The Diagnostic and Statistical Manual of Mental Disorders (5th ed.; DSM–5; American Psychiatric Association [APA], 2013) defines melancholia as “A mental state characterized by very severe depressi...

The Jewish religious tradition summons its adherents to save life. For religious Jews preservation of life is the ultimate religious commandment. At the same time Jewish law recognizes that the agony of a moribund person may not be stretched. When the time to die has come this has to be respected. The process of dying should not needlessly be prolonged. We discuss the position of two prominent Orthodox Jewish authorities – the late Rabbi Moshe Feinstein and Rabbi J David Bleich (...) – towards the role of life-sustaining treatment in end-of-life care. From the review, the characteristic halachic and heterogeneous character of Jewish ethical reasoning appears. The specificity of Jewish dealing with ethical dilemmas in health care indicates the importance for contemporary healthcare professionals of providing care which is sensitive to a patient’s culture and worldview. (shrink)

Various authors of logic texts are cited who either suggest or explicitly state that the Gödel incompleteness result shows that some unprovable sentence of arithmetic is true. Against this, the paper argues that the matter is one of philosophical controversy, that it is not a mathematical or logical issue.

Information?rich environments are created to promote data use in schools for the purpose of self?evaluation and quality assurance. However, providing feedback does not guarantee that schools will actually put it to use. One of the main stumbling blocks relates to the interpretation and diagnosis of the information. This study examines the relationship between data literacy competences, support given in interpreting the information, actual use of the feedback and potential school improvement effect. A randomised field experiment with 188 school principals from (...) primary education was set up and a post?test was used to investigate the effects of a support initiative. The results revealed that a minority of schools invested significantly in the interpretation and diagnosis of the school performance feedback (SPF), despite the fact that most of the respondents showed an interest in the SPF report. In addition, data competence support and the subsequent use of feedback were found to be limited. (shrink)

According to the received view, formalism – interpreted as the thesis that mathematical truth does not outrun the consequences of our maximal mathematical theory – has been refuted by Goedel's theorem. In support of this claim, proponents of the received view usually invoke an informal argument for the truth of the Goedel sentence, an argument which is supposed to reconstruct our reasoning in seeing its truth. Against this, Field has argued in a series of papers that the principles involved in (...) this argument – when applied to our maximal mathematical theory – are unsound. This paper defends the received view by showing that there is a way of seeing the truth of the Goedel sentence which is immune to Field's strategy. (shrink)

Summarizing a surrounding 200 pages, pages 179 to 190 of Shadows of the Mind contain a future dialog between a human identified as "Albert Imperator" and an advanced robot, the "Mathematically Justified Cybersystem", allegedly Albert's creation. The two have been discussing a Gödel sentence for an algorithm by which a robot society named SMIRC certifies mathematical proofs. The sentence, referred to in mathematical notation as Omega(Q*), is to be precisely constructed from on a definition of SMIRC's algorithm. It can (...) be interpreted as stating "SMIRC's algorithm cannot certify this statement." The robot has asserted that SMIRC never makes mistakes. If so, SMIRC's algorithm cannot certify the Goedel sentence, for that would make the statement false. But, if they can't certify it, what is says is true! Humans can understand it is true, but mighty SMIRC cannot certify it. The dialog ends melodramatically as the robot, apparently unhinged by this revelation, claims to be a messenger of god, and the human shuts it down with a secret control. (shrink)

This paper develops in certain directions the work of Meyer in [3], [4], [5] and [6]. In those works, Peano’s axioms for arithmetic were formulated with a logical base of the relevant logic R, and it was proved finitistically that the resulting arithmetic, called R♯, was absolutely consistent. It was pointed out that such a result escapes incau- tious formulations of Goedel’s second incompleteness theorem, and provides a basis for a revived Hilbert programme. The absolute consistency result used as a (...) model arithmetic modulo two. Modulo arithmetics are not or- dinarily thought of as an extension of Peano arithmetic, since some of the propositions of the latter, such as that zero is the successor of no number, fail in the former. Consequently a logical base which, unlike classical logic, tolerates contradictory theories was used for the model. The logical base for the model was the three-valued logic RM3, which has the advantage that while it is an extension of R, it is finite valued and so easier to handle. The resulting model-theoretic structure is interesting in its own right in that the set of sentences true therein consti- tutes a negation inconsistent but absolutely consistent arithmetic which is an extension of R♯. In fact, in the light of the result of [6], it is an extension of Peano arithmetic with a base of a classical logic, P♯. A generalisation of the structure is to modulo arithmetics with the same logical base RM3, but with varying moduli. We first study the properties of these arithmetics in this paper. The study is then generalised by vary- ing the logical base, to give the arithmetics RMni, of logical base RMn and modulus i. Not all of these exist, however, as arithmetical properties and logical properties interact, as we will show. The arithmetics RMni give rise, on intersection, to an inconsistent arithmetic RMω which is not of modulo i for any i. We also study its properties, and, among other results, we show by finitistic means that the more natural relevant arithmetics R♯ and R♯♯ are incomplete. In the rest of the paper we apply these techniques to several topics, particularly relevant quantum arithmetic in which we are able to show that the law of distribution remains unprovable. Aside from its intrinsic interest, we regard the present exercise as a demonstration that inconsistent theories and models are of mathematical worth and interest. (shrink)

