differential fields, it is shown that for every finite free algebra scheme.

The vigorous development of online education has produced massive amounts of education data. How to mine and analyze education big data has become an urgent problem in the field of education and big data knowledge engineering. As for the dynamic learning data, knowledge tracing aims to track learners’ knowledge status over time by analyzing the learners’ exercise data, so as to predict their performance in the next time step. Deep learning knowledge tracking performs well, but they mainly model the (...) knowledge components while ignoring the personalized information of questions and learners, and provide limited interpretability in the interaction between learners’ knowledge status and questions. A context-aware attentive knowledge query network model is proposed in this paper, which combines flexible neural network models with interpretable model components inspired by psychometric theory. We use the Rasch model to regularize the embedding of questions and learners’ interaction tuples, and obtain personalized representations from them. In addition, the long-term short-term memory network and monotonic attention mechanism are used to mine the contextual information of learner interaction sequences and question sequences. It can not only retain the ability to model sequences, but also use the monotonic attention mechanism with exponential decay term to extract the hidden forgetting behavior and other characteristics of learners in the learning process. Finally, the vector dot product is used to simulate the interaction between the learners’ knowledge state and questions to improve the interpretability. A series of experimental results on 4 real-world online learning datasets show that CAKQN has the best performance, and its AUC value is improved by an average of 2.945% compared with the existing optimal model. Furthermore, the CAKQN proposed in this paper can not only track learners’ knowledge status like other models but also model learners’ forgetting behavior. In the future, our research will have high application value in the realization of personalized learning strategies, teaching interventions, and resource recommendations for intelligent online education platforms. (shrink)

Vector spaces over unspecified fields can be axiomatized as one-sorted structures, namely, abelian groups with the relation of parallelism. Parallelism is binary linear dependence. When equipped with the n-ary relation of linear dependence for some positive integer n, a vector-space is existentially closed if and only if it is n-dimensional over an algebraically closed field. In the signature with an n-ary predicate for linear dependence for each positive integer n, the theory of infinite-dimensional vector spaces over algebraically closed (...) fields is the model-completion of the theory of vector spaces. (shrink)

Fields of characteristic zero with several commuting derivations can be treated as fields equipped with a space of derivations that is closed under the Lie bracket. The existentially closed instances of such structures can then be given a coordinate-free characterization in terms of differential forms. The main tool for doing this is a generalization of the Frobenius Theorem of differential geometry.

The quantum mechanical description of the evolution of an unstable system defined initially as a state in a Hilbert space at a given time does not provide a semigroup (exponential) decay, law. The Wigner–Weisskopf survival amplitude, describing reversible quantum transitions, may be dominated by exponential type decay in pole approximation at times not too short or too long, but, in the two channel case, for example, the pole residues are not orthogonal, and the evolution does riot correspond to (...) a semigroup (experiments on the decay of the neutral K-meson system strongly support the semigroup evolution postulated, by Lee, Oehme and Yang, and Yang and Wu). The scattering theory of Lax and Phillips, originally developed for classical wave equations, has been recently extended to the description of the evolution of resonant states in the framework of quantum theory. The resulting evolution law of the unstable system is that of a semigroup, and the resonant state is a well-defined function in the Lax–Phillips Hilbert space. In this paper we apply this theory to a relativistically covariant quantum field theoretical form of the (soluble) Lee model. We construct the translation representations with the help of the wave operators, and show that the resulting Lax–Phillips S-matrix is an inner function (the Lax–Phillips theory is essentially a theory of translation invariant subspaces). In the special case that the S-matrix is a rational inner function, we obtain the resonant state explicitly and analyze its particle (V, N, θ) content. If there is an exponential bound, the general case differs only by a so-called trivial inner factor, which does not change the complex spectrum, but may affect the wave function of the resonant state. (shrink)

