A topos version of Cantor’s back and forth theorem is established and used to prove that the ordered structure of the rational numbers (Q, <) is homogeneous in any topos with natural numbers object. The notion of effective homogeneity is introduced, and it is shown that (Q, <) is a minimal effectively homogeneous structure, that is, it can be embedded in every other effectively homogeneous ordered structure.

In 1996, W. Veldman and F. Waaldijk present a constructive (intuitionistic) proof for the homogeneity of the ordered structure of the Cauchy real numbers, and so this result holds in any topos with natural number object. However, it is well known that the real numbers objects obtained by the traditional constructions of Cauchy sequences and Dedekind cuts are not necessarily isomorphic in an arbitrary topos with natural numbers object. Consequently, Veldman and Waaldijk's result does not (...) apply to the ordered structure of Dedekind real numbers in toposes. The main result to be proved in the present paper is that the ordered structure of the Dedekind real numbers object is homogeneous, in any topos with natural numbers object. This result is obtained within the framework of local set theory. (shrink)

The approximate number system (ANS) enables organisms to represent the approximate number of items in an observed collection, quickly and independently of natural language. Recently, it has been proposed that the ANS goes beyond representing natural numbers by extracting and representing rational numbers (Clarke & Beck, 2021a). Prior work demonstrates that adults and children discriminate ratios in an approximate and ratio-dependent manner, consistent with the hallmarks of the ANS. Here, we use a well-known “connectedness illusion” to provide (...) evidence that these ratio-dependent ratio discriminations are (a) based on the perceived number of items in seen displays (and not just non-numerical confounds), (b) are not dependent on verbal working memory, or explicit counting routines, and (c) involve representations with a part-whole (or subset-superset) format, like a fraction, rather than a part-part format, like a ratio. These results vindicate key predictions of the hypothesis that the ANS represents rational numbers. (shrink)

Solutions to word problems are moderated by the semantic alignment of real-world relations with mathematical operations. Categorical relations between entities are aligned with addition, whereas certain functional relations between entities are aligned with division. Similarly, discreteness vs. continuity of quantities is aligned with different formats for rational numbers. These alignments have been found both in textbooks and in the performance of college students in the USA and in South Korea. The current study examined evidence for alignments in Russia. (...) Textbook analyses revealed semantic alignments for arithmetic word problems, but not for rational numbers. Nonetheless, Russian college students showed semantic alignments both for arithmetic operations and for rational numbers. Since Russian students exhibit semantic alignments for rational numbers in the absence of exposure to examples in school, such alignments likely reflect intuitive understanding of mathematical representations of real-world situations. (shrink)

In late February and early March 2020, Italy became the European epicenter of the COVID-19 pandemic. Despite increasingly stringent containment measures enforced by the government, the health system faced an enormous pressure, and extraordinary efforts were made in order to increase overall hospital beds’ availability and especially ICU capacity. Nevertheless, the hardest-hit hospitals in Northern Italy experienced a shortage of ICU beds and resources that led to hard allocating choices. At the beginning of March 2020, the Italian Society of Anesthesia, (...) Analgesia, Resuscitation, and Intensive Care issued recommendations aimed at supporting physicians in prioritizing patients when the number of critically ill patients overwhelm the capacity of ICUs. One motivating concern for the SIAARTI guidance was that, if no balanced and consistent allocation procedures were applied to prioritize patients, there would be a concrete risk for unfair choices, and that the prevalent “first come, first served” principle would lead to many avoidable deaths. Among the drivers of decision for admission to ICUs, age, comorbidities, and preexisting functional status were included. The recommendations were criticized as ageist and potentially discriminatory against elderly patients. Looking forward to the next steps, the Italian experience can be relevant to other parts of the world that are yet to see a significant surge of COVID-19: the need for transparent triage criteria and commonly shared values give the Italian recommendations even greater legitimacy. (shrink)

We extend the topos-theoretic treatment given in previous papers of assigning values to quantities in quantum theory. In those papers, the main idea was to assign a sieve as a partial and contextual truth-value to a proposition that the value of a quantity lies in a certain set D of real numbers. Here we relate such sieve-valued valuations to valuations that assign to quantities subsets, rather than single elements, of their spectrum (we call these interval valuations). There are (...) two main results. First, there is a natural correspondence between these two kinds of valuation, which uses the notion of a state's support for a quantity (Section 3). Second, if one starts with a more general notion of interval valuation, one sees that our interval valuations based on the notion of support (and correspondingly, our sieve-valued valuations) are a simple way to secure certain natural properties of valuations, such as monotonicity (Section 4). (shrink)

On a now orthodox view, humans and many other animals possess a “number sense,” or approximate number system, that represents number. Recently, this orthodox view has been subject to numerous critiques that question whether the ANS genuinely represents number. We distinguish three lines of critique – the arguments from congruency, confounds, and imprecision – and show that none succeed. We then provide positive reasons to think that the ANS genuinely represents numbers, and not just non-numerical confounds or exotic substitutes (...) for number, such as “numerosities” or “quanticals,” as critics propose. In so doing, we raise a neglected question: numbers of what kind? Proponents of the orthodox view have been remarkably coy on this issue. But this is unsatisfactory since the predictions of the orthodox view, including the situations in which the ANS is expected to succeed or fail, turn on the kind of number being represented. In response, we propose that the ANS represents not only natural numbers, but also non-natural rational numbers. It does not represent irrational numbers, however, and thereby fails to represent the real numbers more generally. This distances our proposal from existing conjectures, refines our understanding of the ANS, and paves the way for future research. (shrink)

Let ƒ be a real number. It is well known [7] that the set of rational numbers which are less than ƒ is a recursive set if and only if ƒ is representable as the limit of a recursive, recursively convergent sequence of rational numbers. In this paper we replace the condition that the set of rational numbers less than ƒ is recursive by the condition that this set is at various points in the (...) Kleene hierarchy, and we replace the recursive, recursively convergent limit by a variety of other recursive limiting processes. (shrink)

We extend the topos-theoretic treatment given in previous papers of assigning values to quantities in quantum theory, and of related issues such as the Kochen-Specker theorem. This extension has two main parts: the use of von Neumann algebras as a base category (Section 2); and the relation of our generalized valuations to (i) the assignment to quantities of intervals of real numbers, and (ii) the idea of a subobject of the coarse-graining presheaf (Section 3).

