Logical and philosophical literature provides different classifications of reasoning. In the Polish literature on the subject, for instance, there are three popular ones accepted by representatives of the Lvov-Warsaw School: Jan Łukasiewicz, Tadeusz Czeżowski and Kazimierz Ajdukiewicz (Ajdukiewicz in Logika pragmatyczna [Pragmatic Logic]. PWN, Warsaw (1965, 2nd ed. 1974). Translated as: Pragmatic Logic. Reidel & PWN, Dordrecht, 1975). The author of this paper, having modified those classifications, distinguished the following types of reasoning: (1) deductive and (2) non-deductive, and additionally two (...) types of them in each of the two, depending on the manner of combining their premises with the conclusion through the relation of classical logical entailment. Consequently, the four types of reasoning: unilateral deductive (incl. its sub-types: deductive inference and proof), bilateral deductive (incl. complete induction), and reductive (incl. the sub-types: explanation and verification), logically nonvaluable (incl. inference by analogy, statistic inference), correspond to four operators of derivability. They are defined formally on the ground of Tarski’s axiomatic theory of deductive systems, by means of the consequence operation _Cn_ (Tarski in Monatshefte Math Phys 37:361–404, 1930a, C R Soc Sci Lett Vars 23:22–29, 1930b). Also, certain metalogical properties of these operators are given, as well as their relations with Tarski’s consequence operations \(Cn^+\) ( \(Cn^+ = Cn\) ) and dual consequences \(Cn^{-1}\) (Słupecki in Zeszyty Naukowe Uniwersytetu Wrocławskiego Seria B Nr 3:33–40, 1959, Słupecki et al. in Stud Log 29:76–123, 1971, Wybraniec-Skardowska, in: Wybraniec-Skardowska, Bryll (eds) Z badań nad teorią zdań odrzuconych [Studies in the Theory of Rejected Propositions], Series B, Studia i Monografie, Zeszyty Naukowe Wyższej Szkoły Pedagogicznej w Opolu, Opole, 1969), and \(Cn^-\) (Wójcicki in Bull Sect Log 2(2):54–57, 1973)). (shrink)

While there are many legal textbooks on the laws of armed conflict and academic works on ethical issues in international relations, this is the first text on the relevance of legal and normative issues in military practice. It covers the entire spectrum of military operations and is written with military deicision-makers particularly in mind.

This chapter addresses some basic ethical questions about psychological operations. It defines PSYOP, then compares and contrasts it with both conventional military activities and contemporary information warfare. Then it briefly clarifies emerging public policy problems, outlines relevant legal particularities, and offers general policy considerations with regard to ethical considerations in its employment.

This is a study in the meaning of natural language probability operators, sentential operators such as probably and likely. We ask what sort of formal structure is required to model the logic and semantics of these operators. Along the way we investigate their deep connections to indicative conditionals and epistemic modals, probe their scalar structure, observe their sensitivity to contex- tually salient contrasts, and explore some of their scopal idiosyncrasies.

Certain passages in Kaplan’s ‘Demonstratives’ are often taken to show that non-vacuous sentential operators associated with a certain parameter of sentential truth require a corresponding relativism concerning assertoric contents: namely, their truth values also must vary with that parameter. Thus, for example, the non-vacuity of a temporal sentential operator ‘always’ would require some of its operands to have contents that have different truth values at different times. While making no claims about Kaplan’s intentions, we provide several reconstructions of how (...) such an argument might go, focusing on the case of time and temporal operators as an illustration. What we regard as the most plausible reconstruction of the argument establishes a conclusion similar enough to that attributed to Kaplan. However, the argument overgenerates, leading to absurd consequences. We conclude that we must distinguish assertoric contents from compositional semantic values, and argue that once they are distinguished, the argument fails to establish any substantial conclusions. We also briefly discuss a related argument commonly attributed to Lewis, and a recent variant due to Weber. (shrink)

I argue that David Lewis is too quick to deny the presentist the right to employ span operators. There is no reason why the presentist could not help herself to both primitive tensed slice operators and primitive span operators. She would then have another device available to eliminate ambiguities and explain why sentences with embedded contradictions may nevertheless be true.

