In the causal modeling literature, it is well known that ill-defined variables may give rise to ambiguous manipulations. Here, we illustrate how ill-defined variables may also induce mistakes in causal inference when standard causal search methods are applied. To address the problem, we introduce a representation framework, which exploits an independent component representation of the data, and demonstrate its potential for detecting ill-defined variables and avoiding mistaken causal inferences.

In the last several decades, a confluence of work in the social sciences, philosophy, statistics, and computer science has developed a theory of causal inference using directed graphs. This theory typically rests either explicitly or implicitly on two major assumptions.

It is argued that there is no agreed definition of disease. Purely biological definitions are inadequate and combined biological and social definitions are not yet satisfactory. One approach has been to say that what doctors treat is disease. We are uncomfortable with that because we feel it releases people from obligations on a basis of convenience. In practice the weight given to the idea of disease varies according to what it will imply about obligations and privileges. It is suggested (...) that what doctors treat can be accepted as disease provided that we recognize that the significance of disease must vary with circumstances. Those circumstances include the agreement, more or less, of all persons affected when someone is considered to be a patient. The individual must also be competent and not constrained except by his own biological or psychological characteristics. Keywords: disease, patient-physician relationship, obligation CiteULike Connotea Del.icio.us What's this? (shrink)

This paper will focus on a philosophically significant construction whose semantics brings together two important notions in Kit Fine’s philosophy, the notion of truthmaking and the notion of a variable embodiment, or its extension, namely what I call a ‘variable object’. This is the construction of definite NPs like 'the number of people that can fit into the bus', 'the book John needs to write', and 'the gifted mathematician John claims to be'. Such NPs are analysed as standing (...) for variable objects, which are part of the 'shallow', construction-driven ontology of natural language, yet are real. (shrink)

Noun phrases like _the number of people that can fit into the bus_ or _the book John needs to write_ are an extremely puzzling linguistic phenomenon. This chapter argues that such noun phrases stand for objects, namely variable objects, entities that have different manifestations (as ordinary entities) in different circumstances. Variable objects unite two important notions of Fine’s philosophy: that of a variable embodiment and that of truthmaking. Variable objects fall under an extension of Fine’s notion (...) of a variable embodiment and involve as circumstances truthmakers of entities like needs. (shrink)

A challenge for relevant logicians is to delimit their area of study. I propose and explore the definition of a relevant logic as a logic satisfying a variable-sharing property and closed under detachment and adjunction. This definition is, I argue, a good definition that captures many familiar logics and raises interesting new questions concerning relevant logics.

Frege’s definitions in Part III of _Begriffsschrift_ introduce novel forms of variable-binding and quantification. Frege’s commentary, however, shows that he did not fully grasp the logical significance of his notation, treating the new variables as themselves somehow defined. In _Grundgesetze_, such issues are avoided by exploiting the value-range notation as a substitute for functional abstraction, relying on the inconsistent Basic Law V. In presenting Frege’s Theorem without appeal to Basic Law V, Richard Heck reinstates a generalized form of the (...) notation of _Begriffsschrift_ by using a higher-order logic employing generalized variable-binding to form names of higher-level functions. Heck and Robert May suggest that by the time of _Grundgesetze_ Frege had achieved the necessary understanding of variable-binding to appreciate Heck’s notation. However, even the later Frege had only a piecemeal characterization of what we now see as falling together as variable-binding. For him, different forms of variable-binding do different logical work, marked by distinct ranges of variables. Eliminating the value-range notation in his definitions after the manner of Heck would require rethinking the role of variable-binding operators. This would not be philosophically cost-free for Frege, though there is some slight evidence that Frege may have begun to move in this direction toward the end of his career. (shrink)

Interventionism is a theory of causation with a pragmatic goal: to define causal concepts that are useful for reasoning about how things could, in principle, be purposely manipulated. In its original presentation, Woodward’s interventionist definition of causation is relativized to an analyzed variable set. In Woodward, Woodward changes the definition of the most general interventionist notion of cause, contributing cause, so that it is no longer relativized to a variable set. This derelativization of interventionism has not (...) gathered much attention, presumably because it is seen as an unproblematic way to save the intuition that causal relations are objective features of the world. This paper first argues that this move has problematic consequences. Derelativization entails two concepts of unmediated causal relation that are not coextensional, but which nonetheless do not entail different conclusions about manipulability relations within any given variable set. This is in conflict with the pragmatic orientation at the core of interventionism. The paper then considers various approaches for resolving this tension but finds them all wanting. It is concluded that interventionist causation should not be derelativized in the first place. Various considerations are offered rendering that conclusion acceptable. (shrink)