The following result is an approximation to the answer of the question of Kokorin about decidability of a quantifier-free theory of field of rational numbers. Let Q0 be a subset of the set of all rational numbers which contains integers 1 and −1. Let be a set containing Q0 and closed by the functions of addition, subtraction and multiplication. For example coincides with Q0 if Q0 is the set of all binary rational numbers or (...) the set of all decimal rational numbers. It is clear that , where Z is the set of all integers and Q is the set of all rational numbers. A negationless theory uses only conjunction and disjunction as logical connectives. Let T be a quantifier-free negationless elementary theory of signature , where Pol is the list of all polynomials with rational coefficients from Q0 in which exponent of the polynomials and rational coefficients are written in binary number system. Theorem 1. Theory T is NP-hard and if is everywhere dense then the theory T is decidable by an algorithm which belongs to EXPTIME. The set of all rational numbers or the set of all binary rational numbers may be taken instead of . The quantifier-free negationless theory of the field of rational numbers may be regarded as a base of constructive mathematics. (shrink)

We prove that each countable rooted K4 -frame is a d-morphic image of a subspace of the space $\mathbb{Q}$ of rational numbers. From this we derive that each modal logic over K4 axiomatizable by variable-free formulas is the d-logic of a subspace of $\mathbb{Q}$ . It follows that subspaces of $\mathbb{Q}$ give rise to continuum many d-logics over K4 , continuum many of which are neither finitely axiomatizable nor decidable. In addition, we exhibit several families of modal logics (...) finitely axiomatizable by variable-free formulas over K4 that d-define interesting classes of topological spaces. Each of these logics has the finite model property and is decidable. Finally, we introduce quasi-scattered and semi-scattered spaces as generalizations of scattered spaces, develop their basic properties, axiomatize their corresponding modal logics, and show that they also arise as the d-logics of some subspaces of $\mathbb{Q}$. (shrink)

Several studies suggest that decisions made in a foreign language are more rational. The authors imply that when thinking in a language which is not our native tongue, analytical, slow, deep-thinking is activated. The question that underlies the present article is whether this is a characteristic of every mental operation in the foreign medium. Studies carried out by Costa et al., Geipel et al. and Hadjichristidis et al. suggest the issue is much more complex than it may seem. The (...) answer to the question above was sought through a study in which 84 Polish advanced users of English as a foreign language were asked to solve mathematical problems from the Cognitive Reflection Test. Initially the subjects were randomly assigned to two groups, who subsequently solved the problems in Polish and in English. The article presents the results, discusses them and arrives at a number of conclusions as well as implications for further research. (shrink)

Evolutionary thinking has expanded in the last decades, spreading from its traditional stronghold – the explanation of speciation and adaptation in biology - to new domains. Fascinating pieces of work, the essays in this collection attest to the illuminating power of evolutionary thinking when applied to the understanding of the human mind. The contributors to_ Cognition, Evolution and Rationality_ use an evolutionary standpoint to approach the nature of the human mind, including both cognitive and behavioural functions. Cognitive science is by (...) its nature an interdisciplinary subject and the essays in this collection investigate the workings of the mind through a variety of disciplines including the philosophy of science, the philosophy of mind, game theory, robotics and computational neuroanatomy. Topics covered range from general methodological issues to long-standing philosophical problems such as how rational human beings actually are. With contributions from leading experts in the areas involved, this book will be of interest across a number of fields, including philosophy, evolutionary theory and cognitive science. (shrink)

Let ${{\mathcal L}^{\square\circ}}$ be a propositional language with standard Boolean connectives plus two modalities: an S4-ish topological modality □ and a temporal modality ◦, understood as ‘next’. We extend the topological semantic for S4 to a semantics for the language ${{\mathcal L}^{\square\circ}}$ by interpreting ${{\mathcal L}^{\square\circ}}$ in dynamic topological systems, i.e., ordered pairs 〈X, f〉, where X is a topological space and f is a continuous function on X. Artemov, Davoren and Nerode have axiomatized a logic S4C, and have shown (...) that S4C is sound and complete for this semantics. S4C is also complete for continuous functions on Cantor space (Mints and Zhang, Kremer), and on the real plane (Fernández Duque); but incomplete for continuous functions on the real line (Kremer and Mints, Slavnov). Here we show that S4C is complete for continuous functions on the rational numbers. (shrink)

This essay analyzes Roman Catholic social teaching on the right to health care and the legitimacy of healthcare rationing. It considers that discussion at two levels: (1) the specific warrants that undergird key terms; and (2) the accessibility and applicability of those warrants to policy choices in a secular society. The essay concludes with a number of broader reflections meant to reserve an appropriate place for religious voices in the process of policy-making, as distinguished from its justification.

The term “synthetic biology” is a popular label of an emerging biotechnological field with strong claims to robustness, modularity, and controlled construction, finally enabling the creation of new organisms. Although the research community is heterogeneous, it advocates a common denominator that seems to define this field: the principles of rational engineering. However, it still remains unclear to what extent rational engineering—rather than “tinkering” or the usage of random based or non-rational processes—actually constitutes the basis for the techniques (...) of synthetic biology. In this article, we present the results of a quantitative bibliometric analysis of the realized extent of rational engineering in synthetic biology. In our analysis, we examine three issues: (1) We evaluate whether work at three levels of synthetic biology (parts, devices, and systems) is consistent with the principles of rational engineering. (2) We estimate the extent of rational engineering in synthetic biology laboratory practice by an evaluation of publications in synthetic biology. (3) We examine the methodological specialization in rational engineering of authors in synthetic biology. Our analysis demonstrates that rational engineering is prevalent in about half of the articles related to synthetic biology. Interestingly, in recent years the relative number of respective publications has decreased. Despite its prominent role among the claims of synthetic biology, rational engineering has not yet entirely replaced biotechnological methods based on “tinkering” and non-rational principles. (shrink)

For a ring R, Hilbert’s Tenth Problem $HTP$ is the set of polynomial equations over R, in several variables, with solutions in R. We view $HTP$ as an enumeration operator, mapping each set W of prime numbers to $HTP$, which is naturally viewed as a set of polynomials in $\mathbb {Z}[X_1,X_2,\ldots ]$. It is known that for almost all W, the jump $W'$ does not $1$ -reduce to $HTP$. In contrast, we show that every Turing degree contains a set (...) W for which such a $1$ -reduction does hold: these W are said to be HTP-complete. Continuing, we derive additional results regarding the impossibility that a decision procedure for $W'$ from $HTP$ can succeed uniformly on a set of measure $1$, and regarding the consequences for the boundary sets of the $HTP$ operator in case $\mathbb {Z}$ has an existential definition in $\mathbb {Q}$. (shrink)

The present study examined whether a dissociation among formats for rational numbers can be obtained in tasks that require comparing a number to a non-symbolic quantity. In Experiment 1, college students saw a discrete or else continuous image followed by a rational number, and had to decide which was numerically larger. In Experiment 2, participants saw the same displays but had to make a judgment about the type of ratio represented by the number. The magnitude task was (...) performed more quickly using decimals, whereas the relation task was performed more accurately with fractions. The pattern observed for percentages was very similar to that for decimals. A dissociation between magnitude comparison and relational processing with rational numbers can be obtained when a symbolic number must be compared to a non-symbolic display. (shrink)

