The formalisation of Natural Language arguments in a formal language close to it in syntax has been a central aim of Moss’s Natural Logic. I examine how the Quantified Argument Calculus (Quarc) can handle the inferences Moss has considered. I show that they can be incorporated in existing versions of Quarc or in straightforward extensions of it, all within sound and complete systems. Moreover, Quarc is closer in some respects to Natural Language than are Moss’s systems – (...) for instance, is does not use negative nouns. The process also sheds light on formal properties and presuppositions of some inferences it formalises. Directions for future work are outlined. (shrink)

We introduce a two-valued and a three-valued truth-valuational substitutional semantics for the Quantified Argument Calculus (Quarc). We then prove that the 2-valid arguments are identical to the 3-valid ones with strict-to-tolerant validity. Next, we introduce a Lemmon-style Natural Deduction system and prove the completeness of Quarc on both two- and three-valued versions, adapting Lindenbaum’s Lemma to truth-valuational semantics. We proceed to investigate the relations of three-valued Quarc and the Predicate Calculus (PC). Adding a logical predicate T (...) to Quarc, true of all singular arguments, allows us to represent PC quantification in Quarc and translate PC into Quarc, preserving validity. Introducing a weak existential quantifier into PC allows us to translate Quarc into PC, also preserving validity. However, unlike the translated systems, neither extended system can have a sound and complete proof system with Cut, supporting the claim that these are basically different calculi. (shrink)

I develop a formal logic in which quantified arguments occur in argument positions of predicates. This logic also incorporates negative predication, anaphora and converse relation terms, namely, additional syntactic features of natural language. In these and additional respects, it represents the logic of natural language more adequately than does any version of Frege’s Predicate Calculus. I first introduce the system’s main ideas and familiarize it by means of translations of natural language sentences. I then develop a formal (...) system built on these principles, the Quantified Argument Calculus or Quarc. I provide a truth-value assignment semantics and a proof system for the Quarc. I next demonstrate the system’s power by a variety of proofs; I prove its soundness; and I comment on its completeness. I then extend the system to modal logic, again providing a proof system and a truth-value assignment semantics. I proceed to show how the Quarc versions of the Barcan formulas, of their converses and of necessary existence come out straightforwardly invalid, which I argue is an advantage of the modal Quarc over modal Predicate Logic as a system intended to capture the logic of natural language. (shrink)

The Quantified Argument Calculus (Quarc) is a formal logic system, first developed by Hanoch Ben-Yami in (Ben-Yami 2014), and since then extended and applied by several authors. The aim of this paper is to further these contributions by, first, providing a philosophical motivation for the truth-valuational, substitutional approach of (Ben-Yami 2014) and defending it against a common objection, a topic also of interest beyond its specific application to Quarc. Second, we fill the formal lacunae left in the (...) original presentation, which did not incorporate identity systematically into Quarc, and although it proved the soundness of the system did not prove its completeness. (shrink)

The Quantified argument calculus (Quarc) has received a lot of attention recently as an interesting system of quantified logic which eschews the use of variables and unrestricted quantification, but nonetheless achieves results similar to the Predicate calculus (PC) by employing quantifiers applied directly to predicates instead. Despite this noted similarity, the issue of the relationship between Quarc and PC has so far not been definitively resolved. We address this question in the present paper, and then (...) expand upon that result. Utilizing recent developments in structural proof theory, we develop a G3-style sequent calculus for Quarc and briefly demonstrate its structural properties. We put these properties to use immediately to construct direct proofs of the meta-theoretical properties of the system. We then incorporate an abstract (and, as we shall see, logical) predicate into the system in a way that preserves all the structural properties. This allows us to identify a system of Quarc which is deductively equivalent to PC, and also yields a constructive method of demonstrating the Craig interpolation theorem (which speaks in favor of the aforementioned predicate being logical). We further generalize this extension to develop a bivalent system of Quarc with defining clauses that still maintains all the desirable properties of a good proof system. (shrink)