Chapin reviewed this 1972 ZEITSCHRIFT paper that proves the completeness theorem for the logic of variable-binding-term operators created by Corcoran and his student John Herring in the 1971 LOGIQUE ET ANALYSE paper in which the theorem was conjectured. This leveraging proof extends completeness of ordinary first-order logic to the extension with vbtos. Newton da Costa independently proved the same theorem about the same time using a Henkin-type proof. This 1972 paper builds on the 1971 “Notes on a Semantic Analysis (...) of Variable Binding Term Operators” (Co-author John Herring), Logique et Analyse 55, 646–57. MR0307874 (46 #6989). A variable binding term operator (vbto) is a non-logical constant, say v, which combines with a variable y and a formula F containing y free to form a term (vy:F) whose free variables are exact ly those of F, excluding y. Kalish-Montague 1964 proposed using vbtos to formalize definite descriptions “the x: x+x=2”, set abstracts {x: F}, minimization in recursive function theory “the least x: x+x>2”, etc. However, they gave no semantics for vbtos. Hatcher 1968 gave a semantics but one that has flaws described in the 1971 paper and admitted by Hatcher. In 1971 we give a correct semantic analysis of vbtos. We also give axioms for using them in deductions. And we conjecture strong completeness for the deductions with respect to the semantics. The conjecture, proved in this paper with Hatcher’s help, was proved independently about the same time by Newton da Costa. (shrink)

This paper presents rules of inference for a binary quantifier I for the formalisation of sentences containing definite descriptions within intuitionist positive free logic. I binds one variable and forms a formula from two formulas. Ix[F,G] means ‘The F is G’. The system is shown to have desirable proof-theoretic properties: it is proved that deductions in it can be brought into normal form. The discussion is rounded up by comparisons between the approach to the formalisation of definite descriptions recommended (...) here and the more usual approach that uses a term-forming operator ι, where ιxF means ‘the F’. (shrink)

This paper presents rules of inference for a binary quantifier I for the formalisation of sentences containing definite descriptions within intuitionist positive free logic. I binds one variable and forms a formula from two formulas. Ix[F, G] means ‘The F is G’. The system is shown to have desirable proof-theoretic properties: it is proved that deductions in it can be brought into normal form. The discussion is rounded up by comparisons between the approach to the formalisation of definite descriptions (...) recommended here and the more usual approach that uses a term-forming operator ι, where ιxF means ‘the F’. (shrink)

The causal Bayes net framework specifies a set of axioms for causal discovery. This article explores the set of causal variables that function as relata in these axioms. Spirtes (2007) showed how a causal system can be equivalently described by two different sets of variables that stand in a non-trivial translation-relation to each other, suggesting that there is no “correct” set of causal variables. I extend Spirtes’ result to the general framework of linear structural equation models and then explore to (...) what extent the possibility to intervene or a preference for simpler causal systems may help in selecting among sets of causal variables. (shrink)

In the present paper we give a precise definition of a hidden-variable theory for quantum mechanics, whereby we adopt the weakest possible definition of a hidden-variable theory, which is compatible with the assumption that the bounded observables of a quantum mechanical system are represented by the elements of the real part Ar of a W*-algebra A (of the most general type) and the states are represented by the “normal states” (in the mathematical sense) of A. We (...) then go on to show that an example put forward by Bell in 1966 satisfies our definition (Sec. 2). Finally we make use of Bell's famous theorem to show that for a sufficiently non-commutative W*-algebra A no hidden-variable theory in our sense exists (Theorem 3.3 and its corollaries). (shrink)

Hidden variables are usually presented as potential completions of the quantum description. We describe an alternative role for these entities, as aids to calculation in quantum mechanics. This is illustrated by the computation of the time-dependence of a massless relativistic spinor field obeying Weyl’s equation from a single-valued continuum of deterministic trajectories (the “hidden variables”). This is achieved by generalizing the exact method of state construction proposed previously for spin 0 systems to a general Riemannian manifold from which the spinor (...) construction is extracted as a special case. The trajectories form a non-covariant structure and the Lorentz covariance of the spinor field theory emerges as a kind of collective effect. The method makes manifest the spin 1/2 analogue of the quantum potential that is tacit in Weyl’s equation. This implies a novel definition of the “classical limit” of Weyl’s equation. (shrink)

Following Asher Peres’s observation that, as in classical physics, in quantum theory, too, a given physical object considered “has a precise position and a precise momentum,” this article examines the question of the definition of quantum variables, and then the new type (as against classical physics) of relationships between mathematics and physics in quantum theory. The article argues that the possibility of the precise definition and determination of quantum variables depends on the particular nature of these relationships.