In 2001, the algebraico-tree-theoretic simplicity hierarchical structure of J. H. Conway’s ordered field ${\mathbf {No}}$ of surreal numbers was brought to the fore by the first author and employed to provide necessary and sufficient conditions for an ordered field to be isomorphic to an initial subfield of ${\mathbf {No}}$, i.e. a subfield of ${\mathbf {No}}$ that is an initial subtree of ${\mathbf {No}}$. In this sequel, analogous results are established for ordered exponential fields, making use of a slight (...) generalization of Schmeling’s conception of a transseries field. It is further shown that a wide range of ordered exponential fields are isomorphic to initial exponential subfields of $$. These include all models of $T$, where ${\mathbb R}_W$ is the reals expanded by a convergent Weierstrass system W. Of these, those we call trigonometric-exponential fields are given particular attention. It is shown that the exponential functions on the initial trigonometric-exponential subfields of ${\mathbf {No}}$, which includes ${\mathbf {No}}$ itself, extend to canonical exponential functions on their surcomplex counterparts. The image of the canonical map of the ordered exponential field ${\mathbb T}^{LE}$ of logarithmic-exponential transseries into ${\mathbf {No}}$ is shown to be initial, as are the ordered exponential fields ${\mathbb R})^{EL}$ and ${\mathbb R}\langle \langle \omega \rangle \rangle $. (shrink)

Time perspective theory provides a robust conceptual framework for analyzing human behavior in the context of time. So far, the concept has been studied and applied in multiple life domains, such as education, health, social relationships, environmental behavior, or financial behavior; however its explanatory potential has been completely neglected within the domain of sport. In the present paper we provide a deepened theoretical analysis of the potential role of temporal framing of human experience for sport-related attitudes, emotions, and athletic (...) performance. We propose a conceptual model in which time perspectives influence psychological functioning and performance of athletes via three major mechanisms: 1) magnitude and persistence of sport motivation and resulting athlete engagement, 2) regulation of affective states during sport performance, and 3) appraisal of one’s performance and coping with resulting emotions. We support the theoretical considerations based on the major assumptions of time perspective theory with research findings regarding the regulatory role of time perspectives in other life domains. We also highlight potential research paths that would allow us to empirically test the present model and determine the actual role of temporal perspectives in shaping crucial aspects of athletes’ psychological functioning, as well as levels of their sport performance. (shrink)

This book contains the material for a first course in pure model theory with applications to differentially closed fields.

Major shifts in the field of model theory in the twentieth century have seen the development of new tools, methods, and motivations for mathematicians and philosophers. In this book, John T. Baldwin places the revolution in its historical context from the ancient Greeks to the last century, argues for local rather than global foundations for mathematics, and provides philosophical viewpoints on the importance of modern model theory for both understanding and undertaking mathematical practice. The volume also (...) addresses the impact of model theory on contemporary algebraic geometry, number theory, combinatorics, and differential equations. This comprehensive and detailed book will interest logicians and mathematicians as well as those working on the history and philosophy of mathematics. (shrink)

The formulation of quantum mechanics developed by Bohm, which can generate well-defined trajectories for the underlying particles in the theory, can equally well be applied to relativistic quantum field theories to generate dynamics for the underlying fields. However, it does not produce trajectories for the particles associated with these fields. Bell has shown that an extension of Bohm’s approach can be used to provide dynamics for the fermionic occupation numbers in a relativistic quantum field theory. In (...) the present paper, Bell’s formulation is adopted and elaborated on, with a full account of all technical detail required to apply his approach to a bosonic quantum field theory on a lattice. This allows an explicit computation of trajectories for massive and massless particles in this theory. Also particle creation and annihilation, and their impact on particle propagation, is illustrated using this model. (shrink)

In response to Cushing it is urged that the vicissitudes of quantum field theory do not press towards a nonrealist attitude towards the theory as strongly as he suggests. A variety of issues which Redhead raises are taken up, including photon localizability, the wave-particle distinction in the classical limit, and the interpretation of quantum statistics, vacuum fluctuations, virtual particles, and creation and annihilation operators. It is urged that quantum field theory harbors an unacknowledged inconsistency connected with the (...) fact that the zero point energy has observable consequences, while to avoid infinities it must be "thrown away". Finally, Redhead's conception of ephemerals is pressed and the paper concludes with the suggestion that the particle concept largely drops out of quantum field theory. (shrink)

A model for U(1) gauge theories over a compact Lie group is described usingR×S 3 as background space. A comparison with other results is given. Electrodynamics equations are obtained. Finally, some considerations and observations about gravity onR×S 3 space are presented.