This paper presents an extended version of the Quantified Argument Calculus (Quarc). Quarc is a logic comparable to the first-order predicate calculus. It employs several nonstandard syntactic and semantic devices, which bring it closer to natural language in several respects. Most notably, quantifiers in this logic are attached to one-place predicates; the resulting quantified constructions are then allowed to occupy the argument places of predicates. The version presented here is capable of straightforwardly translating natural-language (...) sentences involving defining clauses. A three-valued, model-theoretic semantics for Quarc is presented. Interpretations in this semantics are not equipped with domains of quantification: they are just interpretation functions. This reflects the analysis of natural-language quantification on which Quarc is based. A proof system is presented, and a completeness result is obtained. The logic presented here is capable of straightforward translation of the classical first-order predicate calculus, the translation preserving truth values as well as entailment. The first-order predicate calculus and its devices of quantification can be seen as resulting from Quarc on certain semantic and syntactic restrictions, akin to simplifying assumptions. An analogous, straightforward translation of Quarc into the first-order predicate calculus is impossible. (shrink)

This paper extends the investigations into logical properties of the quantified argument calculus (Quarc) by suggesting a series of proper subsystems which, although retaining the entire vocabulary of Quarc, restrict quantification in such a way as to make the result decidable. The proof of decidability is via a procedure that prunes the infinite branches of a derivation tree in what is a syntactic counterpart of semantic filtration. We demonstrate an application of one of these systems by showing (...) that Aristotle’s assertoric syllogistic is embeddable within, thus also providing another method of showing its decidability. (shrink)

This article investigates the proof theory of the Quantified Argument Calculus as developed and systematically studied by Hanoch Ben-Yami [3, 4]. Ben-Yami makes use of natural deduction, we, however, have chosen a sequent calculus presentation, which allows for the proofs of a multitude of significant meta-theoretic results with minor modifications to the Gentzen’s original framework, i.e., LK. As will be made clear in course of the article LK-Quarc will enjoy cut elimination and its corollaries.

The present article employs a model-theoretic semantics to interpret a fragment of the language of the Quantified Argument Calculus (Quarc), a recently introduced logical system whose main aim is capturing the structure of natural language sentences in a closer way than does the language of classical logic. The main contribution is an axiomatization for the set of formulas that are valid in all standard interpretations within the employed semantics.

The Modal Predicate Calculus gives rise to issues surrounding the Barcan formulas, their converses, and necessary existence. I examine these issues by means of the Quantified Argument Calculus, a recently developed, powerful formal logic system. Quarc is closer in syntax and logical properties to Natural Language than is the Predicate Calculus, a fact that lends additional interest to this examination, as Quarc might offer a better representation of our modal concepts. The validity of the Barcan (...) formulas and their converses is shown by Quarc to be a result of the specific incorporation of quantification in the Predicate Calculus, and not as reflecting a feature of the interaction of quantification and modality more generally. Necessary existence is shown to follow from the identification, in the Predicate Calculus on its canonical interpretation, of particular quantification, ascription of existence and the ‘there is’ construction, three constructions which are distinguished in both Quarc and Natural Language. The issues surrounding the Barcan formulas, their converses and necessary existence are thus shown to be an artefact of a specific logic system, not an essential feature of our relevant modal concepts or of formal logic. (shrink)

Aristotle counts as the founder of formal logic. The logic he develops dominated until Frege and others introduced a new logic. This new logic is taken to be more powerful and better capable of capturing inference patterns. The new logic differs from Aristotelian logic in significant respects. It has been argued by Fred Sommers and Hanoch Ben-Yami that the new logic is not well equipped as a logic of natural language, and that a logic closer to Aristotle's is better suited (...) for this task. Each of them developed their own formalism - Sommers in form of term logic, Ben-Yami in form of his Quantified Argument Calculus (QUARC). I discuss Aristotle's logic - a term logic - and attempt a comparison between Aristotelian logic and (i) the new logic, (ii) Sommers' term logic, and (iii) Ben-Yami's QUARC. I consider differences between the systems, and show how they are related to and diverge from the new logic. (shrink)