On a popular view dating back to Russell, descriptions, both definite and indefinite alike, work syntactically and semantically like quantifiers. I have an argument against Russell's view. The argument supports a different picture: descriptions can behave syntactically and semantically like variables. This basic idea can be implemented in very different systematic analyses, but, whichever way one goes, there will be a significant departure from Russell. The claim that descriptions are variables is not new: what I offer is a new way (...) of defending it. The argument centers on attitude reports. I argue that we should recognize a new reading of descriptions under attitude reports, which I call ‘singular opaque’. The existence of this reading cannot be explained on the traditional Russellian view, and demands a switch to the variable view. Along the way, some interesting new facts about attitude reports come to light. (shrink)

Some 55 years after the publication of Russell's seminal ‘On Denoting’, Quine adopted the theory of definite descriptions presented therein to formulate his perspicuous lingua franca for the sciences. This paper illustrates how, in so doing, Quine's lingua franca inherited an old antinomy at the core of Russell's theory of definite descriptions, specifically, the lack of congruency between notation and metaphysical commitments when the variable assumes the role of fundamental singular reference. In this context, the paper contends that the (...) phrase ‘to be is purely and simply to be the value of the variable’ is far from the straightforward solution Quine initially envisioned for his lingua franca. Additionally, it argues that it is unlikely that an attempt to account for a determinate object theory, such as those propounded by Russell and Quine, can prove successful when grounded in a referential theory of quantificational logic where the variable, seen as a simple range of values, holds fundamental singular referent‐position. The paper concludes by suggesting that Meinong's object theory could resolve the problem of the variable, albeit at the cost of potentially undesirable ontological and logical commitments. Alternatively, Kit Fine's recent work on other antinomies in the variable may provide a promising approach to exploring how to salvage the variable as a formal foundation for ontology. (shrink)

A variable binding term operator (vbto) is a non-logical constant, say v, which combines with a variable y and a formula F containing y free to form a term (vy:F) whose free variables are exact ly those of F, excluding y. Kalish-Montague proposed using vbtos to formalize definite descriptions, set abstracts {x: F}, minimalization in recursive function theory, etc. However, they gave no sematics for vbtos. Hatcher gave a semantics but one that has flaws. We give a correct (...) semantic analysis of vbtos. We also give axioms for using them in deductions. And we conjecture strong completeness for the deductions with respect to the semantics. The conjecture was later proved independently by the authors and by Newton da Costa. The expression (vy:F) is called a variable bound term (vbt). In case F has only y free, (vy:F) has the syntactic propreties of an individual constant; and under a suitable interpretation of the language vy:F) denotes an individual. By a semantic analysis of vbtos we mean a proposal for amending the standard notions of (1) "an interpretation o f a first -order language" and (2) " the denotation of a term under an interpretation and an assignment", such that (1') an interpretation o f a first -order language associates a set-theoretic structure with each vbto and (2') under any interpretation and assignment each vb t denotes an individual. (shrink)

What I wish to propose in the present paper is a new form of “career induction” for ambitious young logicians. The basic problem is this: if we look at the n-variable fragments of relevant propositional logics, at what point does undecidability begin? Focus, to be definite, on the logic R. John Slaney showed that the 0-variable fragment of R (where we allow the sentential con- stants t and f) contains exactly 3088 non-equivalent propositions, and so is clearly decidable. (...) In the opposite direction, I claimed in my paper of 1984 that the five variable fragment of R is undecidable. The proof given there was sketchy (to put the matter charitably), and a close examination reveals that although the result claimed is true, the proof given is incorrect. In the present paper, I give a detailed and (I hope) correct proof that the four variable fragments of the principal relevant logics are undecidable. This leaves open the question of the decidability of the n-variable fragments for n = 1, 2, 3. At what point does undecidability set in? (shrink)