We investigate what happens when ‘truth’ is replaced with ‘provability’ in Yablo’s paradox. By diagonalization, appropriate sequences of sentences can be constructed. Such sequences contain no sentence decided by the background consistent and sufficiently strong arithmetical theory. If the provability predicate satisfies the derivability conditions, each such sentence is provably equivalent to the consistency statement and to the Gödel sentence. Thus each two such sentences are provably equivalent to each other. The same holds for the arithmetization of (...) the existential Yablo paradox. We also look at a formulation which employs Rosser’s provability predicate. (shrink)

This paper develops in certain directions the work of Meyer in [3], [4], [5] and [6] (see also Routley [10] and Asenjo [11]). In those works, Peano’s axioms for arithmetic were formulated with a logical base of the relevant logic R, and it was proved finitistically that the resulting arithmetic, called R♯, was absolutely consistent. It was pointed out that such a result escapes incau- tious formulations of Goedel’s second incompleteness theorem, and provides a basis for a revived Hilbert programme. (...) The absolute consistency result used as a model arithmetic modulo two. Modulo arithmetics are not or- dinarily thought of as an extension of Peano arithmetic, since some of the propositions of the latter, such as that zero is the successor of no number, fail in the former. Consequently a logical base which, unlike classical logic, tolerates contradictory theories was used for the model. The logical base for the model was the three-valued logic RM3 (see e.g. [1] or [8]), which has the advantage that while it is an extension of R, it is finite valued and so easier to handle. The resulting model-theoretic structure (called in this paper RM32) is interesting in its own right in that the set of sentences true therein consti- tutes a negation inconsistent but absolutely consistent arithmetic which is an extension of R♯. In fact, in the light of the result of [6], it is an extension of Peano arithmetic with a base of a classical logic, P♯. A generalisation of the structure is to modulo arithmetics with the same logical base RM3, but with varying moduli (called RM3i here). We first study the properties of these arithmetics in this paper. The study is then generalised by vary- ing the logical base, to give the arithmetics RMni, of logical base RMn and modulus i. Not all of these exist, however, as arithmetical properties and logical properties interact, as we will show. The arithmetics RMni give rise, on intersection, to an inconsistent arithmetic RMω which is not of modulo i for any i. We also study its properties, and, among other results, we show by finitistic means that the more natural relevant arithmetics R♯ and R♯♯ are incomplete (whether or not consistent and recursively enumerable). In the rest of the paper we apply these techniques to several topics, particularly relevant quantum arithmetic in which we are able to show (unlike classical quantum arithmetic) that the law of distribution remains unprovable. Aside from its intrinsic interest, we regard the present exercise as a demonstration that inconsistent theories and models are of mathematical worth and interest. (shrink)

The argument is a dialectical one. It is not a direct proof that the mind is something more than a machine, but a schema of disproof for any particular version of mechanism that may be put forward. If the mechanist maintains any specific thesis, I show that [146] a contradiction ensues. But only if. It depends on the mechanist making the first move and putting forward his claim for inspection. I do not think Benacerraf has quite taken the point. He (...) criticizes me both for "failing to notice" that my ability to show that the Gödel sentence of a formal system is true "depends very much on how he is given. (shrink)