Since the time, about a century ago, when DeMorgan, Boole and Jevons, inaugurated the study of the logic of numerically definite reasoning, no one has been concerned to establish the validity rules for a very general type of numerically definite inference which is a strong analogue of the classical syllogism. The reader will readily agree that the traditional rules of syllogistic inference cannot even begin to decide whether the following proportionally quantified syllogism is a valid argument: at most (...) 4/7 p are at most 2/3 not-m and at least 3/5 s are precisely 7/8 m, hence, at most 1/3 s are p. Likely reasons, of broad methodological interest, why this readily definable type of formal inference has been neglected will presently be proposed. Among the masters of twentieth century logic, Hilbert and Bernays have, to be sure, meticulously shown how such numerically definite propositions as “at least 7 individuals have the property p” can be expressed in the predicate calculus with the use of the identity relation. They do not, since their concern with such propositions is indirect, proceed to establish a systematic calculus of classes whose “size” or extent is numerically definite. As we shall always notice, traditional logic and even ordinary Boolean algebra prefer to generalize about the laws governing the interrelationship of classes in inference systems without making any hypotheses concerning class “size” or extent except by the classical quantifier “some”, which quantifier admits the measure or extent of a class only in terms of the proposition that a given class contains or does not contain at least one member. Such a restricted admission of the relevance for inference of class size is among the fundamental reasons for the neglect of proportional quantifiers, i.e., quantifiers where numerical value is any rational number r such that 0/100 ≤ r ≤ 100/100. It can, of course, also be pointed out that the traditional syllogism and ordinary Boolean algebra do not i.e. measure, numerically define, the degree of inclusion of one class in another. Inclusion is taken either as total or partial, with no discrimination of the degree of partial inclusion. (shrink)

J. Richard Gott III (1993) has used the “Copernican principle” to derive a probability density function for the total longevity of any phenomenon, based solely on the phenomenon’s past longevity. John Leslie (1996) and others have used an apparently similar probabilistic argument, the “Doomsday Argument,” to claim that conventional predictions of longevity must be adjusted, based on Bayes’ Theorem, in favor of shorter longevities. Here I show that Gott’s arguments are flawed and contradictory, but that one of his (...) conclusions—his delta t formula—is mathematically equivalent to Laplace’s famous (and notorious) ‘rule of succession’; moreover, Gott’s delta t formula is a plausible worst-case (if one favors greater longevity) bound in some contexts. On the other hand, the Doomsday Argument is fallacious: the argument’s Bayesian formalism is stated in terms of total duration, but all attempted real-life applications of the argument—with one exception, an application by Gott 1994—actually plug in prior probabilities for future duration; moreover, the Self-Sampling Assumption, an essential premise of the Doomsday Argument, is contradicted by the prior information in all known real-life cases. But rejecting the Doomsday Argument does not entail rejecting the possibility of learning about the future from the past. Applying the work of Bruce M. Hill (1968, 1988, 1993) and Frank P.A. Coolen (1998, 2006) in the field of non-parametric predictive inference, I propose and defend an alternative methodology for quantifying how past longevity of any phenomenon does provide evidence for future longevity. In so doing, I identify an objective standard by which to choose among counting time intervals, counting population, or counting any other measure of past longevity in predicting future longevity. This methodology forms the basis of a calculus of induction. (shrink)

This text prepares undergraduate mathematics students to meet two challenges in the study of mathematics, namely, to read mathematics independently and to understand and write proofs. The book begins by teaching how to read mathematics actively, constructing examples, extreme cases, and non-examples to aid in understanding an unfamiliar theorem or definition (a technique famililar to any mathematician, but rarely taught); it provides practice by indicating explicitly where work with pencil and paper must interrupt reading. The book then turns to proofs, (...) showing in detail how to discover the structure of a potential proof from the form of the theorem (especially the conclusion). It shows the logical structure behind proof forms (especially quantifier arguments), and analyzes, thoroughly, the often sketchy coding of these forms in proofs as they are ordinarily written. The common introductroy material (such as sets and functions) is used for the numerous exercises, and the book concludes with a set of "Laboratories" on these topics in which the student can practice the skills learned in the earlier chapters. Intended for use as a supplementary text in courses on introductory real analysis, advanced calculus, abstract algebra, or topology, the book may also be used as the main text for a "transitions" course bridging the gab between calculus and higher mathematics. (shrink)

The goal of this paper is to present a new reconstruction of Aristotle's assertoric logic as he develops it in Prior Analytics, A1-7. This reconstruction will be much closer to Aristotle's original...