For companies involved in the supply chain, proper warehousing management is crucial. Warehouse layout arrangement and operation play a critical role in a company’s ability to maintain and improve its competitiveness. Reducing costs and increasing efficiency are two of the most crucial warehousing goals. Deciding on the best warehouse layout is a remarkable optimization problem. This paper uses an optimization method to set bin allocations within an automated warehouse with particular characteristics. The warehouse’s initial layout and the automated platforms limit (...) the search and define the time required to move goods within the warehouse. With the help of historical data and the definition of the time needed to move goods, a mathematical model of warehouse operation was created. An optimization procedure based on the well-known Variable Neighbourhood Search algorithm is defined and applied to the problem. Experimental results demonstrate increments in the efficiency of warehousing operations. (shrink)

The family of relevant logics can be faceted by a hierarchy of increasingly fine-grained variable sharing properties—requiring that in valid entailments $A\to B$, some atom must appear in both A and B with some additional condition (e.g., with the same sign or nested within the same number of conditionals). In this paper, we consider an incredibly strong variable sharing property of lericone relevance that takes into account the path of negations and conditionals in which an atom appears in (...) the parse trees of the antecedent and consequent. We show that this property of lericone relevance holds of the relevant logic $\mathbf {BM}$ (and that a related property of faithful lericone relevance holds of $\mathbf {B}$ ) and characterize the largest fragments of classical logic with these properties. Along the way, we consider the consequences for lericone relevance for the theory of subject-matter, for Logan’s notion of hyperformalism, and for the very definition of a relevant logic itself. (shrink)

In treatises or advanced textbooks on theoretical physics, it is apparent that the way mathematics is used is very different from what is to be found in books of mathematics. There is, for example, no close connection between books on analysis, on the one hand, and any classical textbook in quantum mechanics, for example, Schiff, [11], or quite recent books, for example Ryder, [10], on quantum field theory. The differences run a good deal deeper than the fact that the books (...) on theoretical physics are not written in the definition-theorem-proof style characteristic of pure mathematics. Although a good many propositions are proved in the books on physics, there are almost with exception no existential proofs, and consequently there is no really serious systematic use of quantifiers. Another important characteristic is the free use of infinitesimals. In fact, most results would not lose anything, from a physicist's point of view, by leaving them in approximate form, i.e., instead of strict equalities or inequalities, using equalities or inequalities only up to an infinitesimal.The discrepancy between the way mathematics is ordinarily done in theoretical physics and the way it is built up from a foundational standpoint in any of the standard modern views raises the question of whether it might be possible to construct quite directly a rigorous foundation that reflects a significant part of this standard practice in theoretical physics. Other parts of standard practice in physics, for example, the use of physically intuitive but nonrigorous arguments, are not present in our system. (shrink)

The consent process for publication of clinical images in medical journals varies widely. The extent of this variation is not known. It is also not known whether journals follow their own stated best practices or the guidance of the International Committee of Medical Journal Editors. We assessed consent requirements in a sample of 10 top impact factor general medicine journals that publish clinical images, examining variability in consent requirements for clinical image publication and congruence of requirements with the recommendations of (...) the ICMJE. Clinical image consent requirements varied widely from journal to journal. None of the studied journals, even amongst n = 4 ICMJE members or n = 8 journals who self-report adherence to ICMJE guidelines, comply with all of the recommendations of the ICMJE. Half of studied journals require a journal-specific consent form. Among top medical journals there is significant heterogeneity in consent requirements for clinical images. Variability of consent requirements is neither practical nor rational; inconsistent requirements create uncertainty for authors, present impediments to dissemination of scholarship, and undermine a shared professional understanding of how best to protect patient privacy. We propose adopting a standardized consent form and process for publication of identifiable images in medical journals, with uniform elements and explicit definitions. (shrink)

