Purely parallel neural networks can model object recognition in brief displays – the same conditions under which illusory conjunctions have been demonstrated empirically. Correcting errors of illusory conjunction is the “tag-assignment” problem for a purely parallel processor: the problem of assigning a spatial tag to nonspatial features, feature combinations, and objects. This problem must be solved to model human object recognition over a longer time scale. Our model simulates both the parallel processes that may underlie illusory conjunctions and the serial (...) processes that may solve the tag-assignment problem in normal perception. One component of the model extracts pooled features and another provides attentional tags that correct illusory conjunctions. Our approach addresses two questions: How can objects be identified from simultaneously attended features in a parallel, distributed representation? How can the spatial selectional requirements of such an attentional process be met by a separation of pathways for spatial and nonspatial processing? Our analysis of these questions yields a neurally plausible simulation of tag assignment based on synchronizing feature processing activity in a spatial focus of attention. (shrink)

Philologus, founded in 1846, is one of the oldest and most respected periodicals in the field of Classics. It publishes articles on Greek and Latin literature, historiography, philosophy, history of religion, linguistics, reception, and the history of scholarship. The journal aims to contribute to our understanding of Greco-Roman culture and its lasting influence on European civilization. The journal Philologus, conceived as a forum for discussion among different methodological approaches to the study of ancient texts and their reception, publishes original scholarly (...) contributions with a strong international focus. Publications languages are: German, English, Italian, French. As of 2014 the publication of supplementary volumes will be resumed. The series Philologus. Supplemente / Philologus. Supplementary Volumes will publish monographs and edited volumes pertaining to all aspects of the study of ancient literature and its reception, with a special focus on topics concerning literary theory, philosophy and the history of scholarship from an interdisciplinary perspective. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Barrow and Newton E. W. STRONG As E. A. Buxrr HAS ADDUCED,Isaac Barrow (1630-1677) in his philosophy of space, time, and mathematical method strongly influenced the thinking of Newton: The recent publication of an early paper written by Newton (his De gravitatione et aequipondio fluidorum)2 affords evidence not known to Burtt of Newton's indebtedness in philosophy to Barrow, his teacher. Prior to its publication in 1962, this paper (...) was utilized by Alexandre Koyrd in his essay, "Newton and Descartes," 3 a study based on the third Horblit Lecture in the History of Science which he gave at Harvard University, March 8, 1961. Koyr8 maintains that there is a radical opposition in Newton's Principia not only to Descartes' purely scientific theories but also to the Cartesian philosophy. Yet, as he remarks, "we do not find in the Principia an open criticism of the philosophy of Descartes.... " He attributes this fact principally "to the very structure of the Principia: it is essentially a book on rational mechanics, which provides principles for physics and astronomy. In such a book there is a normal place for the discussion of Cartesian optics, but not of the conception of the relations of mind and body, and other such things." Koyrd asserts, nonetheless, that the criticism is not absent. It lurks in Newton's carefully worded definitions of fundamental concepts--those of space, time, motion, and matter--and becomes more apparent in the Optice of 1706 and in the second odition of the Principia. In support of this argument, he makes much of young Newton's unfini.~hed paper. He holds that this essay is of exceptional value "as it enables us to get some insight into the formation of Newton's thought, and to recognize that preoccupation with philosophic problems was not an external additatmentum but an integral dement of his thinking." 4 As concerns "young Newton's conception of space in its being and in its relation to God and time," Koyrd remarks that we learn from this essay The Metaphysical Foundations of Modern Physical Science (New York, 1927), p. 144. A. Rupert Hall and Marie Boas Hall, Unpublished Scientific Papers of Isaac Newton (Cambridge, 1962), Introduction, pp. 75-88; Latin text, pp. 90-121; English translation, pp. 121156. " Newtonian Studies (Harvard University Press, 1965), pp. 53-114. " Newtonian Studies, pp. 82-83. In his De gravitatione et aequipondio fluidorum, Newton is indeed engrossed with philosophic problems. With regard, however, to the announced purpose of his paper, namely, "to treat of the science of gravity and solid bodies in fluids by two methods," does Newton represent kis metaphysical "explanation of the nature of body" as an element of his science essential to its completeness7 He does not do so. At the end of his explanation he remarks: "I have already digressed enough; let us return to the main theme." He proceeds to set forth fifteen more definitions and then turns to the demonstration of two "Propositions on Non-Elastic Fluids." [155] 156 HISTORY OF PHILOSOPHY "that space is necessary, eternal, immutz~ble, and unmovable, that though we can imagine that there is nothing in space we cannot think space is not.., and that if there is no space, God would be nowhere. We learn also that all points of space are simultaneous and that, therefore, the divine omnipresence does not introduce composition in God.... " What we here learn from Newton about space in confutation of Descartes is to be found in Barrow's tenth mathematical lecture, "'Of Space, and Impenetrability." 5 In this lecture, Barrow opposes both Descartes and Hobbes. He objects, as does Newton, to the position taken by Descartes in his Principia Philosophiae, namely, "it is necessary.forMatter to be infinitely extended." He proceeds, as does Newton, to show how "very much Cartesius's great Subtility has failed him in this Case" to conclude that there is space empty of matter and distinct from magnitude from which an infinity of matter cannot be deduced. The correspondence of arguments tendered by Barrow and Newton indicates that the tenth lecture constituted a source from which Newton gleaned principal objections to Descartes' Principia Philosophiae. Although Koyr~ makes reference to Burtt's... (shrink)