he model theory of groups of unitriangular matrices over rings is studied. An important tool in these studies is a new notion of a quasiunitriangular group. The models of the theory of all unitriangular groups are algebraically characterized; it turns out that all they are quasiunitriangular groups. It is proved that if R and S are domains or commutative associative rings then two quasiunitriangular groups over R and S are isomorphic only if R and S are isomorphic (...) or antiisomorphic. This algebraic result is new even for ordinary unitriangular groups. The groups elementarily equivalent to a single unitriangular group UTn are studied. If R is a skew field, they are of the form UTn, for some S ≡ R. In general, the situation is not so nice. Examples are constructed demonstrating that such a group need not be a unitriangular group over some ring; moreover, there are rings P and R such that UTn ≡ UTn, but UTn cannot be represented in the form UTn for S ≡ R. We also study the number of models in a power of the theory of a unitriangular group. In particular, we prove that, for any communicative associative ring R and any infinite power λ, I = I). We construct an associative ring such that I = 3 and I) = 2. We also study models of the theory of UTn in the case of categorical R. (shrink)

Software application ontologies have the potential to become the keystone in state-of-the-art information management techniques. It is expected that these ontologies will support the sort of reasoning power required to navigate large and complex terminologies correctly and efficiently. Yet, there is one problem in particular that continues to stand in our way. As these terminological structures increase in size and complexity, and the drive to integrate them inevitably swells, it is clear that the level of consistency required for such navigation (...) will become correspondingly difficult to maintain. While descriptive semantic representations are certainly a necessary component to any adequate ontology-based system, so long as ontology engineers rely solely on semantic information, without a sound ontological theory informing their modeling decisions, this goal will surely remain out of reach. In this paper we describe how Language and Computing nv (L&C), along with The Institute for Formal Ontology and Medical Information Sciences (IFOMIS), are working towards developing and implementing just such a theory, combining the open software architecture of L&C’s LinkSuiteTM with the philosophical rigor of IFOMIS’s Basic Formal Ontology. In this way we aim to move beyond the more or less simple controlled vocabularies that have dominated the industry to date. (shrink)

We prove some results about the model theory of fields with a derivation of the Frobenius map, especially that the model companion of this theory is axiomatizable by axioms used by Wood in the case of the theory $\operatorname {DCF}_p$ and that it eliminates quantifiers after adding the inverse of the Frobenius map to the language. This strengthens the results from [4]. As a by-product, we get a new geometric axiomatization of this model (...) companion. Along the way we also prove a quantifier elimination result, which holds in a much more general context and we suggest a way of giving “one-dimensional” axiomatizations for model companions of some theories of fields with operators. (shrink)

An introduction to category theory as a rigorous, flexible, and coherent modeling language that can be used across the sciences. Category theory was invented in the 1940s to unify and synthesize different areas in mathematics, and it has proven remarkably successful in enabling powerful communication between disparate fields and subfields within mathematics. This book shows that category theory can be useful outside of mathematics as a rigorous, flexible, and coherent modeling language throughout the sciences. Information is (...) inherently dynamic; the same ideas can be organized and reorganized in countless ways, and the ability to translate between such organizational structures is becoming increasingly important in the sciences. Category theory offers a unifying framework for information modeling that can facilitate the translation of knowledge between disciplines. Written in an engaging and straightforward style, and assuming little background in mathematics, the book is rigorous but accessible to non-mathematicians. Using databases as an entry to category theory, it begins with sets and functions, then introduces the reader to notions that are fundamental in mathematics: monoids, groups, orders, and graphs—categories in disguise. After explaining the “big three” concepts of category theory—categories, functors, and natural transformations—the book covers other topics, including limits, colimits, functor categories, sheaves, monads, and operads. The book explains category theory by examples and exercises rather than focusing on theorems and proofs. It includes more than 300 exercises, with solutions. Category Theory for the Sciences is intended to create a bridge between the vast array of mathematical concepts used by mathematicians and the models and frameworks of such scientific disciplines as computation, neuroscience, and physics. (shrink)

In this chapter, the author articulates two Hobbesian models of interpersonal power relations that can be used to understand gender relations: what he will call the dominion model and the deference model. Hobbes himself analyses the relation between men and women through the dominion model. The author lays out Hobbes's model of interpersonal power relations as dominion, including his application of the model to the case of gender relations. The centerpiece of Hobbes's method is his (...) “state of nature” thought experiment. Hobbes's analysis is radical insofar as he understands familial relations according to the general model of interpersonal relations just outlined, without any reference to sui generis principles. The author indicates some shortcomings of the dominion model for grasping contemporary social life. The much‐celebrated social contract between equal male citizens is quietly underpinned by the sexual contract, a contract of domination between men and women. (shrink)