Let K = (p, q...; &, ∨, ~) be a zeroth-order formal language with sentence variables p, q..., two place connectives & (and), ∨ (or) and negation sign ~, and let F be the formula algebra (set of well-formed formulas in K defined in the standard way by induction from the sentence variables). If v is an assignment of truth values 1(true), 0(f alse) to the sentence variables p, q..., then classical propositional logic is characterized by extending v by induction (...) from p, q... to the formula algebra F in such a manner that the extension (called interpretation and also denoted by v) be a “homomorphism” from F into the two-element Boolean algebra B 2 ≡ (1, 0, ⋂, ⋃, ⊥), where “homomorphism” means that the following hold υ(q&p)=υ(q)∩υ(p)υ(q∨p)=υ(q)∪υ(p)υ(∼q)=υ(q)⊥. (shrink)

I present a notion of invariance under arbitrary surjective mappings for operators on a relational finite type hierarchy generalizing the so-called Tarski-Sher criterion for logicality and I characterize the invariant operators as definable in a fragment of the first-order language. These results are compared with those obtained by Feferman and it is argued that further clarification of the notion of invariance is needed if one wants to use it to characterize logicality.

Tarski and Mautner proposed to characterize the "logical" operations on a given domain as those invariant under arbitrary permutations. These operations are the ones that can be obtained as combinations of the operations on the following list: identity; substitution of variables; negation; finite or infinite disjunction; and existential quantification with respect to a finite or infinite block of variables. Inasmuch as every operation on this list is intuitively "logical", this lends support to the Tarski-Mautner proposal.

The properties of the ${\forall^{1}}$ quantifier defined by Kontinen and Väänänen in [13] are studied, and its definition is generalized to that of a family of quantifiers ${\forall^{n}}$ . Furthermore, some epistemic operators δ n for Dependence Logic are also introduced, and the relationship between these ${\forall^{n}}$ quantifiers and the δ n operators are investigated.The Game Theoretic Semantics for Dependence Logic and the corresponding Ehrenfeucht- Fraissé game are then adapted to these new connectives.Finally, it is proved that the (...) ${\forall^{1}}$ quantifier is not uniformly definable in Dependence Logic, thus answering a question posed by Kontinen and Väänänen in the above mentioned paper. (shrink)

The Operator Argument against eternalism holds that having non-vacuous tense operators in the language is incompatible with the claim that every proposition has its truth-value eternally. Assuming that (1) there are non-vacuous tense operators, (2) tense operators operate on propositions and (3) tense operators which operate on eternal entities are vacuous, it may be argued that eternalism is false. In this paper, I examine the Operator Argument. The goal is threefold. First, I want to present some (...) aspects of the debate in a more elaborate way, especially those concerning formal matters. Secondly, I will argue that eternalism can escape the Operator Argument. There are two main strategies for handling the Operator Argument. The first one is based on replacing temporal operators with object-language quantifiers. The second rejects the identification of compositional semantic value with assertoric content. My third goal is to show that none of them is as good as the strategy that adopts Timestamp Semantics (Fritz in Philosl Stud 176:2933–2959, 2019). I am going to argue that the quantificational treatment of tenses is compatible with temporalism and that the arguments for rejecting the identification of compositional semantic value with assertoric content provide, in fact, a motivation for the temporalist position. At the end, I will develop Timestamp Semantics by providing a novel formalization of it, and defend it against three potential counter-arguments. (shrink)

Résumé La linguistique du texte a pour tâche la théorisation et la description des opérations de segmentation qui délimitent des unités de rang et de longueur différentes, et la théorisation et la description des différents effets de continuité créés par les opérations de liage de ces unités. À la structuration phrastique-périodique par la morpho-syntaxe et la prosodie à l’oral, la ponctuation à l’écrit, le palier micro-textuel ajoute six facteurs de texture transphrastique : les liages référentiels et isotopiques, les liages du (...) signifiant, l’ensemble des phénomènes de connexion, les relations d’implicitation, la cohésion énonciative et la cohésion illocutoire. À partir de trois textes, cet article illustre systématiquement et détaille ces six formes de liage transphrastique des unités textuelles de base. (shrink)