Let H be a proof system for quantified propositional calculus (QPC). We define the Σqj-witnessing problem for H to be: given a prenex Σqj-formula A, an H-proof of A, and a truth assignment to the free variables in A, find a witness for the outermost existential quantifiers in A. We point out that the Σq1-witnessing problems for the systems G*1and G1 are complete for polynomial time and PLS (polynomial local search), respectively. We introduce and study the systems G*0 (...) and G0, in which cuts are restricted to quantifier-free formulas, and prove that the Σqj-witnessing problem for each is complete for NC1. Our proof involves proving a polynomial time version of Gentzen’s midsequent theorem for G*0 and proving that G0-proofs are TC0-recognizable. We also introduce QPC systems for TC0 and prove witnessing theorems for them. We introduce a finitely axiomatizable second-order system VNC1 of bounded arithmetic which we prove isomorphic to Arai’s first order theory AID + Σb0-CA for uniform NC1. We describe simple translations of VNC1 proofs of all bounded theorems to polynomial size families of G*0 proofs. From this and the above theorem we get alternative proofs of the NC1 witnessing theorems for VNC1 and AID. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Journal of the History of Philosophy 39.4 (2001) 592-594 [Access article in PDF] John Earman. Hume's Abject Failure: The Argument Against Miracles. New York: Oxford University Press, 2000. Pp. xi + 217. Cloth, $39.95. Paper, $21.95. As his uncompromising title announces, John Earman considers Hume's famous account of miracles in the Enquiry Concerning Human Understanding to be an "abject failure." More than this, the author judges Hume's well-known (...) arguments to have failed in multiple ways. As he states in the opening paragraph: "It is not simply that Hume's [End Page 592] essay does not achieve its goals, but that his goals are ambiguous and confused." Hume's deliberations on this topic, Earman further contends, are unoriginal, and where original, insubstantial. Further, the logic of the position expressed in the essay "reveals the weakness and poverty of Hume's own account of induction and probabilistic reasoning." Finally, "the essay represents the kind of overreaching that gives philosophy a bad name." While there are occasional hints in the book that the author is himself not completely immune to this latter tendency, for the most part these bluntly stated objections to the famous essay are well supported. This book is a comprehensive and persuasive demolition of Hume's much vaunted claims about the credibility of miracle reports, and it issues a serious challenge to standard readings.Hume's Abject Failure is divided into two parts, the first of which takes the form of an analysis and critique of Hume's arguments. This eighty-page section is followed by another hundred pages of primary materials, mostly eighteenth-century, which address issues related to Hume's essay. It is clear from the format of the book that Earman intends to take seriously the intellectual context in which Hume's arguments first appeared. This a most welcome development. Many treatments of Hume's "Of Miracles" tend to be profoundly ahistorical. What becomes immediately apparent from a consideration of this context is the startling unoriginality of Hume's chief argument. The principle that uniform experience overrides testimony to the occurrence of a miracle was aired long before Hume claimed it as his own, although it can be conceded that in Hume's hands it took on a particularly persuasive form.More importantly, however, this is an argument which does not work. Earman claims that Hume would have been aware of this had he availed himself of the developing science of probability, and in particular Thomas Bayes's pioneering attempts to quantify degrees of belief and credibility. Hume's probabilistic arguments, even on the most charitable interpretation, simply fail the test of a Bayesian analysis, and a number of Earman's chapters forcefully demonstrate this. Having exposed the dubious nature of the argument based on competing testimony, Earman goes on to makes good his claim about the inadequacy of Hume's view of induction, showing how it would rule out not merely miracle testimony, but many empirical claims of the kind typically made in the sciences.It is perhaps a little unfair to charge Hume with having articulated a flawed argument the limitations of which only become obvious with the application of a sophisticated calculus unavailable to him. There is no evidence that Hume ever read Bayes. Earman points out that Richard Price, in his 1767 critique of the argument, drew Hume's attention to the possibility of a Bayesian approach, but Hume was apparently reluctant to incorporate quantification into subsequent editions of the Essay. Whether this amounts to a major failing on Hume's part is debatable. It is also worth noting that at times Earman seems to blur the contemporary distinction between "internal" and "external evidences" (miracles were instances of the latter). This distinction is important for understanding why Hume did not adopt the subjective notions of "miracle" of Locke and the Newtonians, and also why in section two of the Essay he deploys the 'contrary miracles' argument. There is also the puzzle as to how so acute a philosophical mind as Hume's could in this instance have... (shrink)

