Six-year-old children's understanding of sentences adjoined with time adverbs

The adjoining of clauses with temporal links is the basis for many sentences that convey sequence of events. The present study attempts to delineate 6-year-old children's (N=30) understanding of the meaning sequences imparted by sentences adjoined with after, before, and until. Their performance of the meaning sequence for each of 24 carefully constructed sentences is compared to an adult model. Analysis of the results (using a Wilcoxon Matched Pairs Signed Rank Test) indicated that: (1)Ss understood sentences adjoined with after according to an adult model more frequently than before adjoined sentences (P<0.01); (b) Until adjoined sentences with a negative marker in the main clause were understood according to an adult model more often than until adjoined sentences with no such negative element, but the difference was not significant at a=0.01; (3)Ss understood before adjoined sentences according to an adult model more often than until adjoined sentences, but the difference was not significant at a=0.01. In general, the results indicated that 6-year-olds have not yet completed development of an adult grammar with respect to adjoining clauses with temporal links, after, before, and until.     

"Solar love": Nietzsche,Merleau-Ponty and the fortunes of perception

Both Nietzsche and Merleau-Ponty repudiate the mirror view of perception and embrace what Nietzsche refers to as solar love or creative perception. I argue that Merleau-Ponty thinks of this type of perception primarily in terms of convergence and Nietzsche in terms of divergence. I then show how, contrary to their own emphases, Merleau-Ponty's notion of flesh and Nietzsche's idea of chaos suggest that convergence and divergence are abstractions from an ontologically prior realm of hybrid perceptions. In this realm, each perception is shot through with the others, simultaneously inside and outside one another. The creative tension among these perceptions continually produces new perspectives or voices, that is, a realm whose very being is metamorphosis. Moreover, this realm of hybrid perceptions suggests a political principle that might prove attractive for communities in an age of diversity and cultural hybridity.     

Inverses for Normal Modal Operators

Given a 1-ary sentence operator , we describe L - another 1-ary operator - as as a left inverse of in a given logic if in that logic every formula is provably equivalent to L. Similarly R is a right inverse of if is always provably equivalent to R. We investigate the behaviour of left and right inverses for taken as the operator of various normal modal logics, paying particular attention to the conditions under which these logics are conservatively extended by the addition of such inverses, as well as to the question of when, in such extensions, the inverses behave as normal modal operators in their own right.     

Why we need a relevant theory of conditionals

This paper presents ConR (Conditional R), a logic of conditionals based on Anderson and Belnap's system R. A Routley-Meyer-style semantics for ConR is given for the system (the completeness of ConR over this semantics is proved in E. Mares and A. Fuhrmann, A Relevant Theory of Conditionals (unpublished MS)). Moreover, it is argued that adopting a relevant theory of conditionals will improve certain theories that utilize conditionals, i.e. Lewis' theory of causation, Lewis' dyadic deontic logic, and Chellas' dyadic deontic logic.I am of course deeply indebted to André Fuhrmann, who co-wrote the paper on which the present effort is based. Perhaps I should also thank the Social Sciences and Humanities Research Council of Canada because the original research for this project was funded by them in the form of a post-doctoral fellowship.     

The politics of situating knowledge: An exercise in social epistemology

This essay forges links between Popperians and feminists by considering the connections between Donna Haraway's situated knowledge and Karl R. Popper's situational logic. It is concerned with the political commitments behind methodological issues, with the degree to which there can be a Popperian contribution to the feminist vision of a successor science, and with ways of dealing with, while not resolving, the political differences between socialist feminists and libertarian Popperians.     

Supererogation in Deontic Logic: Metatheory for DWE and Some Close Neighbours

In "Doing Well Enough: Toward a Logic for Common Sense Morality", Paul McNamara sets out a semantics for a deontic logic which contains the operator It is supererogatory that. As well as having a binary accessibility relation on worlds, that semantics contains a relative ordering relation, . For worlds u, v and w, we say that u w v when v is at least as good as u according to the standards of w. In this paper we axiomatize logics complete over three versions of the semantics. We call the strongest of these logics DWE for Doing Well Enough.     