Philologus, founded in 1846, is one of the oldest and most respected periodicals in the field of Classics. It publishes articles on Greek and Latin literature, historiography, philosophy, history of religion, linguistics, reception, and the history of scholarship. The journal aims to contribute to our understanding of Greco-Roman culture and its lasting influence on European civilization. The journal Philologus, conceived as a forum for discussion among different methodological approaches to the study of ancient texts and their reception, publishes original scholarly (...) contributions with a strong international focus. Publications languages are: German, English, Italian, French. As of 2014 the publication of supplementary volumes will be resumed. The series Philologus. Supplemente / Philologus. Supplementary Volumes will publish monographs and edited volumes pertaining to all aspects of the study of ancient literature and its reception, with a special focus on topics concerning literary theory, philosophy and the history of scholarship from an interdisciplinary perspective. (shrink)

Building upon earlier work of Donna Carr, Don Pelletier, Chris Johnson, Shu-Guo Zhang and others, we show that a normal ideal J on Pκ is strongly normal if and only if J+→< 2 for every μ < κ, and we describe the least normal ideal J on Pκ such that J+ →< 2.

For every uncountable regular cardinalκ and any cardinalλ≧κ,P κ λ denotes the set $\left\{ {x \subseteqq \lambda :\left| x \right|< \kappa } \right\}$ . Furthermore, < denotes the binary operation defined inP κ λ byx (...) + denotes the setP κ λ−I, andI * the filter dual toI.An idealI overP κ λ is said to benormal iff every functionf:P κ λ→λ with the property that {x∈P κ λ:f(x)∈x}∈I + is constant on a set inI +.I is said to bestrongly normal iff every functionf:P κ λ→P κ λ with the property that {x∈P κ λ:x∩xκ≠Ø∧f(x)shrink)

In this paper, we present an extension of λμ-calculus called λμ++-calculus which has the following properties: subject reduction, strong normalization, unicity of the representation of data and thus confluence only on data types. This calculus allows also to program the parallel-or.

In this paper, we present an extension of $lambdamu$-calculus called $lambdamu^{++}$-calculus which has the following properties: subject reduction, strong normalization, unicity of the representation of data and thus confluence only on data types. This calculus allows also to program the parallel-or.

We revisit Kolchin's results on definability of differential Galois groups of strongly normal extensions, in the case where the field of constants is not necessarily algebraically closed. In certain classes of differential topological fields, which encompasses ordered or p‐valued differential fields, we find a partial Galois correspondence and we show one cannot expect more in general. In the class of ordered differential fields, using elimination of imaginaries in, we establish a relative Galois correspondence for relatively definable subgroups of the group (...) of differential order automorphisms. (shrink)

We introduce modal propositional substructural logics with strong negation, and prove the completeness theorems (with respect to Kripke models) for these logics.

In a recent paper by M. Rathjen and the present author it has been shown that the statement “every normal function has a derivative” is equivalent to $\Pi ^1_1$ -bar induction. The equivalence was proved over $\mathbf {ACA_0}$, for a suitable representation of normal functions in terms of dilators. In the present paper, we show that the statement “every normal function has at least one fixed point” is equivalent to $\Pi ^1_1$ -induction along the natural numbers.