Some arguments use ‘generic’, or ‘typical’, objects. An explanation for this idea in terms of ‘almost all’ is suggested. The intuition of ‘almost all’ as ‘but for a few exceptions’ is rendered precise by means of ultrafilters. A logical system, with generalized quantifiers for ‘almost all’, is proposed as a basis for generic reasoning. This logic is monotonic, has a simple sound and complete deductive calculus, and is a conservative extension of classical first-order logic, with which it shares several (...) properties. For generic reasoning, generic individuals are introduced and internalized as generic constants, thereby producing conservative extensions where one can reason about generic objects as intended. A many-sorted version of this logic is introduced to handle distinct notions of ‘large’ subsets. Other possible applications for this logic are indicated. (shrink)

We show that the quantified propositional proof systems Gi are polynomially equivalent to their restricted versions that require all cut formulas to be prenex Σqi . Previously this was known only for the treelike systems G*i. © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

It is known that there is a sound and faithful translation of the full intuitionistic propositional calculus into the atomic polymorphic system F at, a predicative calculus with only two connectives: the conditional and the second-order universal quantifier. The faithfulness of the embedding was established quite recently via a model-theoretic argument based in Kripke structures. In this paper we present a purely proof-theoretic proof of faithfulness. As an application, we give a purely proof-theoretic proof of the disjunction (...) property of the intuitionistic propositional logic in which commuting conversions are not needed. (shrink)

When restricted to proving $\Sigma _{i}^{q}$ formulas, the quantified propositional proof system $G_{i}^{\ast}$ is closely related to the $\Sigma _{i}^{b}$ theorems of Buss's theory $S_{2}^{i}$ . Namely, $G_{i}^{\ast}$ has polynomial-size proofs of the translations of theorems of $S_{2}^{i}$ , and $S_{2}^{i}$ proves that $G_{i}^{\ast}$ is sound. However, little is known about $G_{i}^{\ast}$ when proving more complex formulas. In this paper, we prove a witnessing theorem for $G_{i}^{\ast}$ similar in style to the KPT witnessing theorem for $T_{2}^{i}$ . This witnessing (...) theorem is then used to show that $S_{2}^{i}$ proves $G_{i}^{\ast}$ is sound with respect to $\Sigma _{i+1}^{q}$ formulas. Note that unless the polynomial-time hierarchy collapses $S_{2}^{i}$ is the weakest theory in the s₂ hierarchy for which this is true. The witnessing theorem is also used to show that $G_{i}^{\ast}$ is p-equivalent to a quantified version of extended-Frege for prenex formulas. This is followed by a proof that Gi p-simulates $G_{i+1}^{\ast}$ with respect to all quantified propositional formulas. We finish by proving that S₂ can be axiomatized by $S_{2}^{1}$ plus axioms stating that the cut-free version of $G_{0}^{\ast}$ is sound. All together this shows that connection between $G_{i}^{\ast}$ and $S_{2}^{i}$ does not extend to more complex formulas. (shrink)

This paper gives a semantical account for the (i)ordinary propositional calculus, enriched with quantifiers binding variables standing for sentences, and with an identity-function with sentences as arguments; (ii)the ordinary theory of quantification applied to the special quantifiers; and (iii)ordinary laws of identity applied to the special function. The account includes some thoughts of Roman Suszko as well as some thoughts of Wittgenstein's Tractatus.

General practice consultation has often been characterized by pragma-dialecticians as an argumentative activity type. These characterizations are typically derived from theoretical insights and qualitative analyses. Yet, descriptions that are based on quantitative data are thus far lacking. This paper provides a detailed account of the development of an instrument to guide the quantitative analysis of argumentation in doctor–patient consultation. It describes the implementation and preliminary results of a content analysis of seventy videotaped medical consultations of which the extent and type (...) of doctors’ argumentative support for medical opinions and advice are analyzed. Based on the study results, this paper addresses the merits of observational studies using content analysis as a method for the analysis of argumentative discourse in context as well as some of its key challenges and limitations, laying bare the opportunities for future research. (shrink)