The understanding of the interrelationship between brain and mind remains far from clear. It is well established that the brain's capacity to integrate information from numerous sources forms the basis for cognitive abilities. However, the core unresolved question is how information about the "objective" physical entities of the external world can be integrated, and how unifiedand coherent mental states (or Gestalts) can be established in the internal entities of distributed neuronal systems. The present paper offers a unified methodological and conceptual (...) basis for a possible mechanism of how the transient synchronization of brain operations may construct the unified and relatively stable neural states, which underlie mental states. It was shown that the sequence of metastable spatial EEG mosaics does exist and probably reflects the rapid stabilization periods of the interrelation of large neuron systems. At the EEG level this is reflected in the stabilization of quasi-stationary segments on corresponding channels. Within the introduced framework, physical brain processes and psychological processes are considered as two basic aspects of a single whole informational brain state. The relations between operational process of the brain, mental states and consciousness are discussed. (shrink)

The concept of an operator is used in a variety of practical and theoretical areas. Operators, as both conceptual and physical entities, are found throughout the world as subsystems in nature, the human mind, and the manmade world. Operators, and what they operate, i.e., their substrates, targets, or operands, have a wide variety of forms, functions, and properties. Operators have explicit philosophical significance. On the one hand, they represent important ontological issues of reality. On the other hand, (...) epistemological operators form the basic mechanism of cognition. At the same time, there is no unified theory of the nature and functions of operators. In this work, we elaborate a detailed analysis of operators, which range from the most abstract formal structures and symbols in mathematics and logic to real entities, human and machine, and are responsible for effecting changes at both the individual and collective human levels. Our goal is to find what is common in physical objects called operators and abstract mathematical structures, with the name operator providing foundations for building a unified but flexible theory of operators. The paper concludes with some reflections on functionalism and other philosophical aspects of the ‘operation’ of operators. (shrink)

Based on the theoretical analysis of self-consciousness concepts, we hypothesized that the spatio-temporal pattern of functional connectivity within the default-mode network (DMN) should persist unchanged across a variety of different cognitive tasks or acts, thus being task-unrelated. This supposition is in contrast with current understanding that DMN activated when the subjects are resting and deactivated during any attention-demanding cognitive tasks. To test our proposal, we used, in retrospect, the results from our two early studies ([Fingelkurts, 1998] and [Fingelkurts et al., (...) 2003]). In both studies for the majority of experimental trails we indeed found a constellation of operationally synchronized cortical areas (indexed as DMN) that was persistent across all studied experimental conditions in all subjects. Furthermore, we found three major elements comprising this DMN: two symmetrical occipito-parieto-temporal and one frontal spatio-temporal patterns. This new data directly supports the notion that DMN has a specific functional connotation – it provides neurophysiologic basis for self-processing operations, namely first-person perspective taking and an experience of agency. (shrink)

Although several studies propose that the integrity of neuronal assemblies may underlie a phenomenon referred to as awareness, none of the known studies have explicitly investigated dynamics and functional interactions among neuronal assemblies as a function of consciousness expression. In order to address this question EEG operational architectonics analysis (Fingelkurts and Fingelkurts, 2001, 2008) was conducted in patients in minimally conscious (MCS) and vegetative states (VS) to study the dynamics of neuronal assemblies and operational synchrony among them as a function (...) of consciousness expression. We found that in minimally conscious patients and especially in vegetative patients neuronal assemblies got smaller, their life-span shortened and they became highly unstable. Furthermore, we demonstrated that the extent/volume and strength of operational synchrony among neuronal assemblies was smallest or even absent in VS patients, intermediate in MCS patients and highest in healthy fully-conscious subjects. All findings were similarly observed in EEG alpha as well as beta1 and beta2 frequency oscillations. The presented results support the basic tenets of Operational Architectonics theory of brain-mind functioning and suggest that EEG operational architectonics analysis may provide an objective and accurate means of assessing signs of (un)consciousness in patients with severe brain injuries. Therefore this methodological approach may complement the existing “gold standard” of behavioral assessment of this population of challenging patients and inform the diagnostic and treatment decision-making processes. (shrink)