This article draws attention to several common mistakes in thinking about biomedical enhancement, mistakes that are made even by some supporters of enhancement. We illustrate these mistakes by examining objections that John Harris has recently raised against the use of pharmacological interventions to directly modulate moral decision-making. We then apply these lessons to other influential figures in the debate about enhancement. One upshot of our argument is that many considerations presented as powerful objections to enhancement are really strong considerations (...) in favour of biomedical enhancement, just in a different direction. Another upshot is that it is unfortunate that much of the current debate focuses on interventions that will radically transform normal human capacities. Such interventions are unlikely to be available in the near future, and may not even be feasible. But our argument shows that the enhancement project can still have a radical impact on human life even if biomedical enhancement operated entirely within the normal human range. (shrink)

We discuss the content and significance of John von Neumann’s quantum ergodic theorem (QET) of 1929, a strong result arising from the mere mathematical structure of quantum mechanics. The QET is a precise formulation of what we call normal typicality, i.e., the statement that, for typical large systems, every initial wave function ψ0 from an energy shell is “normal”: it evolves in such a way that |ψt ψt| is, for most t, macroscopically equivalent to the micro-canonical density matrix. The (...) QET has been mostly forgotten after it was criticized as a dynamically vacuous statement in several papers in the 1950s. However, we point out that this criticism does not apply to the actual QET, a correct statement of which does not appear in these papers, but to a different (indeed weaker) statement. Furthermore, we formulate a stronger statement of normal typicality, based on the observation that the bound on the deviations from the average specified by von Neumann is unnecessarily coarse and a much tighter (and more relevant) bound actually follows from his proof. (shrink)

Response to commentary. We are grateful to Crockett and Craigie for their interesting remarks on our paper. We accept Crockett’s claim that there is a need for caution in drawing inferences about patient groups from work on healthy volunteers in the laboratory. However, we believe that the evidence we cited established a strong presumption that many of the patients who are routinely taking a medication, including many people properly prescribed the medication for a medical condition, have morally significant aspects (...) of their cognition and behavior modified in a way that is unintended and may sometimes be unwelcome. Crockett notes that in some cases the effects of long-term drug use may differ, sometimes markedly, from the effects of short-term use. However, if acute use of a drug affects a neural system involved in mediating moral cognition or behavior, this nevertheless provides some evidence that chronic use of the drug may affect that same system and thus have morally significant effects. It is also plausible, in some cases, that an acute moral effect would give rise to a chronic moral effect via cognitive mechanisms. ... (shrink)

Let $R$ be a convergent term rewriting system, and let $CR$-equality on combinatory logic terms be the equality induced by $\beta \eta R$-equality on terms of the lambda calculus under any of the standard translations between these two frameworks for higher-order reasoning. We generalize the classical notion of strong reduction to a reduction relation which generates $CR$-equality and whose irreducibles are exactly the translates of long $\beta R$-normal forms. The classical notion of strong normal form in combinatory logic (...) is also generalized, yielding yet another description of these translates. Their resulting tripartite characterization extends to the combined first-order algebraic and higher-order setting the classical combinatory logic descriptions of the translates of long $\beta$-normal forms in the lambda calculus. As a consequence, the translates of long $\beta R$-normal forms are easily seen to serve as canonical representatives for $CR$-equivalence classes of combinatory logic terms for non-empty, as well as for empty, $R$. (shrink)

The basic bimodal systemK/K can be interpreted as an analysis of the logic of ability developed in [1]. Where in [1] we would express the claimI can bring it about that P using the formula, with its non-normal operator, we will now use the formula. Here is a normal alethic possibilitation operator.is a normal necessitation operator, but it is independent of, and not subject to an alethic interpretation. Rather, is interpreted to meanI bring it about that P. The result is (...) a simplification and clarification of a combined logic of ability and action like that in [2], but employing only normal operators.A number of extensions of the basic systemK/K are constructed, first by strengthening the two normal sublogics independently and then by linking the two sublogics via axiom schemata involving both operators. The result is a series of increasingly strong systems which more and more adequately fulfill our expectations for a satisfactory logic of action and ability. (shrink)

Tetravalent modal logic (TML) was introduced by Font and Rius in 2000. It is an expansion of the Belnap-Dunn four-valued logic FOUR, a logical system that is well-known for the many applications found in several fields. Besides, TML is the logic that preserves degrees of truth with respect to Monteiro’s tetravalent modal algebras. Among other things, Font and Rius showed that TML has a strongly adequate sequent system, but unfortunately this system does not enjoy the cut-elimination property. However, in a (...) previous work we presented a sequent system for TML with the cut-elimination property. Besides, in this same work, it was also presented a sound and complete natural deduction system for this logic. In the present article we continue with the study of TML under a proof-theoretic perspective. In the first place, we show that the natural deduction system that we introduced before admits a normalization theorem. In the second place, taking advantage of the contrapositive implication for the tetravalent modal algebras introduced by A. V. Figallo and P. Landini, we define a decidable tableau system adequate to check validity in the logic TML. Finally, we provide a sound and complete tableau system for TML in the original language. These two tableau systems constitute new (proof-theoretic) decision procedures for checking validity in the variety of tetravalent modal algebras. (shrink)

We present a range of mathematical theorems whose proofs require unexpectedly strong logical methods, which in some cases go well beyond the usual axioms for mathematics.