On Ultrafilter Logic and Special Functions

Logics for generally were introduced for handling assertions with vague notions,such as generally, most, several, etc., by generalized quantifiers, ultrafilter logic being an interesting case. Here, we show that ultrafilter logic can be faithfully embedded into a first-order theory of certain functions, called coherent. We also use generic functions (akin to Skolem functions) to enable elimination of the generalized quantifier. These devices permit using methods for classical first-order logic to reason about consequence in ultrafilter logic.Presented by André Fuhrmann     

Naive realism about operators

A source of much difficulty and confusion in the interpretation of quantum mechanics is a naive realism about operators. By this we refer to various ways of taking too seriously the notion of operator-as-observable, and in particular to the all too casual talk about measuring operators that occurs when the subject is quantum mechanics. Without a specification of what should be meant by measuring a quantum observable, such an expression can have no clear meaning. A definite specification is provided by Bohmian mechanics, a theory that emerges from Schrödinger's equation for a system of particles when we merely insist that particles means particles. Bohmian mechanics clarifies the status and the role of operators as observables in quantum mechanics by providing the operational details absent from standard quantum mechanics. It thereby allows us to readily dismiss all the radical claims traditionally enveloping the transition from the classical to the quantum realm — for example, that we must abandon classical logic or classical probability. The moral is rather simple: Beware naive realism, especially about operators!     

Semantics for existential graphs

This paper examines Charles Peirce's graphical notation for first-order logic with identity. The notation forms a part of his system of existential graphs, which Peirce considered to be his best work in logic. In this paper a Tarskian semantics is provided for the graphical system.     

Converse Ackermann Croperty and semiclassical negation

A prepositional logic S has the Converse Ackermann Property (CAP) if (AB)C is unprovable in S when C does not contain . In A Routley-Meyer semantics for Converse Ackermann Property (Journal of Philosophical Logic, 16 (1987), pp. 65–76) I showed how to derive positive logical systems with the CAP. There I conjectured that each of these positive systems were compatible with a so-called semiclassical negation. In the present paper I prove that this conjecture was right. Relational Routley-Meyer type semantics are provided for each one of the resulting systems (the positive systems plus the semiclassical negation).     

First-order indefinite and uniform neighbourhood semantics

The main purpose of this paper is to define and study a particular variety of Montague-Scott neighborhood semantics for modal propositional logic. We call this variety the first-order neighborhood semantics because it consists of the neighborhood frames whose neighborhood operations are, in a certain sense, first-order definable. The paper consists of two parts. In Part I we begin by presenting a family of modal systems. We recall the Montague-Scott semantics and apply it to some of our systems that have hitherto be uncharacterized. Then, we define the notion of a first-order indefinite semantics, along with the more specific notion of a first-order uniform semantics, the latter containing as special cases the possible world semantics of Kripke. In Part II we prove consistency and completeness for a broad range of the systems considered, with respect to the first-order indefinite semantics, and for a selected list of systems, with respect to the first-order uniform semantics. The completeness proofs are algebraic in character and make essential use of the finite model property. A by-product of our investigations is a result relating provability in S-systems and provability in T-systems, which generalizes a known theorem relating provability in the systems S 2° and C 2.The author would like to thank Prof. Nuel D. Belnap of the University of Pittsburg for many indispensable contributions to earlier versions of this work. The author also thanks the referee for several helpful comments and corrections.     

Illustrating two complementary enterprises at the interface of psychology and religion through reading Winnicott

Our work at the interface of psychology and religion can proceed in two complementary directions. When reading a psychological theory, (1) we may pay special attention to how certain concepts in particular, and the system of ideas as a whole, are being or might be used to interpret religious phenomena. We may focus on how those ideas may be involved in doing psychology of religion: the psychological interpretation of religious phenomena. Alternatively, (2) we may pay special attention to how certain concepts in particular, and the system of ideas as a whole, are being or might be used, either implicitly or explicitly, to make claims about human nature, about the meaning and purpose of life, about God. We may identify the psychology as religion-theology: psychological ideas potentially functioning in a religious-theological manner. I will illustrate this by: (a) examining D. W. Winnicott's article, Transitional Objects and Transitional Phenomena (1953/1986) in terms of three successive concepts or categories: transitional object, transitional phenomena, and a third intermediate area of experiencing; (b) considering how these categories can be used in psychology of religion; (c) reconsidering how the psychological categories may function as religious-theological. The discussion is intended to illustrate how we might more fully appreciate how and why a psychological theory may work well in doing psychology of religion when we more fully appreciate how that psychology implicitly functions as theology.     