We show that the Bohmian approach in terms of persisting particles that move on continuous trajectories following a deterministic law can be literally applied to quantum field theory. By means of the Dirac sea model—exemplified in the electron sector of the standard model neglecting radiation—we explain how starting from persisting particles, one is led to standard QFT employing creation and annihilation operators when tracking the dynamics with respect to a reference state, the so-called vacuum. Since on the (...) level of wave functions, both formalisms are mathematically equivalent, this proposal provides for an ontology of QFT that includes a dynamics of individual processes, solves the measurement problem, and explains the appearance of creation and annihilation events. 1Bohmian Mechanics from Quantum Mechanics to Quantum Field Theory2The Dirac Sea Model3Equilibrium States and the Vacuum4Excitations of the Vacuum and the Fock Space Formalism5The Appearance of Particle Creations and Annihilations6The Merits of the Bohmian Approach. (shrink)

The naive theory of properties states that for every condition there is a property instantiated by exactly the things which satisfy that condition. The naive theory of properties is inconsistent in classical logic, but there are many ways to obtain consistent naive theories of properties in nonclassical logics. The naive theory of classes adds to the naive theory of properties an extensionality rule or axiom, which states roughly that if two classes have exactly the same members, (...) they are identical. In this paper we examine the prospects for obtaining a satisfactory naive theory of classes. We start from a result by Ross Brady, which demonstrates the consistency of something resembling a naive theory of classes. We generalize Brady’s result somewhat and extend it to a recent system developed by Andrew Bacon. All of the theories we prove consistent contain an extensionality rule or axiom. But we argue that given the background logics, the relevant extensionality principles are too weak. For example, in some of these theories, there are universal classes which are not declared coextensive. We elucidate some very modest demands on extensionality, designed to rule out this kind of pathology. But we close by proving that even these modest demands cannot be jointly satisfied. In light of this new impossibility result, the prospects for a naive theory of classes are bleak. (shrink)

We study the deviations from the exponential decay law, both in quantum field theory (QFT) and quantum mechanics (QM), for an unstable particle which can decay in (at least) two decay channels. After a review of general properties of non-exponential decay in QFT and QM, we evaluate in both cases the decay probability that the unstable particle decays in a given channel in the time interval between t and t+dt. An important quantity is the ratio of the (...) probability of decay into the first and the second channel: this ratio is constant in the Breit-Wigner limit (in which the decay law is exponential) and equals the quantity Γ1/Γ2, where Γ1 and Γ2 are the respective tree-level decay widths. However, in the full treatment (both for QFT and QM) it is an oscillating function around the mean value Γ1/Γ2 and the deviations from this mean value can be sizable. Technically, we study the decay properties in QFT in the context of a superrenormalizable Lagrangian with scalar particles and in QM in the context of Lee Hamiltonians, which deliver formally analogous expressions to the QFT case. (shrink)

The collaboration of Language and Computing nv (L&C) and the Institute for Formal Ontology and Medical Information Science (IFOMIS) is guided by the hypothesis that quality constraints on ontologies for software ap-plication purposes closely parallel the constraints salient to the design of sound philosophical theories. The extent of this parallel has been poorly appreciated in the informatics community, and it turns out that importing the benefits of phi-losophical insight and methodology into application domains yields a variety of improvements. L&C’s LinKBase® (...) is one of the world’s largest medical domain ontologies. Its current primary use pertains to natural language processing ap-plications, but it also supports intelligent navigation through a range of struc-tured medical and bioinformatics information resources, such as SNOMED-CT, Swiss-Prot, and the Gene Ontology (GO). In this report we discuss how and why philosophical methods improve both the internal coherence of LinKBase®, and its capacity to serve as a translation hub, improving the interoperability of the ontologies through which it navigates. (shrink)

Volume 500, 2009 On the Infrared Problem for the Dressed Non-Relativistic Electron in a Magnetic Field Laurent Amour, ...

A correspondence theory of truth explains truth in terms of various correspondence relations (e.G., Reference) between words and the extralinguistic world. What are the consequences of quine's doctrine of indeterminacy for correspondence theories? in "ontological relativity" quine implicitly claims that correspondence theories are impossible; that is what the doctrine of 'relative reference' amounts to. But quine's doctrine of relative reference is incoherent. Those who think the indeterminacy thesis valid should not try to relativize reference, They should abandon the relation (...) and replace it by certain more general correspondence relations between words and extralinguistic objects. Doing so will not interfere with the task of defining truth in terms of correspondence relations. (shrink)