The presented paper takes up the attempt to analyse and specify the suspicion that some modal rules of inference are paralogical in application to non-logical reasonings (s.c. modal fallacy). The considerations have been limited to modal prepositional calculi: K and S5, which are intended to be a formal base of these non-logical reasonings - proofs of so called specific thesis on the grounds of the particular specific theories. Pointing out the properties of being permitted, being valid and being derivable in (...) case of inferences rules and also semantical relations of point, structure, frame and inferential consequence in standard semantics of possible worlds, enables to define two kinds of paralogism: point and structural. Justification of the suspicion of modal fallacy occurrence in the case of a given inference rule, depends on pointed metalogical properties of this rule and also on what kind of the notion of paralogism is being discussed. It appears that when a given rule is paralogical only pointly (and not structurally), the sufficient condition of avoiding modal fallacy is to consider the specific axioms of the given specific theory as the sentences which are structurally true (structural truth is of course not equivalent to logical truth). If we want to treat these axioms as sentences which are pointly true, we have to eliminate pointly paralogical rules. In this case it is enough to construct such axiomatisation of calculi K and S5, in which we use the notion of modal closure (it eliminates the primitive rule of Goedel and all rules derivable from it - rules which are structurally but not pointly correct). (shrink)

The Goedelian approach is discussed as a prime example of a science towards the origins. While mere self­referential objectification locks in to its own by­products, self­releasing objectification informs the formation of objects at hand and their different levels of interconnection. Guided by the spirit of Goedel's work a self­reflective science can open the road where old tenets see only blocked paths. “This is, as it were, an analysis of the analysis itself, but if that is done it forms the fundamental (...) of human science, as far as this kind of things is concerned.” G. Leibniz, ('Methodus Nova ...', 1673) . (shrink)

Hawking, in his book, A Brief History of Time, concludes with a conditional remark: If we find a complete theory to explain the physical world, then we will come to understand God’s mind. With Goedel in mind, we can raise questions about the completeness of our scientific understanding and the nature of our understanding with regard to God’s mind. We need to ask about the higher order of our understanding when we move to knowing God’s mind. We go onto develop (...) these problems with Nietzsche’s thoughts on the death of God, and the emergence of super human intelligences. Then, we come to Buddha, a logical genius, to see how the Buddhistic enlightenment exemplifies the super human intelligence, as well as the higher order understanding in our knowledge of God’s mind. (shrink)

It is unfortunate for the philosophical community generally, and for those philosophers who pursue various versions of idealism in particular, that a logician of Kurt Goedel’s genius published very little of non-mathematical philosophical interest. Amongst his unpublished papers at Princeton there are, however, several versions of a paper he wrote on the relevance of contemporary relativity to the philosophy of Kant. The purpose of the present paper is to give a partial exposition and defence of Goedel’s view that contemporary relativity (...) supports a neo-Kantian idealistic position with regard to time. (shrink)

This accessible book gives a new, detailed and elementary explanation of the Gödel incompleteness theorems and presents the Chaitin results and their relation to the da Costa-Doria results, which are given in full, but with no ...

I argue for an alternative to Quine’s conception of observation sentences, one that better satisfies the roles Quine envisages for them, and that otherwise respects Quinean constraints. After reviewing a certain predicament Quine got into in balancing the needs of the intersubjectivity of observation sentences with his notion of the stimulus meaning of an observation sentence, I push for replacing the latter with what I call the ‘stimulus field’ of an observation sentence, a notion that remains ‘proximate’ but (...) is shared between different language users. Throughout, I emphasize the epistemological role of observation sentences. (shrink)

Sentence boundary detection (SBD) represents an important first step in natural language processing since accurately identifying sentence boundaries significantly impacts downstream applications. Nevertheless, detecting sentence boundaries within legal texts poses a unique and challenging problem due to their distinct structural and linguistic features. Our approach utilizes deep learning models to leverage delimiter and surrounding context information as input, enabling precise detection of sentence boundaries in English legal texts. We evaluate various deep learning models, including domain-specific transformer models like LegalBERT and (...) CaseLawBERT. To assess the efficacy of our deep learning models, we compare them with a state-of-the-art domain-specific statistical conditional random field (CRF) model. After considering model size, F1-score, and inference time, we identify the Convolutional Neural Network Model (CNN) as the top-performing deep learning model. To further enhance performance, we integrate the features of the CNN model into the subsequent CRF model, creating a hybrid architecture that combines the strengths of both models. Our experiments demonstrate that the hybrid model outperforms the baseline model, achieving a 4% improvement in the F1-score. Additional experiments showcase the superiority of the hybrid model over SBD open-source libraries when confronted with an out-of-domain test set. These findings underscore the importance of efficient SBD in legal texts and emphasize the advantages of employing deep learning models and hybrid architectures to achieve optimal performance. (shrink)