This paper explores a notion of “the strong version” of a sentential logic S, initially defined in terms of the notion of a Leibniz filter, and shown to coincide with the logic determined by the matrices of S whose filter is the least S-filter in the algebra of the matrix. The paper makes a general study of this notion, which appears to unify under an abstract framework the relationships between many pairs of logics in the literature. The paradigmatic examples (...) are the local and the global consequences associated with a normal modal logic, and the logics preserving degrees of truth and preserving truth associated with certain substructural and many-valued logics. For protoalgebraic logics the results in the paper coincide with those obtained by two of the authors in 2001, so the main novelty of the approach is its suitability for all kinds of logics. The paper also studies three kinds of definability of the Leibniz filters, and their consequences for the determination of the strong version. In a second part of the paper several case studies are developed, comprising positive modal logic, Dunn–Belnap’s four-valued logic, the large family of substructural logics, and some relevance logics. (shrink)

A filter of a sentential logic ? is Leibniz when it is the smallest one among all the ?-filters on the same algebra having the same Leibniz congruence. This paper studies these filters and the sentential logic ?+ defined by the class of all ?-matrices whose filter is Leibniz, which is called the strong version of ?, in the context of protoalgebraic logics with theorems. Topics studied include an enhanced Correspondence Theorem, characterizations of the weak algebraizability of ?+ and (...) of the explicit definability of Leibniz filters, and several theorems of transfer of metalogical properties from ? to ?+. For finitely equivalential logics stronger results are obtained. Besides the general theory, the paper examines the examples of modal logics, quantum logics and Łukasiewicz's finitely-valued logics. One finds that in some cases the existence of a weak and a strong version of a logic corresponds to well-known situations in the literature, such as the local and the global consequences for normal modal logics; while in others these constructions give an independent interest to the study of other lesser-known logics, such as the lattice-based many-valued logics. (shrink)

A method is described for obtaining conjunctive normal forms for logics using Gentzen-style rules possessing a special kind of strong invertibility. This method is then applied to a number of prominent fuzzy logics using hypersequent rules adapted from calculi defined in the literature. In particular, a normal form with simple McNaughton functions as literals is generated for łukasiewicz logic, and normal forms with simple implicational formulas as literals are obtained for Gödel logic, Product logic, and Cancellative hoop logic.

The health theories of Nordenfelt and Boorse are compared. Critical attention is focused on Nordenfelt's description of his theory as one of holistic welfare, contrasting with Boorse's analytical and statistical approach. Neither theory is found to give an entirely satisfactory account of ‘health’ in scientific medicine or common usage. Because Nordenfelt attenuates the ontological significance of organs and organ parts and simplifies the role of statistics, his theory is regarded as weakly holistic. Boorse underrates the importance of non-statistical evaluation. A (...) mediating position, termed ‘strong holism’ is suggested as a way of integrating normative and statistical elements in a more adequate health concept. (shrink)

This paper explores a notion of “the strong version” of a sentential logic S, initially defined in terms of the notion of a Leibniz filter, and shown to coincide with the logic determined by the matrices of S whose filter is the least S-filter in the algebra of the matrix. The paper makes a general study of this notion, which appears to unify under an abstract framework the relationships between many pairs of logics in the literature. The paradigmatic examples (...) are the local and the global consequences associated with a normal modal logic, and the logics preserving degrees of truth and preserving truth associated with certain substructural and many-valued logics. For protoalgebraic logics the results in the paper coincide with those obtained by two of the authors in 2001, so the main novelty of the approach is its suitability for all kinds of logics. The paper also studies three kinds of definability of the Leibniz filters, and their consequences for the determination of the strong version. In a second part of the paper several case studies are developed, comprising positive modal logic, Dunn–Belnap’s four-valued logic, the large family of substructural logics, and some relevance logics. (shrink)

Ordinary semantic compositionality (meaning of whole determined from meanings of parts plus composition) can serve to explain how a hearer manages to assign an appropriate meaning to a new sentence. But it does not serve to explain how the speaker manages to find an appropriate sentence for expressing a new thought. For this we would need a principle of inverse compositionality, by which the expression of a complex content is determined by the expressions of it parts and the mode of (...) composition. But this presupposes that contents have constituent structure, and this cannot be taken for granted. However, it can be proved that if a certain principle of substitutivity is valid for a particular language, then the meanings expressed by its sentences can justifiably be treated as structured. In its simplest form, this principle says that if in a complex expression a constituent is replaced by another constituent with a different meaning, the new complex has a meaning different from the original. This principle is again inversely related to the normal compositional principle of substitutivity. The combination of ordinary and inverse compositionality is here called 'strong compositionality'. The proof is carried out in the algebraic framework developed by Wilfrid Hodges and Dag Westerståhl. (shrink)