Predicates are term-to-sentence devices, and operators are sentence-to-sentence devices. What Kaplan and Montague's Paradox of the Knower demonstrates is that necessity and other modalities cannot be treated as predicates, consistent with arithmetic; they must be treated as operators instead. Such is the current wisdom.A number of previous pieces have challenged such a view by showing that a predicative treatment of modalities neednot raise the Paradox of the Knower. This paper attempts to challenge the current wisdom in another way (...) as well: to show that mere appeal to modal operators in the sense of sentence-to-sentence devices is insufficient toescape the Paradox of the Knower. A family of systems is outlined in which closed formulae can encode other formulae and in which the diagonal lemma and Paradox of the Knower are thereby demonstrable for operators in this sense. (shrink)

Recently, new types of independence of a pair of C *- or W *-subalgebras (1,2) of a C *- or W *-algebra have been introduced: operational C *- and W *-independence (Rédei and Summers, http://arxiv.org/abs/0810.5294, 2008) and operational C *- and W *-separability (Rédei and Valente, How local are local operations in local quantum field theory? 2009). In this paper it is shown that operational C *-independence is equivalent to operational C *-separability and that operational W *-independence is equivalent to (...) operational W *-separability. Specific further sub-types of both operational C *- and W *-separability and operational C *- and W *-independence are defined and the problem of characterization of the logical interdependencies of the independence notions is raised. (shrink)

Relational, operator, and predicate systems are distinguished on the basis that they correspond to the three possible pair-wise bracketings into two constituents of the three parts of a proposition: relation, subject, and object. It is asserted that the verbal propositional modality (left hemisphere) uses a predicate grammar, while the spatial-image operational modality (right hemisphere) uses an operator grammar. Verbal propositional memory has the capacity for extensive propositional embedding while spatial operational memory does not.

Behavior that solves a problem is distinguished by the fact that it changes another part of the solver's behavior and is strengthened when it does so. Problem solving typically involves the construction of discriminative stimuli. Verbal responses produce especially useful stimuli, because they affect other people. As a culture formulates maxims, laws, grammar, and science, its members behave more effectively without direct or prolonged contact with the contingencies thus formulated. The culture solves problems for its members, and does so by (...) transmitting the verbal discriminative stimuli called rules. Induction, deduction, and the construction of models are ways of producing rules. Behavior that solves a problem may result from direct shaping by contingencies or from rules constructed either by the problem solver or by others. Because different controlling variables are involved, contingency-shaped behavior is never exactly like rule-governed behavior. The distinction must take account of a system which establishes certain contingencies of reinforcement, such as some part of the natural environment, a piece of equipment, or a verbal community; the behavior shaped and maintained by these contingencies; rules, derived from the contingencies, which specify discriminative stimuli, responses, and consequences, and the behavior occasioned by the rules. (shrink)

Several important terms in biology have recently been criticized for not being "operational." In this paper the course of operationism in physics, psychology and genetics is sketched to show what effect this particular view on the meaning of scientific terms had on these disciplines. Then the biological species concept and the concept of homology are examined to see in what respects they are or are not "operational." One of the primary conclusions of this investigation is that few terms in science (...) are completely operational or completely nonoperational. Some scientific terms, especially theoretical terms, are a good deal less operational than others; but, far from being regrettable, this situation is essential if theoretical terms are to fulfill their systematizing function and if scientific theories are to be capable of growth. (shrink)

We trace the difference between the ways in which apes and humans co–operate to differences in communicative abilities, claiming that the pressure for future–directed co–operation was a major force behind the evolution of language. Competitive co–operation concerns goals that are present in the environment and have stable values. It relies on either signalling or joint attention. Future–directed co–operation concerns new goals that lack fixed values. It requires symbolic communication and context–independent representations of means and goals. We analyse these ways of (...) co–operating in game–theoretic terms and submit that the co–operative strategy of games that involve shared representations of future goals may provide new equilibrium solutions. (shrink)