The sum, difference, product and quotient of two functions with different domains are usually defined only on their common domain. This paper extends these definitions so that the sum and other operations are essentially defined anywhere that at least one of the components is defined. This idea is applied to propositions and events, expressed as indicator functions, to define conditional propositions and conditional events as three-valued indicator functions that are undefined when their condition is false. Extended operations of "and", "or", (...) "not" and "conditioning" are then defined on these conditional events with variable conditions. The probabilities of the disjunction and of the conjunction of two conditionals are expressed in terms of the conditional probabilities of the component conditionals. In a special case, these are shown to be weighted averages of the component conditional probabilities where the weights are the relative probabilities of the various conditions. Next, conditional random variables are defined to be random variables X whose domain has been restricted by a condition on a second random variable Y. The extended sum, difference, product and conditioning operations on functions are then applied to these conditional random variables. The expectation of a random variable and the conditional expectation of a conditional random variable are recounted. Theorem 1 generalizes the standard result that the conditional expectation of the sum of two conditional random variables with disjoint and exhaustive conditions is a weighted sum of the conditional expectations of the component conditional random variables. Because of the extended operations, the theorem is true for arbitrary conditions. Theorem 2 gives a formula for the expectation of the product of two conditional random variables. After the definition of independence of two random variables is extended to accommodate the extended operations, it is applied to the formula of Theorem 2 to simplify the expectation of a product of conditional random variables. Two examples end the paper. The first concerns a work force of n workers of different output levels and work shifts. The second example involves two radars with overlapping surveillance regions and different detection error rates. One radar's error rate is assumed to be sensitive to fog and the other radar's error rate is assumed to be sensitive to air traffic density. The combined error rate over the combined surveillance region given heavy fog and moderate air traffic is computed. (shrink)

This paper investigates the nature of the emotive meaning (or expressive force) of words commonly referred to as “thick” or “emotive,” which include slurs, derogative or pejorative words, and ethical terms. The inclusion of an expressive component in the semantic representation of a slur is assessed by considering the notion of definition and the related inferential tests developed in the dialectical tradition. The failure of such tests shows how the expressive force cannot be accounted for in terms of lexical (...) meaning. Emotive meaning is analyzed by distinguishing the evaluative component from the emotive one, which results from the former. The negative evaluation is explained as a stable but defeasible inference resulting from different types of triggers, which can be classified into three categories: a specific definitional component (often revealed through its etymology), the denotation, or the “expression” level of a word (connotation). In this sense, instead of considering emotive meaning as a unique concept, it is more adequate to refer to distinct emotive meanings, which vary according to their triggers. At the same time, this approach can account for the characteristics of stability, force variability, historical variability, and cancellability in specific contexts of use. (shrink)

I will argue that the Peres-Mermin square does not necessarily rule out a value-definite (deterministic) noncontextual hidden variable model if the operators are not given a physical interpretation satisfying the following two requirements: (i) each operator is uniquely realized by a single physical measurement; (ii) commuting operators are realized by simultaneous measurements. To underpin this claim, I will construct three hidden variable models for three different physical realizations of the Peres-Mermin square: one violating (i), another violating (ii), and (...) a third one violating both (i) and (ii). (shrink)

In this paper, we present a theory of interaction between definiteness and quantifier structure, where the definite determiner (D) performs the function of contextually restricting the domain of quantificational determiners (Qs). Our motivating data come from Greek and Basque, where D appears to compose with the Q itself. Similar compositions are found in Hungarian and Bulgarian. Following earlier work (Giannakidou 2004, Etxeberria 2005, Etxeberria and Giannakidou 2009) we define a domain restricting function DDR, in which D modifies the Q and (...) supplies the contextual variable C to intersect with Q’s domain. DDR can also modify the NP in which case it works like an intersective modfier— and we suggest that this is the case in St’át’imcets Salish (drawing on data from Matthewson’s work). The result of DDR will be restricting the domain of Q by C, a weakly familiar property (in the sense of Roberts 2003, 2010), i.e. it is entailed in the common ground of the context. As a result of intersecting with this property, the Q that undergoes DDR becomes presuppositional, and we hypothesize that all presuppositional Qs (each-like Qs) have an underlying derivation of the domain restriction via D that we see in Greek and Basque overtly. Our analysis provides support for the program that domain restriction is grammatically represented, but we propose an important refinement: domain restriction can affect the Q itself (in agreement with von Fintel 1998, Martí 2003, Giannakidou 2004; pace Stanley 2002), and in fact quite systematically. We also show that the Q that is affected by DDR is a strong one, and explain the inability of weak Qs to undergo DDR as following from their status as adjectival. (shrink)