This article surveys the latest research on risky-choice framing effects, focusing on the implications for rational decision-making. An influential program of psychological research suggests that people's judgements and decisions depend on the way in which information is presented, or ‘framed’. In a central choice paradigm, decision-makers seem to adopt different preferences, and different attitudes to risk, depending on whether the options specify the number of people who will be saved or the corresponding number who will die. It is standardly (...) assumed that such responses violate a foundational tenet of rational decision-making, known as the principle of description invariance. We discuss recent theoretical and empirical research that challenges the dominant ‘irrationalist’ narrative. These approaches typically pay close attention to how decision-makers represent decision problems (including their interpretation of numerical quantifiers or predicate choice) and they highlight the need for a more robust characterization of the description invariance principle. We conclude by indicating avenues for future research that could bring us closer to a complete—and potentially rationalizing—explanation of framing effects. (shrink)

Klein’s Erlangen program contains the postulate to study thegroup of automorphisms instead of a structure itself. This postulate, takenliterally, sometimes means a substantial loss of information. For example, thegroup of automorphisms of the field of rational numbers is trivial. Howeverin the case of Euclidean plane geometry the situation is different. We shallprove that the plane Euclidean geometry is mutually interpretable with theelementary theory of the group of authomorphisms of its standard model.Thus both theories differ practically in the language (...) only. (shrink)

Objective: To explore the relationship between the presentation of suffering and support for euthanasia in the British news media.Method: Data was retrieved by searching the British newspaper database LexisNexis from 1996 to 2000. Twenty-nine articles covering three cases of family assisted suicide were found. Presentations of suffering were analysed employing Heidegger’s distinction between technological ordering and poetic revealing.Findings: With few exceptions, the press constructed the complex terrain of FAS as an orderly or orderable performance. This was enabled by containing the (...) contradictions of FAS through a number of journalistic strategies: treating degenerative dying as an aberrant condition, smoothing over botched attempts, locating the object of ethical evaluation in persons, not contexts, abbreviating the decision making process, constructing community consensus and marginalising opposing views.Conclusion: The findings of this study support the view that news reporting of FAS is not neutral or inconsequential. In particular, those reports presenting FAS as an orderly, rational performance were biased in favor of technical solutions by way of the legalisation of euthanasia and/or the involvement of medical professionals. In contrast, while news reports sensitive to contradiction did not necessarily oppose euthanasia, they were less inclined to overtly support technical solutions, recognising the importance of a trial to address the complexity of FAS. (shrink)

People sometimes make moral judgments on the basis of brief emotional episodes. I follow the widely established practice of referring to such affective responses as intuitions (Haidt 2001, 2012; Bedke 2012, Copp 2012). Recently, a number of moral psychologists have argued that moral judgments are never more than emotion- or intuition-based pronouncements on what is right or wrong (Haidt 2001, Nichols 2004, Prinz 2007). A wide variety of empirical findings seem to support this claim. For example, some argue that arbitrary (...) emotional responses or intuitions induced under hypnosis elicit moral judgments (Wheatly and Haidt 2005). Furthermore, intuitions function as the point of last resort in attempts to justify moral judgments (Haidt, Björklund, and Murphy 2000). On the basis of such evidence, psychologists such as Jonathan Haidt (2001, 2012) and philosophers such as Shaun Nichols (2004) and Jesse Prinz (2007) defend what I call ‘Subjective Sentimentalism’, which consists of three claims a. (shrink)

The recent reemergence of theories that emphasize the semantic and conceptual aspects of emotions has also brought to attention questions about their rationality. There are essentially two standard senses in which emotions can be assessed for their rationality. First, emotions can be said to be categorically rational insofar as they presuppose our psychological capacities to be clearly conscious of distinctions, to engage and manipulate concepts, and hence to provide intentional descriptions as reasons for what we feel and are moved (...) to do. For this "cognitive" rationality we can apply the usual standards intrinsic to the processes of belief formation such as coherence, consistency, inferential validity, and appropriateness of evidence. Secondly, and derivatively of "rationality" as a teleological or strategic notion, emotions can be thought of as rational or irrational depending upon their function in fulfilling certain specified human purposes. While neither adhering to nor dismissing what these two mainstream perspectives afford, the following thesis is an alternative, yet complementary, project. Its aim is to "rationalize" emotions through insights obtained in programmatic examinations of their relationship to a number of critical features of being human: intentionality, expression and language, sense of self, responsibility, self-deception, and value cognition and moral agency. The idea is less to fit emotions within some formulaic description of rationality and more to let its potential definition emerge subsequently to these investigations. This reflects a conviction that rationality is not a unitary property of our minds but a complex stance towards the world. It also exhibits an awareness that, as evidenced by current debates, "rationality" is very much a contested notion. (shrink)