Penrose proved that a computational or formalizable theory of the brainís cognitive functioning is impossible, but suggested that a physical non-computational and non-formalizable one may be viable. Arguments as to why Penroseís program is unrealizable are presented. The main argument is that a non-formalizable theory should be verbal. However, verbal paradoxes based on Cantorís diagonal processes show the impossibility of a consistent verbal theory of the brain comprising its arithmetical cognition. It is suggested that comprehensive theories of the human brain (...) and of physical experience are Kantian rather than Platonic ideas. This suggestion is likewise based on arguments related to diagonal processes. (shrink)

Sentence comprehension - the way we process and understand spoken and written language - is a central and important area of research within psycholinguistics. This book explores the contribution of computational linguistics to the field, showing how computational models of sentence processing can help scientists in their investigation of human cognitive processes. It presents the leading computational model of retrieval processes in sentence processing, the Lewis and Vasishth cue-based retrieval mode, and develops a principled methodology for parameter estimation and model (...) comparison/evaluation using benchmark data, to enable researchers to test their own models of retrieval against the present model. It also provides readers with an overview of the last 20 years of research on the topic of retrieval processes in sentence comprehension, along with source code that allows researchers to extend the model and carry out new research. Comprehensive in its scope, this book is essential reading for researchers in cognitive science. (shrink)

Gödel’s Ontological argument is distinctive because it is the most sophisticated and formal of ontological arguments and relies heavily on the notion of _positive property_. Gödel uses a third-order modal logic with a property abstraction operator and property quantification into modal contexts. Gödel describes _positive property_ as "independent of the accidental structure of the world"; "pure attribution," as opposed to privation; "positive in the 'moral aesthetic sense.'" _Pure attribution_ seems likely to be related to the Leibnizian concept (...) of perfection. By a careful examination of the formal semantics of third-order modal logic with property abstraction together with a Completeness result for third-order modal logic with property abstraction for faithful models that I previously developed in 2000 in my work, _Gödel’s Ontological Argument_, I argue that it is not possible to develop a sufficient applied third-order modal semantics for Gödel’s ontological argument. As I explore possible approaches for an applied semantics including anti-Realist accounts of the semantics of modal logic compatible with Actualism, I argue that Gödel makes implicit philosophical assumptions which commit him to both possibilism and modal realism. (shrink)

Gödel’s Ontological argument is distinctive because it is the most sophisticated and formal of ontological arguments and relies heavily on the notion of positive property. Gödel uses a third-order modal logic with a property abstraction operator and property quantification into modal contexts. Gödel describes positive property as "independent of the accidental structure of the world"; "pure attribution," as opposed to privation; "positive in the 'moral aesthetic sense.'" Pure attribution seems likely to be related to the Leibnizian concept (...) of perfection.By a careful examination of the formal semantics of third-order modal logic with property abstraction together with a Completeness result for third-order modal logic with property abstraction for faithful models that I previously developed in 2000 in my work, Gödel’s Ontological Argument, I argue that it is not possible to develop a sufficient applied third-order modal semantics for Gödel’s ontological argument. As I explore possible approaches for an applied semantics including anti-Realist accounts of the semantics of modal logic compatible with Actualism, I argue that Gödel makes implicit philosophical assumptions which commit him to both possibilism (the belief in merely possible objects) and modal realism (the belief in possible worlds). (shrink)

Read this book to get a deeper understanding of a wide range of semantics research on complex sentences and meaning in discourse. These in-depth articles from leading names in their fields cover the core concepts of sentential semantics such as tense, modality, conditionality, propositional attitudes, scope, negation, and coordination. The highly cited material, covers questions, imperatives, copular clauses, and existential sentences. It also includes essential research on sentence types, and explains central concepts in the theory of information structure (...) and discourse structure, such as topics, cohesion and coherence, accessibility and discourse particles. (shrink)