De Re Significance accounts of moral appraisal consider an agent’s responsiveness to a particular kind of reason, normative moral reasons de re, to be of central significance for moral appraisal. Here, I argue that such accounts find it difficult to accommodate some neuroatypical agents. I offer an alternative account of how an agent’s responsiveness to normative moral reasons affects moral appraisal – the Reasonable Expectations Account. According to this account, what is significant for appraisal is not the content of the (...) reasons an agent is responsive to, but rather whether she is responsive to the reasons it is reasonable to expect her to be responsive to, irrespective of their content. I argue that this account does a better job of dealing with neuroatypical agents, while agreeing with the De Re Significance accounts on more ordinary cases. (shrink)

Bayesian decision theory can be viewed as the core of psychological theory for idealized agents. To get a complete psychological theory for such agents, you have to supplement it with input and output laws. On a Bayesian theory that employs strict conditionalization, the input laws are easy to give. On a Bayesian theory that employs Jeffrey conditionalization, there appears to be a considerable problem with giving the input laws. However, Jeffrey conditionalization can be reformulated so (...) that the problem disappears, and in fact the reformulated version is more natural and easier to work with on independent grounds. (shrink)

If properties are to play a useful role in semantics, it is hard to avoid assuming the naïve theory of properties: for any predicate Θ(x), there is a property such that an object o has it if and only if Θ(o). Yet this appears to lead to various paradoxes. I show that no paradoxes arise as long as the logic is weakened appropriately; the main difficulty is finding a semantics that can handle a conditional obeying reasonable laws without engendering (...) paradox. I employ a semantics which is infinite-valued, with the values only partially ordered. Can the solution be adapted to naïve set theory? Probably not, but limiting naïve comprehension in set theory is perfectly satisfactory, whereas this is not so in a property theory used for semantics. (shrink)

We show that in 4-spacetime modified at very short distances due to the weakening of classical logic, the higher dimensions emerge. We analyse the case of some smooth topoi, and the case of some class of pointless topoi. The pointless topoi raise the dimensionality due to the forcing adding “string” objects and thus replacing classical points in spacetime. Turning to strings would be something fundamental and connected with set theoretical forcing. The field theory/strings dualities originate at the set theoretical (...) level of the theories. It is argued that this fundamental level can help solving some difficulties of the physical dualities. (shrink)

1. Of what use is the concept of causation? Bertrand Russell [1912-13] argued that it is not useful: it is “a relic of a bygone age, surviving, like the monarchy, only because it is erroneously supposed to do no harm.” His argument for this was that the kind of physical theories that we have come to regard as fundamental leave no place for the notion of causation: not only does the word ‘cause’ not appear in the advanced sciences, but the (...) laws that these sciences state are incompatible with causation as we normally understand it. But Nancy Cartwright has argued [1979] that abandoning the concept of causation would cripple science; her conclusion was based not on fundamental physics, but on more ordinary science such as the search for the causes of cancer. She argues that Russell was right that the fundamental theories of modern physics say nothing, even implicitly, about causation, and concludes on this basis that such theories are incomplete. It is with this cluster of issues that I will begin my discussion. (shrink)

This book offers a detailed study of the political philosophies of Thomas Hobbes and Benedict de Spinoza, focussing on their concept of power as potentia, concrete power, rather than power as potestas, authorised power. The focus on power as potentia generates a new conception of popular power. Radical democrats–whether drawing on Hobbes's 'sleeping sovereign' or on Spinoza's 'multitude'–understand popular power as something that transcends ordinary institutional politics, as for instance popular plebsites or mass movements. However, the book argues that these (...) understandings reflect a residual scholasticism which Hobbes and Spinoza ultimately repudiate. Instead, on the book's revisionist conception, a political phenomenon should be said to express popular power when it is both popular (it eliminates oligarchy and encompasses the whole polity), and also powerful (it robustly determines political and social outcomes). Two possible institutional forms that this popular power might take are distinguished: Hobbesian repressive egalitarianism, or Spinozist civic strengthening. But despite divergent institutional proposals, the book argues that both Hobbes and Spinoza share the conviction that there is nothing spontaneously egalitarian or good about human collective existence. From this point of view, the book accuses radical democrats of pernicious romanticism; the slow, meticulous work of organizational design and maintenance is the true centre of popular power. Three minute video summary available via HPBin3. Extended discussion on The Political Theory Review podcast. First chapter open access available via Oxford Scholarship Online. Videos of book talks at National University of Singapore (Centre for Legal Theory) and Universidad de Buenos Aires (Instituto de Investigaciones Gino Germani) available via YouTube. (See links below.). (shrink)