In the present note, we study a generalization of Dedekind cuts in the context of constructive Zermelo–Fraenkel set theory CZF. For this purpose, we single out an equivalent of CZF's axiom of fullness and show that it is sufficient to derive that the Dedekind cuts in this generalized sense form a set. We also discuss the instance of this equivalent of fullness that is tantamount to the assertion that the class of Dedekind cuts in the rational numbers, in (...) the customary constructive sense including locatedness, is a set. This is to be compared with the situation for the partial reals, a generalization in a different direction: if one drops locatedness from the notion of a Dedekind real, then it becomes inherently impredicative. We make this precise, and further present the curiosity that the irrational Dedekind reals form a set already with exponentiation. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:684 JOURNAL OF THE HISTORY OF PHILOSOPHY 33:4 OCTOBER 1995 "Private I.anguage" and the pivotal paper in the Stoic section, "The Conjunctive Model," bring out a third feature of Brunschwig's method. Many of his essays take their start from a small text or a relatively local problem, one which does not primafacie bear significantly on large philosophical issues. Yet in a rigorously conceived philosophical system, the whole is often (...) reflected in the details; where possible Brunschwig elicits the larger significance. He shows how Epicurean physics provides a normative model for Epicurean psychology without falling into the reductionist error; the Epicurean does extrapolate from physical theory to human experience, but in so doing he does not forget that human beings are not just atomic; they are atomic compounds. Reductionism does not follow from materialism, for Epicurus or for us. Similarly in "The Conjunctive Model" Brunschwig connects, in a manner which is speculative but nevertheless compelling, a important Stoic thesis in logic (that a conjunction is false if even one of its conjuncts is false) with a comprehensive understanding of Stoic ethics and physics, thereby giving definite content to the Stoic claims about the coherence of their system. The other Stoic papers focus on ontology and logic, showing how central these are to Stoicism. The titles speak for themselves: "Remarks on the Stoic Theory of the Proper Noun," "Remarks on the Classification of Simple Propositions in Hellenistic Logics," "The Stoic Theory of the Supreme Genus and Platonic Ontology," and "Did Diogenes of Babylon Invent the Ontological Argument?" (the answer is 'no'). One essay ("On a Stoic Way of Not Being") disguises by its title a crucial contribution to the philosophy of mind. The papers on Scepticism include "The 6oov ~t~ x~ ~.6"f.t 9 Formula in Sextus Empiricus," a definitive treatment of a verbal formula crucial to understanding the precise character of his sceptical stance, and "Sextus Empiricus on the xptxfl0tov," the only paper in the volume which has previously appeared in English. The papers "Once Again on Eusebius on Aristocles on Timon on Pyrrho" and "The Title of Timon's lndalmoi: From Odysseus to Pyrrho" deal with early Pyrrhonism, for which the evidence is so thin that no firm conclusions can be drawn. Yet even here Brunschwig's care and skill are exemplary, and his argument that we should look to Timon rather than Pyrrho as the creator of Pyrrhonism is as convincing as anything could be in this area. This is a collection which specialists must read and even nonspecialists will value for its elegant combination of rigor, intellectual honesty, and philosophical insight. BRAD INWOOD University of Toronto Michael J. B. Allen. Nuptial Arithmetic: Marsilio Ficino's Commentary on the Fatal Number in Book VIII of Plato's Republic. Berkeley: University of California Press, 1994. PP. x + 291. Cloth, $5o.oo. Marsilio Ficino was born in 1433 and died in 1499 at the age of 66. He would have been pleased if he could have known that. For three years before in 1496 (or slightly earlier) he declared in his Commentary on the Fatal Number that 6 was the perfect number and BOOK R~VIEWS 685 that contemplations of the sextile relations of the planets might lead to the return of the golden age of Saturn "some day," This is the fifth volume of Michael Allen's seminal studies of Ficino's Platonic commentaries; if his notable additional articles on further Ficino commentaries were assembled, as they sometime must be, it would be his sixth--not that he takes the same pleasure in numbers as his subject Ficino did. But 6 is the key to Ficino's unraveling of Plato's "fatal number" in Republic 546. To end the suspense, Ficino's solution, aided by Aristotle, Politics V. 1316, is (4 + 3 + 5)3or (6 x 2)3 or 1728. But 1728 what? There is no clue. The book is itself a valuable contribution to the history of philosophy. Allen reviews the history of this topos up to Brumbaugh and Rees. Although Ficino's entry was known and discussed in the sixteenth century, it has been lost from sight since, and Alien restores it importantly to... (shrink)

The Eurotransplant Kidney Allocation System (ETKAS) emerged from the XCOMB model by Wujciak and Opelz (1993a,b), who applied computer simulation studies to create an allocation algorithm. The present study investigated how experts would allocate a donated organ to patients on the waiting list with respect to the five allocation factors proposed in the ETKAS (number of mismatches, mismatch probability, waiting time, distance, international exchange balance). The experts’ evaluations were compared to the ETKAS points as well as to factor weights established (...) in mandatory allocation guidelines which are based on the German law for organ allocation (Transplantationsgesetz). The investigation was carried out using a conjoint analysis. Overall, the results indicate a fairly high degree of agreement between the experts’ opinions and the existing allocation system ETKAS and even more so for the allocation guidelines, in particular, with respect to the factors Mismatches, Mismatch probability, and Waiting time. (shrink)

This paper develops some ideas from previous work (coauthored, mostly with C.J.Isham). In that work, the main proposal is to assign as the value of a physical quantity in quantum theory (or classical physics), not a real number, but a certain kind of set (a sieve) of quantities that are functions of the given quantity. The motivation was in part physical---such a valuation illuminates the Kochen-Specker theorem; in part mathematical---the valuations arise naturally in the theory of presheaves; and in part (...) conceptual---the valuations arise from applying to propositions about the values of physical quantities some general axioms governing partial truth for any kind of proposition. In this paper, I give another conceptual motivation for the proposal. I develop (in Sections 2 and 3) the notion of a topos (of which presheaves give just one kind of example); and explain how this notion gives a satisfactory general framework for making sense of the idea of partial truth. Then I review (in Section 4) how our proposal applies this framework to the case of physical theories. (shrink)

Background There is broad international agreement from clinicians and academics that healthcare rationing should be undertaken as explicitly as possible, and the BMA have publicly supported the call for more accountable priority setting for some time. However, studies in the UK and elsewhere suggest that clinicians experience a number of barriers to rationing openly, and the information needs of patients at the point of provision are largely unknown. Methodology In-depth interviews were undertaken with NHS professionals working at the community level (...) of provision, and with patients and professionals receiving or providing treatment for morbid obesity and breast cancer (n=52). Results Nearly all patients wanted to know about healthcare rationing and had high expectations of their clinical professionals to provide all relevant information about treatment options. However, professionals did not always understand these information requirements, and cases of implicit rationing were common. The existence of relevant national guidance was not always known about, meaning that patients were often reliant on other sources of information about treatment options, which included the popular media, the internet, patient advocacy groups and informal networks of support. Discussion Clinical professionals need to understand patients' need for detailed information when it comes to rationing, and to understand that they are the main gateway for this to be provided. However, disclosure could be distressing for both patients and professionals, and thus the most sensitive and acceptable ways to make this information available requires further investigation. (shrink)

The increased focus on issues of gender and schooling in India over the last decade has produced several gains that include more incentive schemes to make girls attend school, greater employment of women teachers and improved efforts to incorporate female protagonists in textbooks. However, a closer reading of this ‘gender’ focus reveals an inordinate concern with numbers, i.e. enrolment. The instrumentalism that underlies these efforts is revealed through a double-move effected by existing discourses. The first is to locate the (...) reasons why girls are out of school strictly within a reading of cultural and familial practices and (secondly) to therefore fail to recognize normative practices of schooling and State policies as already deeply ‘gendered’. This double-move is epitomized in the Indian State’s more recent efforts to set up residential elementary schools for girls (Kasturba Gandhi Vidyalayas) in each district of the country; an effort that has been publicly lauded as the most effective way to overcome cultural barriers to girls’ schooling. Through a focus on policy documents that discuss this scheme, the article will interrogate the existing conflation of ‘gender’ with a biological/culturalist reading of the ‘girl child’. In what ways does this narrow focus naturalize a binary frame of reference around the traditional family/community and the empowered girl child? Why have State efforts around educating the ‘girl child’ not been subject to greater critical analysis amongst feminist scholars in India? (shrink)

In this paper we extend the usual notion of model (asa structure) to the more general notion of CauchySequence of Structures in a similar way as rationalsare extending to real numbers by means of Cauchysequences of rationals. We show that the structurespace St is dense in thecomplete space CSt of Cauchysequences of structures and that CSt is compact in the (topo)logicalsense.