This is part I of a two-part essay introducing case-intensional first order logic, an easy-to-use, uniform, powerful, and useful combination of first-order logic with modal logic resulting from philosophical and technical modifications of Bressan’s General interpreted modal calculus. CIFOL starts with a set of cases; each expression has an extension in each case and an intension, which is the function from the cases to the respective case-relative extensions. Predication is intensional; identity is extensional. Definite descriptions are context-independent terms, and (...) lambda-predicates and -operators can be introduced without constraints. These logical resources allow one to define, within CIFOL, important properties of properties, viz., extensionality and absoluteness, Bressan’s chief innovation that allows tracing an individual across cases without recourse to any notion of “rigid designation” or “trans-world identity.” Thereby CIFOL abstains from incorporating any metaphysical principles into the quantificational machinery, unlike extant frameworks of quantified modal logic. We claim that this neutrality makes CIFOL a useful tool for discussing both metaphysical and scientific arguments involving modality and quantification, and we illustrate by discussing in diagrammatic detail a number of such arguments involving the extensional identification of individuals via absolute properties, essential properties, de re vs. de dicto, and the results of possible tests. (shrink)

Frege analyzed the grammatical subject-term 'S' in quantified subject-predicate sentences, 'q S are P', as being logically predicative. This is in contrast to Aristotelian Logic, according to which it is a logical subject-term, like the proper name 'a' in 'a is P' – albeit a plural one, designating many particulars. I show that Frege's arguments for his analysis are unsound, and explain how he was misled to his position by the mathematical concept of function. If common nouns in this (...) grammatical subject position are indeed logical subject-terms, this should require a thorough reevaluation of the adequacy of Frege's Predicate Calculus as a tool for the analysis of the logic and semantics of natural language. (shrink)

Recently a number of works in meta-ontology have used a variant of J.H. Harris's collapse argument in the philosophy of logic as an argument against Eli Hirsch's quantifier variance. There have been several responses to the argument in the literature, but none of them have identified the central failing of the argument, viz., the argument has two readings: one on which it is sound but doesn't refute quantifier variance and another on which it is unsound. (...) The central lesson I draw is that arguments against quantifier variance must pay strict attention to issues of translation and interpretation. The paper also has a substantial appendix in which I prove the equivalence of plural mereological nihilism and standard first-order atomistic mereology; results of this kind are often appealed to in the literature on quantifier variance but without many details on the nature or proof of the result. (shrink)

In "The Existence of God," Richard Swinburne presents a detailed examination of the various arguments for and against God's existence. Methodologically, Swinburne's approach is to develop a cumulative case argument wherein the various theistic arguments constitute the accumulated evidences. Additionally, Swinburne attempts to utilise the formal probability calculus (Bayes's Theorem) to quantify the probability of God's existence in light of the various evidences. However, many have been disappointed with the anticlimactic nature of Swinburne's conclusion. This essay suggest that (...) a much more positive conclusion follows directly from Swinburne's arguments. (shrink)

This clearly written book is designed to introduce the student to the content and methods of formal logic up to and including the lower predicate calculus with identity. There is also a final chapter on undecidability and incompleteness in which the theorems of Church and a version of Gödel's incompleteness theorem are discussed. Primary attention is paid throughout to the development of a system of natural deduction, and the author makes recourse at numerous points to examples drawn from arguments (...) in ordinary natural language. Aside from the material in the last chapter, the principal novelty of the book lies in its use of a method of trees to test for validity. While this device is often informative and pedagogically helpful, it occasionally takes on some of the hallmarks of gimmickry, and sometimes encourages the student to apply a predesigned program, rather than his mind. On the other hand, Jeffrey does provide a good treatment of topics which often baffle beginning logic students, such as tensed verbs, the use of multiple quantifiers, selection of a universe of discourse and relation to elementary set-theoretical notions. There is also a brief section on restricted quantifiers. Each chapter contains numerous exercises for the student.—H. P. K. (shrink)

How important is the concept of solidarity in our society's calculus of consent as regards the legitimacy and ethical and political support for public health, health policy, and health services? By the term “calculus of consent,” we refer to the answer that people give to rationalize and justify their obedience to laws, rules, and policies that benefit others. The calculus of consent answers questions such as, Why should I care? Why should I help? Why should I contribute (...) to the public provision of others? Consent here does not have to be a deliberate, explicit act of informed agreement. And a calculus does not have to be a quantifiable, quasimathematical operation; more often, such a calculus takes narrative form in stories that a society tells about itself and that individuals tell about their place in it. One vital function of bioethics is to inform and shape those stories. Bioethics has the potential to offer society a keener insight into and perception of what is ethically at stake in controversies concerning health, science, and society. This insight is what we shall refer to as a “moral imagination,” by which we do not mean make-believe or fantasy but, rather, the capacity to take a critical distance from the given, to think reality otherwise. The moral imagination enables one to see connections between factors at work in history, in large social and communal structures, and in the shape of one's own life, thoughts, and feelings. Here we are especially concerned with the contribution that the concept of solidarity can make to the moral imagination of bioethics. We contend that solidarity must become more widely active and explicit in bioethics analysis and argumentation as it endeavors to shape reasons for obeying norms and rules of common benefit in an open, diverse society. (shrink)

The aim of this paper is to give a geometric interpretation of quantifiers in the intutionistic predicate calculus. We obtain it treating formulae withn free variables as functions withn arguments which run over an abstract set whereas the values of functions are open subsets of a suitable topological space.