A Revenge-Immune Solution to the Semantic Paradoxes

The paper offers a solution to the semantic paradoxes, one in which (1) we keep the unrestricted truth schema True(A)A, and (2) the object language can include its own metalanguage. Because of the first feature, classical logic must be restricted, but full classical reasoning applies in ordinary contexts, including standard set theory. The more general logic that replaces classical logic includes a principle of substitutivity of equivalents, which with the truth schema leads to the general intersubstitutivity of True(A) with A within the language.The logic is also shown to have the resources required to represent the way in which sentences (like the Liar sentence and the Curry sentence) that lead to paradox in classical logic are defective. We can in fact define a hierarchy of defectiveness predicates within the language. Contrary to claims that any solution to the paradoxes just breeds further paradoxes (revenge problems) involving defectiveness predicates, there is a general consistency/conservativeness proof that shows that talk of truth and the various levels of defectiveness can all be made coherent together within a single object language.     

A Sound and Complete Tableau Calculus for Reasoning about only Knowing and Knowing at Most

We define a tableau calculus for the logic of only knowing and knowing at most ON, which is an extension of Levesque's logic of only knowing O. The method is based on the possible-world semantics of the logic ON, and can be considered as an extension of known tableau calculi for modal logic K45. From the technical viewpoint, the main features of such an extension are the explicit representation of "unreachable" worlds in the tableau, and an additional branch closure condition implementing the property that each world must be either reachable or unreachable. The calculus allows for establishing the computational complexity of reasoning about only knowing and knowing at most. Moreover, we prove that the method matches the worst-case complexity lower bound of the satisfiability problem for both ON and O. With respect to [22], in which the tableau calculus was originally presented, in this paper we both provide a formal proof of soundness and completeness of the calculus, and prove the complexity results for the logic ON.     

Inferential Intensionality

The paper is a study of properties of quasi-consequence operation which is a key notion of the so-called inferential approach in the theory of sentential calculi established in [5]. The principal motivation behind the quasi-consequence, q-consequence for short, stems from the mathematical practice which treats some auxiliary assumptions as mere hypotheses rather than axioms and their further occurrence in place of conclusions may be justified or not. The main semantic feature of the q-consequence reflecting the idea is that its rules lead from the non-rejected assumptions to the accepted conclusions.First, we focus on the syntactic features of the framework and present the q-consequence as related to the notion of proof. Such a presentation uncovers the reasons for which the adjective inferential is used to characterize the approach and, possibly, the term inference operation replaces q-consequence. It also shows that the inferential approach is a generalisation of the Tarski setting and, therefore, it may potentially absorb several concepts from the theory of sentential calculi, cf. [10]. However, as some concrete applications show, see e.g.[4], the new approach opens perspectives for further exploration.The main part of the paper is devoted to some notions absent, in Tarski approach. We show that for a given q-consequence operation W instead of one W-equivalence established by the properties of W we may consider two congruence relations. For one of them the current name is kept preserved and for the other the term W-equality is adopted. While the two relations coincide for any W which is a consequence operation, for an arbitrary W the inferential equality and the inferential equivalence may differ. Further to this we introduce the concepts of inferential extensionality and intensionality for q-consequence operations and connectives. Some general results obtained in Section 2 sufficiently confirm the importance of these notions. To complete a view, in Section 4 we apply the new intensionality-extensionality distinction to inferential extensions of a version of the ukasiewicz four valued modal logic.     

The artist as transgressor in Mandel'štam's poetry

In Mandel'tam's writing, artistic creativity is described as based on the indispensable yet contradictory modes of compliance and deviation. The artist, by his artistic nature, must be an obedient disciple to the tradition that inspires him, and, at the same time, a violator who renders what inspires him in an individual form. Thus, art implies iterability through novelty. In the totalitarian state, this double nature of art acquires a sinister context and brings the artist to an unavoidable conflict with the state. He has a choice between a servile compliance with the state's command and artistic independence. If the artist complies, he loses his ingenuity; if, on the other hand, he has the courage to break away from the established order, his fate is martyrdom. The criteria of truth and falsehood, the issue of loyalty, of compromise and collaboration or resistance become most relevant. Such words as outcast or non-contemporary acquire the meaning of non-collaborationist or enemy of the people. In the totalitarian state a genuine artist is viewed as a law-breaker, and his art leads him to crime. The notions of compliance and deviation cease being merely aesthetic terms and assume in Mandel'tam's poetry complex, subtle and tragic overtones.I would like to express my gratitude to John Barnstead, Thomas Blakeley, James Doull, Elena Glazov-Corrigan, Gregory Glazov, Leonard Kazdan, Peter Kussmaul, Malcolm Ross, Detlev Steffen, and Ieva Vitins for their valuable criticism, suggestions, and revisions of my English.     