The aim of this paper is to introduce the instrumental variables technique to the discussion about causal inference in econometrics. I show that it may lead to causally incorrect conclusions unless some fairly strong causal background assumptions are made, assumptions which are usually left implicit by econometricians. These assumptions are very similar to, albeit not identical with, James Woodward's definition of an ‘intervention’. I discuss similarities and differences of the two points of view and argue that—understood as a practical (...) method of causal inference—the set presented here is superior. (shrink)

The Narrative Gravity operator (Ng) has been criticized as lacking operational definition — as a conceptual label rather than a calculable variable. This paper provides the complete mathematical formalization of Ng = Ma / Sn squared, operationalizes its input variables, and demonstrates calculability through three benchmark cases. -/- Narrative Mass (Ma) is operationalized through four sub-variables scored 0.0-2.5: Causal Density (Cd), Informational Opacity (Io), Temporal Persistence (Tp), and Structural Centrality (Sc). Ma = Cd + Io + Tp + (...) Sc, range 0.0-10.0. -/- Narrative Entropy (Sn) is operationalized through Information Friction (If, scored 0.0-5.0) and Causal Branching (Cb, scored 0.0-5.0). Sn = If x Cb. Three benchmark calculations demonstrate the formula's calculability: Pulp Fiction (Ma=10.0, Sn=18.0, Ng=0.031 — edge of structural collapse through maximum entropy and maximum Vacuum Variable attractor), Crime and Punishment (Ma=7.8, Sn=5.0, Ng=0.312 — high stability through controlled entropy), and Moby Dick (Ma=9.4, Sn=7.5, Ng=0.167). -/- The Vacuum Variable is formally defined as an attractor with Io=2.5 (maximum informational opacity) and distinguished from Hitchcock's MacGuffin through precise mathematical criteria. Four testable predictions are derived, falsifiable through standard reader response methodology without biometric equipment. -/- The paper demonstrates that Ng constitutes a genuine structural contribution distinct from Shannon's Information Theory through three mathematical elements absent from Shannon: temporal integration of entropy, a formal counterforce mechanism, and a squared denominator capturing exponential attractor requirements of high-entropy systems. (shrink)

The usual definition of (non-contextual) hidden variables is found to be too restrictive, in the sense that, according to it, even some classical systems do not admit hidden variables. A more general concept is introduced and the term “approximate hidden variables” is used for it. This new concept avoids the aforementioned problems, since all classical systems admit approximate hidden variables. Standard quantum systems do not admit approximate hidden variables, unless the corresponding Hilbert space is 2-dimensional. However, an appropriate non-standard (...) quantum system, which arises by focussing on momentum and position and neglecting the remaining observables, admits approximate hidden variables. Systems associated with JBW-algebras (resp. von Neumann algebras) and satisfying some mild conditions admit approximate hidden variables iff they are classical, that is, iff the corresponding JBW-algebra (resp. von Neumann algebra) is associative (resp. commutative). (shrink)

This paper contributes to the debate regarding the semantic type of singular referential names. According to one view, known as referentialism, names rigidly designate individuals (Kripke 1972, Abbott 2002, Leckie 2013, Jeshion 2015, Schoubye 2017). According to another view, known as predicativism, names designate properties of individuals (Burge 1973, Geurts 1997, Bach 2002, Elbourne 2005, Matushansky 2008, Fara 2015). Most predicativist accounts claim that bare names in English occur with a phonologically null determiner, a proposal that is based on languages (...) like Greek where names require a determiner in argument position. Novel data from both English and Greek show that names can be nonrigid designators under modal operators ("Aristotle may teach Socrates") and bound variables under quantifiers ("in every set of twins, Helen is a musician"), challenging referentialism. As for rigidity, one possible source of this phenomenon is the proprial article, a name-specific determiner found in Catalan and other languages that may be null in English and homophonous with the definite article in Greek (Ghomeshi and Massam 2009, Muñoz 2019, Izumi and Erickson 2021). While much further research is needed, the data suggest that the proper analysis of names is grounded in predicativism rather than referentialism. (shrink)