How do we measure happiness? Focusing on subjective measures as a proxy for welfare and well-being, this book finds ways to do that. Subjective measures have been used by psychologists, sociologists, political scientists, and, more recently, economists to answer a variety of scientifically and politically relevant questions. Van Praag, a pioneer in this field since 1971, and Ferrer-i-Carbonell present in this book a generally applicable methodology for the analysis of subjective satisfaction. Drawing on a range of surveys on people's satisfaction (...) with their jobs, income, housing, marriages, and government policy, among other areas of life, this book shows how satisfaction with life "as a whole" is an aggregate of these domain satisfactions. Using German, British, Dutch, and Russian data, the authors cover a wide range of topics, even some not usually considered part of economic study.The book makes a distinction between actual satisfaction levels and individual norms, and in this way complements Van Praag's earlier work within the Leyden School with his later work in "happiness research". Among the many topics covered, the authors discuss: individuals' memory and anticipation processes and the estimation of adaptation phenomena ; the effect of reference groups on income norms and satisfaction with income; the importance of climate for well-being, including the development of a climate-equivalence index; the trade-offs between chronic diseases and income when well-being is kept constant; the damage of aircraft noise on well-being; the construction of a new talent tax tariff; and inequality from a satisfaction perspective, including the definition of "satisfaction inequalities", a natural extension of income inequality and poverty.This groundbreaking book presents new and fruitful methodology that consitutes a welcome addition to the social sciences. (shrink)

Combinatory logic (Curry and Feys 1958) is a “variable-free” alternative to the lambda calculus. The two have the same expressive power but build their expressions differently. “Variable-free” semantics is, more precisely, “free of variable binding”: it has no operation like abstraction that turns a free variable into a bound one; it uses combinators—operations on functions—instead. For the general linguistic motivation of this approach, see the works of Steedman, Szabolcsi, and Jacobson, among others. The standard view in linguistics is that (...) reflexive and personal pronouns are free variables that get bound by an antecedent through some coindexing mechanism. In variable free semantics the same task is performed by some combinator that identifies two arguments of the function it operates on (a duplicator). This combinator may be built into the lexical semantics of the pronoun, into that of the antecedent, or it may be a free-floating operation applicable to predicates or larger chunks of texts, i.e. a typeshifter. This note is concerned with the case of cross-sentential anaphora. It adopts Hepple’s and Jacobson’s interpretation of pronouns as identity maps and asks how this can be extended to the cross-sentential case, assuming the dynamic semantic view of anaphora. It first outlines the possibility of interpreting indefinites that antecede non-ccommanded pronouns as existential quantifiers enriched with a duplicator. Then it argues that it is preferable to use the duplicator as a type-shifter that applies “on the fly”. The proposal has consequences for two central ingredients of the classical dynamic semantic treatment: it does away with abstraction over assignments and with treating indefinites as inherently existentially quantified. However, cross-sentential anaphora remains a matter of binding, and the idea of propositions as context change potentials is retained. (shrink)

Cirquent calculus is a novel proof theory permitting component-sharing between logical expressions. Using it, the predecessor article ‘Elementary-base cirquent calculus I: Parallel and choice connectives’ built the sound and complete axiomatization $\textbf{CL16}$ of a propositional fragment of computability logic. The atoms of the language of $\textbf{CL16}$ represent elementary, i.e. moveless, games and the logical vocabulary consists of negation, parallel connectives and choice connectives. The present paper constructs the first-order version $\textbf{CL17}$ of $\textbf{CL16}$, also enjoying soundness and completeness. The (...) language of $\textbf{CL17}$ augments that of $\textbf{CL16}$ by including choice quantifiers. Unlike classical predicate calculus, $\textbf{CL17}$ turns out to be decidable. (shrink)