There are two foundational, but not fully developed, ideas in paraconsistency, namely, the duality between paraconsistent and intuitionistic paradigms, and the introduction of logical operators that express metalogical notions in the object language. The aim of this paper is to show how these two ideas can be adequately accomplished by the logics of formal inconsistency and by the logics of formal undeterminedness. LFIs recover the validity of the principle of explosion in a paraconsistent scenario, while LFUs recover the validity (...) of the principle of excluded middle in a paracomplete scenario. We introduce definitions of duality between inference rules and connectives that allow comparing rules and connectives that belong to different logics. Two formal systems are studied, the logics mbC and mbD, that display the duality between paraconsistency and paracompleteness as a duality between inference rules added to a common core—in the case studied here, this common core is classical positive propositional logic. The logics mbC and mbD are equipped with recovery operators that restore classical logic for, respectively, consistent and determined propositions. These two logics are then combined obtaining a pair of LFI and undeterminedness, namely, mbCD and mbCDE. The logic mbCDE exhibits some nice duality properties. Besides, it is simultaneously paraconsistent and paracomplete, and able to recover the principles of excluded middle and explosion one at a time. The last sections offer an algebraic account for such logics by adapting the swap structures semantics framework of the LFIs the LFUs. This semantics highlights some subtle aspects of these logics, and allows us to prove decidability by means of finite nondeterministic matrices. (shrink)

According to operator theories, "if" denotes a two-place operator. According to restrictor theories, "if" doesn't contribute an operator of its own but instead merely restricts the domain of some co-occurring quantifier. The standard arguments (Lewis 1975, Kratzer 1986) for restrictor theories have it that operator theories (but not restrictor theories) struggle to predict the truth conditions of quantified conditionals like -/- (1) a. If John didn't work at home, he usually worked in his office. b. If John didn't work at (...) home, he must have worked in his office. -/- Gillies (2010) offers a context-shifty conditional operator theory that predicts the right truth conditions for epistemically modalized conditionals like (1b), thus undercutting one standard argument for restrictor theories. I explore how we might generalize Gillies' theory to adverbially quantified conditionals like (1a) and deontic conditionals, and argue that a natural generalization of Gillies' theory -- following his strategy for handling epistemically modalized conditionals -- won't work for these other conditionals because a crucial assumption that epistemic modal bases are closed (used to neutralize the epistemic quantification contributed by "if") doesn't have plausible analogs in these other domains. (shrink)

This work extend to residuated lattices the results of [ 7 ]. It also provides a possible generalization to this context of frontal operators in the sense of [ 9 ]. Let L be a residuated lattice, and f : L k → L a function. We give a necessary and sufficient condition for f to be compatible with respect to every congruence on L . We use this characterization of compatible functions in order to prove that the variety (...) of residuated lattices is locally affine complete. We study some compatible functions on residuated lattices which are a generalization of frontal operators. We also give conditions for two operations P ( x , y ) and Q ( x , y ) on a residuated lattice L which imply that the function $${x \mapsto min\{y \in L : P(x, y) \leq Q(x, y)\}}$$ when defined, is equational and compatible. Finally we discuss the affine completeness of residuated lattices equipped with some additional operators. (shrink)

How can we critique political theory when all we have to use are its own conceptual tools? As Hannah Arendt observed, it can only be done through leaps, inversions, and the turning of concepts upside-down. But this twisting operation must be done in order to turn those who philosophize back to the hard work of real life change. In Turning Operations, renowned theorist Mary G. Dietz challenges specific contemporary modes of theorizing politics-from feminist theory to Habermasian discourse- -while appropriating some (...) of political theory's own approaches and some of its most striking figures, including Aristotle, Nietzsche, Weber, Beauvoir, and Arendt in order to foment some leaps, inversions, reversals and turns on politics along the way. Dietz confronts a number of current debates, arguing that most are filled with artificial division and empty terms. She argues that we must abandon commonly supported dichotomies-masculine versus feminine, speech versus action, liberty versus community -to create abetter discourse, and a better world. Turning Operations is an essential new contribution to democratic and feminist political thought. (shrink)

Four consequence operators based on hypergraph satisfiability are defined. Their properties are explored and interconnections are displayed. Finally their relation to the case of the Classical Propositional Calculus is shown.