While 3/11 has altered energy policies around the world, insufficient attention has focused on reactions from local nuclear power plant host communities and their neighbors throughout Japan. Using site visits to such towns, interviews with relevant actors, and secondary and tertiary literature, this article investigates the community crisis management strategies of two types of cities, towns, and villages: those which have nuclear plants directly in their backyards and neighboring cities further away (within a 30 mile radius). Responses to the disaster (...) have varied with distance to nuclear facilities but in a way contrary to the standard theories based on the concept of the . Officials in communities directly proximal to nuclear power plants by and large remain supportive of Japan's nuclear power program, while those in cities and towns at a distance (along with much of the general public) have displayed strong opposition to the pre 3/11 status quo. Using qualitative data, this article underscores how national energy and crisis response policies rest strongly on the political economy, experiences of, and decisions made at the subnational level. (shrink)

When someone believes something that is justified for her, what part does the subject play in her state of being justified? I will answer this question by developing a strong internalist account of justification according to which the justification of a believing for a subject consists in her having grounds for her belief, and holding the belief in recognition of those grounds. But the internalist theory I defend incorporates key elements of reliabilism into its account. Using perception as a (...) model for justification, I show how ordinary perceivers would appeal to external factors to support their perceptual beliefs, and normally suppose that their beliefs are reliably connected to the objects their beliefs are about. I find in this feature of our common justificatory practice a sufficient basis for positing an externalist condition on justification—namely that subjects are only justified if their beliefs are reliably connected to their objects. (shrink)

The storage operators were introduced by J.L. Krivine ([6]); they are closed λ-terms which, for some fixed data type (the integers for example), allow to simulate “call by value” while using “call by name”. J.L. Krivine showed that such operators can be typed, in the type system, using Gödel's translation from classical to intuitionistic logic ([8]).This paper studies the existence of storage operators which give a normal form as result (strong storage operators) for recursive and iterative representation of data (...) in λ-calculus. We obtain the following result:We can find typed strong storage operators for the recursive representations of data type, but that is not the case for the iterative representations of an infinite data type.We give the proof of this result in the case of integers. (shrink)

We prove that each intermediate or normal modal logic is strongly complete with respect to a class of finite Kripke frames iff it is tabular, i.e. the respective variety of pseudo-Boolean or modal algebras, corresponding to it, is generated by a finite algebra.

Social Deviations, Labelling and Normality This paper discusses the issues of labelling, normality and social deviation. I focus on the sociological and socio-psychological aspects of these topics in light of their importance for pedagogy. Labelling mainly concerns the ways in which the formal and constitutive institutions of social control, including schools, respond to behaviour. Mainly children and young people are "marked" or labelled according to both their existing and presumed patterns of deviant behaviour. School, as a social institution, expects its (...) students to be normal. It has the power to define normality and, moreover, a network of social control to achieve it. However, from the perspective of the school it is very important not to prematurely label pupils negatively during the selection process. On the contrary, school should enable as many pupils as possible to contribute successfully towards the requirements of a knowledge society. Research indicates that there is a correlation between a child's school performance and the perceptions and expectations held by the teacher. Recent studies, concerning for example violence at school, have shown how strongly the aggressive behaviour of pupils is connected to the teacher's behaviour. The theory of labelling is concerned with the fundamental question of why some individuals and groups are branded as deviating from norms more often than others. Stigma is a relative phenomenon; it is the result of successful labelling, delivering a punitive and disapproving response. In order to better understand labelling, the concepts of social norms and social deviance also require clarification. (shrink)

We generalize a theorem of Mundici relating compactness of a regular logic L to a strong form of normality of the associated spaces of models. Moreover, it is shown that compactness is in fact equivalent to ordinary normality of the model spaces when L has uniform reduction for infinite disjoint sums of structures. Some applications follow. For example, a countably generated logic is countably compact if and only if every clopen class in the model spaces is elementary. The model (...) spaces of L are not normal for vocabularies of uncountable power ωα. It also follows that first-order logic is the only finite-dependence logic having normal model spaces and satisfying at the same time the downward Löwenheim-Skolem theorem and uniform reduction for pairs. (shrink)

We study two logics of knowledge and belief stemming from the work of Stalnaker, omitting positive introspection for knowledge. The two systems are equivalent with positive introspection, but not without. We show that while the logic of beliefs remains unaffected by omitting introspection for knowledge in one system, it brings significant changes to the other. The resulting logic of belief is non-normal, and its complete axiomatization uses an infinite hierarchy of coherence constraints. We conclude by returning to the philosophical interpretation (...) underlying both models of belief, showing that neither is strong enough to support a probabilistic interpretation, nor an interpretation in terms of certainty or the “mental component” of knowledge. (shrink)