The term ‘social capital’ is a way of defining the intangible resources of community, shared values and trust upon which we draw in daily life. It has achieved considerable international currency across the social sciences through the very different work of Pierre Bourdieu in France and James Coleman and Robert Putnam in the United States, and has been widely taken up within politics and sociology as an explanation for the decline in social cohesion and community values in western societies. It (...) has also been adopted by policy makers, particularly in international governmental bodies such as the World Bank. (shrink)

The relationship between philosophy and research on artificial intelligence (AI) has been difficult since its beginning, with mutual misunderstanding and sometimes even hostility. By contrast, we show how an approach informed by both philosophy and AI can be productive. After reviewing some popular frameworks for computation and learning, we apply the AI methodology of “build it and see” to tackle the philosophical and psychological problem of characterizing perception as distinct from sensation. Our model comprises a network of very simple, (...) but interacting agents which have binary experiences of the “yes/no”-type and communicate their experiences with each other. When does such a network refer to a single agent instead of a distributed network of entities? We apply machine learning techniques to address the following related questions: i) how can the model explain stability of compound entities, and ii) how could the model implement a single task such as perceptual inference? We thereby find consistency with previous work on “interface” strategies from perception research. While this reflects some necessary conditions for the ascription of agency, we suggest that it is not sufficient. Here, AI research, if it is intended to contribute to conceptual understanding, would benefit from issues previously raised by philosophy. We thus conclude the article with a discussion of action-selection, the role of embodiment, and consciousness to make this more explicit. We conjecture that a combination of AI research and philosophy allows general principles of mind and being to emerge from a “quasi-empirical” investigation. (shrink)

In this paper we give a differential lifting principle which provides a general method to geometrically axiomatize the model companion (if it exists) of some theories of differential topological fields. The topological fields we consider here are in fact topological systems in the sense of van den Dries, and the lifting principle we develop is a generalization of the geometric axiomatization of the theory DCF₀ given by Pierce and Pillay. Moreover, it provides a geometric alternative to (...) the axiomatizations obtained by Tressl and Guzy/Point in separate papers where the authors also build general schemes of axioms for some model complete theories of differential fields. We first characterize the existentially closed models of a given theory of differential topological fields and then, under an additional hypothesis of largeness, we show how to modify this characterization to get a general scheme of first-order axioms for the model companion of any large theory of differential topological fields. We conclude with an application of this lifting principle proving that, in existentially closed models of a large theory of differential topological fields, the jet-spaces are dense in their ambient topological space. (shrink)

The paper distinguishes two approaches to understanding the representational content of sentences and intentional states, and its role in describing people, predicting and explaining their behavior, and so forth. It sets forth the case for one of these approaches, the “egocentric” one, initially on the basis of its ability to explain the near‐indefeasibility of ascriptions of content to our own terms (“‘dogs’ as I use it means dogs”), but more generally on the basis of its providing an attractive overall picture (...) of the descriptive and explanatory role of representational content. In doing this, the paper relates the egocentric view to an “immanent” or “deflationary” view of reference and truth conditions, and also to the view of reference‐talk and truth‐talk as anaphoric devices. It discusses the indeterminacy of content ascriptions to those in communities with radically different theories, a phenomenon that is unsurprising on the egocentric approach, and connects this to the thesis of the normativity of meaning. (It does all this in rather broad brush: many strands of the egocentric account will be familiar, and are the subject of familiar controversies; the point of the paper is less to address these controversies individually than to tie the strands together into what is hoped to be an appealing package.). (shrink)

It might be thought that we could argue for the consistency of a mathematical theory T within T, by giving an inductive argument that all theorems of T are true and inferring consistency. By Gödel's second incompleteness theorem any such argument must break down, but just how it breaks down depends on the kind of theory of truth that is built into T. The paper surveys the possibilities, and suggests that some theories of truth give far more intuitive (...) diagnoses of the breakdown than do others. The paper concludes with some morals about the nature of validity and about a possible alternative to the idea that mathematical theories are indefinitely extensible. (shrink)

The purpose of this paper is to study an analogue of Hilbert's seventeenth problem for functions over a valued field which are integral definite on some definable set; that is, that map the given set into the valuation ring. We use model theory to exhibit a uniform method, on various theories of valued fields, for deriving an algebraic characterization of such functions. As part of this method we refine the concept of a function being integral at a (...) point, and make it dependent on the relevant class of valued fields. We apply our framework to algebraically closed valued fields, model complete theories of difference and differential valued fields, and real closed valued fields. (shrink)