The article identifies essential features characteristic of different stages of development and types of humor, and discusses the role of humor in historical changes, social and cul­tural evolution. Humor gets external definitions and criteria that allow to distinguish two stages of proto-humor, and the criterion of full-fledged humor is set. The classical theo­ries of humor (superiority, relief, and incongruity) and main modern theories (benign vio­lation, appropriate incongruity, false alarm, attitude shift, etc.) treat diverse phenomena but have definite invariants. Successful humor (...) episodes (when people involuntarily laugh at an amusing combination of meanings) have main features of interactive rituals (E. Durkheim, E. Goffman, R. Collins), which allows us to reconstruct the hidden mean­ings and bases of participants’ reactions. Such well-known phenomena as joint intention­ality, synchronization of emotional states, bursts of emotional energy, positive reinforce­ment, group membership dynamics, etc. are significant in each successful humor episode. The main features of the combination of meanings in the stimulus of humor according to the most plausible theories, taken disjunctively, form a “confusion” as a basic comic factor. Humor manages to survive in human prehistory and history because its functiona­lity as a provision for individual, group, as well as long-term social needs and concerns. Humor makes a significant impact in affirmation of social norms, orders, and cultural pat­terns by hidden symbols of worship in humor episodes as interactive rituals. At the same time, laughter and humor play a substantial role for loosening and changing orders, and these processes have attracted the attention of researchers in recent years. A sketch model presents how laughter and humor act in “strengthening” and “undermining” roles in dif­ferent phases of historical cycles and the evolutionary spiral. (shrink)

Moral capacity is an important feature of what it means to be human. In this volume, the contributors have taken on the daunting task of trying to distinguish between legal and moral capacity. This distinction is difficult at times for clinicians, philosophers and legal scholars alike. Part of the challenge of defining moral capacity lies in the difficulty of adequately categorizing it. For this reason, the editors have chosen to divide the book into three parts. The first looks at the (...) concepts involved in the discussion of moral capacity; the second considers the role of moral capacity in the lives of professionals; and the final part reflects on case studies of moral capacity or incapacity illustrating the challenge that moral capacity presents - its definition lying between two seemingly incommensurable models, those of the threshold and continuum. This volume takes a multidisciplinary approach to the subject, and ties the disciplines of medicine, philosophy and law into the health context. It will be of interest to medical health professionals as well as researchers working in the areas of philosophy and law. (shrink)

In order to block controversial predictions of 2D semantics (The Nesting Problem), Chalmers and Rabern (2014) propose adding an additional constriction called “the liveness constraint” in definitions of epistemic modals. Without this constraint, all scenario‐world pairs counterfactual to a scenario‐world pair considered as actual in a 2D matrix for a contingenta prioripropositionϕappear problematic for 2D semantics. This is because, although it is false thatϕin such pairs, it isa prioritrue thatϕ. I consider two versions of 2D semantics, those with unstructured and (...) structured intensions. I argue that the unstructured version of 2D semantics is over‐simplified and due to this, it has controversial predictions for counterfactual scenario‐world pairs – the definition of epistemic conceivability with the liveness constraint causes some contingent propositions to appear inconceivable in counterfactual scenario‐world pairs, while some other contingent propositions remain conceivable. In turn, the structured version of the 2D account of propositions has no explanation of how it is possible to possess purely qualitative knowledge without its being dependent on a particular individual or on a particular actual world. (shrink)

This essay considers arguments for and against syntactical constraints on the proper formalization of definitions, originally owing to Alfred Tarski. It discusses and refutes an application of the constraints generalized to include a prohibition against not only object-place but also predicate-place variables in higher-order logic in a criticism of a recent effort to define the concept of heterologicality in a strengthened derivation of Grelling's paradox within type theory requirements. If the objections were correct, they would offer a more general moral (...) for the proper formal definition of terms in philosophical logic. The criticism nevertheless seems mistaken both in the substance and specific application with respect to legitimate synctactical constraints on definitions of key concepts in the case of Grelling's paradox. As such, the critique provides no justification for overturning previous conclusions concerning the possibility of resurrecting a type-observant version of Grelling's heterologicality paradox. (shrink)

The sudden onset of severe traumatic brain injury (sTBI) is an event suffered by millions of individuals each year. Regardless of this frequency in occurrence, accurate prognostication remains difficult to achieve among physicians. There are many variables that affect this prognosis. Physicians are expected to assess the clinical indications of the brain injury while considering other factors such as patient quality of life, patient preferences, and environmental context. However, this lack of certainty in prognosis can ultimately affect treatment recommendations and (...) prompt clinical ethical issues at the bedside, as it leaves room for physician bias and interpretation. In this article, we introduce data on neurosurgeon values that may shed light on the process physicians and patients involved in sTBI undergo. In doing so, we highlight the many nuances in decision-making for patients suffering from sTBI and discuss potential solutions to better patient-physician or surrogate-physician interactions. (shrink)