We study two logics of knowledge and belief stemming from the work of Stalnaker, omitting positive introspection for knowledge. The two systems are equivalent with positive introspection, but not without. We show that while the logic of beliefs remains unaffected by omitting introspection for knowledge in one system, it brings significant changes to the other. The resulting logic of belief is non-normal, and its complete axiomatization uses an infinite hierarchy of coherence constraints. We conclude by returning to the philosophical interpretation (...) underlying both models of belief, showing that neither is strong enough to support a probabilistic interpretation, nor an interpretation in terms of certainty or the “mental component” of knowledge. (shrink)

A variety of recent work in epistemology employs a notion of normality to provide novel theories of knowledge or justification. While such theories are commonly advertised as affording particularly strong epistemic logics, they often make substantive assumptions about the background notion of normality and its logic. This article takes recent normality-based defences of the KK principle as a case study to submit such assumptions to scrutiny. After clarifying issues regarding the natural language use of normality claims, the article isolates (...) a number of choice points regarding the role of contingency, context-sensitivity and similarity in our theorizing with normality. It turns out that both weaker and stronger logics of normality can be motivated depending on how such choices are resolved. And yet securing logics of normality strong enough for normality to play its envisaged role in epistemology may have unwelcome downstream consequences for the resultant theories of knowledge or justification. (shrink)

The epistemic modal auxiliaries must and might are vehicles for expressing the force with which a proposition follows from some body of evidence or information. Standard approaches model these operators using quantificational modal logic, but probabilistic approaches are becoming increasingly influential. According to a traditional view, must is a maximally strong epistemic operator and might is a bare possibility one. A competing account—popular amongst proponents of a probabilisitic turn—says that, given a body of evidence, must \ entails that \\) (...) is high but non-maximal and might \ that \\) is significantly greater than 0. Drawing on several observations concerning the behavior of must, might and similar epistemic operators in evidential contexts, deductive inferences, downplaying and retractions scenarios, and expressions of epistemic tension, I argue that those two influential accounts have systematic descriptive shortcomings. To better make sense of their complex behavior, I propose instead a broadly Kratzerian account according to which must \ entails that \ = 1\) and might \ that \ > 0\), given a body of evidence and a set of normality assumptions about the world. From this perspective, must and might are vehicles for expressing a common mode of reasoning whereby we draw inferences from specific bits of evidence against a rich set of background assumptions—some of which we represent as defeasible—which capture our general expectations about the world. I will show that the predictions of this Kratzerian account can be substantially refined once it is combined with a specific yet independently motivated ‘grammatical’ approach to the computation of scalar implicatures. Finally, I discuss some implications of these results for more general discussions concerning the empirical and theoretical motivation to adopt a probabilisitic semantic framework. (shrink)

The human being as a constituted objectivity is a fragile ‘figure’ who lives in through their individual and shared experience. As a constituted objectivity, it influences our experiences, actions and the constitution of our community. Nevertheless, it appears to us, who actually constitute it, as a completely independent and immutable object, as a mere fact our experience has to comply with, and as a normative representation of the human being. This paper inquires - from a phenomenological point of view - (...) about the structure that underlies the norm at work in our experience, as well as in the high- and low-level dimensions of the intersubjective community. Indirectly, such a structure can be identified through the connection between Husserl’s understanding of normality and objectivity. My claim is that normativity can be understood as a necessary function and thus can be distinguished from objectivity and normality. Normativity appears, therefore, as a function of objectivity, which allows one to distinguish the latter from normality. As such, normativity should not be confused with an active agreement or regulation, but rather identified as a necessary constitutive structure arising from experiential intersubjective sense-borrowing performance. At the same time, due to its connection to objectivity, normativity also appears to strongly influence the social production of validity, therefore being endorsed by institutions. (shrink)

Modern microscopic theory is employed to construct a powerful analytical algorithm that permits a clear description of characteristic features of strongly correlated quantum fluids in thermodynamic equilibrium. Using recently developed formal results we uncover an intricate relationship between strongly correlated systems and free quantum gases of appropriately defined constituents. The latter entities are precisely defined renormalized bosons or fermions. They carry all the information contained in the statistical correlations of the strongly interacting many-particle system by virtue of their effective masses. (...) The mass of such a renormalized boson or fermion depends in a specific form on temperature, bulk particle number density of the many-body system, and eventually on momentum. Due to these properties the renormalized bosons and fermions determine in particular the location and nature of the transition to non-normal phases. (shrink)