It is common in the literature on classical electrodynamics and relativity theory that the transformation rules for the basic electrodynamical quantities are derived from the pre-assumption that the equations of electrodynamics are covariant against these---unknown---transformation rules. There are several problems to be raised concerning these derivations. This is, however, not our main concern in this paper. Even if these derivations were completely correct, they leave open the following fundamental question: Are the so-obtained transformation rules indeed identical with the true transformation (...) rules of the fundamental electrodynamical quantities? In other words, is it indeed the case that the values calculated from the quantities in one inertial frame by means of the transformation rules we derived are equal to the values of the same quantities obtained by the same operations with the same measuring equipments when they are co-moving with the other inertial frame? This is of course an empirical question. In this paper, we will investigate the problem in a purely theoretical framework by applying what J. S. Bell calls “Lorentzian pedagogy”---according to which the laws of physics in any one reference frame account for all physical phenomena. We will show that the transformation rules of the electrodynamical quantities are indeed identical with the ones obtained by presuming the covariance of the equations of electrodynamics, and that the covariance is indeed satisfied. Beforehand, however, we need to clarify the operational definitions of the fundamental electrodynamical quantities. As we will see, these semantic issues are not as trivial as one might think. (shrink)

For the tradition, an action is rational if maximizing; for Gauthier, if expressive of a disposition it maximized to adopt; for me, if maximizing on rational preferences, ones whose possession maximizes given one's prior preferences. Decision and Game Theory and their recommendations for choice need revamping to reflect this new standard for the rationality of preferences and choices. It would not be rational when facing a Prisoner's Dilemma to adopt or co-operate from Amartya Sen's "Assurance Game" or "Other Regarding" preferences. (...) But there are preferences which it maximizes to adopt and co-operate from. (shrink)

The major contributions of operationism have been negative, largely because operationists failed to distinguish logical theories of reference from empirical accounts of language. Behaviorism never finished an adequate formulation of verbal reports and therefore could not convincingly embrace subjective terms. But verbal responses to private stimuli can arise as social products through the contingencies of reinforcement arranged by verbal communities.

Berichte zur Wissenschaftsgeschichte, EarlyView.

For regular sets in Euclidean space, previous work has identified twelve ‘basic’ computability notions to which many previous notions considered in literature were shown to be equivalent. With respect to those basic notions we now investigate on the computability of natural operations on regular sets: union, intersection, complement, convex hull, image, and pre-image under suitable classes of functions. It turns out that only few of these notions are suitable in the sense of rendering all those operations uniformly computable.

In the October 1937 number of Philosophy of Science Lindsay has made certain criticisms of the adequacy of the “operational method” of analyzing and giving meaning to the concepts of physics, documenting his criticisms chiefly from my own writings. In these criticisms he has made statements as to the method which I would by no means accept. This is not characteristic of his paper only, for I have seldom indeed seen a printed discussion of the method which I would accept (...) as being an adequate or sometimes even fair representation of what I understand by it. It will perhaps pay therefore if I attempt to state what I conceive it to be all about, particularly since I have never attempted such a comprehensive statement and since my own ideas on the subject have been developing since I first wrote in the Logic of Modern Physics. For one reason I have hesitated to do this, for fear of seeming to subscribe to the not uncommon idea that we are dealing with some elaborate and profound new theory of the nature of knowledge or of meaning. I believe that I myself have never talked of “operationalism” or “operationism”, but I have a distaste for these grandiloquent words which imply something more philosophic and esoteric than the simple thing that I see. What we are here concerned with is an observation and description of methods which at least some physicists had already, perhaps unconsciously, adopted and found successful—the practise of the methods already existed. What I have attempted is to analyze these successful methods, not to set up a philosophical system and a theory of the properties that any method must have if it hopes to be successful. Since I was concerned with a technique already extant, my principal method of getting others to see what the technique involved has been to exhibit examples of the technique in action, rather than to attempt any exhaustive characterization of the technique itself. (shrink)

It is shown, within constructive mathematics, that the unit ball B1 of the set of bounded operators on a Hilbert space H is weak-operator totally bounded. This result is then used to prove that the weak-operator continuity of the mapping T → AT on B1 is equivalent to the existence of the adjoint of A.