It is widely agreed that Hume’s description of human inductive reasoning is inadequate. But many philosophers think that this inadequacy in no way affects the force of Hume’s argument for the unjustifiability of inductive reasoning. I argue that this constellation of opinions contains a serious tension, given that Hume was not merely pointing out that induction is fallible. I then explore a recent diagnosis of where Hume’s sceptical argument goes wrong, due to Elliott Sober. Sober argues that Hume (...) committed a quantifier-shift fallacy, i.e. inferred a statement of ∃∀ form from one of V∀∃ form. The implications of this diagnosis for the traditional problem of induction are briefly examined. The author suggests that, were his philosophy received, we must alter from the foundation the greatest part of the sciences. Hume 1740. (shrink)

One of the premises of the argument from design is the need for the order of a designer. This premise has been explained in various ways, one of which is the calculus of probabilities. It posits that the likelihood of an ordered thing coming into existence by chance is so low that human beings consider it nearly impossible; therefore, this order requires an intelligent designer. However, some contemporary Muslim philosophers, such as Ayatollah Jawādī Āmulī, along with certain Western (...) philosophers, have contested the validity of the calculus of probabilities. They argue that the calculus of probabilities does not reveal reality but is merely practically useful. They assert that undesigned states have the same probability as designed states. In this article, I address these objections, refute them, and ultimately demonstrate the soundness of the argument from design based on the calculus of probabilities. (shrink)

This book is designed for an introductory course in logic on the freshman-sophomore level. The approach to logic through set theory is justified by the fundamental importance of set theory in mathematics, and by the fact that most students entering college are acquainted with set theory. The author begins by explaining the basic notions and laws of set theory, and shows how the four standard types of propositions are translated into the notation of set theory. Propositional logic is introduced and (...) related to set theory by interpreting truth-tables in terms of sets and subsets. A simplified first order functional calculus is developed without quantifiers by using an unconventional notation resembling that of set theory as closely as possible. The nature and techniques of deductive proof are treated at length. Beyond these formal topics there are interesting discussions of the application of logical laws in ordinary language arguments, in probability theory, and in circuit theory. The material is organized in units suitable for fifty minute classes with excellent exercises at the end of each unit. Answers are provided to half the questions in the exercises to allow the student to test himself. The book ends with a brief note on scientific discovery and axiomatics.--T. D. Z. (shrink)

Quantifier variantists accept multiple alternative ontological languages in which quantifiers obey the usual inference rules despite having different meanings. But collapse arguments seem to show that these quantifiers would be provably equivalent to one another. Cian Dorr has pushed this discussion forward by formulating the collapse argument in terms of an algebra of meanings that are common amongst the languages. I attempt to show that quantifier variantists can respond. But an important distinction between types of quantifier variance emerges, between (...) those in which quantifier meanings draw on a single objective backbone of “portions of reality,” and those (such as the type that is arguably associated with neo-Fregeanism) in which they do not. (shrink)

Quantifier variance holds that different languages can have unrestricted quantifier expressions that differ in meaning, where an expression is a “quantifier” just in case it plays the right inferential role. Several critics argued that J.H. Harris’s “collapse” argument refutes variance by showing that identity of inferential role is incompatible with meaning variance. This standard, syntactic collapse argument has generated several responses. More recently, Cian Dorr proved semantic collapse theorems to generate a semantic collapse argument against variance. The (...) argument is significantly different from standard collapse, so it requires a new response. Here I clarify and analyze the semantic collapse argument, and explain how variantists can and should respond to it. The paper also includes an appendix showing the difficulties of positing identity variance without quantifier variance. The argument in the appendix has yet to appear in print, but is familiar to specialists. (shrink)

It is widely agreed that Hume's description of human inductive reasoning is inadequate. But many philosophers think that this inadequacy in no way affects the force of Hume's argument for the unjustifiability of inductive reasoning. I argue that this constellation of opinions contains a serious tension, given that Hume was not merely pointing out that induction is fallible. I then explore a recent diagnosis of where Hume's sceptical argument goes wrong, due to Elliott Sober. Sober argues that Hume (...) committed a quantifier-shift fallacy, i.e. inferred a statement of ?? form from one of ?? form. The implications of this diagnosis for the traditional problem of induction are briefly examined. (shrink)