The thesis deals with the concept of truth and the paradoxes of truth. Philosophical theories usually consider the concept of truth from a wider perspective. They are concerned with questions such as - Is there any connection between the truth and the world? And, if there is - What is the nature of the connection? Contrary to these theories, this analysis is of a logical nature. It deals with the internal semantic structure of language, the mutual semantic connection of sentences, (...) above all the connection of sentences that speak about the truth of other sentences and sentences whose truth they speak about. Truth paradoxes show that there is a problem in our basic understanding of the language meaning and they are a test for any proposed solution. It is important to make a distinction between the normative and analytical aspect of the solution. The former tries to ensure that paradoxes will not emerge. The latter tries to explain paradoxes. Of course, the practical aspect of the solution is also important. It tries to ensure a good framework for logical foundations of knowledge, for related problems in Artificial Intelligence and for the analysis of the natural language. Tarski’s analysis emphasized the T-scheme as the basic intuitive principle for the concept of truth, but it also showed its inconsistency with the classical logic. Tarski’s solution is to preserve the classical logic and to restrict the scheme: we can talk about the truth of sentences of a language only inside another essentially richer metalanguage. This solution is in harmony with the idea of reflexivity of thinking and it has become very fertile for mathematics and science in general. But it has normative nature | truth paradoxes are avoided in a way that in such frame we cannot even express paradoxical sentences. It is also too restrictive because, for the same reason we cannot express a situation in which there is a circular reference of some sentences to other sentences, no matter how common and harmless such a situation may be. Kripke showed that there is no natural restriction to the T-scheme and we have to accept it. But then we must also accept the riskiness of sentences | the possibility that under some circumstances a sentence does not have the classical truth value but it is undetermined. This leads to languages with three-valued semantics. Kripke did not give any definite model, but he gave a theoretical frame for investigations of various models | each fixed point in each three-valued semantics can be a model for the concept of truth. The solutions also have normative nature | we can express the paradoxical sentences, but we escape a contradiction by declaring them undetermined. Such a solution could become an analytical solution only if we provide the analysis that would show in a substantial way that it is the solution that models the concept of truth. Kripke took some steps in the direction of finding an analytical solution. He preferred the strong Kleene three-valued semantics for which he wrote it was "appropriate" but did not explain why it was appropriate. One reason for such a choice is probably that Kripke finds paradoxical sentences meaningful. This eliminates the weak Kleene three valued semantics which corresponds to the idea that paradoxical sentences are meaningless, and thus indeterminate. Another reason could be that the strong Kleene three valued semantics has the so-called investigative interpretation. According to this interpretation, this semantics corresponds to the classical determination of truth, whereby all sentences that do not have an already determined value are temporarily considered indeterminate. When we determine the truth value of these sentences, then we can also determine the truth value of the sentences that are composed of them. Kripke supplemented this investigative interpretation with an intuition about learning the concept of truth. That intuition deals with how we can teach someone who is a competent user of an initial language (without the predicate of truth T) to use sentences that contain the predicate T. That person knows which sentences of the initial language are true and which are not. We give her the rule to assign the T attribute to the former and deny that attribute to the latter. In that way, some new sentences that contain the predicate of truth, and which were indeterminate until then, become determinate. So the person gets a new set of true and false sentences with which he continues the procedure. This intuition leads directly to the smallest fixed point of strong Kleene semantics as an analytically acceptable model for the logical notion of truth. However, since this process is usually saturated only on some transfinite ordinal, this intuition, by climbing on ordinals, increasingly becomes a metaphor. This thesis is an attempt to give an analytical solution to truth paradoxes. It gives an analysis of why and how some sentences lack the classical truth value. The starting point is basic intuition according to which paradoxical sentences are meaningful (because we understand what they are talking about well, moreover we use it for determining their truth values), but they witness the failure of the classical procedure of determining their truth value in some "extreme" circumstances. Paradoxes emerge because the classical procedure of the truth value determination does not always give a classically supposed (and expected) answer. The analysis shows that such an assumption is an unjustified generalization from common situations to all situations. We can accept the classical procedure of the truth value determination and consequently the internal semantic structure of the language, but we must reject the universality of the exterior assumption of a successful ending of the procedure. The consciousness of this transforms paradoxes to normal situations inherent to the classical procedure. Some sentences, although meaningful, when we evaluate them according to the classical truth conditions, the classical conditions do not assign them a unique value. We can assign to them the third value, \undetermined", as a sign of definitive failure of the classical procedure. An analysis of the propagation of the failure in the structure of sentences gives exactly the strong Kleene three-valued semantics, not as an investigative procedure, as it occurs in Kripke, but as the classical truth determination procedure accompanied by the propagation of its own failure. An analysis of the circularities in the determination of the classical truth value gives the criterion of when the classical procedure succeeds and when it fails, when the sentences will have the classical truth value and when they will not. It turns out that the truth values of sentences thus obtained give exactly the largest intrinsic fixed point of the strong Kleene three-valued semantics. In that way, the argumentation is given for that choice among all fixed points of all monotone three-valued semantics for the model of the logical concept of truth. An immediate mathematical description of the fixed point is given, too. It has also been shown how this language can be semantically completed to the classical language which in many respects appears a natural completion of the process of thinking about the truth values of the sentences of a given language. Thus the final model is a language that has one interpretation and two systems of sentence truth evaluation, primary and final evaluation. The language through the symbol T speaks of its primary truth valuation, which is precisely the largest intrinsic fixed point of the strong Kleene three valued semantics. Its final truth valuation is the semantic completion of the first in such a way that all sentences that are not true in the primary valuation are false in the final valuation. (shrink)