Roughly characterized, solipsism is the skeptical thesis that there is no reason to think that anything exists other than oneself and one’s present experience. Since its inception in the reflections of Descartes, the thesis has taken three broad and sometimes overlapping forms: Internal World Solipsism that arises from an account of perception in terms of representations of an external world; Observed World Solipsism that arises from doubts as to the existence of what is not actually present sensuously in experience; Unreal (...) World Solipsism that arises from doubts as to the reality of the perceived world. This book attempts to give a rationally warranted refutation of all three forms. Over time, a vast number of putative rebuttals of solipsism have been proposed. The first half of the book clears the terrain for more productive investigation by showing in detail how each of these various responses fails. Among the simpler of such responses is the claim to have knowledge and certainty about everyday matters (Moore, Austin, Quinton, Pollock). Another is to appeal to pragmatic considerations dictated by the fact of one’s living in the world (Wittgenstein, Rescher, Ayer, Will, Strawson). Yet another is to undermine the skeptical thesis by applying it to itself (Plato, Hume, Russell, Johnson). All of these simpler approaches are found to be inadequate or irrelevant (Chapters 2 and 3). Other responses are more complex in that they presuppose certain basic positions with regard to the nature of cognition, meaning, language, or thought. Consequently, showing how they fail often involves showing the falsity of their underlying views. One such approach maintains that any empirical enquiry presupposes the existence of material objects (Neurath, Wittgenstein, Sellars, Quine, Gurwitsch, Williams, Rorty, BonJour), and that consequently solipsism is a problem peculiar to a mistaken foundationalist epistemology that purports to derive all warranted belief about the world from sensuous data. However, on examination, the various lines of reasoning advanced are found to be fallacious (Chapter 4). A closely-related approach is to claim that any empirical enquiry presupposes background truths, and that consequently solipsism is parasitic in the sense that it is based on truths that it purports to deny (Heidegger, Wittgenstein, Sellars, Quine). Such a self-contradictory situation is shown to obtain for only one form of solipsism, representational solipsism with its classical external world problem dating back to Descartes (Chapter 5). Another approach is to appeal to linguistic considerations in order to level charges of meaninglessness against solipsism (Wittgenstein, Austin, Ryle, Putnam, Clarke, Stroud). However, the charges are easily shown to be unwarranted (Chapter 6), a conclusion subsequently corroborated by a briefly sketched first-person account of meaning (Chapter 7). A further approach is to claim that all philosophical thinking must involve linguistic concepts, that language is intersubjective and tied to objects, and hence that solipsism is conceptually parasitic, and hence calls into question a conceptual scheme that it presupposes (Kant, Strawson, Wittgenstein, Sellars, Quine, Rorty). However, it may be shown that language is not incorrigibly wedded to objects, and in revised form it may be used to state solipsistic theses (Chapter 8). This conclusion is further supported by a refutation of various arguments against the possibility of private language (Wittgenstein, Sellars, Goodman, Rorty, Gadamer), as well as by the empirical evidence of everyday thinking that commonly takes place without reliance on the structures of public language (Chapter 9). The final chapters are more directly constructive. Following foundationalist procedure, a survey is undertaken of the sensuous data of first-person experience in its various modalities and their interrelationships (Chapter 10). An account is given of the bodily nature of the experiencing subject or self that feels, that wills, and that thinks, as well as of the spontaneity of the self or its capacity for free choice (Chapter 11). Rational warrant is then provided for thinking that items randomly perceived through a subject’s spontaneity or free will, continue to exist when unperceived, thus refuting forms of Observed World Solipsism that deny the existence of unperceived objects (Chapter 12). Finally, it is argued with regard to Unreal World Solipsism that while the scenarios it proposes cannot be dismissed as impossible, the absence of any supporting evidence whatever in their favor makes the espousal of any of them both arbitrary and an irrational leap (Chapter 13). (shrink)

Numerous recent discoveries in China of ancient tombs have greatly increased our knowledge of ritual and religious practices. These discoveries include excavated oracle bones, bronze, jade, stone and pottery objects, and bamboo manuscripts dating from the twelfth to fourth century BCE. Inscribed upon these artifacts are a large number of records of numerical sequences, for which no explanation has been found of how they were produced. Structural links to the Book of Changes, a divination manual that entered the Confucian canon, (...) are evident; yet, the algorithm described therein dates to the slightly later second to first century BCE. By combining archeological and statistical evidence, we propose a new methodology that enables us to reconstruct and test cleromantic techniques which can explain how these numerical sequences were generated. Dice and divination stalk use, either in combination or separately, appear in fact to have been underlying the rather stable numerical patterns in ancient China all the way back to the late Shang dynasty (1300–1046 BCE). Bringing to light such a long-standing technique, which awaits further confirmation from the ever-growing database of newly discovered numerical and textual records, can change drastically our understanding of early Chinese history and of the historical development of sophisticated arithmetical practices and the rationalization of chance. (shrink)

Decisions concerning proof of facts in criminal law must be rational because of what is at stake, but the decision‐making process must also be cognitively feasible because of cognitive limitations, and it must obey the relevant legal–procedural constraints. In this topic three approaches to rational reasoning about evidence in criminal law are compared in light of these demands: arguments, probabilities, and scenarios. This is done in six case studies in which different authors analyze a manslaughter case from different (...) theoretical perspectives, plus four commentaries on these case studies. The aim of this topic is to obtain more insight into how the different approaches can be applied in a legal context. This will advance the discussion on rational reasoning about evidence in law and will contribute more widely to cognitive science on a number of topics, including the value of probabilistic accounts of cognition and the problem of dealing with cognitive biases in reasoning under uncertainty in practical contexts. (shrink)

The development of Plato's dialectical method is traced through a number of dialogues. Beginning with the Meno, the evolution of a "pre-critical" dialectic ending with the Phaedo is considered. This first dialectic is described as an ascending or inductive movement from sensible things, through which the Forms are apprehended intuitively and independently. The problem of the mutual participation of the Forms, and of sensible things in them, occasions a growing crisis which comes to a head in the first part of (...) the Parmenides, where, according to Montes, the inadequacy of such a dialectic is established. The second part of that dialogue is then interpreted as an exercise in a new "critical dialectic," which is to be applied later in the Sophist to a rational deduction of the Forms in which the problems of participation are overcome. As might be expected of a work originally in thesis form, the book is heavy with footnotes, references, and Greek quotations, making for cumbersome reading.--A. T. (shrink)