Allgemeinpsychologische Untersuchungen zum Vigilanzverhalten

Zusammenfassung Mit Hilfe eines 2×2×2-Designs wurde die Wirkung der Anzahl der Signalflächen, Anzahl der irrelevanten Reize und Art der Motivation auf die Vigilanzleistung untersucht. Dabei zeigte sich, daß die Wahrscheinlichkeiten von verpaßten Signalen und falschen Alarmen mit der Anzahl der Signalquellen zunehmen. Die Menge der Nicht-Signale gleicher Modalität wie die Signalreize beeinflußt weder die Signalentdeckungen noch die falschen Alarme.Weiterhin wurde versucht, eine Systematisierung von Motivationswirkungen in Vigilanzaufgaben im Rahmen des detection-Modells vorzunehmen. Bei großen Gewinnen für richtige Signalentdeckungen und geringen Verlusten für falsche Alarme (Risiko-Motivation) ergab sich eine wesentlich höhere Entdeckungswahrscheinlichkeit und eine geringfügig höhere Rate von falschen Alarmen als bei geringen Gewinnen für richtige Signalentdeckungen und hohen Kosten für falsche Alarme (Vorsichts-Motivation). Weiterhin zeigte sich unter Risiko-Motivation ein Abfall der Entdeckungswahrscheinlichkeit und bei Vorsichts-Motivation ein Anstieg, während sich die entsprechenden Raten der falschen Alarme im Verlauf der Aufgabe nicht signifikant veränderten.

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Experimental application of detection theory to vigilance behaviour

Summary In a 2×2×2-design the effects of number of dials, number of irrelevant stimuli and kind of motivation were combined. It was found out, that probabilities of missed signals and false alarms increased with spatial uncertainty. The number of irrelevant stimuli, which were of equal sensory modality as the relevant stimuli, had no influence either on detection probability or on false alarms rate.Further attempt was made to systematize effects of motivation on vigilance performance in the detection model. With great values for hits and small costs for false alarms (risky motivation) there was an essentially higher detection pobability and a slightly higher false alarms rate than with small values for hits and high costs for false detections (cautious motivation). The probabilities of detections decreased under risky motivation and increased under cautious motivation as the watch prolonged, whereas the corresponding probabilities of false alarms showed no significant changes.

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Teil I der Dissertation, die im Januar 1969 der Philosophischen Fakultät der Freien Universität Berlin vorgelegt wurde.     

The "Natural" and the "Formal"

The paper presents an argument against a metaphysical conception of logic according to which logic spells out a specific kind of mathematical structure that is somehow inherently related to our factual reasoning. In contrast, it is argued that it is always an empirical question as to whether a given mathematical structure really does captures a principle of reasoning. (More generally, it is argued that it is not meaningful to replace an empirical investigation of a thing by an investigation of its a priori analyzable structure without paying due attention to the question of whether it really is the structure of the thing in question.) It is proposed to elucidate the situation by distinguishing two essentially different realms with which our reason must deal: the realm of the natural, constituted by the things of our empirical world, and the realm of the formal, constituted by the structures that we use as prisms to view, to make sense of, and to reconstruct the world. It is suggested that this vantage point may throw light on many foundational problems of logic.     

A Chemically Induced “Shadow”?

Stevenson's classic yarn, Dr. Jekyll and Mr. Hyde, is explored as a vivid, insightful story of addiction. In spite of clinical temptations to chase deeper issues connected with the dark side, this article suggests that pastoral counselors and psychotherapists need to first ask whether a client's shadow may be chemically induced.     

The ω-rule

We prove that all proofs in -logic (a first order logic with -rule added) in which -rule is used finitely many times can be turned into proofs in which the -rule is used at most one time. Next, we prove that the word finitely above cannot be changed by the word infinitely.