We define a logic capable of expressing dependence of a variable on designated variables only. Thus has similar goals to the Henkin quantifiers of [4] and the independence friendly logic of [6] that it much resembles. The logic achieves these goals by realizing the desired dependence declarations of variables on the level of atomic formulas. By [3] and [17], ability to limit dependence relations between variables leads to existential second order expressive power. Our avoids some difficulties arising in the (...) original independence friendly logic from coupling the dependence declarations with existential quantifiers. As is the case with independence friendly logic, truth of is definable inside . We give such a definition for in the spirit of [11] and [2] and [1]. (shrink)

We prove that the set of properties describable by a uniform sequence of first-order sentences using at most k + 1 distinct variables is exactly equal to the set of properties checkable by a Turing machine in DSPACE[n k ] (where n is the size of the universe). This set is also equal to the set of properties describable using an iterative definition for a finite set of relations of arity k. This is a refinement of the theorem PSPACE (...) = VAR[O[1]] [8]. We suggest some directions for exploiting this result to derive trade-offs between the number of variables and the quantifier depth in descriptive complexity. (shrink)

In this paper we study proof procedures for some variants of first-order modal logics, where domains may be either cumulative or freely varying and terms may be either rigid or non-rigid, local or non-local. We define both ground and free variable tableau methods, parametric with respect to the variants of the considered logics. The treatment of each variant is equally simple and is based on the annotation of functional symbols by natural numbers, conveying some semantical information on the worlds (...) where they are meant to be interpreted.This paper is an extended version of a previous work where full proofs were not included. Proofs are in some points rather tricky and may help in understanding the reasons for some details in basic definitions. (shrink)

Several types of definitions and means of assessing welfare are discussed in an attempt to reconcile differences which may be counter-productive in addressing welfare issues. Various groups should use similar terminology and it is suggested that well-being be used in the context of the current state of the animal, while welfare refer to a more general concept including past, present and future implications for the animal's well-being. Legal, public and technical definitions of welfare serve different purposes and will necessarily differ. (...) All of these definitions are interdependent and are affected by, and affect, each other. It is suggested that all definitions should attempt to reflect the animals' perspective on their own welfare. Although the ideal means of assessing welfare may lie in determining animals' mental experiences, our ability to do this is limited at this time. A more practical approach is to assess several behavioural, physiological and pathological variables. Reliance on a specific variable or a "cut-off" point may be appropriate in a legal definition of welfare, but should be avoided in scientific studies. The study of animal welfare should not focus only on assessing well-being or the effects of poor welfare, but should also determine behavioural, physiological and pathological factors which predispose animals to environmental stressors. Only then can we focus on developing improved management systems rather than eliminating poor ones. (shrink)

The shortest definition of a number by a first order formula with one free variable, where the notion of a formula defining a number extends a notion used by Boolos in a proof of the Incompleteness Theorem, is shown to be non computable. This is followed by an examination of the complexity of sets associated with this function.

Uncertainty around the role ‘super-spreaders’ play in the transmission and escalation of infectious disease is compounded by its broad and vague definition. It is a term that has been much used in relation to COVID-19, particularly in social media. On its widest definition, it refers to a propensity to infect a larger than average number of people. Given the biological, behavioural and environmental variables relevant to infectivity, this might be pertinent to almost any infected individual who is not (...) physically isolated from others. Nor is the term confined to individuals with a propensity to spread infectious disease: it can potentially be used to describe events, policies or settings. This article explores the use of the term and considers circumstances in which the wide definition can be problematic. One problem is that it can lead to undeserved apportionment of moral blame to alleged super-spreaders. Another is that it can detract from scientific investigation of the heterogeneity of COVID-19 transmission. The author calls for a clearer epidemiological definition. (shrink)

NPs with intensional relative clauses such as 'the book John needs to write' pose a significant challenge for semantic theory. Such NPs act like referential terms, yet they do not stand for a particular actual object. This paper will develop a semantic analysis of such NPs on the basis of the notion of a variable object. The analysis avoids a range of difficulties that a more standard analysis based on the notion of an individual concept would face. Most importantly, (...) unlike the latter, the proposed analysis can be carried over NPs such as 'the number of people that fit into the bus', which describe tropes (particularized properties). (shrink)