Moral dissensus is a distinct feature of our time. This is not only true of our post-modern culture in general, but also of business culture specifically. In this paper I start by explaining how modernist rationality has produced moral dissensus without offering any hope of bringing an end to it in the foreseeable future. Opting for a form of post-modernist rationality as the only viable way of dealing with moral dissensus, I then make an analysis of a number of ways (...) proposed by both specialists in the field of business ethics, as well as philosophers to deal with moral decision-making in this situation of moral dissensus. The conclusion reached is that none of these attempts succeeds in coming to terms with moral dissensus. I then formulate an alternative approach to moral decision-making which I call: Rational interaction for moral sensitivity. After explaining this approach, I defend it against some of the most obvious objections that might be raised against it in a business environment. When you''re talking birth control, what blocks it and freezes it out is that it''s not a matter of more or fewer babies being argued. That''s just on the surface. What''s underneath is a conflict of faith, of faith in empirical social planning versus faith in the authority of God as revealed by the teachings of the Catholic Church. You can prove the practicality of planned parenthood till you get tired of listening to yourself and it''s going to get nowhere because your antagonist isn''t buying the assumption that anything socially practical is good per se. Goodness for him has other sources which he values as much as or more than social practicality. (Robert M. Pirsig, Zen and the Art of Motorcycle Maintenance.). (shrink)

The main contribution of this article is to apply Herbert Marcuse’s work in contemporary neoliberal society. Specifically, this article will focus on Marcuse’s critique of advanced industrial society and the role that technology plays in the quantification of the self. In this article, I will argue that in recent years, the development of technology has created the possibility to measure, calculate and quantify even the most trivial aspects of our lives, reducing people to numbers. The quantification of people is (...) done with the specific purpose of enhancing efficacy and productivity. I will unpack this notion by first looking to Marcuse’s critique of an advanced industrial society which he argues has the unique purpose of quantifying people to achieve a universal norm of calculated efficiency. Specifically, I will refer to Marcuse’s critique of industrial rationality as the prevailing rationality in advanced industrial societies which encourages the quantification of people. Secondly, I argue that Marcuse’s critique has evolved in the work of contemporary thinkers such as political economist Wendy Brown and cultural theorist Byung-Chul Han. I argue that Brown expands on Marcuse’s theories and contextualises those theories in contemporary neoliberalism. Specifically, I will focus on the concept of governmentality as a political rationality in neoliberal societies and how it advances a one-dimensional political passivity in neoliberal subjects. Finally, I refer to Han, whose theories explore the influence of new forms of technology in a neoliberal society and the development of the neoliberal subject as a “quantified self”. (shrink)

In a familiar passage from Plato's Euthyphro, Socrates points to a contrast between "matters of difference that cause hatred and anger," and matters where agreement is reached by seemingly rational means. Where a dispute concerns number, size or weight, we arrive at a decision by counting or measuring. But there are matters of disagreement where such convergence is not to be expected: "the just and the unjust, the beautiful and the ugly, the good and the bad" notorious among them. (...) Socrates's point, in drawing what a modern reader might take to be a contrast between facts and values, is not so easily understood. The Euthyphro passage elicits a concern-call it a concern about "objectivity"-which is often addressed in a characteristically narrow way. How we approach a given concern depends on how we articulate that concern, and this is what I propose to consider here. (shrink)

I argue that it was rational for chemists to eliminate phlogiston, but that it also would have been rational for them to retain it. I do so on the grounds that a number of prominent phlogiston theorists identified phlogiston with hydrogen in the late 18th century, and this identification became fairly well entrenched by the early 19th century. In light of this identification, I critically evaluate Hasok Chang’s argument that chemists should have retained phlogiston, and that doing so (...) would have benefited science. I argue that these benefits would have been unlikely, and I go on to consider some more likely benefits and harms of retaining phlogiston. I conclude that there is a sense in which scientific rationality concerns what is permissible, as opposed to what is required, so that retention and elimination may, at least sometimes, both be rationally permissible options. (shrink)

Two questions are central to the “rationality debate” in the philosophy of social science. First, should we acknowledge differences in basic norms of epistemic and agential rationality, or in the content of perceptual experience, as the “best explanation” of radical differences in belief and practice? Second, can genuine understanding be achieved between cultures and research traditions that so differ in their beliefs and practices? I survey a number of responses to these questions, and suggest that one of these, “dialogical optimism”, (...) while attractive, is in need of further clarification. Such clarification may be forthcoming if we attend to recent work by John McDowell. McDowell claims that perceptual experience, as our primary mode of epistemic access to the world, must be located within what Sellars termed the “space of reasons” if we are to make sense of our conception of ourselves as thinking creatures. I develop a reading of this claim in terms of a fundamental duality in human perceptual experience, and use this conception of experience to illuminate the dialogical optimist strategy in the rationality debate. (shrink)