Several conclusions depend on a version of signal detection theory that assumes performance is based on underlying equal-variance normal distributions of trace strength. Such conclusions are questionable without empirical justification for that assumption. A thought experiment is presented to show how the assumption is probably invalid, and empirical evidence is cited for the assumption's invalidity in research on human memory.

The underutilization of base rates is a consistent finding. The strong claim that base rates are ignored has been rejected and this needs no further emphasis. Following the path of “normal science,” research examines the conditions predicting changes in the degree of underutilization. A scientific revolution that might dethrone the heuristics and biases paradigm is not in sight.

ABSTRACT Drawing upon Edmund Husserl’s concept of the natural attitude, our taken-for-granted understandings of what is normal, natural, and what should be the case, I argue that when one’s everyday routines are radically disrupted in a sustained way, as has happened with the COVID-19 global pandemic, adjustments are also needed in our natural attitudes so that the latter accurately reflect our actual situation. And yet, the tendency to resist altering one’s natural attitude in response to major changes in one’s life (...) is very strong, as we see with Gregor Samsa in Franz Kafka’s The Metamorphosis and Vashti in E. M. Forster’s story, “The Machine Stops.” Both characters, I suggest, offer important cautionary tales as we assess the impact of the “new normal” that has come to characterize daily existence during a global pandemic as well as nostalgic appeals to return, as quickly as possible, to the “old normal” of our pre-pandemic lives. This critical analysis is an especially urgent task given the fact that this pre-pandemic normal was clearly not as positive an experience for some people as for others. (shrink)

A number of significant contributions in the last four decades show that non-normal modal logics can be fruitfully employed in several applied fields. Well-known domains are epistemic logic, deontic logic, and systems capturing different aspects of action and agency such as the modal logic of agency, concurrent propositional dynamic logic, game logic, and coalition logic. Semantics for such logics are traditionally based on neighbourhood models. However, other model-theoretic semantics can be used for this purpose. Here, we systematically study multi-relational structures, (...) whose investigation is still relatively underdeveloped. After a brief introduction to two different versions of multi-relational semantics – which we call strong and weak multi-relational semantics – we proceed to study several modal schemata. Special attention is paid to the schemata CON and D. Finally we offer completeness proofs for several systems using both strong and weak semantic tools: The proofs thus cover both classical system.. (shrink)

ABSTRACT The two main directions pursued in the present paper are the following. The first direction was started by Pigozzi in 1969. In [Mak 91] and [Mak 79] Maksimova proved that a normal modal logic has the Craig interpolation property iff the corresponding class of algebras has the superamalgamation property. In this paper we extend Maksimova's theorem to normal multi-modal logics with arbitrarily many, not necessarily unary modalities, and to not necessarily normal multi-modal logics with modalities of ranks smaller than (...) 2. To extend the characterization beyond multi-modal logics, we look at arbitrary algebraizable logics. We will introduce an algebraic property equivalent with the Craig interpolation property in algebraizable logics, and prove that the superamalgamation property implies the Craig interpolation property. The problem of extending the characterization result to non-normal non-unary modal logics also will be discussed. In the second direction pursued herein: for non-normal modal logic with one unary modality Lemmon [Lem 66] gave a possible worlds semantics. Here we give a more general possible worlds semantics for not necessarily normal multi-modal logics with arbitrarily many not necessarily unary modalities. Strongly related to the above is the theorem, proved, e.g., in Jóns son-Tarski [JT 52] and Henkin-Monk-Tarski [HMT 71], that every normal Boolean algebra with operators can be represented as a subalgebra of the complex algebra of some relational structure. We extend this result to not necessarily normal BAO's as follows. We define partial relational structures and show that every not necessarily normal BAO is embeddable into the complex algebra of a partial relational structure. This gives a possible worlds semantics for not necessarily normal multi-modal logics. (shrink)