In the 1950s, Noam Chomsky offered a new vision for linguistic research and syntacticians. This chapter explores some ways in which Chomsky's linguistic work has influenced research on one domain of linguistic performance, sentence processing, over the last half century. It shows that Chomsky's claim in Aspects of the Theory of Syntax is largely borne out: "the study of performance will proceed only as far as the study of the underlying competence permits". The chapter briefly addresses a question about the (...) scope of modern sentence processing research and its relationship to specific grammatical formalisms. It reviews the literature on incremental ambiguity resolution, moves to the processing of long‐distance filler‐gap dependency processing, and provides information on the processing of anaphoric relations. In order to illustrate how the phenomenon has contributed to psycholinguistic theorizing, the chapter outlines a well‐known model and then considers how other models diverge. (shrink)

Introduction: the emergence of the proportionate sentence -- Sentence proportionality sketched briefly -- Why should the criminal sanction exist? -- Why punish proportionately? -- Ordinal and cardinal proportionality -- Seriousness, severity and the living-standard -- The role of previous convictions -- Proportionate non-custodial sanctions -- A "modified" desert model? -- The politics of the desert model -- Proportionate sentences for juveniles -- Appendix: the desert model's evolution : a brief chronology.

Substitution and simple sentences -- Simple sentences and semantics -- Simple sentences and implicatures -- The enlightenment problem and a common assumption -- Abandoning (EOI) -- Beyond matching propositions -- App. A : extending the account -- App. B : belief reporting.

This book looks at the relationship between the structure of the sentence and the organization of discourse. While a sentence obeys specific grammatical rules, the coherence of a discourse is instead dependent on the relations between the sentences it contains. In this volume, leading syntacticians, semanticists, and philosophers examine the nature of these relations, where they come from, and how they apply. Chapters in Part I address points of sentence grammar in different languages, including mood and tense in Spanish, (...) definite determiners in French and Bulgarian, and the influence of aktionsart on the acquisition of tense by English, French, and Chinese children. Part II looks at modes of discourse, showing for example how discourse relations create implicatures and how Indirect Discourse differs from Free Indirect Discourse. The studies conclude that the relations between sentences that make a discourse coherent are already encoded in sentence grammar and that, once established, these relations influence the meaning of individual sentences. (shrink)

The paper proposes the first unified account of deictic/sentence-external and sentence-internal readings of singular different . The empirical motivation for such an account is provided by a cross-linguistic survey and an analysis of the differences in distribution and interpretation between singular different , plural different and same (singular or plural) in English. The main proposal is that distributive quantification temporarily makes available two discourse referents within its nuclear scope, the values of which are required by sentence-internal uses of singular different (...) to be distinct, much as its deictic uses require the values of two discourse referents to be distinct. Thus, we take sentence-internal readings to be a form of ‘association with distributivity’ that is similar to association with focus. The contrast between singular different , plural different and same is explained in terms of several kinds of quantificational distributors that license their internal readings. The analysis is executed in a stack-based dynamic system couched in type logic, so we get compositionality in the usual Montagovian way. Quantificational subordination and dependent indefinites in various languages provide additional motivation for the account. Investigating the connections between items with sentence-internal readings and the quantificational licensors of these readings opens up a larger project of formally investigating (i) the typology of quantificational distributors and distributivity-dependent items and (ii) the fine-grained contexts of evaluation needed to capture this typological variation. (shrink)

Introduction: what is a sentence? -- Slogans and other one-liners -- The poetic line -- Sentences terminable and interminable -- The democratic sentence -- Conclusion: the sentence fetish.

The principle that a sentence should be proportionate to the seriousness of the offence remains at the centre of penal practice and scholarly debate. This volume explores highly topical aspects of proportionality theory that require examination and further analysis. von Hirsch and Ashworth explore the relevance of the principle of proportionality to the sentencing of young offenders, the possible reasons for departing from the principle when sentencing dangerous offenders, and the application of the principle to socially deprived offenders. They examine (...) the claim that the principle tends to be associated with greater severity in sentencing, and explore the relevance of penance and of restorative justice to proportionality theory. Their examination of arguments and counter-arguments culminates in a re-statement of the main criteria for proportionate sentencing.The authors are well known for their previous writings on proportionality theory, and this volume broadens the theory to deal with important contemporary issues in crime and punishment. (shrink)

Presents a set-theoretic version of the analysis of "there be" as predicating instantiation of a property, a property-theoretic version of which was developed in McNally 1992. This paper provides a solution to the criticism that McNally 1992's analysis could not account for sentences in which postverbal nominal contains a monotone decreasing or nonmonotonic determiner.