This textbook is designed for an Introduction to Proofs course organized around the themes of number and space. Concepts are illustrated using both geometric and number examples, while frequent analogies and applications help build intuition and context in the humanities, arts, and sciences. Sophisticated mathematical ideas are introduced early and then revisited several times in a spiral structure, allowing students to progressively develop rigorous thinking. Throughout, the presentation is enlivened with whimsical illustrations, apt quotations, and glimpses of mathematical history and (...) culture. Early chapters integrate an introduction to sets, logic, and beginning proof techniques with a first exposure to more advanced mathematical structures. The middle chapters focus on equivalence relations, functions, and induction. Carefully chosen examples elucidate familiar topics, such as natural and rational numbers and angle measurements, as well as new mathematics, such as modular arithmetic and beginning graph theory. The book concludes with a thorough exploration of the cardinalities of finite and infinite sets and, in two optional chapters, brings all the topics together by constructing the real numbers and other complete metric spaces. Designed to foster the mental flexibility and rigorous thinking needed for advanced mathematics, Introduction to Mathematics suits either a lecture-based or flipped classroom. A year of mathematics, statistics, or computer science at the university level is assumed, but the main prerequisite is the willingness to engage in a new challenge. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Unmodern Philosophy and Modern Philosophy by John DeweyCharles A. HobbsJohn Dewey. Unmodern Philosophy and Modern Philosophy. Carbondale and Edwardsville: Southern Illinois University Press, 2012, 351 pp., index.John Dewey’s latest publication marks a watershed moment for scholarship in American philosophy, and, in addition to Dewey himself, we have editor Phillip Deen to thank for discovering it (among the Dewey papers in Special Collections at Morris Library of Southern Illinois (...) University) and editing it. We see Dewey late in life (early 1940s) engaged mainly in a critique of the modern, ancient, and (fragmentarily) medieval philosophical periods, which Dewey argues, are eras not nearly as distinct as traditional understanding admits. In the Introduction, Deen helpfully explains how we are now bequeathed incomplete but in most [End Page 122] cases quite robust chapter drafts that amount to another substantial work by Dewey. While published by Southern Illinois University Press, this volume is not itself part of The Collected Works of John Dewey. Still, the careful editing (of what are actually a number of manuscripts) is comparable in its excellence. There is also a well-done Index.The scope is twofold: retrospective and prospective. Chapters one through seven trace the development of so-called modern philosophy along with its central epistemological problem, with the aim being to demonstrate how thoroughly “unmodern” such philosophy has been. Then, chapters eight through fourteen constitute a genuinely modern approach that naturalistically and functionally undercuts the epistemic problem of subject/object and points to a revolution in the process of knowing.We turn to the retrospective, beginning in the first chapter with the acknowledgement that Dewey comes to philosophy itself as a kind of anthropologist, something we note as consistent with the influence of Franz Boas on Dewey (with whom Dewey was a colleague and intellectual ally at Columbia for about thirty-five years). This is further underscored by a lengthy quotation of anthropologist Bronislaw Malinowski on the meaning of culture (p. 290). The ongoing history of philosophy is itself a cultural activity. Indeed, citing James, Dewey declares that “The sickliest way in which a student of philosophy can approach his subject-matter is that of a search for ultimate impersonal revelation of truth.” (p. 16) Rather, let the philosopher have the pragmatic attitude of openness “... to truth from whatever source it comes” (ibid).With that, Dewey once again turns to the Greeks, who initiated “The Discovery of Rational Discourse” (Ch. III) as underscored by the Socratic means of cooperative discourse, with the dialogues—not lectures—being evidence of the Athenian philosophical revolution in turning “from discussing nature and giving an account of it to the examination of the nature and procedure of discussion and report” (p. 38). Yet this project, despite its initial promise, failed for lack of a genuine logic of experimentation or inquiry. Then philosophy focused on going beyond the natural, beginning with the medieval “Search for Salvation” (Ch. IV, a significantly less developed and unified chapter draft). “Modern” philosophers then rightly replaced grand cosmic schemes with a focus on human nature (Ch. V), but they went too far with their introspective methods, gradually resulting in the same consequence supernaturalism had produced: a dualism of mind and nature, as if human nature is somehow not a part of nature. As we recall from Human Nature and Conduct (1922), human nature is not independent of but rather interdependent (or, using Dewey’s later term, transactional) with the rest of nature. The key is to avoid hypostatizing mind and better to talk of culture as nature. [End Page 123]With the Renaissance onward, humans have been “Wandering between Two Worlds” (Ch. VI), and endless arguments between “rationalists” and “empiricists” overlook what these camps share, namely a psychology assuming a fundamental split between subjective/objective and assumptions about certainty as founded upon various first principles or substances. The result is the stagnation of philosophy while science flourishes. Dewey cites Bertrand Russell as an example of continued insistence on such a priori principles (p. 106).We find ourselves in an epoch split between scientism and moral and religious fundamentalism, the result of a lingering tenacious investment in bad elements from ancient and medieval... (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Kennedy Institute of Ethics Journal 10.1 (2000) 103-108 [Access article in PDF] Letters "Small Sacrifices" in Stem Cell Research Madam: I agree with Professors McGee and Caplan (in their article "The Ethics and Politics of Small Sacrifices in Stem Cell Research," KIEJ, June 1999) that the question of the nature and status of the source of stem cells must be addressed. However, in their eagerness to convince us of (...) the smallness of the sacrifices, I think the authors use some unfortunate rhetorical devices and move much too quickly over some necessary distinctions.The rhetorical display is unfortunate if the article is intended to be a fair and rational development of an argument--e.g., those who hold a position in opposition to the authors do not argue they "inveigh." The section on the political area of the controversy seems particularly dismissive of other's positions.However, I will focus on just two areas where I think a more nuanced consideration would make the question of the moral legitimacy of the "small sacrifices" of embryos less obvious than the authors' rhetoric would suggest.First, they claim that opponents of such research assume some sort of "super status" for an embryo. The rights generally conceded to born human beings may not be as "weak" as they characterize. But even considering only the "negative right against unwarranted violence," I think the authors misdescribe the situation. Contrary to their assertion, I do not know when "adults and even children are... forced to give life... in the defense or at least interest of the community's highest ideals and most pressing interests" (p. 153). Could they be speaking of capital punishment, justified in the name of protecting the community? But then why mention children?It is true that not everyone can be guaranteed every means to preserving and enhancing life. But this limitation on positive rights is not a "forced giving." Adults may be compelled to risk life--e.g. in a draft for the sake of a war. But, again, the more or less justifiable imposition of a risk is not the same as selecting out one particular individual or class to be directly killed. Neither adults nor born children are compelled to be killed for the sake of organ "donation," even if a greater number might be saved. If one grants equivalent status to the embryo (as the authors seem to do here for the sake of argument), opponents do not have to claim a "super status" for embryos, just the ordinary human right not to be killed even for "compassionate" motives.A second area where I think the authors move too quickly is in their impoverished definition of the essential humanity of the early embryo as exhaustively represented by the physical structure of its DNA. The authors seem to recognize [End Page 103] that, ordinarily, there is more to personhood than sheer physical structure. For example, they mention memories and habits (p. 154). They could also speak of relationships, attitudes, and the like. Since an early embryo has no such components of personality as we experience it, the authors hold that its identity could only be contained in its DNA. Since this DNA is preserved, even spread far and wide, by the use of stem cells, it almost seems as if we are doing the early embryo a favor by breaking it up.However, just because the embryo does not have any conscious memories or other attributes of character or personality, that does not mean its identity is constituted only by its physical structure described statically. The early embryo is not just a bundle of discrete structures, and its DNA is not just an inert lump made up of certain smaller lumps. Both the embryo and its DNA are active. Thus the identity of even an early embryo includes both its current processes and the innate potential for further activity and development. Although lacking a conscious will, the early embryo is already in a sense an agent, already doing things--growing, changing, and heading toward something that... (shrink)

In this paper, I review the literature on rational choice theory to scrutinize a number of criticisms that philosophers have voiced against its usefulness in economics. The paper has three goals: first, I argue that the debates about RCT have been characterized by disunity and confusion about the object under scrutiny, which calls into question the effectiveness of those criticisms. Second, I argue that RCT is not a single and unified choice theory—let alone an empirical theory of human behavior—as (...) some critics seem to suppose. Rather, there are several variants of RCT used in economics. Third, I propose that we think of RCT as a set of distinct research strategies to appreciate its diversity. This account implies that the effectiveness of any criticism depends on the variant of RCT we are considering. (shrink)

Given a class ℱ oft otal functions in the set oft he natural numbers, one could study the real numbers that have arbitrarily close rational approximations explicitly expressible by means of functions from ℱ. We do this for classes ℱsatisfying certain closedness conditions. The conditions in question are satisfied for example by the class of all recursive functions, by the class of the primitive recursive ones, by any of the Grzegorczyk classes ℰnwith n ≥ 2, by the (...) class of all functions recursive in a given function and by the class of the functions primitive recursive in it, as well as by the class of all total functions in the set of the natural numbers. (shrink)