Two different concepts of iconicity compete in Peirce's diagrammatical logic. One is articulated in his general reflections on the role of diagrams in thought, in what could be termed his diagrammatology — the other is articulated in his construction of Existential Graphs as an iconic system for representing logic. One is operational and defines iconicity in terms of which information may be derived from a given diagram or diagram system — the other has stronger demands on iconicity, adding to the (...) operational criterion a demand for as high a degree of similarity as possible and may be termed optimal iconicity. Peirce himself does not clearly distinguish these two iconicity notions, a fact that has caused some confusion. By isolating them, we get a clearer and more refined conceptual apparatus for analyzing iconic signs, from pictures to logic. (shrink)

Scheduling surgical procedures among operating rooms is mistakenly regarded as merely a tedious administrative task. However, the growing demand for surgical care and finite hours in a day qualify OR time as a limited resource. Accordingly, the objective of this manuscript is to reframe the process of OR scheduling as an ethical dilemma of allocating scarce medical resources. Recommendations for ethical allocation of OR time—based on both familiar and novel ethical values—are provided for healthcare institutions and individual surgeons.

Traditionally, “the operator calculus of Born and Wiener” has been considered one of the four formulations of quantum mechanics that existed in 1926. The present paper reviews the operator calculus as applied by Max Born and Norbert Wiener during the last months of 1925 and the early months of 1926 and its connections with the rise of the new quantum theory. Despite the relevance of this operator calculus, Born–Wiener’s joint contribution to the topic is generally bypassed in historical accounts of (...) quantum mechanics. In this study, we analyse the paper that epitomises the contribution, and we explain the main reasons for the apparent lack of interest in Born and Wiener’s work. We argue that they did not solve the main problem for which the tool was intended, that of linear motion, because of their reluctance to use Dirac delta functions. (shrink)

In 1990, J. L. Krivine introduced the notion of storage operator to simulate “call by value” in the “call by name” strategy. J. L. Krivine has showed that, using Gödel translation of classical into intuitionistic logic, one can find a simple type for the storage operators in AF2 type system. This paper studies the ∀-positive types and the Gödel transformations of TTR type system. We generalize by using syntactical methods Krivine's theorem about these types and for these transformations. We (...) give a proof of this result in the case of the type of recursive integers. (shrink)

A REFERENCE UUH FOR Llb^nv, J'-t ONLY Operations Research With Special Reference to Non-Military Applications A Comprehensive Scientific Aid to Executive Decisions OPERATIONS Research (or, as the British say, Operational Research) is ...

I shall be dealing, throughout this book, with a set of related problems: the relationship between morality and reasoning in general, the way in which moral reasoning is properly to be carried on, and why morality is not arbitrary. The solutions to these problems come out of the same train of argument. Morality is not arbitrary, I shall argue, because the acceptance of certain qualities of character as virtues and the rejection of others as vices is forced on us by (...) the co-operative basis of human life. The co-operation in human life is unavoidable; the alternative is a literal Hobbesian state of nature, and that is impossible. It is not that co-operation between people is a good thing or even a very good thing; it is simply unavoidable in human life, and it is impossible unless the qualities of character counted as virtues are encouraged and are at least fairly common. The possibility of human life presupposes a theory of human nature, and working out that theory of human nature is the main job of moral philosophy. These virtues or qualities of character or attitudes lead us towards a theory of reasons. A person with a sense of justice is a person inclined to accept certain sorts of facts as reasons for acting, and if the virtues are presupposed by human life then the acceptance of those sorts of facts as reasons for acting is presupposed by human life. A condition of the life of reasoning beings (a more accurate term here than 'human beings') is that moral reasons are reasons for acting and are at the very basis of reasoning. And from this it follows that properly conducted moral reasoning is ultimately guided by the virtues rather than ultimately guided by a set of rules. (shrink)