Students systematically and deliberately apply rule‐based but erroneous algorithms to solving unfamiliar arithmetic problems. These algorithms result in erroneous solutions termed rational errors. Computationally, students' erroneous algorithms can be represented by perturbations or bugs in otherwise correct arithmetic algorithms (Brown & VanLehn, 1980; Langley & Ohilson, 1984; VanLehn, 1983, 1986, 1990; Young S O'Sheo, 1981). Bugs are useful for describing how rational errors occur but bugs are not sufficient for explaining their origin. A possible explanation for this is (...) that rational errors are the result of incorrect induction from examples. This prediction is termed the “induction hypothesis” (VanLehn, 1986). The purpose of the present study was to: (a) expand on post formulations of the induction hypothesis, and (b) use a new methodology to test the induction hypothesis more carefully than has been done previously. The first step involved teaching participants a new number system called NewAbacus, a written modification of the abacus system. The second step consisted of dividing them into different groups, where each individual received an example of only one port of the NewAbacus addition algorithm. During the third and final step, participants were instructed to solve both familiar and unfamiliar types of addition problems in NewAbacus. The induction hypothesis was supported by using both empirical and computational investigations. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:121. HUME'S Of Scepticism with regard to reason: A STUDY IN CONTRASTING THEMES.* This paper attempts to describe the complex dialectical interplay among the contrasting rational, sceptical and naturalist elements which appear in Section I, Part IV of Book I of Hume's Treatise of Human Nature. At the same time we shall try to show that, contrary to Hume's own evaluation of that section, it is the sceptical (...) element, in which the unreliability of reason is supposedly demonstrated, as opposed to the naturalist element, in which its unreliability is supposed to remain hidden from us, that deserves to triumph. With these two goals in mind and in order to make it easier for the reader to follow the inevitable twists and turns of the dialectic, we have divided the paper into two three-sectioned parts. The first part bears the title "Reason and Scepticism", while the second part bears the title "Naturalism". The first section of Part I is concerned with proving that Hume's attempted reduction of all knowledge to probability is frustrated by his failure to explain how we can make mistakes in simple operations with small numbers. If so, the first phase of his sceptical assault against reason fails to dislodge her from her throne. If the second section is right, the second stage of the sceptical assault fares no better. For Hume's attempted reduction of all probabilities to zero is shown to rely on an unsatisfactory formula for calculating the probabilities in question. In the third section an effort is made to show that the attempted reduction of the second section, i_f it had been a success instead of a failure, would have destroyed reason but left scepticism intact. *I should like to thank Howard Sobel for his penetrating and unsparing criticism of an earlier version of this paper. 122. Hume's conviction, on the other hand, that the flawed reduction in question is unflawed and destroys both leads to a prolonged discussion, initiated in the first section of Part II, of his naturalism. Indeed, this theme dominates the rest of the paper. Thus it deserves a part to itself. If we are correct in the first section of Part II, Hume's naturalism is best interpreted as a doctrine of instincts relying for its doctrinal status upon a failure to accept the conclusion of the sceptical argument directed against reason. But, as we try to bring out in the second section, the specific psychological inability with which Hume could in the final analysis give substance to this failure of acceptance is left without any causal foundation. Finally, in the third section that inability is seen to run afoul of reason as Hume himself understands it. And note is taken of the fact that reason so understood and the sceptical argument directed against reason that Hume adopts for his own both commit him willy-nilly to rejecting for good or ill one standard definition of knowledge. Reason and Scepticism Nowhere are the rational elements in Hume's philosophy more in evidence, ironically enough, than in Section I, Part IV of Book I of the Treatise entitled Of Scepticism with regard to reason. For it is there we are told in the very first paragraph that in all demonstrative sciences the rules are certain and infallible. Our reason, moreover, must be consider ' d as a kind of cause, of which truth is the natural effect. (T180) In other words, reason, left to its own devices, would produce truth and, presumably, only truth. Anyone who steadfastly adheres to such principles will reject out of hand one kind of scepticism with regard 123. to reason. That is the kind which results from the alleged discovery that reason, left to its own devices, compels us to embrace one or more contradictions, an obvious form of 2 falsity. It is a kind of scepticism which Bayle cultivated so assiduously. And yet, despite the influence which Bayle 's writings exerted upon Hume, they never convinced him of the viability of this kind of scepticism. On the contrary, apart from some wavering in the Enquiry, he was as adamant as any Leibnizian rationalist that right reason3 ing leads only... (shrink)

In this article, I present some worries about the possible impact of global efforts to aid the needy in some of the world’s most desperate regions. Among the worries I address are possible unintended negative consequences that may occur elsewhere in a society when aid agencies hire highly qualified local people to promote their agendas; the possibility that foreign interests and priorities may have undue influence on a country’s direction and priorities, negatively impacting local authority and autonomy; and the related (...) problem of outside interventions undermining the responsiveness of local and national governments to their citizens. -/- Another issue I discuss is the possibility that efforts to aid the needy may involve an Each-We Dilemma, in which case conflicts may arise between what is individually rational or moral, and what is collectively rational or moral. Unfortunately, it is possible that if each of us does what we have most reason to do, morally, in aiding the needy, we together will bring about an outcome which is worse, morally, in terms of its overall impact on the global needy. -/- The article ends by briefly noting a number of claims and arguments that I made in my 2017 Uehiro Lectures regarding how good people should respond in a world of need. As I have long argued, I have no doubt that those who are well off are open to serious moral criticism if they ignore the plight of the needy. Unfortunately, however, for a host of both empirical and philosophical reasons, what one should do in light of that truth is much more complex, and murky, than most people have realized. (shrink)

The 8th National Congress of Philosophy has been held at the National University of Mar del Plata 27 November - 1 December 1995. Although the number of papers was unexpectedly high, only three of them were devoted to Leibniz' thought: Oscar Esquisabel on “Ratio universalis. The Leibnizian Order of the Sciences: Analysis and Synthesis,” Evelyn Vargas on “Juridical Topic and Mathematical Tradition in the Leibnizian Concept of 'Case',” and A. Guillermo Ranea on “Monads on the Silk Road: How to keep (...) an Empire within the Pinhead of Rationality.” Two outstanding Leibniz scholars attending the Congress, Quentín Racionero Carmona and E. de Olaso devoted their contributions to the forthcoming celebration of the fourth centenary of Descartes' birth. (shrink)

Newcomb's problem is regularly described as a problem arising from equally defensible yet contradictory models of rationality. Braess’ paradox is regularly described as nothing more than the existence of non‐intuitive (but ultimately non‐contradictory) equilibrium points within physical networks of various kinds. Yet it can be shown that Newcomb's problem is structurally identical to Braess’ paradox. Both are instances of a well‐known result in game theory, namely that equilibria of non‐cooperative games are generally Pareto‐inefficient. Newcomb's problem is simply a limiting case (...) in which the number of players equals one. Braess’ paradox is another limiting case in which the ‘players’ need not be assumed to be discrete individuals. The result is that Newcomb's problem is no more difficult to solve than (the easy to solve) Braess’ paradox. (shrink)